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InHawK

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llama2-summarize-dataset

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SECTION 1. SHORT TITLE. This Act may be cited as the ``Mortgage Disclosure Enhancement Act of 2007''. SEC. 2. AMENDMENTS TO THE TRUTH IN LENDING ACT. The Truth In Lending Act (15 U.S.C. 1601 et seq.) is amended by inserting after section 129 the following new section: ``SEC. 129A. ENHANCED MORTGAGE DISCLOSURES. ``(a) Definitions.--As used in this section, the term `mortgage loan' means any consumer credit transaction in which a security interest is or will be retained or acquired in any real property located in the United States which is or, upon completion of the transaction, will be used as the dwelling of the consumer. ``(b) Disclosures for Mortgage Loans.--Subject to the rules of the Board, with respect to a mortgage loan, the creditor shall disclose to the consumer, in addition to any other disclosures required under this title-- ``(1) the amount of the loan; ``(2) the percentage of the loan, as compared to the appraised value of the property; ``(3) the term of the loan; ``(4) the monthly income of the borrower, as relied upon in making the loan; ``(5) if the annual percentage rate of interest is fixed-- ``(A) the applicable annual percentage rate of interest for the loan; ``(B) the amount of the monthly payment on the loan; ``(C) an estimate of the monthly payment, plus taxes and insurance; and ``(D) the percentage of the stated monthly income of the borrower represented by the monthly payment, plus taxes and insurance; ``(6) if the annual percentage rate of interest is variable-- ``(A) the initial interest rate; ``(B) the duration of the initial interest rate; ``(C) an estimate of the monthly payment amount associated with the initial interest rate; ``(D) an estimate of the monthly payment associated with the initial interest rate, plus taxes and insurance; ``(E) the percentage of the stated monthly income of the borrower represented by the estimated monthly payment associated with the initial interest rate, plus taxes and insurance; ``(F) the date on which the interest rate will be adjusted or reset; ``(G) the fully indexed rate (expressed as an estimate of the interest rate after it is adjusted or reset); ``(H) an estimate of the monthly payment amount associated with the fully indexed interest rate; ``(I) the percentage of the stated monthly income of the borrower represented by the estimated monthly payment associated with the fully indexed interest rate; ``(J) an estimate of the monthly payment associated with the fully indexed rate, plus taxes and insurance; and ``(K) an estimate of the maximum possible applicable annual percentage rate of interest, including language expressing that if there is no maximum rate, the applicable State usury rate shall be disclosed; ``(7) if the loan represents a subordinate lien (also referred to as a `piggyback loan') on the real property securing the loan, a brief statement that the loan is subordinate to an existing primary lien, and that the amount of the loan and estimated monthly payments described in the disclosure are in addition to any amounts arising from existing loan obligations; ``(8) in any case in which a prepayment fee or penalty may be imposed with respect to the loan-- ``(A) the amount of such fee or penalty; and ``(B) a brief description, in plain English, of the circumstances or events which would trigger the imposition of the prepayment fee or penalty; ``(9) in any case in which a balloon payment may be required with respect to the loan-- ``(A) the date on which the balloon payment is due, and the estimated amount of the balloon payment; and ``(B) a brief statement, in plain English, that a balloon payment mortgage does not fully pay off the loan, that a large balloon payment of the remaining principal will be required at the end of the loan term, and that many borrowers must secure another loan to make the balloon payment; ``(10) if the borrower has a `payment option' loan-- ``(A) a disclosure that the loan is a payment option loan; and ``(B) a brief statement, in plain English, that a payment option loan has negative amortization, which can result in the loan balance becoming higher than the original amount of the loan, even if the borrower makes all payments on time; ``(11) total points to be paid at closing, with an explanation that points are a fee that the borrower pays to the lender, expressed as a percentage of the total loan; and ``(12) the total actual closing costs, including points, if known, and if not known, the total estimated closing costs, including points. ``(c) Timing of Disclosures.--The disclosures required by this section shall be provided to the consumer at the time of approval of the mortgage loan, but in no case later than 7 days before the date on which the mortgage loan is consummated. ``(d) Format.--Disclosures required by this section shall be presented to the consumer in the form and manner which the Board shall prescribe by regulation-- ``(1) in a simple, clearly legible, and uniform tabular format, in accordance with subsection (e); ``(2) to the extent possible, as a one-page, single document; ``(3) when provided in conjunction with or at the same time as other required written disclosures, as the first of such documents; and ``(4) in an easily readable font size. ``(e) Tabular Format.-- ``(1) In general.--In the regulations prescribed under subsection (d)(1), the Board shall require that the disclosure of such information shall be in the form of a table, which-- ``(A) contains clear and concise headings for each item of such information; and ``(B) provides a clear and concise form for stating each item of information required to be disclosed under each such heading. ``(2) Board discretion in prescribing order and wording of table.--In prescribing the form of the table under paragraph (1), the Board may-- ``(A) list the items required to be included in the table in a different order than the order in which such items are set forth in subsection (b); and ``(B) employ terminology which is different from the terminology employed in subsection (b), if such terminology conveys substantially the same meaning. ``(f) Rules for Reduction of Time Limit of Disclosure Requirements to 24 Hours.--The Board shall, by rule, provide for procedures to reduce the time limit described in subsection (c) to 24 hours prior to the consummation of the mortgage, to the extent that the Board determines necessary and appropriate, except that such rules shall provide for a time limit reduction only at the request of the borrower, and only in those limited circumstances in which the borrower needs to consummate the mortgage transaction in a more expedited manner than would otherwise be permitted under this section. ``(g) Tolerances for Accuracy.--The provisions of section 106(f), relating to tolerances for accuracy, and any rules of the Board issued under that subsection, shall apply to disclosures required under this section.''. SEC. 3. AMENDMENT TO REAL ESTATE SETTLEMENT PROCEDURES. Section 4 of the Real Estate Settlement Procedures Act of 1974 (12 U.S.C. 2603) is amended by adding at the end the following: ``(c) Truth in Lending Act Disclosures.--The form required under section 129A of the Truth in Lending Act shall be provided to the borrower at the time of settlement by the person conducting the settlement, in addition to any other disclosures required by this Act. In no case may a federally related mortgage loan be consummated if such form has not been provided to the borrower, both at the time of the approval of the loan, in accordance with that section 129A, and at settlement.''.

Mortgage Disclosure Enhancement Act of 2007 - Amends the Truth In Lending Act to require additional mortgage loan disclosures by a creditor to a consumer, including: (1) ) the percentage of the loan, as compared to the appraised value of the property; (2) the term of the loan; (3) the monthly income of the borrower, as relied upon in making the loan; (4) the annual percentage rate of interest for loans that are fixed, and for loans that are variable; (5) prepayment fees; and (6) balloon payments. Amends the Real Estate Settlement Procedures Act of 1974 to conform with this Act.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Mortgage Disclosure Enhancement Act of 2007''. SEC. 2. AMENDMENTS TO THE TRUTH IN LENDING ACT. The Truth In Lending Act (15 U.S.C. 1601 et seq.) is amended by inserting after section 129 the following new section: ``SEC. 129A. ENHANCED MORTGAGE DISCLOSURES. ``(a) Definitions.--As used in this section, the term `mortgage loan' means any consumer credit transaction in which a security interest is or will be retained or acquired in any real property located in the United States which is or, upon completion of the transaction, will be used as the dwelling of the consumer. ``(b) Disclosures for Mortgage Loans.--Subject to the rules of the Board, with respect to a mortgage loan, the creditor shall disclose to the consumer, in addition to any other disclosures required under this title-- ``(1) the amount of the loan; ``(2) the percentage of the loan, as compared to the appraised value of the property; ``(3) the term of the loan; ``(4) the monthly income of the borrower, as relied upon in making the loan; ``(5) if the annual percentage rate of interest is fixed-- ``(A) the applicable annual percentage rate of interest for the loan; ``(B) the amount of the monthly payment on the loan; ``(C) an estimate of the monthly payment, plus taxes and insurance; and ``(D) the percentage of the stated monthly income of the borrower represented by the monthly payment, plus taxes and insurance; ``(6) if the annual percentage rate of interest is variable-- ``(A) the initial interest rate; ``(B) the duration of the initial interest rate; ``(C) an estimate of the monthly payment amount associated with the initial interest rate; ``(D) an estimate of the monthly payment associated with the initial interest rate, plus taxes and insurance; ``(E) the percentage of the stated monthly income of the borrower represented by the estimated monthly payment associated with the initial interest rate, plus taxes and insurance; ``(F) the date on which the interest rate will be adjusted or reset; ``(G) the fully indexed rate (expressed as an estimate of the interest rate after it is adjusted or reset); ``(H) an estimate of the monthly payment amount associated with the fully indexed interest rate; ``(I) the percentage of the stated monthly income of the borrower represented by the estimated monthly payment associated with the fully indexed interest rate; ``(J) an estimate of the monthly payment associated with the fully indexed rate, plus taxes and insurance; and ``(K) an estimate of the maximum possible applicable annual percentage rate of interest, including language expressing that if there is no maximum rate, the applicable State usury rate shall be disclosed; ``(7) if the loan represents a subordinate lien (also referred to as a `piggyback loan') on the real property securing the loan, a brief statement that the loan is subordinate to an existing primary lien, and that the amount of the loan and estimated monthly payments described in the disclosure are in addition to any amounts arising from existing loan obligations; ``(8) in any case in which a prepayment fee or penalty may be imposed with respect to the loan-- ``(A) the amount of such fee or penalty; and ``(B) a brief description, in plain English, of the circumstances or events which would trigger the imposition of the prepayment fee or penalty; ``(9) in any case in which a balloon payment may be required with respect to the loan-- ``(A) the date on which the balloon payment is due, and the estimated amount of the balloon payment; and ``(B) a brief statement, in plain English, that a balloon payment mortgage does not fully pay off the loan, that a large balloon payment of the remaining principal will be required at the end of the loan term, and that many borrowers must secure another loan to make the balloon payment; ``(10) if the borrower has a `payment option' loan-- ``(A) a disclosure that the loan is a payment option loan; and ``(B) a brief statement, in plain English, that a payment option loan has negative amortization, which can result in the loan balance becoming higher than the original amount of the loan, even if the borrower makes all payments on time; ``(11) total points to be paid at closing, with an explanation that points are a fee that the borrower pays to the lender, expressed as a percentage of the total loan; and ``(12) the total actual closing costs, including points, if known, and if not known, the total estimated closing costs, including points. ``(c) Timing of Disclosures.--The disclosures required by this section shall be provided to the consumer at the time of approval of the mortgage loan, but in no case later than 7 days before the date on which the mortgage loan is consummated. ``(d) Format.--Disclosures required by this section shall be presented to the consumer in the form and manner which the Board shall prescribe by regulation-- ``(1) in a simple, clearly legible, and uniform tabular format, in accordance with subsection (e); ``(2) to the extent possible, as a one-page, single document; ``(3) when provided in conjunction with or at the same time as other required written disclosures, as the first of such documents; and ``(4) in an easily readable font size. ``(e) Tabular Format.-- ``(1) In general.--In the regulations prescribed under subsection (d)(1), the Board shall require that the disclosure of such information shall be in the form of a table, which-- ``(A) contains clear and concise headings for each item of such information; and ``(B) provides a clear and concise form for stating each item of information required to be disclosed under each such heading. ``(2) Board discretion in prescribing order and wording of table.--In prescribing the form of the table under paragraph (1), the Board may-- ``(A) list the items required to be included in the table in a different order than the order in which such items are set forth in subsection (b); and ``(B) employ terminology which is different from the terminology employed in subsection (b), if such terminology conveys substantially the same meaning. ``(f) Rules for Reduction of Time Limit of Disclosure Requirements to 24 Hours.--The Board shall, by rule, provide for procedures to reduce the time limit described in subsection (c) to 24 hours prior to the consummation of the mortgage, to the extent that the Board determines necessary and appropriate, except that such rules shall provide for a time limit reduction only at the request of the borrower, and only in those limited circumstances in which the borrower needs to consummate the mortgage transaction in a more expedited manner than would otherwise be permitted under this section. ``(g) Tolerances for Accuracy.--The provisions of section 106(f), relating to tolerances for accuracy, and any rules of the Board issued under that subsection, shall apply to disclosures required under this section.''. SEC. 3. AMENDMENT TO REAL ESTATE SETTLEMENT PROCEDURES. Section 4 of the Real Estate Settlement Procedures Act of 1974 (12 U.S.C. 2603) is amended by adding at the end the following: ``(c) Truth in Lending Act Disclosures.--The form required under section 129A of the Truth in Lending Act shall be provided to the borrower at the time of settlement by the person conducting the settlement, in addition to any other disclosures required by this Act. In no case may a federally related mortgage loan be consummated if such form has not been provided to the borrower, both at the time of the approval of the loan, in accordance with that section 129A, and at settlement.''.[/INST]Mortgage Disclosure Enhancement Act of 2007 - Amends the Truth In Lending Act to require additional mortgage loan disclosures by a creditor to a consumer, including: (1) ) the percentage of the loan, as compared to the appraised value of the property; (2) the term of the loan; (3) the monthly income of the borrower, as relied upon in making the loan; (4) the annual percentage rate of interest for loans that are fixed, and for loans that are variable; (5) prepayment fees; and (6) balloon payments. Amends the Real Estate Settlement Procedures Act of 1974 to conform with this Act.</s>

quantile regression is one of a popular alternative to mean regression when the data is non - normal , skewed or heteroscedastic . quantile regression is also useful when our objective is to make inferences about the population at different quantile levels . linear quantile regression was first proposed in @xcite . various other frequentist methods for quantile regression can be found in @xcite . @xcite first introduced the quantile regression using bayesian methods . later @xcite , @xcite , @xcite , @xcite proposed a few methods on generalization and extension of single level quantile regression under different possible scenarios . the main disadvantage of considering separate quantile regression using single level quantile regression is that the natural ordering among different quantiles can not be ensured . addressing the non - crossing issue , @xcite proposed a quantile regression method assuming the response variable to be heteroskedastic . @xcite proposed a method to estimate the quantile curve using linear interpolation from a estimated gird of quantile curves . @xcite and @xcite proposed non - crossing quantile regression methods using support vector machine ( svm , @xcite ) . later @xcite used doubly penalized kernal machine ( dpkm ) for estimating non - crossing quantile curves . @xcite and @xcite proposed quantile regression methods for a grid of quantiles addressing the monotonicity constraint . later @xcite , @xcite , @xcite , @xcite proposed linear quantile regression methods addressing the non - crossing issues . recently , @xcite and @xcite proposed simultaneous linear quantile regression methods for univariate explanatory variables . @xcite extended that simultaneous linear quantile regression method to handle multivariate predictor case . @xcite also extended the method proposed in @xcite in the spatio - temporal simultaneous quantile regression context where the response variable is assumed to be linearly dependent on one of the explanatory variables and varying non - parametrically with rest of the explanatory variables . one of the shortcomings of using linear quantile regression method is that it is not able to reveal a higher degree polynomial trend in the quantile curves . for example , while regressing household income data of a country over time , lower quantile levels maybe linear with time but the upper quantile levels may evolve very differently , for instance lower quantile level may increase linearly with time but upper quantile level may increase faster . in that case , using linear quantile regression will not be appropriate since it would only give the closest possible linear approximation of the quantile curves . quantile regression methods addressing this issue were proposed in @xcite , @xcite . @xcite proposed the local linear quantile regression method based on the techniques proposed in @xcite , @xcite , @xcite . @xcite and @xcite proposed alternative methods of quantile regressions . a few other non - parametric quantile regression methods were proposed in @xcite , @xcite and @xcite . @xcite provided a detailed description of local linear quantile regression method using software r. alongside , he also proposed an alternative method called local spline quantile regression . as long as non - linear quantile regression is concerned , most of the above - mentioned methods do not take care of the non - crossing issues . although , @xcite proposed a non - parametric quantile regression method addressing the non - crossing issue , it can only estimate a set of non - crossing curves for a given grid of quantiles and it does not estimate the whole quantile regression function . secondly , the quantile regression estimates obtained by this method is sensitive to the number and location of chosen quantile grids . instead of estimating the quantile curves at a given set of quantiles , it is more desirable to estimate the whole quantile curve simultaneously to emerge the broader picture . in this paper , we propose two bayesian methods for quantile regression using b - spline . in the first method , the entire quantile function is modeled by a b - spline series expansion . for each of the explanatory variables , a corresponding b - spline basis function is considered . the whole quantile function is obtained via tensor product of b - spline basis functions corresponding to each dimension of explanatory variables and one corresponding to the quantile level . the prior on the b - spline coefficients is put in such a way that the monotonicity of the quantile curves is maintained . we name this method ` non - parametric simultaneous quantile regression ( npsqr ) ' . in the second method , instead of the quantile function , the conditional distribution function is estimated non - parametrically using b - spline basis expansion . similar to npsqr , in this method also , corresponding to each dimension of the explanatory variable , a b - spline basis is considered . again , the prior of the coefficients of the b - spline basis functions is put in such a way that the monotonicity of the distribution function is maintained . in this case also the whole distribution function is given by tensor product of the b - spline basis functions . the conditional distribution function is inverted to obtain the quantile regression function . the use of splines , which are piece - wise polynomials , allow efficient inversion through a combination of analytical and numerical technique . we name this method to be ` non - parametric distribution function simultaneous quantile regression ( npdfsqr ) ' . further using both of these two approaches , we propose the method of estimating the quantile curves when only the data with frequencies of the observations in each quantile range are available . suppose @xmath0 and @xmath1 denote the @xmath2-dimensional explanatory variable and the response variable respectively . using monotonic transformation , each coordinates of the explanatory variable and the response variable are transformed into unit interval . suppose @xmath3 denotes the conditional quantile function of @xmath4 given @xmath5 . a b - spline function of degree @xmath6 ( i.e. , degree of piece - wise polynomial is @xmath7 ) with knot sequence @xmath8 has @xmath9 basis functions . let @xmath10 denote b - spline basis functions of degree @xmath6 on the above - mentioned knot sequence . for simplicity we consider equidistant knots , i.e. , @xmath11 for @xmath12 . hence the quantile function is given by @xmath13 where @xmath14 , are the coefficients of b - splines basis expansion of @xmath3 . thus in the above - mentioned equation it is noted that the coefficients of the basis functions used to expand the quantile function are dependent on the explanatory variable @xmath15 . secondly , the imposed monotonicity condition on the b - spline coefficients @xmath16 ensures the monotoniticy of the quantile levels ( @xcite ) . now to put a prior , the functions @xmath16 , it is expanded using @xmath2-dimensional tensor product of the b - spline basis functions of degree @xmath17 . we use the knot sequence @xmath18 such that @xmath19 for all the coordinates of the explanatory variable @xmath15 . then @xmath20 is given by @xmath21 then the parameters which need to be estimated are given by @xmath22 for modeling the distribution function with b - spline basis functions , we adopt a similar technique . suppose @xmath23 denotes the conditional distribution function of @xmath4 at @xmath5 . suppose @xmath10 denotes the b - spline coefficients of degree @xmath6 on the knot sequence @xmath24 as mentioned earlier . then the conditional distribution @xmath23 is given by @xmath25 it is noted that again the coefficients @xmath26 are taken in such a way that the monotonicity of the distribution function is preserved . to put a prior on @xmath26 , we use the same technique as mentioned in section [ npsqr_model ] . then @xmath27 is given by @xmath28 hence the parameters to be estimated are given by @xmath29 . in this section we describe the likelihood evaluation for both complete data and grouped data where only the frequencies of observations at each range of quantiles are given with the corresponding values of the explanatory variables . suppose that the explanatory and the response variables in the data are given by @xmath1 and @xmath30 where @xmath31 denotes the sample size and @xmath2 denotes the dimension of the explanatory variable . in the case of npsqr , the likelihood derived from the quantile function is given by @xmath32 where @xmath33 is given by @xmath34 here @xmath35 solves the equation @xmath36 as described in section [ npsqr_model ] , @xmath37 is constructed in such a way that it is monotonically increasing in @xmath38 . hence equation has a unique solution . in case we consider piece - wise quadratic b - spline ( i.e. , @xmath6=2 ) , an advantage of our proposed method is that equation reduces to a quadratic equation and hence it can be solved analytically . solving it analytically provides the exact solution in lesser time . now to compute the likelihood , using the properties of derivative of b - spline ( @xcite ) , we get @xmath39 where @xmath40 thus the log - likelihood in case of npsqr is given by @xmath41 in case of npdfsqr , the log - likelihood function is given by @xmath42 where @xmath43 in the case of grid data suppose the partition of the quantiles of the response are given by @xmath44 and for each observation it is given between which two consecutive quantile divisions it belongs . define @xmath45 for @xmath46 . given the value of the explanatory variable for the @xmath47-th subject @xmath48 , the probability of an observation @xmath49 belonging between @xmath50 and @xmath51-th quantile is given by @xmath52 . here @xmath53 denotes the @xmath54-th quantile @xmath55 of @xmath4 . hence the total likelihood is given by @xmath56 we assume that the values @xmath57 are provided and with @xmath58 , @xmath59 for all @xmath46 . now for npsqr , it should be noted that @xmath60 is the solution of the equation @xmath37@xmath61 since @xmath62 implies @xmath63 . hence @xmath60 can be obtained solving the following equation in terms of @xmath38 @xmath64 in case of npdfsqr , once the values of @xmath65 are evaluated , likelihood evaluation is straightforward and can be easily obtained using equation . to estimate the parameters for npsqr and npdfsqr methods ( given by equations and respectively ) we use block metropolis - hastings markov chain monte carlo algorithm ( @xcite ) . it should be noted that the parameter space which needs to be estimated are of the same form for npsqr and npdfsqr and hence we use the similar steps and same prior distribution for both the cases . recall that for npsqr the parameter space is given by @xmath66 now define @xmath67 for @xmath68 . then it can be noted that @xmath69 belongs to the unit - simplex for any given @xmath68 since @xmath70for @xmath68 . we put the uniform prior on each simplex block . the number of simplex blocks is given by @xmath71 where @xmath72 is the equidistant knot sequence used for each coordinate of the explanatory variables and @xmath17 is the degree of the piece - wise polynomials use for b - spline regression ( as mentioned in section [ npsqr_model ] ) . within an iteration , one simplex block is updated at a time . hence there will be @xmath71 updates performed one at a time during a single iteration . to make movements on the simplex block , we use the same strategy as explained in @xcite and @xcite . first we fix @xmath68 . we generate independent sequence @xmath73 from @xmath74 for some @xmath75 . it should be noted that @xmath76 works as a tuning parameter of the mcmc . smaller value of @xmath76 yields sticky movement with higher acceptance probability while larger value of @xmath76 would result in bigger jumps with less acceptance probability . define @xmath77 . hence the proposal move @xmath78 is given by @xmath79 the conditional distribution of @xmath80 given @xmath69 is given by ( see section [ section_mcmc_1 ] for the derivation ) @xmath81 where @xmath82 suppose @xmath83 and @xmath84 denote the likelihood for npsqr ( either corresponding to complete data or quantile grid data ) for the parameter values @xmath85 and @xmath86 respectively . then a single block update for @xmath87 is given by @xmath88 where @xmath89 and @xmath90 denotes the uniform prior density . for npdfsqr we define @xmath91 for @xmath68 . hence in this case also the parameter space is given by a collection of @xmath71 simplex blocks . hence in case of npdfsqr ( for complete data and quantile grid data ) , the update steps are performed similar to that of npsqr ( as mentioned above ) . in this case also , inside each iteration step of mcmc , @xmath71 simplex blocks are updated one by one . in case of very large parameter space , the strategy of warm - start in general helps in reducing the burn - in for metropolis - hastings mcmc . in the proposed method , instead of using a randomly generated starting point , we use the maximum likelihood estimator ( mle ) as the starting point . in section [ mcmc_here ] , it is noted that for both npsqr and npdfsqr methods , the parameter space is given by a collection of simplex blocks . one of the challenging aspect of finding mle under this scenario is that the parameter space is constrained and for npsqr , the likelihood function does not have any closed form . it is almost impossible to verify whether the negative of the likelihood of npsqr is convex or not ( in case negative likelihood is convex , there exists only one global maximum and convex optimization techniques can be used to find it ) . thus optimization should be performed assuming the possibility of existence of multiple local maximums of the likelihood function . secondly , due to the absence of a closed form likelihood in the case of npsqr , the derivative of the likelihood function does not have any closed form . in this case , one of the disadvantages of using derivative based optimization methods is that derivatives can be evaluated only numerically which is computationally intensive . hence , this is an ideal scenario to use black - box optimization technique since black - box optimization technique does not use analytically derivative and is used to optimize any function with ( possibly ) multiple maximums or minimums . recently @xcite proposed an black - box optimization technique on a hyper - rectangular parameter space which has been shown to perform better ( in terms of computing time , accuracy and successful convergence ) than black - box optimization techniques genetic algorithm ( @xcite , @xcite , @xcite ) and simulated annealing ( @xcite , @xcite ) yielding better solutions . following that strategy , @xcite modified that algorithm to optimize any function on an unit simplex . later @xcite extended that method and proposed ` greedy coordinate descent of varying step sizes on multiple simplexes ' ( gcdvsms ) algorithm which efficiently minimizes ( or maximizes ) any black - box function of parameters given by a collection of unit simplex blocks . the main idea of the this algorithm is to make jumps of varying step - sizes within each unit simplex blocks parallelly and searching for the most favorable direction of movement . we use gcdvsms algorithm to find the warm starting point before initializing the mcmc . as mentioned section [ mcmc_here ] , @xmath76 plays a critical role in controlling the acceptance probability . instead of fixing the value of @xmath76 , we propose an adaptive strategy so that during the mcmc iterations , acceptance probability is maintained within a desirable range of 0.15 to 0.45 . for both npsqr and npdfsqr , we start the first iteration with @xmath92 . it should be noted that in each iteration , @xmath71 simplex blocks are updated ; hence , @xmath71 acceptance - rejection decisions are taken . after each iteration , the cumulative acceptance ratio is calculated . at the end of an iteration , if the cumulative acceptance probability drops below 0.15 , @xmath76 is updated to @xmath93 and if the cumulative acceptance probability goes above 0.45 , the value of @xmath76 is updated to @xmath94 . note that in this way , the value of @xmath76 will always be greater than 1 . for simulation purpose , we consider the following true models and we generate sample of sizes @xmath95 for each case . 1 . * first simulation study :* we consider the explanatory variable @xmath96 in coming from @xmath97 . the dependence of the response variable @xmath4 on @xmath96 is given by @xmath98 where @xmath99 follows @xmath100 ( i.e. , skewed normal distribution with scale parameter 4 , mean 0 and standard deviation 1 ) . * second simulation study :* we consider the explanatory variable @xmath96 in coming from @xmath101 . the dependence of the response variable @xmath4 on @xmath96 is given by @xmath102 where @xmath103 follows discrete uniform @xmath104 and @xmath99 follows gamma distribution with shape and scale parameters 5 and 1 respectively . for each of the cases given by equation ( [ sim_1_eq ] ) and ( [ sim_2_eq ] ) , the quantiles are estimated using non - parametric simultaneous quantile regression ( npsqr ) , non - parametric distribution function simultaneous quantile regression ( npdfsqr ) , local linear quantile regression ( llqr ) and local spline quantile regression ( lsqr ) ( see @xcite , @xcite ) . + for npsqr and npdfsqr , first the explanatory variable and the response variables are transformed into unit interval separately by linear transformation . we use piece - wise quadratic b - spline for expanding both the quantile function as well as the explanatory variable ( i.e. , @xmath105 ) . one of the biggest advantage of quadratic b - spline is that equations and reduce to quadratic equation which can be solved analytically very easily . suppose @xmath24 and @xmath72 denote the equidistant knots on unit interval such that @xmath106 in case of npsqr , for b - spline expansion , we consider @xmath24 and @xmath72 knot sequences for expanding the quantile function and transformed explanatory variable respectively . we consider @xmath107 and choose the best model using the akaike information criteria ( aic ) criterion . for npdfsqr , suppose that knot sequences @xmath24 and @xmath72 are used for expanding the distribution function and transformed explanatory variable respectively . for npdfsqr , it is noted that taking @xmath108 , yields poorly estimated posterior quantile curves under different simulation studies . the possible reason is that in case of npdfsqr , a lot of estimated b - spline coefficients ( which are used to estimate the distribution function of the response variable ) are coming to be nearly zero which might be an indicator of usage of less number of knots to represent the variability of the distribution function . therefore , for npdfsqr , we omit the cases @xmath108 and consider the cases @xmath109 . then we choose the best model via the aic criterion . 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] + 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] + @ccccc@ .(first simulation study ( complete data ) ) prediction mean squared errors using npsqr , npdfsqr , llqr and lsqr based on simulation studies for sample sizes @xmath111 . [ cols="^ " , ] + & 5 & 510.31 & 537.40 + ( l)2 - 4 & 10 & 524.79 & 568.91 + ( l)2 - 4 & 20 & 559.10 & 580.08 + & 5 & 550.09 & 548.82 + ( l)2 - 4 & 10 & 578.09 & 571.07 + ( l)2 - 4 & 20 & 573.44 & 575.94 + & 5 & 497.74 & 541.71 + ( l)2 - 4 & 10 & 535.20 & 539.61 + ( l)2 - 4 & 20 & 540.32 & 549.71 + @xcite made an argument that the hurricanes with higher velocities in the north atlantic basin have got stronger in the last couple of decades . we apply npsqr method to estimate the simultaneous quantiles of the hurricane velocities in the north atlantic basin using the hurricane intensity data during the period 19812006 . first the explanatory variable time is linearly transformed to unit interval such that the years 1981 and 2006 are mapped to 0 and 1 respectively . to transform the hurricane velocities into the unit interval , we assume the hurricane velocities follow the power - pareto distribution . the power - pareto density is given by @xmath112 the distribution function is given by @xmath113 @xcite proposed the parameter values as @xmath114 , @xmath115 and @xmath116 in the same context . we transform the hurricane velocities into unit interval using equation ( [ eq : pareto_dist_here ] ) . after transforming both @xmath96 and @xmath4 values into unit interval , we use npsqr method to estimate the simultaneous quantiles of the hurricane wind velocities . similar to the approach considered in section [ sec_complete ] , we start the block - metropolis hastings algorithm with a warm starting point found using gcdvsms algorithm . we consider 10000 posterior samples discarding the first 1000 samples as burn - in . the number of equidistant knots to be used for b - spline basis expansion is selected using the aic . after the quantile curves are estimated , corresponding inverse transformations are performed on the response and the explanatory variables before plotting them . in figure [ figfighurricane ] we note that unlike the upper quantiles , the lower quantiles of the hurricane velocities have changed little over the time . we note a periodic pattern in the upper quantiles . specially this pattern becomes more prominent with increasing values of the quantile . a increasing pattern of the higher quantile curves is noted during the period 1987 - 1994 and 2002 - 2005 while a decreasing pattern is prominent during 1994 - 2002 . historical tables for us household income data can be found in this site . in the data tables , the 20 , 40 , 60 , 80 and 95-th quantiles of the household income in current dollars ( accessed 11 - 25 - 2016 ) of all population ( combined ) , asian , black , hispanic , white and white non - hispanic population have been provided for a few years . along with that , the total population of each category at each considered year has been given . a snapshot of the data table showing the household income distribution of all population during 2010 - 2015 is given in table [ snapshot ] . for analysis , we transform the years linearly to the the unit interval . for example , for hispanic population since the data is available during 1972 - 2015 , we transform it linearly to the unit interval such that 1972 and 2015 get mapped to 0 and 1 respectively . to transform the incomes into unit interval , we use a log - linear transformation . first we take logarithms of all income values of all races . after the @xmath117 transformation , suppose @xmath118 and @xmath119 denote the smallest and the biggest values . define @xmath120 and @xmath121 . we use the transformation @xmath122 to transform all the incomes to unit interval and the values of @xmath123 and @xmath124 come out to be @xmath125 and @xmath126 respectively . after the analysis , inverse transformations are performed before plotting the quantile curves to return to the original scale . it is noted that this data is somewhat different from the data considered for simulation study in section [ sec_grid ] . firstly , the value of quantile grids ( i.e. , @xmath127 ) in this data is different for each year ( or time - point ) . for example , as seen in table [ snapshot ] , the values of income at different quantile levels in 2015 is different than that of 2014 . secondly , unlike the data considered in section [ sec_grid ] , here for each value of @xmath96 ( i.e. , time - point ) , there are multiple observations . the quantile grid considered here is given by @xmath128 where @xmath129 and @xmath130 . so if at @xmath31 time - points @xmath131 , the number of observations ( i.e. , population ) are @xmath132 then the likelihood is given by @xmath133 clearly , the value of @xmath134 can be found using the same technique as used described in section [ sec_grid ] . to estimate the quantile curves we use the npsqr method . we start the block metropolis - hastings mcmc algorithm with warm starting point found using the gcdvsms algorithm . unlike all the previous studies , this data represent the population , not the sample . hereby , instead of choosing the optimal number of knots for fitting the b - spline , we can fix their values anywhere depending on desired smoothness level . we set @xmath135 for the whole analysis . in figure [ income ] we plot the estimated simultaneous quantiles of household income of all population ( during 1967 - 2015 ) , asian ( during 2002 - 2015 ) , black ( during 1967 - 2015 ) , hispanic ( during 1972 - 2015 ) , white ( during 1967 - 2015 ) and white non - hispanic ( during 1972 - 2015 ) population . irrespective of the races , it is noted that the higher quantile curves increase at higher rates while the lower quantile curves are roughly constant over the years . household incomes seem to be more evenly distributed among asian people compared with other races . among other races white and white non - hispanic population have lesser gaps across different quantile levels of income distribution compared with that of black and hispanic population . the estimated quantile levels of household income of asian population is greater than other populations . it should be also noted that the gaps between the quantile levels are more or less increasing over time . 0.5 for @xmath110 using npsqr.,title="fig : " ] 0.5 for @xmath110 using npsqr.,title="fig : " ] 0.5 for @xmath110 using npsqr.,title="fig : " ] 0.5 for @xmath110 using npsqr.,title="fig : " ] + 0.5 for @xmath110 using npsqr.,title="fig : " ] 0.5 for @xmath110 using npsqr.,title="fig : " ] + in this paper two novel methods for non - parametric simultaneous quantile regression methods have been proposed . in the first method , the quantile function is estimated non - parametrically using tensor products of quadratic b - splines basis expansion and in the second method the distribution function is estimated by a non - parametric approach using tensor product of quadratic b - splines basis expansion . these methods have been further developed for estimating the quantiles for the quantile grid data . we consider the block metropolis - hastings mcmc algorithm to estimate the coefficients of the b - spline basis functions . before initializing the mcmc , the maximum likelihood estimator ( mle ) is evaluated using gcdvsms algorithm and it is used as the starting point . the optimal number of knots for the b - spline basis expansion is selected using the aic criterion . unlike the existing popular methods of non - linear quantile regression , e.g. , local linear and local spline quantile regression , the monotonicity of the quantile curves are maintained using the proposed methods . in the simulation studies it is shown that both of the proposed methods generally perform better than llqr and lsqr in terms of the pmse . it is also observed that for the quantile grid data , npsqr performs slightly better than npdfsqr in terms of pmse . the npsqr method has been used to analyze the hurricane intensity data of north atlantic region for the years 1981 - 2006 . a periodic nature is noted at higher quantile levels while estimated lower quantile curves are relatively stable and with respect to time . npsqr method has been also used to analyze the historical household income data of different races in us given in the form of quantile grids . it is noted that the higher quantile curves are increasing generally at higher rates than the lower quantile curves . the differences between the household income levels tend to increase over time . p. das , s. ghosal ( 2016 ) . _ bayesian quantile regression using random b - spline series prior , computational statistics and data analysis ( to appear , doi : 10.1016/j.csda.2016.11.014 ) , arxiv.org / abs/1609.04843v1_. r. koenker , s. portnoy , s. , p.t . ng , a. zeileis , p. grosjean , b.d . ripley ( 2016 ) . _ quantreg : quantile regression , r package version 5.29 , https://cran.r - project.org / web / packages / quantreg / quantreg.pdf_. b. j. reich ( 2012 ) . _ spatiotemporal quantile regression for detecting distributional changes in environmental processes , journal of royal statistical society series c ( applied statistics ) , 61(4 ) , 535 - 553_.

in this paper , we consider bayesian methods for non - parametric quantile regressions with multiple continuous predictors ranging values in the unit interval . in the first method , the quantile function is assumed to be smooth over the explanatory variable and is expanded in tensor product of b - spline basis functions . while in the second method , the distribution function is assumed to be smooth over the explanatory variable and is expanded in tensor product of b - spline basis functions . unlike other existing methods of non - parametric quantile regressions , the proposed methods estimate the whole quantile function instead of estimating on a grid of quantiles . priors on the b - spline coefficients are put in such a way that the monotonicity of the estimated quantile levels are maintained unlike local polynomial quantile regression methods . the proposed methods have also been modified for quantile grid data where only the percentile range of each response observations are known . simulations studies have been provided for both complete and quantile grid data . the proposed method has been used to estimate the quantiles of us household income data and north atlantic hurricane intensity data . * * keywords:**b - spline prior ; block metropolis - hastings ; non - parametric quantile regression ; north atlantic hurricane data ; us household income data

<s>[INST]quantile regression is one of a popular alternative to mean regression when the data is non - normal , skewed or heteroscedastic . quantile regression is also useful when our objective is to make inferences about the population at different quantile levels . linear quantile regression was first proposed in @xcite . various other frequentist methods for quantile regression can be found in @xcite . @xcite first introduced the quantile regression using bayesian methods . later @xcite , @xcite , @xcite , @xcite proposed a few methods on generalization and extension of single level quantile regression under different possible scenarios . the main disadvantage of considering separate quantile regression using single level quantile regression is that the natural ordering among different quantiles can not be ensured . addressing the non - crossing issue , @xcite proposed a quantile regression method assuming the response variable to be heteroskedastic . @xcite proposed a method to estimate the quantile curve using linear interpolation from a estimated gird of quantile curves . @xcite and @xcite proposed non - crossing quantile regression methods using support vector machine ( svm , @xcite ) . later @xcite used doubly penalized kernal machine ( dpkm ) for estimating non - crossing quantile curves . @xcite and @xcite proposed quantile regression methods for a grid of quantiles addressing the monotonicity constraint . later @xcite , @xcite , @xcite , @xcite proposed linear quantile regression methods addressing the non - crossing issues . recently , @xcite and @xcite proposed simultaneous linear quantile regression methods for univariate explanatory variables . @xcite extended that simultaneous linear quantile regression method to handle multivariate predictor case . @xcite also extended the method proposed in @xcite in the spatio - temporal simultaneous quantile regression context where the response variable is assumed to be linearly dependent on one of the explanatory variables and varying non - parametrically with rest of the explanatory variables . one of the shortcomings of using linear quantile regression method is that it is not able to reveal a higher degree polynomial trend in the quantile curves . for example , while regressing household income data of a country over time , lower quantile levels maybe linear with time but the upper quantile levels may evolve very differently , for instance lower quantile level may increase linearly with time but upper quantile level may increase faster . in that case , using linear quantile regression will not be appropriate since it would only give the closest possible linear approximation of the quantile curves . quantile regression methods addressing this issue were proposed in @xcite , @xcite . @xcite proposed the local linear quantile regression method based on the techniques proposed in @xcite , @xcite , @xcite . @xcite and @xcite proposed alternative methods of quantile regressions . a few other non - parametric quantile regression methods were proposed in @xcite , @xcite and @xcite . @xcite provided a detailed description of local linear quantile regression method using software r. alongside , he also proposed an alternative method called local spline quantile regression . as long as non - linear quantile regression is concerned , most of the above - mentioned methods do not take care of the non - crossing issues . although , @xcite proposed a non - parametric quantile regression method addressing the non - crossing issue , it can only estimate a set of non - crossing curves for a given grid of quantiles and it does not estimate the whole quantile regression function . secondly , the quantile regression estimates obtained by this method is sensitive to the number and location of chosen quantile grids . instead of estimating the quantile curves at a given set of quantiles , it is more desirable to estimate the whole quantile curve simultaneously to emerge the broader picture . in this paper , we propose two bayesian methods for quantile regression using b - spline . in the first method , the entire quantile function is modeled by a b - spline series expansion . for each of the explanatory variables , a corresponding b - spline basis function is considered . the whole quantile function is obtained via tensor product of b - spline basis functions corresponding to each dimension of explanatory variables and one corresponding to the quantile level . the prior on the b - spline coefficients is put in such a way that the monotonicity of the quantile curves is maintained . we name this method ` non - parametric simultaneous quantile regression ( npsqr ) ' . in the second method , instead of the quantile function , the conditional distribution function is estimated non - parametrically using b - spline basis expansion . similar to npsqr , in this method also , corresponding to each dimension of the explanatory variable , a b - spline basis is considered . again , the prior of the coefficients of the b - spline basis functions is put in such a way that the monotonicity of the distribution function is maintained . in this case also the whole distribution function is given by tensor product of the b - spline basis functions . the conditional distribution function is inverted to obtain the quantile regression function . the use of splines , which are piece - wise polynomials , allow efficient inversion through a combination of analytical and numerical technique . we name this method to be ` non - parametric distribution function simultaneous quantile regression ( npdfsqr ) ' . further using both of these two approaches , we propose the method of estimating the quantile curves when only the data with frequencies of the observations in each quantile range are available . suppose @xmath0 and @xmath1 denote the @xmath2-dimensional explanatory variable and the response variable respectively . using monotonic transformation , each coordinates of the explanatory variable and the response variable are transformed into unit interval . suppose @xmath3 denotes the conditional quantile function of @xmath4 given @xmath5 . a b - spline function of degree @xmath6 ( i.e. , degree of piece - wise polynomial is @xmath7 ) with knot sequence @xmath8 has @xmath9 basis functions . let @xmath10 denote b - spline basis functions of degree @xmath6 on the above - mentioned knot sequence . for simplicity we consider equidistant knots , i.e. , @xmath11 for @xmath12 . hence the quantile function is given by @xmath13 where @xmath14 , are the coefficients of b - splines basis expansion of @xmath3 . thus in the above - mentioned equation it is noted that the coefficients of the basis functions used to expand the quantile function are dependent on the explanatory variable @xmath15 . secondly , the imposed monotonicity condition on the b - spline coefficients @xmath16 ensures the monotoniticy of the quantile levels ( @xcite ) . now to put a prior , the functions @xmath16 , it is expanded using @xmath2-dimensional tensor product of the b - spline basis functions of degree @xmath17 . we use the knot sequence @xmath18 such that @xmath19 for all the coordinates of the explanatory variable @xmath15 . then @xmath20 is given by @xmath21 then the parameters which need to be estimated are given by @xmath22 for modeling the distribution function with b - spline basis functions , we adopt a similar technique . suppose @xmath23 denotes the conditional distribution function of @xmath4 at @xmath5 . suppose @xmath10 denotes the b - spline coefficients of degree @xmath6 on the knot sequence @xmath24 as mentioned earlier . then the conditional distribution @xmath23 is given by @xmath25 it is noted that again the coefficients @xmath26 are taken in such a way that the monotonicity of the distribution function is preserved . to put a prior on @xmath26 , we use the same technique as mentioned in section [ npsqr_model ] . then @xmath27 is given by @xmath28 hence the parameters to be estimated are given by @xmath29 . in this section we describe the likelihood evaluation for both complete data and grouped data where only the frequencies of observations at each range of quantiles are given with the corresponding values of the explanatory variables . suppose that the explanatory and the response variables in the data are given by @xmath1 and @xmath30 where @xmath31 denotes the sample size and @xmath2 denotes the dimension of the explanatory variable . in the case of npsqr , the likelihood derived from the quantile function is given by @xmath32 where @xmath33 is given by @xmath34 here @xmath35 solves the equation @xmath36 as described in section [ npsqr_model ] , @xmath37 is constructed in such a way that it is monotonically increasing in @xmath38 . hence equation has a unique solution . in case we consider piece - wise quadratic b - spline ( i.e. , @xmath6=2 ) , an advantage of our proposed method is that equation reduces to a quadratic equation and hence it can be solved analytically . solving it analytically provides the exact solution in lesser time . now to compute the likelihood , using the properties of derivative of b - spline ( @xcite ) , we get @xmath39 where @xmath40 thus the log - likelihood in case of npsqr is given by @xmath41 in case of npdfsqr , the log - likelihood function is given by @xmath42 where @xmath43 in the case of grid data suppose the partition of the quantiles of the response are given by @xmath44 and for each observation it is given between which two consecutive quantile divisions it belongs . define @xmath45 for @xmath46 . given the value of the explanatory variable for the @xmath47-th subject @xmath48 , the probability of an observation @xmath49 belonging between @xmath50 and @xmath51-th quantile is given by @xmath52 . here @xmath53 denotes the @xmath54-th quantile @xmath55 of @xmath4 . hence the total likelihood is given by @xmath56 we assume that the values @xmath57 are provided and with @xmath58 , @xmath59 for all @xmath46 . now for npsqr , it should be noted that @xmath60 is the solution of the equation @xmath37@xmath61 since @xmath62 implies @xmath63 . hence @xmath60 can be obtained solving the following equation in terms of @xmath38 @xmath64 in case of npdfsqr , once the values of @xmath65 are evaluated , likelihood evaluation is straightforward and can be easily obtained using equation . to estimate the parameters for npsqr and npdfsqr methods ( given by equations and respectively ) we use block metropolis - hastings markov chain monte carlo algorithm ( @xcite ) . it should be noted that the parameter space which needs to be estimated are of the same form for npsqr and npdfsqr and hence we use the similar steps and same prior distribution for both the cases . recall that for npsqr the parameter space is given by @xmath66 now define @xmath67 for @xmath68 . then it can be noted that @xmath69 belongs to the unit - simplex for any given @xmath68 since @xmath70for @xmath68 . we put the uniform prior on each simplex block . the number of simplex blocks is given by @xmath71 where @xmath72 is the equidistant knot sequence used for each coordinate of the explanatory variables and @xmath17 is the degree of the piece - wise polynomials use for b - spline regression ( as mentioned in section [ npsqr_model ] ) . within an iteration , one simplex block is updated at a time . hence there will be @xmath71 updates performed one at a time during a single iteration . to make movements on the simplex block , we use the same strategy as explained in @xcite and @xcite . first we fix @xmath68 . we generate independent sequence @xmath73 from @xmath74 for some @xmath75 . it should be noted that @xmath76 works as a tuning parameter of the mcmc . smaller value of @xmath76 yields sticky movement with higher acceptance probability while larger value of @xmath76 would result in bigger jumps with less acceptance probability . define @xmath77 . hence the proposal move @xmath78 is given by @xmath79 the conditional distribution of @xmath80 given @xmath69 is given by ( see section [ section_mcmc_1 ] for the derivation ) @xmath81 where @xmath82 suppose @xmath83 and @xmath84 denote the likelihood for npsqr ( either corresponding to complete data or quantile grid data ) for the parameter values @xmath85 and @xmath86 respectively . then a single block update for @xmath87 is given by @xmath88 where @xmath89 and @xmath90 denotes the uniform prior density . for npdfsqr we define @xmath91 for @xmath68 . hence in this case also the parameter space is given by a collection of @xmath71 simplex blocks . hence in case of npdfsqr ( for complete data and quantile grid data ) , the update steps are performed similar to that of npsqr ( as mentioned above ) . in this case also , inside each iteration step of mcmc , @xmath71 simplex blocks are updated one by one . in case of very large parameter space , the strategy of warm - start in general helps in reducing the burn - in for metropolis - hastings mcmc . in the proposed method , instead of using a randomly generated starting point , we use the maximum likelihood estimator ( mle ) as the starting point . in section [ mcmc_here ] , it is noted that for both npsqr and npdfsqr methods , the parameter space is given by a collection of simplex blocks . one of the challenging aspect of finding mle under this scenario is that the parameter space is constrained and for npsqr , the likelihood function does not have any closed form . it is almost impossible to verify whether the negative of the likelihood of npsqr is convex or not ( in case negative likelihood is convex , there exists only one global maximum and convex optimization techniques can be used to find it ) . thus optimization should be performed assuming the possibility of existence of multiple local maximums of the likelihood function . secondly , due to the absence of a closed form likelihood in the case of npsqr , the derivative of the likelihood function does not have any closed form . in this case , one of the disadvantages of using derivative based optimization methods is that derivatives can be evaluated only numerically which is computationally intensive . hence , this is an ideal scenario to use black - box optimization technique since black - box optimization technique does not use analytically derivative and is used to optimize any function with ( possibly ) multiple maximums or minimums . recently @xcite proposed an black - box optimization technique on a hyper - rectangular parameter space which has been shown to perform better ( in terms of computing time , accuracy and successful convergence ) than black - box optimization techniques genetic algorithm ( @xcite , @xcite , @xcite ) and simulated annealing ( @xcite , @xcite ) yielding better solutions . following that strategy , @xcite modified that algorithm to optimize any function on an unit simplex . later @xcite extended that method and proposed ` greedy coordinate descent of varying step sizes on multiple simplexes ' ( gcdvsms ) algorithm which efficiently minimizes ( or maximizes ) any black - box function of parameters given by a collection of unit simplex blocks . the main idea of the this algorithm is to make jumps of varying step - sizes within each unit simplex blocks parallelly and searching for the most favorable direction of movement . we use gcdvsms algorithm to find the warm starting point before initializing the mcmc . as mentioned section [ mcmc_here ] , @xmath76 plays a critical role in controlling the acceptance probability . instead of fixing the value of @xmath76 , we propose an adaptive strategy so that during the mcmc iterations , acceptance probability is maintained within a desirable range of 0.15 to 0.45 . for both npsqr and npdfsqr , we start the first iteration with @xmath92 . it should be noted that in each iteration , @xmath71 simplex blocks are updated ; hence , @xmath71 acceptance - rejection decisions are taken . after each iteration , the cumulative acceptance ratio is calculated . at the end of an iteration , if the cumulative acceptance probability drops below 0.15 , @xmath76 is updated to @xmath93 and if the cumulative acceptance probability goes above 0.45 , the value of @xmath76 is updated to @xmath94 . note that in this way , the value of @xmath76 will always be greater than 1 . for simulation purpose , we consider the following true models and we generate sample of sizes @xmath95 for each case . 1 . * first simulation study :* we consider the explanatory variable @xmath96 in coming from @xmath97 . the dependence of the response variable @xmath4 on @xmath96 is given by @xmath98 where @xmath99 follows @xmath100 ( i.e. , skewed normal distribution with scale parameter 4 , mean 0 and standard deviation 1 ) . * second simulation study :* we consider the explanatory variable @xmath96 in coming from @xmath101 . the dependence of the response variable @xmath4 on @xmath96 is given by @xmath102 where @xmath103 follows discrete uniform @xmath104 and @xmath99 follows gamma distribution with shape and scale parameters 5 and 1 respectively . for each of the cases given by equation ( [ sim_1_eq ] ) and ( [ sim_2_eq ] ) , the quantiles are estimated using non - parametric simultaneous quantile regression ( npsqr ) , non - parametric distribution function simultaneous quantile regression ( npdfsqr ) , local linear quantile regression ( llqr ) and local spline quantile regression ( lsqr ) ( see @xcite , @xcite ) . + for npsqr and npdfsqr , first the explanatory variable and the response variables are transformed into unit interval separately by linear transformation . we use piece - wise quadratic b - spline for expanding both the quantile function as well as the explanatory variable ( i.e. , @xmath105 ) . one of the biggest advantage of quadratic b - spline is that equations and reduce to quadratic equation which can be solved analytically very easily . suppose @xmath24 and @xmath72 denote the equidistant knots on unit interval such that @xmath106 in case of npsqr , for b - spline expansion , we consider @xmath24 and @xmath72 knot sequences for expanding the quantile function and transformed explanatory variable respectively . we consider @xmath107 and choose the best model using the akaike information criteria ( aic ) criterion . for npdfsqr , suppose that knot sequences @xmath24 and @xmath72 are used for expanding the distribution function and transformed explanatory variable respectively . for npdfsqr , it is noted that taking @xmath108 , yields poorly estimated posterior quantile curves under different simulation studies . the possible reason is that in case of npdfsqr , a lot of estimated b - spline coefficients ( which are used to estimate the distribution function of the response variable ) are coming to be nearly zero which might be an indicator of usage of less number of knots to represent the variability of the distribution function . therefore , for npdfsqr , we omit the cases @xmath108 and consider the cases @xmath109 . then we choose the best model via the aic criterion . 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] + 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] 0.5 for @xmath110 using npsqr , npdfsqr , llqr and lsqr with the data points.,title="fig : " ] + @ccccc@ .(first simulation study ( complete data ) ) prediction mean squared errors using npsqr , npdfsqr , llqr and lsqr based on simulation studies for sample sizes @xmath111 . [ cols="^ " , ] + & 5 & 510.31 & 537.40 + ( l)2 - 4 & 10 & 524.79 & 568.91 + ( l)2 - 4 & 20 & 559.10 & 580.08 + & 5 & 550.09 & 548.82 + ( l)2 - 4 & 10 & 578.09 & 571.07 + ( l)2 - 4 & 20 & 573.44 & 575.94 + & 5 & 497.74 & 541.71 + ( l)2 - 4 & 10 & 535.20 & 539.61 + ( l)2 - 4 & 20 & 540.32 & 549.71 + @xcite made an argument that the hurricanes with higher velocities in the north atlantic basin have got stronger in the last couple of decades . we apply npsqr method to estimate the simultaneous quantiles of the hurricane velocities in the north atlantic basin using the hurricane intensity data during the period 19812006 . first the explanatory variable time is linearly transformed to unit interval such that the years 1981 and 2006 are mapped to 0 and 1 respectively . to transform the hurricane velocities into the unit interval , we assume the hurricane velocities follow the power - pareto distribution . the power - pareto density is given by @xmath112 the distribution function is given by @xmath113 @xcite proposed the parameter values as @xmath114 , @xmath115 and @xmath116 in the same context . we transform the hurricane velocities into unit interval using equation ( [ eq : pareto_dist_here ] ) . after transforming both @xmath96 and @xmath4 values into unit interval , we use npsqr method to estimate the simultaneous quantiles of the hurricane wind velocities . similar to the approach considered in section [ sec_complete ] , we start the block - metropolis hastings algorithm with a warm starting point found using gcdvsms algorithm . we consider 10000 posterior samples discarding the first 1000 samples as burn - in . the number of equidistant knots to be used for b - spline basis expansion is selected using the aic . after the quantile curves are estimated , corresponding inverse transformations are performed on the response and the explanatory variables before plotting them . in figure [ figfighurricane ] we note that unlike the upper quantiles , the lower quantiles of the hurricane velocities have changed little over the time . we note a periodic pattern in the upper quantiles . specially this pattern becomes more prominent with increasing values of the quantile . a increasing pattern of the higher quantile curves is noted during the period 1987 - 1994 and 2002 - 2005 while a decreasing pattern is prominent during 1994 - 2002 . historical tables for us household income data can be found in this site . in the data tables , the 20 , 40 , 60 , 80 and 95-th quantiles of the household income in current dollars ( accessed 11 - 25 - 2016 ) of all population ( combined ) , asian , black , hispanic , white and white non - hispanic population have been provided for a few years . along with that , the total population of each category at each considered year has been given . a snapshot of the data table showing the household income distribution of all population during 2010 - 2015 is given in table [ snapshot ] . for analysis , we transform the years linearly to the the unit interval . for example , for hispanic population since the data is available during 1972 - 2015 , we transform it linearly to the unit interval such that 1972 and 2015 get mapped to 0 and 1 respectively . to transform the incomes into unit interval , we use a log - linear transformation . first we take logarithms of all income values of all races . after the @xmath117 transformation , suppose @xmath118 and @xmath119 denote the smallest and the biggest values . define @xmath120 and @xmath121 . we use the transformation @xmath122 to transform all the incomes to unit interval and the values of @xmath123 and @xmath124 come out to be @xmath125 and @xmath126 respectively . after the analysis , inverse transformations are performed before plotting the quantile curves to return to the original scale . it is noted that this data is somewhat different from the data considered for simulation study in section [ sec_grid ] . firstly , the value of quantile grids ( i.e. , @xmath127 ) in this data is different for each year ( or time - point ) . for example , as seen in table [ snapshot ] , the values of income at different quantile levels in 2015 is different than that of 2014 . secondly , unlike the data considered in section [ sec_grid ] , here for each value of @xmath96 ( i.e. , time - point ) , there are multiple observations . the quantile grid considered here is given by @xmath128 where @xmath129 and @xmath130 . so if at @xmath31 time - points @xmath131 , the number of observations ( i.e. , population ) are @xmath132 then the likelihood is given by @xmath133 clearly , the value of @xmath134 can be found using the same technique as used described in section [ sec_grid ] . to estimate the quantile curves we use the npsqr method . we start the block metropolis - hastings mcmc algorithm with warm starting point found using the gcdvsms algorithm . unlike all the previous studies , this data represent the population , not the sample . hereby , instead of choosing the optimal number of knots for fitting the b - spline , we can fix their values anywhere depending on desired smoothness level . we set @xmath135 for the whole analysis . in figure [ income ] we plot the estimated simultaneous quantiles of household income of all population ( during 1967 - 2015 ) , asian ( during 2002 - 2015 ) , black ( during 1967 - 2015 ) , hispanic ( during 1972 - 2015 ) , white ( during 1967 - 2015 ) and white non - hispanic ( during 1972 - 2015 ) population . irrespective of the races , it is noted that the higher quantile curves increase at higher rates while the lower quantile curves are roughly constant over the years . household incomes seem to be more evenly distributed among asian people compared with other races . among other races white and white non - hispanic population have lesser gaps across different quantile levels of income distribution compared with that of black and hispanic population . the estimated quantile levels of household income of asian population is greater than other populations . it should be also noted that the gaps between the quantile levels are more or less increasing over time . 0.5 for @xmath110 using npsqr.,title="fig : " ] 0.5 for @xmath110 using npsqr.,title="fig : " ] 0.5 for @xmath110 using npsqr.,title="fig : " ] 0.5 for @xmath110 using npsqr.,title="fig : " ] + 0.5 for @xmath110 using npsqr.,title="fig : " ] 0.5 for @xmath110 using npsqr.,title="fig : " ] + in this paper two novel methods for non - parametric simultaneous quantile regression methods have been proposed . in the first method , the quantile function is estimated non - parametrically using tensor products of quadratic b - splines basis expansion and in the second method the distribution function is estimated by a non - parametric approach using tensor product of quadratic b - splines basis expansion . these methods have been further developed for estimating the quantiles for the quantile grid data . we consider the block metropolis - hastings mcmc algorithm to estimate the coefficients of the b - spline basis functions . before initializing the mcmc , the maximum likelihood estimator ( mle ) is evaluated using gcdvsms algorithm and it is used as the starting point . the optimal number of knots for the b - spline basis expansion is selected using the aic criterion . unlike the existing popular methods of non - linear quantile regression , e.g. , local linear and local spline quantile regression , the monotonicity of the quantile curves are maintained using the proposed methods . in the simulation studies it is shown that both of the proposed methods generally perform better than llqr and lsqr in terms of the pmse . it is also observed that for the quantile grid data , npsqr performs slightly better than npdfsqr in terms of pmse . the npsqr method has been used to analyze the hurricane intensity data of north atlantic region for the years 1981 - 2006 . a periodic nature is noted at higher quantile levels while estimated lower quantile curves are relatively stable and with respect to time . npsqr method has been also used to analyze the historical household income data of different races in us given in the form of quantile grids . it is noted that the higher quantile curves are increasing generally at higher rates than the lower quantile curves . the differences between the household income levels tend to increase over time . p. das , s. ghosal ( 2016 ) . _ bayesian quantile regression using random b - spline series prior , computational statistics and data analysis ( to appear , doi : 10.1016/j.csda.2016.11.014 ) , arxiv.org / abs/1609.04843v1_. r. koenker , s. portnoy , s. , p.t . ng , a. zeileis , p. grosjean , b.d . ripley ( 2016 ) . _ quantreg : quantile regression , r package version 5.29 , https://cran.r - project.org / web / packages / quantreg / quantreg.pdf_. b. j. reich ( 2012 ) . _ spatiotemporal quantile regression for detecting distributional changes in environmental processes , journal of royal statistical society series c ( applied statistics ) , 61(4 ) , 535 - 553_.[/INST] in this paper , we consider bayesian methods for non - parametric quantile regressions with multiple continuous predictors ranging values in the unit interval . in the first method , the quantile function is assumed to be smooth over the explanatory variable and is expanded in tensor product of b - spline basis functions . while in the second method , the distribution function is assumed to be smooth over the explanatory variable and is expanded in tensor product of b - spline basis functions . unlike other existing methods of non - parametric quantile regressions , the proposed methods estimate the whole quantile function instead of estimating on a grid of quantiles . priors on the b - spline coefficients are put in such a way that the monotonicity of the estimated quantile levels are maintained unlike local polynomial quantile regression methods . the proposed methods have also been modified for quantile grid data where only the percentile range of each response observations are known . simulations studies have been provided for both complete and quantile grid data . the proposed method has been used to estimate the quantiles of us household income data and north atlantic hurricane intensity data . * * keywords:**b - spline prior ; block metropolis - hastings ; non - parametric quantile regression ; north atlantic hurricane data ; us household income data </s>

SECTION 1. SHORT TITLE; AMENDMENT OF 1986 CODE. (a) Short Title.--This Act may be cited as the ``Medical Cost Containment Act of 1993''. (b) Amendment of 1986 Code.--Except as otherwise expressly provided, whenever in this Act an amendment or repeal is expressed in terms of an amendment to, or repeal of, a section or other provision, the reference shall be considered to be made to a section or other provision of the Internal Revenue Code of 1986. SEC. 2. Section 125A is added to the Code to read as follows: ``SEC. 125A. MEDICAL CARE SAVINGS BENEFITS. ``(a) In General.--A medical care savings benefit is a qualified benefit which consists of a Health Plan meeting the requirements of this section that includes, as part thereof, a Medical Care Savings Account, as set forth in section 408A. ``(b) Establishment of Medical Care Savings Benefit.--A medical care savings benefit shall be established as a Health Plan which provides that all or part of the premium differential realized by instituting a Qualified Higher Deductible Health Plan is credited to a participating employee during a plan year to pay for medical care described in section 213(d) subject to the limitations set forth in subsection (e) hereof. To the extent that any amount remains credited to that participant at the end of each plan year, such amount shall be deposited to a section 408(A) medical care savings account (which may also be referred to as a `Medical IRA') for that participant. ``(c) Payments from Account Balance.--If the plan provides for level installment payments, the plan may also provide that the maximum amount of reimbursement at a particular time during the period of coverage may be limited to the amount of actual contributions to the participant's benefit account. A participant may be advanced, interest free, such amounts necessary to cover incurred medical expenses which exceed the amount then credited to the participant's benefit account, upon the participant's agreement to repay such advancement from future installments or upon ceasing to be a participant. ``(d) Reporting.--Employers shall cause to be issued to participating employees, not less frequently than quarterly, a statement setting forth amounts remaining in their accounts. ``(e) Limitations on Medical Care Savings Benefits.--For purposes of this section-- ``(1) In general.--In the case of an Employer who has a Health Plan in existence immediately prior to the adoption of the Medical Care Savings Benefit, the maximum amount that may be contributed annually to a participant's benefit account shall be equal to-- ``(A) the cost of that Health Plan for that participant's type of coverage; plus ``(B) a cost of living adjustment for the calendar year in which the plan year begins, determined under section 1(f)(3) of the Code as adjusted annually based on the CPI-Medical cost of living component. ``(2) Other employers.--In the case of an Employer to whom paragraph (1) does not apply, the contribution limit shall be equal to the 67th percentile of the per employee health plan expenditures (for the calendar year for which such plan begins) for the type of coverage applicable to such employee based on a broad representative survey using methodology the same as or similar to that used by States to develop an average market premium for small group guarantee access legislation. Such study may be no broader than each State and may be broken down into representative surveys for areas within a State. The amount of such contribution shall be adjusted annually in accordance with the cost of living adjustment provided for in subsection (1)(b) of this section. ``(3) Overall limitation.--In no event may any contribution described above exceed the deductible amount of the Qualified Higher Deductible Plan. ``(f) Health Plan.--The term `Health Plan' means an employee welfare benefit plan providing medical care (as defined in section 213(d) of the Internal Revenue Code of 1954) to participants or beneficiaries directly or through insurance, reimbursement, or otherwise. ``(g) Qualified Higher Deductible Plan.--The term `Qualified Higher Deductible Plan' is a Health Plan which provides for payment of covered benefits in excess of the higher deductible, which higher deductible shall not exceed $5,000 in 1993 and, adjusted annually thereafter for increases in the cost of living in accordance with regulations prescribed by the Secretary. ``(h) Coordination With Health Flexible Spending Accounts.--If, during a Plan Year, a participating employee has a Medical Care Savings Benefit in effect and a health flexible spending account established under section 125, coverage under the health flexible spending account, for the type of medical expenses that may be reimbursed under the Medical Care Savings Benefit, would be limited to 100 percent of the deductible under the Qualified Higher Deductible Plan, less the amount credited in the current year to the Employee's Medical Care Savings Benefit Account. For purposes of section 125, a Medical Care Savings Benefit is not considered to involve the deferral of compensation for purposes of the Code. ``(i) Separate Determinations for Categories of Employees and Separate Lines of Business.--Contributions to Health Plans established by an Employer may be separately determined on the basis of: ``(1) Types of coverage. ``(2) Reasonable classifications of employees based on such classifications as hours of work per week, retirement status, coverage by a collective bargaining agreement. ``(3) Employees within separate lines of business, within the meaning of section 414(r). ``(j) Other Definitions for Purposes of this Section.-- ``(1) Employee.--The term `employee' means any individual employed by an Employer, including-- ``(A) an individual who is employee within the meaning of section 401(c)(1); and ``(B) former employees. ``(2) Types of coverage.--The types of coverage are-- ``(A) self-only coverage; and ``(B) coverage other than self-only coverage. ``(k) Preventative Health Care.--By allowing medical expenses payable from a medical care savings benefit to be those permitted under section 213(d) of the Internal Revenue Code, participating employees are encouraged to use this benefit to promote good health, to use preventative medical and health procedures, and to seek appropriate consultative and second opinions. ``(l) Nonduplication of Benefits.--Policies issued as a part of a medical care savings benefit shall not be required to duplicate expenses that may be proper expenses covered by the medical care savings benefit. Additionally, the Qualified Higher Deductible Plan may provide that the deductible specified in the insurance policy may be increased by the amount of any benefits payable by any other health benefits program or plan.''. SEC. 3. MEDICAL CARE SAVINGS ACCOUNT. (a) In General.--Chapter 1 (relating to normal taxes and surcharge) is amended by adding after section 408 the following new section: ``SEC. 408A. MEDICAL CARE SAVINGS ACCOUNTS. ``(a) Medical Care Savings Accounts.--For purposes of this section, the term `medical care savings account' (which may also be referred to as a `Medical IRA') means a trust created or organized in the United States for the exclusive benefit of an individual, the individual's dependents (as defined in section 152) or beneficiaries, but only if the written instrument creating the trust meets the following requirements: ``(1) No contribution will be accepted unless it is in cash. ``(2) The trustee is a bank (as defined in subsection (d)), insurance company (as defined in section 816), or such other person who demonstrates to the satisfaction of the Secretary that the manner in which such other person will administer the trust will be consistent with the requirements of this section. ``(3) No part of the trust funds will be invested in life insurance contracts. ``(4) The interest of an individual in the balance of the account is nonforfeitable. ``(5) The assets of the trust will not be commingled with other property except in a common trust fund or common investment fund. ``(b) Tax Treatment of Accounts.-- ``(1) Exemption from tax.--Any medical care savings account is exempt from taxation under this subtitle unless such account has ceased to be a medical care savings account by reason of paragraph (2) or (3): Provided, however, That earnings on such account shall be taxable. Notwithstanding the preceding sentence, any such account is subject to the taxes imposed by section 511 (relating to imposition of tax on unrelated business income of charitable, etc. organizations). ``(2) Loss of exemption of account where employee engages in prohibited transaction.-- ``(A) In general.--If, during any taxable year of the individual for whose benefit any medical care savings account is established, that individual, dependent, or his beneficiary engages in any transaction prohibited by section 4975 with respect to such account, such account ceases to be a medical care savings account as of the first day of such taxable year. For purposes of this paragraph the individual for whose benefit any account was established is treated as the creator of such account. ``(B) Account treated as distributing all its assets.--In any case in which any account ceases to be a medical savings account by reason of subparagraph (A) as of the first day of any taxable year, section 511 shall apply as if there were a distribution on such first day in an amount equal to the fair market value (on such first day) of all assets in the account (on such first day). ``(3) Effect of pledging account as security.--If, during any taxable year of the individual for whose benefit a medical care savings account is established, that individual uses the account or any portion thereof as security for a loan, the portion so used is treated as distributed to that individual. ``(4) Commingling medical care savings account amounts in certain common trust funds and common investment funds.--Any common trust fund or common investment fund of individual medical care savings account assets which is exempt from taxation under this subtitle does not cease to be exempt on account of the participation or inclusion of assets of a trust exempt from taxation under section 501(a) which is described in section 401(a). ``(c) Treatment of Distributions.-- ``(1) In general.--Except as otherwise provided in this subsection, any amount paid or distributed out of a medical savings account shall be included in gross income by the distributee. ``(2) Distributions for medical expenses.--Distributions from a medical care savings account shall not be taxable to the distributee, for amounts paid directly or indirectly for medical expenses as defined in section 213(d). ``(3) 10 percent additional tax for early withdrawals.-- Distributions described in paragraph 1 and not described in paragraph 2 shall be subject to an additional 10 percent tax for distributions made prior to age 59\1/2\ of the distributee. ``(4) Rollover contribution.--An amount is described in this paragraph as a rollover contribution which shall not be included in the gross income of the distributee if it meets the requirements of subparagraphs (A) and (B). ``(A) In general.--Paragraph (1) does not apply to any amount paid or distributed out of a medical care savings account to the individual for whose benefit the account is maintained if the entire amount received is paid into a medical care savings account for the benefit of such individual not later than the sixtieth day after the day on which he receives the payment or distribution. ``(B) Limitation.--This paragraph does not apply to any amount described in paragraph (A) received by an individual from a medical savings account if at any time during the one-year period ending on the day of such receipt such individual received any other amount described in that subparagraph from a medical care savings account which was not includible in his gross income because of the application of this paragraph. ``(C) Denial of rollover treatment for inherited accounts, etc.-- ``(i) In general.--In the case of an inherited medical savings account-- ``(I) this paragraph shall not apply to any amount received by an individual from such an account (and no amount transferred from such account to another medical care savings account shall be excluded from gross income by reason of such transfer), and ``(II) such inherited account shall not be treated as a medical care savings account for purposes of determining whether any other amount is a rollover contribution. ``(ii) Inherited medical care savings account.-- ``(I) the individual for whose benefit the account is maintained acquired such account by reason of the death of another individual, and ``(II) such individual was not the surviving spouse of such other individual. ``(d) Bank.--For purposes of subsection (a)(2), the term `bank' means-- ``(1) a bank (as defined in section 581), ``(2) an insured credit union (within the meaning of section 101(6) of the Federal Credit Union Act), and ``(3) a corporation which, under the laws of the State of its incorporation, is subject to supervision and examination by the Commissioner of Banking or other officer of such State in charge of the administration of the banking laws of such State.''. SEC. 4. EFFECTIVE DATES. The amendments made by this Act shall apply to years beginning after December 31, 1993. SEC. 5. OVERALL EFFECT ON TAX DEDUCTIBILITY. This Act is not intended to change the Code's current tax treatment of employer-provided coverage under accident and health plans.

Medical Cost Containment Act of 1993 - Amends the Internal Revenue Code to exclude from gross income medical care savings benefits. Describes such benefits as a health plan which provides that all or part of the premium differential realized by instituting a qualified higher deductible health plan is credited to participating employees to pay for medical care for a plan year. Requires amounts remaining at the end of such plan year to be deposited into a tax-exempt medical care savings account (subject to rules similar to those for retirement plans) for use by the participant for medical expenses.

<s>[INST]SECTION 1. SHORT TITLE; AMENDMENT OF 1986 CODE. (a) Short Title.--This Act may be cited as the ``Medical Cost Containment Act of 1993''. (b) Amendment of 1986 Code.--Except as otherwise expressly provided, whenever in this Act an amendment or repeal is expressed in terms of an amendment to, or repeal of, a section or other provision, the reference shall be considered to be made to a section or other provision of the Internal Revenue Code of 1986. SEC. 2. Section 125A is added to the Code to read as follows: ``SEC. 125A. MEDICAL CARE SAVINGS BENEFITS. ``(a) In General.--A medical care savings benefit is a qualified benefit which consists of a Health Plan meeting the requirements of this section that includes, as part thereof, a Medical Care Savings Account, as set forth in section 408A. ``(b) Establishment of Medical Care Savings Benefit.--A medical care savings benefit shall be established as a Health Plan which provides that all or part of the premium differential realized by instituting a Qualified Higher Deductible Health Plan is credited to a participating employee during a plan year to pay for medical care described in section 213(d) subject to the limitations set forth in subsection (e) hereof. To the extent that any amount remains credited to that participant at the end of each plan year, such amount shall be deposited to a section 408(A) medical care savings account (which may also be referred to as a `Medical IRA') for that participant. ``(c) Payments from Account Balance.--If the plan provides for level installment payments, the plan may also provide that the maximum amount of reimbursement at a particular time during the period of coverage may be limited to the amount of actual contributions to the participant's benefit account. A participant may be advanced, interest free, such amounts necessary to cover incurred medical expenses which exceed the amount then credited to the participant's benefit account, upon the participant's agreement to repay such advancement from future installments or upon ceasing to be a participant. ``(d) Reporting.--Employers shall cause to be issued to participating employees, not less frequently than quarterly, a statement setting forth amounts remaining in their accounts. ``(e) Limitations on Medical Care Savings Benefits.--For purposes of this section-- ``(1) In general.--In the case of an Employer who has a Health Plan in existence immediately prior to the adoption of the Medical Care Savings Benefit, the maximum amount that may be contributed annually to a participant's benefit account shall be equal to-- ``(A) the cost of that Health Plan for that participant's type of coverage; plus ``(B) a cost of living adjustment for the calendar year in which the plan year begins, determined under section 1(f)(3) of the Code as adjusted annually based on the CPI-Medical cost of living component. ``(2) Other employers.--In the case of an Employer to whom paragraph (1) does not apply, the contribution limit shall be equal to the 67th percentile of the per employee health plan expenditures (for the calendar year for which such plan begins) for the type of coverage applicable to such employee based on a broad representative survey using methodology the same as or similar to that used by States to develop an average market premium for small group guarantee access legislation. Such study may be no broader than each State and may be broken down into representative surveys for areas within a State. The amount of such contribution shall be adjusted annually in accordance with the cost of living adjustment provided for in subsection (1)(b) of this section. ``(3) Overall limitation.--In no event may any contribution described above exceed the deductible amount of the Qualified Higher Deductible Plan. ``(f) Health Plan.--The term `Health Plan' means an employee welfare benefit plan providing medical care (as defined in section 213(d) of the Internal Revenue Code of 1954) to participants or beneficiaries directly or through insurance, reimbursement, or otherwise. ``(g) Qualified Higher Deductible Plan.--The term `Qualified Higher Deductible Plan' is a Health Plan which provides for payment of covered benefits in excess of the higher deductible, which higher deductible shall not exceed $5,000 in 1993 and, adjusted annually thereafter for increases in the cost of living in accordance with regulations prescribed by the Secretary. ``(h) Coordination With Health Flexible Spending Accounts.--If, during a Plan Year, a participating employee has a Medical Care Savings Benefit in effect and a health flexible spending account established under section 125, coverage under the health flexible spending account, for the type of medical expenses that may be reimbursed under the Medical Care Savings Benefit, would be limited to 100 percent of the deductible under the Qualified Higher Deductible Plan, less the amount credited in the current year to the Employee's Medical Care Savings Benefit Account. For purposes of section 125, a Medical Care Savings Benefit is not considered to involve the deferral of compensation for purposes of the Code. ``(i) Separate Determinations for Categories of Employees and Separate Lines of Business.--Contributions to Health Plans established by an Employer may be separately determined on the basis of: ``(1) Types of coverage. ``(2) Reasonable classifications of employees based on such classifications as hours of work per week, retirement status, coverage by a collective bargaining agreement. ``(3) Employees within separate lines of business, within the meaning of section 414(r). ``(j) Other Definitions for Purposes of this Section.-- ``(1) Employee.--The term `employee' means any individual employed by an Employer, including-- ``(A) an individual who is employee within the meaning of section 401(c)(1); and ``(B) former employees. ``(2) Types of coverage.--The types of coverage are-- ``(A) self-only coverage; and ``(B) coverage other than self-only coverage. ``(k) Preventative Health Care.--By allowing medical expenses payable from a medical care savings benefit to be those permitted under section 213(d) of the Internal Revenue Code, participating employees are encouraged to use this benefit to promote good health, to use preventative medical and health procedures, and to seek appropriate consultative and second opinions. ``(l) Nonduplication of Benefits.--Policies issued as a part of a medical care savings benefit shall not be required to duplicate expenses that may be proper expenses covered by the medical care savings benefit. Additionally, the Qualified Higher Deductible Plan may provide that the deductible specified in the insurance policy may be increased by the amount of any benefits payable by any other health benefits program or plan.''. SEC. 3. MEDICAL CARE SAVINGS ACCOUNT. (a) In General.--Chapter 1 (relating to normal taxes and surcharge) is amended by adding after section 408 the following new section: ``SEC. 408A. MEDICAL CARE SAVINGS ACCOUNTS. ``(a) Medical Care Savings Accounts.--For purposes of this section, the term `medical care savings account' (which may also be referred to as a `Medical IRA') means a trust created or organized in the United States for the exclusive benefit of an individual, the individual's dependents (as defined in section 152) or beneficiaries, but only if the written instrument creating the trust meets the following requirements: ``(1) No contribution will be accepted unless it is in cash. ``(2) The trustee is a bank (as defined in subsection (d)), insurance company (as defined in section 816), or such other person who demonstrates to the satisfaction of the Secretary that the manner in which such other person will administer the trust will be consistent with the requirements of this section. ``(3) No part of the trust funds will be invested in life insurance contracts. ``(4) The interest of an individual in the balance of the account is nonforfeitable. ``(5) The assets of the trust will not be commingled with other property except in a common trust fund or common investment fund. ``(b) Tax Treatment of Accounts.-- ``(1) Exemption from tax.--Any medical care savings account is exempt from taxation under this subtitle unless such account has ceased to be a medical care savings account by reason of paragraph (2) or (3): Provided, however, That earnings on such account shall be taxable. Notwithstanding the preceding sentence, any such account is subject to the taxes imposed by section 511 (relating to imposition of tax on unrelated business income of charitable, etc. organizations). ``(2) Loss of exemption of account where employee engages in prohibited transaction.-- ``(A) In general.--If, during any taxable year of the individual for whose benefit any medical care savings account is established, that individual, dependent, or his beneficiary engages in any transaction prohibited by section 4975 with respect to such account, such account ceases to be a medical care savings account as of the first day of such taxable year. For purposes of this paragraph the individual for whose benefit any account was established is treated as the creator of such account. ``(B) Account treated as distributing all its assets.--In any case in which any account ceases to be a medical savings account by reason of subparagraph (A) as of the first day of any taxable year, section 511 shall apply as if there were a distribution on such first day in an amount equal to the fair market value (on such first day) of all assets in the account (on such first day). ``(3) Effect of pledging account as security.--If, during any taxable year of the individual for whose benefit a medical care savings account is established, that individual uses the account or any portion thereof as security for a loan, the portion so used is treated as distributed to that individual. ``(4) Commingling medical care savings account amounts in certain common trust funds and common investment funds.--Any common trust fund or common investment fund of individual medical care savings account assets which is exempt from taxation under this subtitle does not cease to be exempt on account of the participation or inclusion of assets of a trust exempt from taxation under section 501(a) which is described in section 401(a). ``(c) Treatment of Distributions.-- ``(1) In general.--Except as otherwise provided in this subsection, any amount paid or distributed out of a medical savings account shall be included in gross income by the distributee. ``(2) Distributions for medical expenses.--Distributions from a medical care savings account shall not be taxable to the distributee, for amounts paid directly or indirectly for medical expenses as defined in section 213(d). ``(3) 10 percent additional tax for early withdrawals.-- Distributions described in paragraph 1 and not described in paragraph 2 shall be subject to an additional 10 percent tax for distributions made prior to age 59\1/2\ of the distributee. ``(4) Rollover contribution.--An amount is described in this paragraph as a rollover contribution which shall not be included in the gross income of the distributee if it meets the requirements of subparagraphs (A) and (B). ``(A) In general.--Paragraph (1) does not apply to any amount paid or distributed out of a medical care savings account to the individual for whose benefit the account is maintained if the entire amount received is paid into a medical care savings account for the benefit of such individual not later than the sixtieth day after the day on which he receives the payment or distribution. ``(B) Limitation.--This paragraph does not apply to any amount described in paragraph (A) received by an individual from a medical savings account if at any time during the one-year period ending on the day of such receipt such individual received any other amount described in that subparagraph from a medical care savings account which was not includible in his gross income because of the application of this paragraph. ``(C) Denial of rollover treatment for inherited accounts, etc.-- ``(i) In general.--In the case of an inherited medical savings account-- ``(I) this paragraph shall not apply to any amount received by an individual from such an account (and no amount transferred from such account to another medical care savings account shall be excluded from gross income by reason of such transfer), and ``(II) such inherited account shall not be treated as a medical care savings account for purposes of determining whether any other amount is a rollover contribution. ``(ii) Inherited medical care savings account.-- ``(I) the individual for whose benefit the account is maintained acquired such account by reason of the death of another individual, and ``(II) such individual was not the surviving spouse of such other individual. ``(d) Bank.--For purposes of subsection (a)(2), the term `bank' means-- ``(1) a bank (as defined in section 581), ``(2) an insured credit union (within the meaning of section 101(6) of the Federal Credit Union Act), and ``(3) a corporation which, under the laws of the State of its incorporation, is subject to supervision and examination by the Commissioner of Banking or other officer of such State in charge of the administration of the banking laws of such State.''. SEC. 4. EFFECTIVE DATES. The amendments made by this Act shall apply to years beginning after December 31, 1993. SEC. 5. OVERALL EFFECT ON TAX DEDUCTIBILITY. This Act is not intended to change the Code's current tax treatment of employer-provided coverage under accident and health plans.[/INST]Medical Cost Containment Act of 1993 - Amends the Internal Revenue Code to exclude from gross income medical care savings benefits. Describes such benefits as a health plan which provides that all or part of the premium differential realized by instituting a qualified higher deductible health plan is credited to participating employees to pay for medical care for a plan year. Requires amounts remaining at the end of such plan year to be deposited into a tax-exempt medical care savings account (subject to rules similar to those for retirement plans) for use by the participant for medical expenses.</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Comprehensive Wildlife Disease Testing Acceleration Act of 2002''. SEC. 2. DEFINITIONS. In this Act: (1) Chronic wasting disease.--The term ``chronic wasting disease'' means the animal disease that afflicts deer and elk-- (A) that is a transmissible disease of the nervous system resulting in distinctive lesions in the brain; and (B) that belongs to the group of diseases-- (i) that is known as transmissible spongiform encephalopathies; and (ii) that includes scrapie, bovine spongiform encephalopathy, and Cruetzfeldt- Jakob disease. (2) Epizootic hemorrhagic disease.--The term ``epizootic hemorrhagic disease'' means the animal disease afflicting deer and other wild ruminants-- (A) that is an insect-borne transmissible viral disease; and (B) that results in spontaneous hemorraging in the muscles and organs of the afflicted animals. (3) Secretary.--The term ``Secretary'' means the Secretary of Agriculture. (4) Task force.--The term ``Task Force'' means the Interagency Task Force on Epizootic Hemorrhagic Disease established by section 4(a). SEC. 3. CHRONIC WASTING DISEASE SAMPLING GUIDELINES AND TESTING PROTOCOL. (a) Sampling Guidelines.-- (1) In general.--Not later than 30 days after the date of enactment of this Act, the Secretary shall issue guidelines for the collection of animal tissue by Federal, State, tribal, and local agencies for testing for chronic wasting disease. (2) Requirements.--Guidelines issued under paragraph (1) shall-- (A) include procedures for the stabilization of tissue samples for transport to a laboratory for assessment; and (B) be updated as the Secretary determines to be appropriate. (b) Testing Protocol.--Not later than 30 days after the date of enactment of this Act, the Secretary shall issue a protocol to be used in the laboratory assessment of samples of animal tissue that may be contaminated with chronic wasting disease. (c) Laboratory Certification and Inspection Program.-- (1) In general.--Not later than 30 days after the date of enactment of this Act, the Secretary shall establish a program for the certification and inspection of Federal and non-Federal laboratories (including private laboratories) under which the Secretary shall authorize laboratories certified under the program to conduct tests for chronic wasting disease. (2) Verification.--In carrying out the program established under paragraph (1), the Secretary may require that the results of any tests conducted by private laboratories shall be verified by Federal laboratories. (d) Development of New Tests.--Not later than 45 days after the date of enactment of this Act, the Secretary shall accelerate research into-- (1) the development of animal tests for chronic wasting disease, including-- (A) tests for live animals; and (B) field diagnostic tests; and (2) the development of testing protocols that reduce laboratory test processing time. SEC. 4. INTERAGENCY TASK FORCE ON EPIZOOTIC HEMORRHAGIC DISEASE. (a) In General.--There is established a Federal interagency task force to be known as the ``Interagency Task Force on Epizootic Hemorrhagic Disease'' to coordinate activities to prevent the outbreak of epizootic hemorrhagic disease and related diseases in the United States. (b) Membership.--The Task Force shall be composed of-- (1) the Secretary, who shall serve as the chairperson of the Task Force; (2) the Secretary of the Interior; (3) the Secretary of Commerce; (4) the Secretary of Health and Human Services; (5) the Secretary of the Treasury; (6) the Commissioner of Food and Drugs; (7) the Director of the National Institutes of Health; (8) the Director of the Centers for Disease Control and Prevention; (9) the Commissioner of Customs; and (10) the heads of any other Federal agencies that the President determines to be appropriate. (c) Report.--Not later than 60 days after the date of enactment of this Act, the Task Force shall submit to Congress a report that-- (1) describes any activities that are being carried out, or that will be carried out, to prevent-- (A) the outbreak of epizootic hemorrhagic disease and related diseases in the United States; and (B) the spread or transmission of epizootic hemorrhagic disease and related diseases to dairy cattle or other livestock; and (2) includes recommendations for-- (A) legislation that should be enacted or regulations that should be promulgated to prevent the outbreak of epizootic hemorrhagic disease and related diseases in the United States; and (B) coordination of the surveillance of and diagnostic testing for epizootic hemorrhagic disease, chronic wasting disease, and related diseases. SEC. 5. FUNDING. To carry out this Act, the Secretary may use funds made available to the Secretary for administrative purposes.

Comprehensive Wildlife Disease Testing Acceleration Act of 2002 - Directs the Secretary of Agriculture, with respect to chronic wasting disease (a disease affecting deer and elk), to: (1) issue guidelines for animal tissue collecting and laboratory testing; (2) establish a laboratory certification and inspection program; and (3) accelerate testing research.Establishes the Interagency Task Force on Epizootic Hemorrhagic Disease to coordinate epizootic hemorrhagic disease (a disease affecting deer and other wild ruminants) prevention activities.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Comprehensive Wildlife Disease Testing Acceleration Act of 2002''. SEC. 2. DEFINITIONS. In this Act: (1) Chronic wasting disease.--The term ``chronic wasting disease'' means the animal disease that afflicts deer and elk-- (A) that is a transmissible disease of the nervous system resulting in distinctive lesions in the brain; and (B) that belongs to the group of diseases-- (i) that is known as transmissible spongiform encephalopathies; and (ii) that includes scrapie, bovine spongiform encephalopathy, and Cruetzfeldt- Jakob disease. (2) Epizootic hemorrhagic disease.--The term ``epizootic hemorrhagic disease'' means the animal disease afflicting deer and other wild ruminants-- (A) that is an insect-borne transmissible viral disease; and (B) that results in spontaneous hemorraging in the muscles and organs of the afflicted animals. (3) Secretary.--The term ``Secretary'' means the Secretary of Agriculture. (4) Task force.--The term ``Task Force'' means the Interagency Task Force on Epizootic Hemorrhagic Disease established by section 4(a). SEC. 3. CHRONIC WASTING DISEASE SAMPLING GUIDELINES AND TESTING PROTOCOL. (a) Sampling Guidelines.-- (1) In general.--Not later than 30 days after the date of enactment of this Act, the Secretary shall issue guidelines for the collection of animal tissue by Federal, State, tribal, and local agencies for testing for chronic wasting disease. (2) Requirements.--Guidelines issued under paragraph (1) shall-- (A) include procedures for the stabilization of tissue samples for transport to a laboratory for assessment; and (B) be updated as the Secretary determines to be appropriate. (b) Testing Protocol.--Not later than 30 days after the date of enactment of this Act, the Secretary shall issue a protocol to be used in the laboratory assessment of samples of animal tissue that may be contaminated with chronic wasting disease. (c) Laboratory Certification and Inspection Program.-- (1) In general.--Not later than 30 days after the date of enactment of this Act, the Secretary shall establish a program for the certification and inspection of Federal and non-Federal laboratories (including private laboratories) under which the Secretary shall authorize laboratories certified under the program to conduct tests for chronic wasting disease. (2) Verification.--In carrying out the program established under paragraph (1), the Secretary may require that the results of any tests conducted by private laboratories shall be verified by Federal laboratories. (d) Development of New Tests.--Not later than 45 days after the date of enactment of this Act, the Secretary shall accelerate research into-- (1) the development of animal tests for chronic wasting disease, including-- (A) tests for live animals; and (B) field diagnostic tests; and (2) the development of testing protocols that reduce laboratory test processing time. SEC. 4. INTERAGENCY TASK FORCE ON EPIZOOTIC HEMORRHAGIC DISEASE. (a) In General.--There is established a Federal interagency task force to be known as the ``Interagency Task Force on Epizootic Hemorrhagic Disease'' to coordinate activities to prevent the outbreak of epizootic hemorrhagic disease and related diseases in the United States. (b) Membership.--The Task Force shall be composed of-- (1) the Secretary, who shall serve as the chairperson of the Task Force; (2) the Secretary of the Interior; (3) the Secretary of Commerce; (4) the Secretary of Health and Human Services; (5) the Secretary of the Treasury; (6) the Commissioner of Food and Drugs; (7) the Director of the National Institutes of Health; (8) the Director of the Centers for Disease Control and Prevention; (9) the Commissioner of Customs; and (10) the heads of any other Federal agencies that the President determines to be appropriate. (c) Report.--Not later than 60 days after the date of enactment of this Act, the Task Force shall submit to Congress a report that-- (1) describes any activities that are being carried out, or that will be carried out, to prevent-- (A) the outbreak of epizootic hemorrhagic disease and related diseases in the United States; and (B) the spread or transmission of epizootic hemorrhagic disease and related diseases to dairy cattle or other livestock; and (2) includes recommendations for-- (A) legislation that should be enacted or regulations that should be promulgated to prevent the outbreak of epizootic hemorrhagic disease and related diseases in the United States; and (B) coordination of the surveillance of and diagnostic testing for epizootic hemorrhagic disease, chronic wasting disease, and related diseases. SEC. 5. FUNDING. To carry out this Act, the Secretary may use funds made available to the Secretary for administrative purposes.[/INST]Comprehensive Wildlife Disease Testing Acceleration Act of 2002 - Directs the Secretary of Agriculture, with respect to chronic wasting disease (a disease affecting deer and elk), to: (1) issue guidelines for animal tissue collecting and laboratory testing; (2) establish a laboratory certification and inspection program; and (3) accelerate testing research.Establishes the Interagency Task Force on Epizootic Hemorrhagic Disease to coordinate epizootic hemorrhagic disease (a disease affecting deer and other wild ruminants) prevention activities.</s>

the crl-2302 ( arpe-19 ) ( atcc , usa ) was used for this study . these human retinal pigment epithelial cells were cultured in dulbecco 's modified eagle 's medium ( dmem ) ( sigma , st louis , mo , usa ) , which is composed of 10% fetal bovine serum ( fbs ) , penicillin ( 100 u / ml ) , streptomycin ( 100 u / ml ) , and nystatin ( 25 ug / ml ) . the cell line was maintained in a humidified incubator in an atmosphere of 95% air and 5% co2 at 37 and the culture medium was changed every 48 hours . the cells were plated in t75 or t150 flasks ( falcon , nj , usa ) and allowed to grow until the cultures were confluent . human retinal pigment epithelial cells were irradiated for 30 seconds with an irradiance of 3.3 mw / cm after removal of serum - free growth medium . uv irradiance was modulated by adjusting lamp output and calibrated with a uv sensor on a uv lamp ( fs-20 t12-uvb , national biological corp . ) . the uvb spectrum was between 280 nm and 320 nm with peak irradiance at 312 nm . human retinal pigment epithelial cells were cultured for 1 day and the experiments were performed on 3 divided groups : the normal control group , which was not exposed to uv light ( group i ) ; the second group , which was exposed to uv light without administration of egcg ( sigma , st louis , mo , usa ) ( group ii ) ; and the third group , which was exposed to uv light with administration of egcg ( group iii ) . egcg was dissolved in dimethyl sulfoxide ( dmso ) ( sigma , st louis , mo , usa ) and added to the culture medium concomitantly with the tnf - a stimulus . five minutes and 1 hour after uv irradiation , different concentration of egcg ( 5 , 10 , 15 , 25 , 50 , and 100 m ) were administered to group iii . after 24 hours incubation , the cell count was determined under a microscope using a counting chamber , cell activity was evaluated by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide ( mtt ) assay . briefly , mtt is reduced to purple formazan in the mitochondria of living cells . a solubilizing liquid optical density was measured at 570 nm using a spectrophotometer . to increase the reliability of the data , the data were analyzed for significance using repeated measures , followed by a duncan 's multiple range test of post hoc tests . the data were expressed as a mean percentage of the control value plus s.e.m . a p - value of < 0.05 was considered significant . the crl-2302 ( arpe-19 ) ( atcc , usa ) was used for this study . these human retinal pigment epithelial cells were cultured in dulbecco 's modified eagle 's medium ( dmem ) ( sigma , st louis , mo , usa ) , which is composed of 10% fetal bovine serum ( fbs ) , penicillin ( 100 u / ml ) , streptomycin ( 100 u / ml ) , and nystatin ( 25 ug / ml ) . the cell line was maintained in a humidified incubator in an atmosphere of 95% air and 5% co2 at 37 and the culture medium was changed every 48 hours . the cells were plated in t75 or t150 flasks ( falcon , nj , usa ) and allowed to grow until the cultures were confluent . human retinal pigment epithelial cells were irradiated for 30 seconds with an irradiance of 3.3 mw / cm after removal of serum - free growth medium . uv irradiance was modulated by adjusting lamp output and calibrated with a uv sensor on a uv lamp ( fs-20 t12-uvb , national biological corp . ) . the uvb spectrum was between 280 nm and 320 nm with peak irradiance at 312 nm . human retinal pigment epithelial cells were cultured for 1 day and the experiments were performed on 3 divided groups : the normal control group , which was not exposed to uv light ( group i ) ; the second group , which was exposed to uv light without administration of egcg ( sigma , st louis , mo , usa ) ( group ii ) ; and the third group , which was exposed to uv light with administration of egcg ( group iii ) . egcg was dissolved in dimethyl sulfoxide ( dmso ) ( sigma , st louis , mo , usa ) and added to the culture medium concomitantly with the tnf - a stimulus . five minutes and 1 hour after uv irradiation , different concentration of egcg ( 5 , 10 , 15 , 25 , 50 , and 100 m ) were administered to group iii . after 24 hours incubation , the cell count was determined under a microscope using a counting chamber , cell activity was evaluated by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide ( mtt ) assay . briefly , mtt is reduced to purple formazan in the mitochondria of living cells . a solubilizing liquid to increase the reliability of the data , all experiments were repeated 3 times and the average values were obtained . the data were analyzed for significance using repeated measures , followed by a duncan 's multiple range test of post hoc tests . the data were expressed as a mean percentage of the control value plus s.e.m . a p - value of < 0.05 was considered significant . epigallocatechin gallate ( egcg ) effectively protected cultured human retinal pigment epithelial ( rpe ) cells from oxidative - stress - induced cytotoxicity . compared with the control group , which was not exposed to uv irradiation ( fig . 1a ) , exposure to uv irradiation without administration of egcg showed significant cell loss ( fig . 1d ) after uv irradiation , experienced an increased cell count compared with that of the control group . the cell count of cultured human rpe cells after uv irradiation was markedly increased in the egcg administration group , compared with the group that did not receive egcg ( fig . 2 ) . there was no significant relationship between the time to administration of egcg and cell loss ( p=0.279 ) . cell activity of the cultured human rpe cells after uv irradiation was markedly increased with egcg administration , and it increased in a dose - dependent way , as determined by the mtt assay ( fig . significant differences were shown between 5 m ( mean=8.003.630 ) and 10 m ( m=25.835.399 ) and between 10 m ( m=25.835.399 ) and 15 m ( m=58.904.623 ) ( p<0.001 ) . there were no significant differences between 0 m ( m=0.000.000 ) and 5 m ( m=8.003.630 ) ( p=0.260 ) among 15 m ( m=58.904.623 ) , 25 m ( m=61.275.206 ) , 50 m ( m=63.301.871 ) , and 100 m ( m=68.105.229 ) ( p=0.072 ) . in comparison with the group that did not receive egcg , cell activity was increased by approximately 43.9% , 68.1% respectively in 100 m of the egcg administration group . moreover , post - treatment of rpe cells with egcg ( 100 m ) after 1 hour showed significantly reduced cell deaths as a result of uv irradiation . there was a significant relationship between the time to administration of egcg and cell activity ( p=0.001 ) . increasing interest in the health benefits of tea has led to the inclusion of tea extracts in dietary supplements and functional foods . while tea contains a number of bioactive chemicals , it is particularly rich in catechins . the main catechin group consists of eight polyphenolic flavonoid - type compounds : ( + ) -catechin ( c ) , ( -)-epicatechin ( ec ) , ( + ) - gallocatechin ( gc ) , ( -)-epigallocatechin ( egc ) , ( + ) -catechin gallate ( cg ) , ( -)-epicatechin gallate ( ecg ) , ( + ) -gallocatechin gallate ( gcg ) , and ( -)-epigallocatechin gallate ( egcg ) . ( -)-epigallocatechin gallate is the most abundant of the tea catechins and is thought to be responsible for the majority of the green tea extracts 's biological activity , such as its anti - cancer and antioxidant properties.19,20 although a number of in vitro and in vivo studies have shown egcg acts as an antioxidant21 - 24 and an antiapoptotic agent,25 the actual mechanism of its action as an antioxidant remains unclear . importantly , total plasma antioxidant activity has been shown to increase following significant intake of green tea26,27 in laboratory studies . moreover , an increase in plasma catalase activity and a decrease in the nitric oxide levels28 occurred , suggesting that catechins have both direct antioxidant effects and indirect influences on increasing the activity of other antioxidants or enzymes . that catechins like egcg elicit antioxidant actions in a number of ways.29 egcg promotes human keratinocyte survival and inhibits ultraviolet light - induced apoptosis by dual mechanisms , namely by phosphorylating bad protein through erk and akt pathways , respectively , and by increasing the bcl-2 to bax ratio.30 retinal pigment epithelial cells may produce a large amount of oxygen radicals because they consume a large amount of oxygen . these reactive oxygen species may peroxidize the unsaturated fatty acids in cell membranes , damaging the protein and dna , thereby causing oxidative cell injury . an investigation about ultraviolet light and apoptosis in retinal pigment epithelial cells has been performed with various methods . yu et al . suggested the possibility that an oxidative injury by uv irradiation is a cause of apoptosis in retinal pigment epithelial cells.8 although research for suppression and protection against apoptosis of retinal pigmented epithelium is continuing , the correct mechanism has not been identified yet . armd is a leading cause for blindness in developed countries and will be more of a problem as life expectancy increases . support for the involvement of oxidative stress in armd comes from the finding that daily administration of antioxidant vitamins and/or zinc significantly slowed the rate of progression in patients from high risk atrophic armd to neovascular armd.14 a number of age - related pathologies have been attributed to cumulative oxidative damage caused by ros , such as nitric oxide ( no ) , hydrogen peroxide ( h2o2 ) , singlet oxygen , superoxide anion , and hydroxyl radicals . ros arise as by - products of cellular metabolism or photochemical reactions.31,32 furthermore , the oxygen supply to the photoreceptors via the choroidal and retinal vessels can cause an elevated oxygen tension in the retinal pigment epithelium and photoreceptors.33,34 moreover , uv radiation can cause damage to dna , leading to single - strand dna breaks in the retina.4,35 egcg attenuates the effect of an ischemia/ reperfusion insult to the intact retina , where oxidative stress is implicated,37 and to neurons in vitro by h2o2 , an oxidant . it is generally thought that oxidative stress plays a part in the pathogenesis of glaucoma,37,38 initiated by ischemia to the optic nerve head components,39,40 because of a reduced optic nerve head blood supply.40 egcg , besides being a powerful antioxidant,24 also has anti - inflammatory41,42 and vasodilator43 effects ; both inflammation and vasoconstriction36,44 are strongly suspected of playing a part in the pathogenesis of glaucoma . moreover , egcg can intervene in other cellular mechanisms that are relevant to retinal ganglion cell loss in glaucoma , independently from its antioxidant properties . it is known that the oxidative damage to the retinal pigment epithelial cells play an important role in the development of armd and glaucoma . in conclusion , the results of this study have shown that egcg increases the cell count and cell activity after uv irradiation in cultured human retinal pigment epithelial cells ; we can conclude that egcg provides protective effects against uv damage in cultured human retinal pigment epithelial cells . although the results show thategcg can protect human retinal pigment epithelial cells from uv induced damage , further in vivo and in vitro studies investigating areas such as mitochondrial damage , nucleic acid damage , phagocytotic activity after uv exposure in human retinal pigment epithelial cells will be required .

purposeto evaluate the protective effects of epigallocatechin gallate ( egcg ) against uv irradiation in cultured human retinal pigment epithelial ( rpe ) cells.methodsuv irradiation was produced by a uv lamp for 30 seconds with an irradiance of 3.3 mw / cm2 . after 5 minutes and 1 hour , we administered different concentrations of egcg ( 0 , 5 , 10 , 15 , 25 , 50 , 100 um ) . the cell count was determined under a microscope using a counting chamber and the cell activity was evaluated by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide ( mtt ) assay.resultsthe cell count of cultured human rpe cells after uv irradiation was markedly increased in the egcg administration group , compared with the non - administrated group . the cell activity of the cultured human rpe cells after uv irradiation was markedly increased in the egcg administration group and was increased in a dose - dependent way as determined by the mtt assay.conclusionsthe administration of egcg increased the cell count and the cell activity after uv irradiation in cultured human retinal pigment epithelial cells ; this suggests that egcg provided protection against uv damage in cultured human retinal pigmented epithelial cells .

<s>[INST]the crl-2302 ( arpe-19 ) ( atcc , usa ) was used for this study . these human retinal pigment epithelial cells were cultured in dulbecco 's modified eagle 's medium ( dmem ) ( sigma , st louis , mo , usa ) , which is composed of 10% fetal bovine serum ( fbs ) , penicillin ( 100 u / ml ) , streptomycin ( 100 u / ml ) , and nystatin ( 25 ug / ml ) . the cell line was maintained in a humidified incubator in an atmosphere of 95% air and 5% co2 at 37 and the culture medium was changed every 48 hours . the cells were plated in t75 or t150 flasks ( falcon , nj , usa ) and allowed to grow until the cultures were confluent . human retinal pigment epithelial cells were irradiated for 30 seconds with an irradiance of 3.3 mw / cm after removal of serum - free growth medium . uv irradiance was modulated by adjusting lamp output and calibrated with a uv sensor on a uv lamp ( fs-20 t12-uvb , national biological corp . ) . the uvb spectrum was between 280 nm and 320 nm with peak irradiance at 312 nm . human retinal pigment epithelial cells were cultured for 1 day and the experiments were performed on 3 divided groups : the normal control group , which was not exposed to uv light ( group i ) ; the second group , which was exposed to uv light without administration of egcg ( sigma , st louis , mo , usa ) ( group ii ) ; and the third group , which was exposed to uv light with administration of egcg ( group iii ) . egcg was dissolved in dimethyl sulfoxide ( dmso ) ( sigma , st louis , mo , usa ) and added to the culture medium concomitantly with the tnf - a stimulus . five minutes and 1 hour after uv irradiation , different concentration of egcg ( 5 , 10 , 15 , 25 , 50 , and 100 m ) were administered to group iii . after 24 hours incubation , the cell count was determined under a microscope using a counting chamber , cell activity was evaluated by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide ( mtt ) assay . briefly , mtt is reduced to purple formazan in the mitochondria of living cells . a solubilizing liquid optical density was measured at 570 nm using a spectrophotometer . to increase the reliability of the data , the data were analyzed for significance using repeated measures , followed by a duncan 's multiple range test of post hoc tests . the data were expressed as a mean percentage of the control value plus s.e.m . a p - value of < 0.05 was considered significant . the crl-2302 ( arpe-19 ) ( atcc , usa ) was used for this study . these human retinal pigment epithelial cells were cultured in dulbecco 's modified eagle 's medium ( dmem ) ( sigma , st louis , mo , usa ) , which is composed of 10% fetal bovine serum ( fbs ) , penicillin ( 100 u / ml ) , streptomycin ( 100 u / ml ) , and nystatin ( 25 ug / ml ) . the cell line was maintained in a humidified incubator in an atmosphere of 95% air and 5% co2 at 37 and the culture medium was changed every 48 hours . the cells were plated in t75 or t150 flasks ( falcon , nj , usa ) and allowed to grow until the cultures were confluent . human retinal pigment epithelial cells were irradiated for 30 seconds with an irradiance of 3.3 mw / cm after removal of serum - free growth medium . uv irradiance was modulated by adjusting lamp output and calibrated with a uv sensor on a uv lamp ( fs-20 t12-uvb , national biological corp . ) . the uvb spectrum was between 280 nm and 320 nm with peak irradiance at 312 nm . human retinal pigment epithelial cells were cultured for 1 day and the experiments were performed on 3 divided groups : the normal control group , which was not exposed to uv light ( group i ) ; the second group , which was exposed to uv light without administration of egcg ( sigma , st louis , mo , usa ) ( group ii ) ; and the third group , which was exposed to uv light with administration of egcg ( group iii ) . egcg was dissolved in dimethyl sulfoxide ( dmso ) ( sigma , st louis , mo , usa ) and added to the culture medium concomitantly with the tnf - a stimulus . five minutes and 1 hour after uv irradiation , different concentration of egcg ( 5 , 10 , 15 , 25 , 50 , and 100 m ) were administered to group iii . after 24 hours incubation , the cell count was determined under a microscope using a counting chamber , cell activity was evaluated by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide ( mtt ) assay . briefly , mtt is reduced to purple formazan in the mitochondria of living cells . a solubilizing liquid to increase the reliability of the data , all experiments were repeated 3 times and the average values were obtained . the data were analyzed for significance using repeated measures , followed by a duncan 's multiple range test of post hoc tests . the data were expressed as a mean percentage of the control value plus s.e.m . a p - value of < 0.05 was considered significant . epigallocatechin gallate ( egcg ) effectively protected cultured human retinal pigment epithelial ( rpe ) cells from oxidative - stress - induced cytotoxicity . compared with the control group , which was not exposed to uv irradiation ( fig . 1a ) , exposure to uv irradiation without administration of egcg showed significant cell loss ( fig . 1d ) after uv irradiation , experienced an increased cell count compared with that of the control group . the cell count of cultured human rpe cells after uv irradiation was markedly increased in the egcg administration group , compared with the group that did not receive egcg ( fig . 2 ) . there was no significant relationship between the time to administration of egcg and cell loss ( p=0.279 ) . cell activity of the cultured human rpe cells after uv irradiation was markedly increased with egcg administration , and it increased in a dose - dependent way , as determined by the mtt assay ( fig . significant differences were shown between 5 m ( mean=8.003.630 ) and 10 m ( m=25.835.399 ) and between 10 m ( m=25.835.399 ) and 15 m ( m=58.904.623 ) ( p<0.001 ) . there were no significant differences between 0 m ( m=0.000.000 ) and 5 m ( m=8.003.630 ) ( p=0.260 ) among 15 m ( m=58.904.623 ) , 25 m ( m=61.275.206 ) , 50 m ( m=63.301.871 ) , and 100 m ( m=68.105.229 ) ( p=0.072 ) . in comparison with the group that did not receive egcg , cell activity was increased by approximately 43.9% , 68.1% respectively in 100 m of the egcg administration group . moreover , post - treatment of rpe cells with egcg ( 100 m ) after 1 hour showed significantly reduced cell deaths as a result of uv irradiation . there was a significant relationship between the time to administration of egcg and cell activity ( p=0.001 ) . increasing interest in the health benefits of tea has led to the inclusion of tea extracts in dietary supplements and functional foods . while tea contains a number of bioactive chemicals , it is particularly rich in catechins . the main catechin group consists of eight polyphenolic flavonoid - type compounds : ( + ) -catechin ( c ) , ( -)-epicatechin ( ec ) , ( + ) - gallocatechin ( gc ) , ( -)-epigallocatechin ( egc ) , ( + ) -catechin gallate ( cg ) , ( -)-epicatechin gallate ( ecg ) , ( + ) -gallocatechin gallate ( gcg ) , and ( -)-epigallocatechin gallate ( egcg ) . ( -)-epigallocatechin gallate is the most abundant of the tea catechins and is thought to be responsible for the majority of the green tea extracts 's biological activity , such as its anti - cancer and antioxidant properties.19,20 although a number of in vitro and in vivo studies have shown egcg acts as an antioxidant21 - 24 and an antiapoptotic agent,25 the actual mechanism of its action as an antioxidant remains unclear . importantly , total plasma antioxidant activity has been shown to increase following significant intake of green tea26,27 in laboratory studies . moreover , an increase in plasma catalase activity and a decrease in the nitric oxide levels28 occurred , suggesting that catechins have both direct antioxidant effects and indirect influences on increasing the activity of other antioxidants or enzymes . that catechins like egcg elicit antioxidant actions in a number of ways.29 egcg promotes human keratinocyte survival and inhibits ultraviolet light - induced apoptosis by dual mechanisms , namely by phosphorylating bad protein through erk and akt pathways , respectively , and by increasing the bcl-2 to bax ratio.30 retinal pigment epithelial cells may produce a large amount of oxygen radicals because they consume a large amount of oxygen . these reactive oxygen species may peroxidize the unsaturated fatty acids in cell membranes , damaging the protein and dna , thereby causing oxidative cell injury . an investigation about ultraviolet light and apoptosis in retinal pigment epithelial cells has been performed with various methods . yu et al . suggested the possibility that an oxidative injury by uv irradiation is a cause of apoptosis in retinal pigment epithelial cells.8 although research for suppression and protection against apoptosis of retinal pigmented epithelium is continuing , the correct mechanism has not been identified yet . armd is a leading cause for blindness in developed countries and will be more of a problem as life expectancy increases . support for the involvement of oxidative stress in armd comes from the finding that daily administration of antioxidant vitamins and/or zinc significantly slowed the rate of progression in patients from high risk atrophic armd to neovascular armd.14 a number of age - related pathologies have been attributed to cumulative oxidative damage caused by ros , such as nitric oxide ( no ) , hydrogen peroxide ( h2o2 ) , singlet oxygen , superoxide anion , and hydroxyl radicals . ros arise as by - products of cellular metabolism or photochemical reactions.31,32 furthermore , the oxygen supply to the photoreceptors via the choroidal and retinal vessels can cause an elevated oxygen tension in the retinal pigment epithelium and photoreceptors.33,34 moreover , uv radiation can cause damage to dna , leading to single - strand dna breaks in the retina.4,35 egcg attenuates the effect of an ischemia/ reperfusion insult to the intact retina , where oxidative stress is implicated,37 and to neurons in vitro by h2o2 , an oxidant . it is generally thought that oxidative stress plays a part in the pathogenesis of glaucoma,37,38 initiated by ischemia to the optic nerve head components,39,40 because of a reduced optic nerve head blood supply.40 egcg , besides being a powerful antioxidant,24 also has anti - inflammatory41,42 and vasodilator43 effects ; both inflammation and vasoconstriction36,44 are strongly suspected of playing a part in the pathogenesis of glaucoma . moreover , egcg can intervene in other cellular mechanisms that are relevant to retinal ganglion cell loss in glaucoma , independently from its antioxidant properties . it is known that the oxidative damage to the retinal pigment epithelial cells play an important role in the development of armd and glaucoma . in conclusion , the results of this study have shown that egcg increases the cell count and cell activity after uv irradiation in cultured human retinal pigment epithelial cells ; we can conclude that egcg provides protective effects against uv damage in cultured human retinal pigment epithelial cells . although the results show thategcg can protect human retinal pigment epithelial cells from uv induced damage , further in vivo and in vitro studies investigating areas such as mitochondrial damage , nucleic acid damage , phagocytotic activity after uv exposure in human retinal pigment epithelial cells will be required .[/INST]purposeto evaluate the protective effects of epigallocatechin gallate ( egcg ) against uv irradiation in cultured human retinal pigment epithelial ( rpe ) cells.methodsuv irradiation was produced by a uv lamp for 30 seconds with an irradiance of 3.3 mw / cm2 . after 5 minutes and 1 hour , we administered different concentrations of egcg ( 0 , 5 , 10 , 15 , 25 , 50 , 100 um ) . the cell count was determined under a microscope using a counting chamber and the cell activity was evaluated by 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide ( mtt ) assay.resultsthe cell count of cultured human rpe cells after uv irradiation was markedly increased in the egcg administration group , compared with the non - administrated group . the cell activity of the cultured human rpe cells after uv irradiation was markedly increased in the egcg administration group and was increased in a dose - dependent way as determined by the mtt assay.conclusionsthe administration of egcg increased the cell count and the cell activity after uv irradiation in cultured human retinal pigment epithelial cells ; this suggests that egcg provided protection against uv damage in cultured human retinal pigmented epithelial cells .</s>

the study of @xmath3 hypernuclei has provided us with important information on the properties of @xmath3 in a nuclear medium and the effective @xmath3-n interaction @xcite . on the other hand , the situation for @xmath4 and @xmath5 hypernuclei is quite different . the special case of @xmath6he aside , there is no experimental evidence for any @xmath4 hypernuclei @xcite , despite extensive searches . it seems likely that the @xmath4-nucleus interaction is somewhat repulsive and that there are no bound @xmath4 hypernuclei beyond a=4 . in the case of the @xmath5 , the experimental situation is very challenging , but we eagerly await studies of @xmath5 hypernuclei with new facilities at j - parc and gsi - fair . to understand further the properties of hypernuclei , we apply the latest version of the quark - meson coupling ( qmc ) model @xcite , and calculate the single - particle energies @xcite and phtoproduction cross sections @xcite . the major improvement in the latest version is the inclusion of the effect of the medium on the color - hyperfine interaction . this has the effect of increasing the splitting between the @xmath3 and @xmath4 masses as the density rises . this is the prime reason why our results yield no middle and heavy mass @xmath4 hypernuclei @xcite . the qmc model was created to provide insight into the structure of nuclear matter , starting at the quark level @xcite . nucleon internal structure was modeled using the mit bag , while the binding was described by the self - consistent coupling of the confined quarks to the scalar-@xmath7 and vector-@xmath8 meson fields generated by the confined quarks in the other `` nucleons '' in the medium . the self - consistent response of the bound quarks to the mean @xmath7 field leads to a novel saturation mechanism for nuclear matter , with the enhancement of the lower components of the valence dirac wave functions . the model has been successfully used to study various nuclear phenomena @xcite . to calculate the hyperon levels , we use a relativistic shell model . details on the calculations are described in refs . results for the hypernuclear single - particle energies are shown in tables [ spe1 ] and [ spe2 ] . first , we emphasize that the present calculation yields no @xmath4 hypernuclei in the nuclei considered . this is consistent with the empirical fact of no finding of the middle and heavy mass @xmath4 hypernuclei . second , overall agreement with the experimental energy levels of @xmath3 hypernuclei across the periodic table is quite good . in particular , the parameter free result of -26.9 mev for the @xmath9 level of @xmath10pb is impressive . the discrepancies which remain may well be resolved by small effective hyperon - nucleon interactions which go beyond the simple , single - particle shell model . once again , we stress the very small spin - orbit force experienced by the @xmath3 , which is a natural property of the qmc model @xcite . finally , this model supports the existence of a variety of bound @xmath5-hypernuclei . for the @xmath11 the binding of the @xmath9 level varies from 5 mev in @xmath12o to 15 mev in @xmath13pb . the experimental search for such states at facilities such as j - parc and gsi - fair will be very important . [ spe1 ] [ spe2 ] concerning the absence of the @xmath4 hypernuclei in the present calculation , it is especially interesting to examine the effective non - relativistic potential felt by the @xmath14 in a finite nucleus . this is shown in fig . [ fig : pot ] for @xmath15ca and @xmath10pb nuclei . in the central region the vector interaction dominates over the scalar one leading to a repulsive effective potential which reaches respectively 30 mev and 12 mev at the center . it is only at the surface that the scalar attraction becomes dominant . in existing several theoretical studies of photoproduction of hypernuclei , it has been usually employed nonrelativistic models to obtain the relevant initial and final state wave functions ( except for ref . @xcite ) . in this study , we follow ref . @xcite and use a fully covariant model to calculate the cross sections for the @xmath0c ( @xmath16b reaction . we explore the feasibility of studying the photoproduction of hypernuclei within the relativistic model of ref . @xcite , but employing the bound @xmath3 spinors obtained by the latest qmc model @xcite . this provides an opportunity to investigate the role of the quark degrees of freedom in the hypernuclear production , which may be a novel feature . the relevant processes included in the present study are shown in figs . 1(a ) and 1(b ) , the elementary @xmath17 and the hypernuclear production reactions , @xmath18 , respectively . in principle , although the @xmath19- and @xmath20-channels should also be included , they contribute to the non - resonant background terms which are insignificant to both elementary as well as in - medium photon induced reactions for energies below 1.5 gev . ( see , e.g. , refs . we use plane waves to describe the relative motion of the outgoing particle which is justified by the relatively weaker kaon - nucleus interaction in the final channel . all ingredients necessary in the calculation , such as effective lagrangians and resonance propagators , are described in refs . the coupling constants have been determined by comparing our calculations [ graph 1(a ) ] with the total and differential cross section data for the elementary @xmath21 reaction in the relevant photon energy region @xcite . the threshold for the kaon photoproduction on @xmath0c is about 695 mev . the momentum transfer involved in the reaction at 10@xmath22 kaon angle , in which we focus , varies between approximately 2 @xmath23 to 1.4 @xmath23 in the photon energy range of 0.7 gev to 1.2 gev @xcite . in fig . [ dsigma ] , we compare the differential cross section calculated @xcite with the bound @xmath3 spinors obtained in the latest qmc model @xcite , and the phenomenological models @xcite for the @xmath0c ( @xmath16b reaction . the hole state spinor is taken from the phenomenological model @xcite in both cases . the cross sections are shown for photon energies in the range of 0.7 - 1.2 gev corresponding to the outgoing kaon angle of 10@xmath22 . the hypernuclear states populated are @xmath24 , @xmath25 , and @xmath26 , @xmath27 corresponding to the particle - hole configurations of @xmath28 and @xmath29 , respectively . we see that in each case the qmc cross sections are smaller than those obtained with phenomenological hyperon spinors . in this figure we further note that the peaks of the qmc cross sections are somewhat shifted toward lower photon energies as compared to those of the phenomenological model . detailed explanations for these features are given in ref . @xcite . we further note that within each group the highest @xmath30 state is most strongly excited , which is in line with the results presented in refs . furthermore , unnatural parity states within each group are preferentially excited by this reaction . the unnatural parity states are excited through the spin flip process . thus , this confirms that kaon photo- and also electro - production reactions on nuclei are ideal tools for investigating the structure of unnatural parity hypernuclear states . we have studied the properties of hypernuclei using the latest version of the quark - meson coupling model , which includes the effect of the medium on the color - hyperfine interaction between quarks . this latest version leads to some important results : ( 1 ) the agreement between the parameter free calculations and the experimental ground state levels for @xmath3-hypernuclei from calcium to lead is impressive . ( 2 ) a number of @xmath5-hypernuclei are predicted to be bound , although not as deeply as in the @xmath3 case . ( 3 ) the additional repulsion arising from the enhancement of the color - hyperfine interaction in the @xmath4-hyperon in - medium ( together with the effect of the @xmath31 channel coupling on the intermediate range scalar attraction @xcite ) yields to predict `` no bound '' @xmath4-hypernuclei . we have also studied photoproduction of hypernucleus by the @xmath0c ( @xmath16b reaction within a covariant model , using the bound @xmath3 spinors obtained by the latest quark - meson coupling model . this is the first time that quark degrees of freedom has been explicitly invoked in the description of the hypernuclear production . k.t . would like to thank the organizers of sendai08 , o. hashimoto , h. tamura , s. n. nakamura and k. maeda for a warm hospitality in entire period of the conference . notice : authored by jefferson science associates , llc under u.s . doe contract no . de - ac05 - 06or23177 . government retains a non - exclusive , paid - up , irrevocable , world - wide license to publish or reproduce this manuscript for u.s . government purposes . 99 for example , o. hashimoto and h. tamura , _ prog . part . phys . _ * 57 * , 564 ( 2006 ) . k. saha _ et al . _ , _ phys . c _ * 70 * , 044613 ( 2004 ) . j. rikovska - stone , p. a. m. guichon , h. h. matevosyan and a. w. thomas , _ nucl . a _ * 792 * , 341 ( 2007 ) . p. a. m. guichon , a. w. thomas and k. tsushima , _ nucl . a _ * 814 * , 66 ( 2008 ) . r. shyam , k. tsushima and a. w. thomas , arxiv:0812.1547 [ nucl - th ] . a. m. guichon , _ phys . b _ * 200 * , 235 ( 1988 ) . for a review , k. saito , k. tsushima and a. w. thomas , _ prog . phys . _ * 58 * , 1 ( 2007 ) . k. tsushima , k. saito , j. haidenbauer and a. w. thomas , _ nucl . phys . a _ * 630 * , 691 ( 1998 ) ; k. tsushima , k. saito and a. w. thomas , _ phys . lett . b _ * 411 * , 9 ( 1997 ) [ _ erratum - ibid . b _ * 421 * , 413 ( 1998 ) ] . c. bennhold and l.e . wright , _ phys . c _ * 39 * 927 , ( 1989 ) ; + _ phys . _ * b191 * , 11 ( 1987 ) . r. shyam , h. lenske and u. mosel , _ phys . c _ * 77 * , 052201(r ) ( 2008 ) . lee , t. mart , c. bennhold , h. haberzettl , and l. e. wright , _ nucl . * a695 * , 237 ( 2001 ) . r. shyam and o. scholten , _ phys . c _ * 78 * , 065201 ( 2008 ) . r. shyam , h. lenske and u. mosel , _ phys c _ * 69 * , 065205 ( 2004 ) ; + r. shyam , h. lenske and u. mosel , _ nucl . phys . _ * a764 * , 313 ( 2006 ) . r. shyam , _ progr . phys . _ * 61 * , 212 ( 2008 ) . a. s. rosenthal et al . , _ ann . ( n.y . ) * 184 * , 33 ( 1988 ) .

we study the binding of hypernuclei based on the latest version of quark - meson coupling model , and estimate the phtoproduction cross sections for the @xmath0c(@xmath1)@xmath2b reaction using the bound @xmath3 spinors obtained in the model .

<s>[INST]the study of @xmath3 hypernuclei has provided us with important information on the properties of @xmath3 in a nuclear medium and the effective @xmath3-n interaction @xcite . on the other hand , the situation for @xmath4 and @xmath5 hypernuclei is quite different . the special case of @xmath6he aside , there is no experimental evidence for any @xmath4 hypernuclei @xcite , despite extensive searches . it seems likely that the @xmath4-nucleus interaction is somewhat repulsive and that there are no bound @xmath4 hypernuclei beyond a=4 . in the case of the @xmath5 , the experimental situation is very challenging , but we eagerly await studies of @xmath5 hypernuclei with new facilities at j - parc and gsi - fair . to understand further the properties of hypernuclei , we apply the latest version of the quark - meson coupling ( qmc ) model @xcite , and calculate the single - particle energies @xcite and phtoproduction cross sections @xcite . the major improvement in the latest version is the inclusion of the effect of the medium on the color - hyperfine interaction . this has the effect of increasing the splitting between the @xmath3 and @xmath4 masses as the density rises . this is the prime reason why our results yield no middle and heavy mass @xmath4 hypernuclei @xcite . the qmc model was created to provide insight into the structure of nuclear matter , starting at the quark level @xcite . nucleon internal structure was modeled using the mit bag , while the binding was described by the self - consistent coupling of the confined quarks to the scalar-@xmath7 and vector-@xmath8 meson fields generated by the confined quarks in the other `` nucleons '' in the medium . the self - consistent response of the bound quarks to the mean @xmath7 field leads to a novel saturation mechanism for nuclear matter , with the enhancement of the lower components of the valence dirac wave functions . the model has been successfully used to study various nuclear phenomena @xcite . to calculate the hyperon levels , we use a relativistic shell model . details on the calculations are described in refs . results for the hypernuclear single - particle energies are shown in tables [ spe1 ] and [ spe2 ] . first , we emphasize that the present calculation yields no @xmath4 hypernuclei in the nuclei considered . this is consistent with the empirical fact of no finding of the middle and heavy mass @xmath4 hypernuclei . second , overall agreement with the experimental energy levels of @xmath3 hypernuclei across the periodic table is quite good . in particular , the parameter free result of -26.9 mev for the @xmath9 level of @xmath10pb is impressive . the discrepancies which remain may well be resolved by small effective hyperon - nucleon interactions which go beyond the simple , single - particle shell model . once again , we stress the very small spin - orbit force experienced by the @xmath3 , which is a natural property of the qmc model @xcite . finally , this model supports the existence of a variety of bound @xmath5-hypernuclei . for the @xmath11 the binding of the @xmath9 level varies from 5 mev in @xmath12o to 15 mev in @xmath13pb . the experimental search for such states at facilities such as j - parc and gsi - fair will be very important . [ spe1 ] [ spe2 ] concerning the absence of the @xmath4 hypernuclei in the present calculation , it is especially interesting to examine the effective non - relativistic potential felt by the @xmath14 in a finite nucleus . this is shown in fig . [ fig : pot ] for @xmath15ca and @xmath10pb nuclei . in the central region the vector interaction dominates over the scalar one leading to a repulsive effective potential which reaches respectively 30 mev and 12 mev at the center . it is only at the surface that the scalar attraction becomes dominant . in existing several theoretical studies of photoproduction of hypernuclei , it has been usually employed nonrelativistic models to obtain the relevant initial and final state wave functions ( except for ref . @xcite ) . in this study , we follow ref . @xcite and use a fully covariant model to calculate the cross sections for the @xmath0c ( @xmath16b reaction . we explore the feasibility of studying the photoproduction of hypernuclei within the relativistic model of ref . @xcite , but employing the bound @xmath3 spinors obtained by the latest qmc model @xcite . this provides an opportunity to investigate the role of the quark degrees of freedom in the hypernuclear production , which may be a novel feature . the relevant processes included in the present study are shown in figs . 1(a ) and 1(b ) , the elementary @xmath17 and the hypernuclear production reactions , @xmath18 , respectively . in principle , although the @xmath19- and @xmath20-channels should also be included , they contribute to the non - resonant background terms which are insignificant to both elementary as well as in - medium photon induced reactions for energies below 1.5 gev . ( see , e.g. , refs . we use plane waves to describe the relative motion of the outgoing particle which is justified by the relatively weaker kaon - nucleus interaction in the final channel . all ingredients necessary in the calculation , such as effective lagrangians and resonance propagators , are described in refs . the coupling constants have been determined by comparing our calculations [ graph 1(a ) ] with the total and differential cross section data for the elementary @xmath21 reaction in the relevant photon energy region @xcite . the threshold for the kaon photoproduction on @xmath0c is about 695 mev . the momentum transfer involved in the reaction at 10@xmath22 kaon angle , in which we focus , varies between approximately 2 @xmath23 to 1.4 @xmath23 in the photon energy range of 0.7 gev to 1.2 gev @xcite . in fig . [ dsigma ] , we compare the differential cross section calculated @xcite with the bound @xmath3 spinors obtained in the latest qmc model @xcite , and the phenomenological models @xcite for the @xmath0c ( @xmath16b reaction . the hole state spinor is taken from the phenomenological model @xcite in both cases . the cross sections are shown for photon energies in the range of 0.7 - 1.2 gev corresponding to the outgoing kaon angle of 10@xmath22 . the hypernuclear states populated are @xmath24 , @xmath25 , and @xmath26 , @xmath27 corresponding to the particle - hole configurations of @xmath28 and @xmath29 , respectively . we see that in each case the qmc cross sections are smaller than those obtained with phenomenological hyperon spinors . in this figure we further note that the peaks of the qmc cross sections are somewhat shifted toward lower photon energies as compared to those of the phenomenological model . detailed explanations for these features are given in ref . @xcite . we further note that within each group the highest @xmath30 state is most strongly excited , which is in line with the results presented in refs . furthermore , unnatural parity states within each group are preferentially excited by this reaction . the unnatural parity states are excited through the spin flip process . thus , this confirms that kaon photo- and also electro - production reactions on nuclei are ideal tools for investigating the structure of unnatural parity hypernuclear states . we have studied the properties of hypernuclei using the latest version of the quark - meson coupling model , which includes the effect of the medium on the color - hyperfine interaction between quarks . this latest version leads to some important results : ( 1 ) the agreement between the parameter free calculations and the experimental ground state levels for @xmath3-hypernuclei from calcium to lead is impressive . ( 2 ) a number of @xmath5-hypernuclei are predicted to be bound , although not as deeply as in the @xmath3 case . ( 3 ) the additional repulsion arising from the enhancement of the color - hyperfine interaction in the @xmath4-hyperon in - medium ( together with the effect of the @xmath31 channel coupling on the intermediate range scalar attraction @xcite ) yields to predict `` no bound '' @xmath4-hypernuclei . we have also studied photoproduction of hypernucleus by the @xmath0c ( @xmath16b reaction within a covariant model , using the bound @xmath3 spinors obtained by the latest quark - meson coupling model . this is the first time that quark degrees of freedom has been explicitly invoked in the description of the hypernuclear production . k.t . would like to thank the organizers of sendai08 , o. hashimoto , h. tamura , s. n. nakamura and k. maeda for a warm hospitality in entire period of the conference . notice : authored by jefferson science associates , llc under u.s . doe contract no . de - ac05 - 06or23177 . government retains a non - exclusive , paid - up , irrevocable , world - wide license to publish or reproduce this manuscript for u.s . government purposes . 99 for example , o. hashimoto and h. tamura , _ prog . part . phys . _ * 57 * , 564 ( 2006 ) . k. saha _ et al . _ , _ phys . c _ * 70 * , 044613 ( 2004 ) . j. rikovska - stone , p. a. m. guichon , h. h. matevosyan and a. w. thomas , _ nucl . a _ * 792 * , 341 ( 2007 ) . p. a. m. guichon , a. w. thomas and k. tsushima , _ nucl . a _ * 814 * , 66 ( 2008 ) . r. shyam , k. tsushima and a. w. thomas , arxiv:0812.1547 [ nucl - th ] . a. m. guichon , _ phys . b _ * 200 * , 235 ( 1988 ) . for a review , k. saito , k. tsushima and a. w. thomas , _ prog . phys . _ * 58 * , 1 ( 2007 ) . k. tsushima , k. saito , j. haidenbauer and a. w. thomas , _ nucl . phys . a _ * 630 * , 691 ( 1998 ) ; k. tsushima , k. saito and a. w. thomas , _ phys . lett . b _ * 411 * , 9 ( 1997 ) [ _ erratum - ibid . b _ * 421 * , 413 ( 1998 ) ] . c. bennhold and l.e . wright , _ phys . c _ * 39 * 927 , ( 1989 ) ; + _ phys . _ * b191 * , 11 ( 1987 ) . r. shyam , h. lenske and u. mosel , _ phys . c _ * 77 * , 052201(r ) ( 2008 ) . lee , t. mart , c. bennhold , h. haberzettl , and l. e. wright , _ nucl . * a695 * , 237 ( 2001 ) . r. shyam and o. scholten , _ phys . c _ * 78 * , 065201 ( 2008 ) . r. shyam , h. lenske and u. mosel , _ phys c _ * 69 * , 065205 ( 2004 ) ; + r. shyam , h. lenske and u. mosel , _ nucl . phys . _ * a764 * , 313 ( 2006 ) . r. shyam , _ progr . phys . _ * 61 * , 212 ( 2008 ) . a. s. rosenthal et al . , _ ann . ( n.y . ) * 184 * , 33 ( 1988 ) .[/INST] we study the binding of hypernuclei based on the latest version of quark - meson coupling model , and estimate the phtoproduction cross sections for the @xmath0c(@xmath1)@xmath2b reaction using the bound @xmath3 spinors obtained in the model . </s>

the core accretion scenario is a key ingredient of our current theory for planet formation ( see reviews by * ? ? ? * ; * ? ? ? * and references therein ) . in this model , solid bodies ranging from micron - sized dust grains to kilometer - sized planetesimals are the building blocks from which planetary cores assemble and ultimately form giant planets orbiting stars . the dynamics of planetesimals and planetary cores may be strongly influenced by their natal protoplanetary gas disks . in particular , type i migration due to angular momentum exchange with the gas disk could drive a planetary core into the host star in a short timescale ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) compared to a typical disk lifetime of @xmath210 myr ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? this remains one of the major obstacles to planet formation in the core accretion scenario unless recent models of the countervailing effects of type iii migration in non - adiabatic disks are confirmed @xcite . turbulent transport in young protoplanetary disks seems required for mass accretion to occur at observed rates . the most likely cause of this turbulence is that disks are unstable to linear perturbations if they are weakly magnetized @xcite . although this magneto - rotational instability ( mri ) is the most promising mechanism to drive turbulence in protoplanetary disks , the numerical convergence of simulations with increasing resolution continues to be an open issue . it has been shown that mri - driven turbulence in ideal , magnetized , unstratified disks without mean magnetic fields decreases with increasing resolution and might be negligible when resolution is high and numerical dissipation is small @xcite . to maintain a nonzero , convergent level of turbulent accretion , it has been argued that simulated disks might require stratification @xcite , explicit dissipation ( e.g. , * ? ? ? * ; * ? ? ? * ) , or nonzero magnetic flux ( e.g. , * ? ? ? * ; * ? ? ? furthermore , the conductivity near the mid - plane of a protoplanetary disk may be too low for the mri to operate , at least over some range of radii , resulting in a quiescent region known as a dead zone ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? disks containing dead zones will , nevertheless , be stirred by turbulent regions near the disk surface @xcite . the turbulent nature of protoplanetary disks might lead to scenarios for the formation and migration of planetesimals and planetary cores that are rather different from those suggested for the better - studied case of a laminar disk . the turbulence driven by the mri causes density enhancements significant enough to exert gravitational torques that turn the orbital motion of low - mass objects into a random walk ( ( * ? ? ? * hereafter lsa04 ) ; @xcite ) . it has been shown that radial excursions and eccentricities of planetesimals or protoplanets could be excited through such a process ( ( * ? ? ? * hereafter n05 ) ; ( * ? ? ? * hereafter oim07 ) ) . since some protoplanets could diffuse their way radially outward in the process , type i migration might be effectively delayed and some objects might more easily survive past the gas disk depletion ( ( * ? ? ? * hereafter jgm06 ) ; @xcite ) . even if the disk contains a dead zone , ( * ? ? ? * hereafter omm07 ) have shown that low - mass objects within the dead zone still experience some of the turbulent torques generated by the active layers . * hereafter igm08 ) suggest , on the other hand , that the velocity dispersion of planetesimals excited by hydromagnetic turbulence might be so strong that kilometer - sized objects suffer from collisional destruction . the survivability of planetesimals or protoplanets under type i migration or collisional destruction sensitively depends on their orbital dynamics in a turbulent gas disk . previous direct orbital integrations of planetesimals or protoplanets embedded in a turbulent gas disk were conducted in global disk models ( lsa04 ; n05 ; oim07 ; igm08 ) . in contrast to global disk models , it can be advantageous to employ the local shearing box approximation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) because of its high resolving power on turbulence structures and the possibility of integrating for long times . @xcite and omm07 first measured the stochastic torques generated by hydromagnetic turbulence at the center of a local shearing box . in this paper , we pursue this topic further by using direct orbital integration of planetesimals moving as massless particles under the gravitational influence of mri - driven turbulence in a local shearing box . we focus our attention on unstratified disks in the context of ideal magnetohydrodynamics ( mhd ) . to maintain a nonzero , numerically convergent level of stochastic perturbations driven by the mri , we impose a constant vertical magnetic flux . we describe our numerical models in [ s : nm ] and present the simulations in [ s : sr ] , along with statistical analyses of the disk properties and the planetesimal orbits . in [ s : ipf ] , we use our results to revisit the issue of survivability of planetesimals and planetary cores , before reaching our conclusions in [ s : conc ] . we use the parallelized , cache - efficient , pencil code described by @xcite . it solves the non - ideal mhd equations by sixth - order finite differences in space and third - order runge - kutta steps in time . the induction equation is solved using the magnetic vector potential @xmath3 so that zero divergence of magnetic field @xmath4 is guaranteed at all time . to save memory usage , the runge - kutta time integration is performed using the @xmath5-method @xcite . the scheme is not written in conservative form . instead , conserved quantities like total mass are monitored to evaluate the quality of the solution . in the following subsections , we describe the equations assumed in our models as well as the numerical constructs . we use the local shearing box approximation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) to simulate a small cartesian box carved out of a keplerian disk at a large distance from the host star . the center of the box co - rotates with the disk at keplerian angular speed @xmath6 , the @xmath7-axis is directed radially , and the @xmath8-axis is directed azimuthally . the vertical component of gravity from the host star is ignored and thus the disk is unstratified . we impose a vertical , external magnetic field @xmath9 to maintain a finite magnetic flux . the mhd equations then become @xmath10 in which @xmath11 is gas density , @xmath12 is gas velocity relative to the background shear flow , @xmath13 is gas pressure , @xmath14 is the electric current density , @xmath15 , and @xmath16 is permeability . the terms @xmath17 , @xmath18 , and @xmath19 , and those containing scalar variables @xmath20 and @xmath21 are numerical dissipation terms needed to stabilize the scheme , which are described below . they are needed to resolve shocks , and because the difference scheme formally has vanishing dissipation . we assume an isothermal equation of state , @xmath22 , where @xmath23 is the isothermal speed of sound . the mass diffusion term @xmath24 in the continuity equation ( [ e : mhd_cont ] ) and the bulk viscosity term @xmath25 in the momentum equation ( [ e : mhd_mom ] ) are implemented to broaden shocks . the artificial kinematic viscosity @xmath20 is of von neumann type ( c.f . * ; * ? ? ? * ) : @xmath26 where @xmath27 is grid spacing . it is smoothed by taking a maximum over nearest neighbors and then convolved with a gaussian kernel having a standard deviation of @xmath27 . note that the threshold for the velocity divergence is set for eliminating artificial diffusion where hydrodynamic shocks are unlikely to be present . we also include the ohmic term @xmath28 in the induction equation ( [ e : mhd_ind ] ) to broaden strong current sheets . the artificial resistivity @xmath21 assumes the same form used by @xcite but with a lower cutoff : @xmath29 where @xmath30 is the alvn speed . although simple , this form may perform better to resolve sharp magnetic structures than a resistivity proportional to the magnitude of current density itself @xcite . we apply a lower cutoff in equation ( [ e : nr ] ) to only treat regions where fast magnetic reconnection may occur . in addition to applying artificial diffusions addressing shocks and current sheets , we also implement hyper - diffusion @xmath17 , hyper - viscosity @xmath18 , and hyper - resistivity @xmath19 in the respective mhd equations ( [ e : mhd_cont])([e : mhd_ind ] ) ( e.g. , * ? ? ? * ; * ? ? ? * ) : @xmath31 where @xmath32 is a constant , the tensor @xmath33 is defined by @xmath34 , and the sixth - order differential operator @xmath35 . these terms are included in order to stabilize the high - order finite - difference scheme implemented by the pencil code . the corresponding diffusivity is proportional to @xmath36 , where @xmath37 is the wavenumber of a signal in the simulation , so features at small scales dissipate at a much higher rate than those at larger scales . therefore , by adjusting the coefficient @xmath32 , we can maintain numerical stability by damping oscillations near the grid scale while still preserving much of the inertial range of the modeled turbulence resolved in the simulation . in our models , we choose @xmath32 such that the mesh reynolds number @xmath38 where @xmath39 is the absolute maximum of @xmath40 over the computational domain . this criterion states that dissipation at the nyquist frequency should be comparable to or stronger than gas advection . notice that since all the adopted hyper - diffusive terms have the same coefficient @xmath32 , the effective magnetic prandtl number @xmath41 in our simulations should be reasonably close to unity , where @xmath42 and @xmath43 are the effective viscosity and resistivity in the simulations , respectively . in this work , we consider particles of zero mass to study the effect of hydromagnetic turbulence on the orbital properties of planetesimals . although simple , this offers a good approximation for kilometer - sized planetesimals as they are large enough that gaseous drag force can be neglected , but small enough that type i migration does not dominate . for the approximation to be valid , the mass of a particle must lie between roughly @xmath44 g and @xmath45 g , corresponding to a size range of about 0.11000 km ( omm07 ) . furthermore , if the action of hydromagnetic turbulence on the particles is separable from effects due to other interactions , our measurements can be applied to all stages of planet formation . in our models , therefore , we consider particles moving under only the gravitational influence of the host star and that of the protoplanetary gas disk . we ignore drag forces between the particles and the gas and the gravity of the particles . because the particles exert no force on the gas or themselves , no migration torques act . given deterministic keplerian shear flow and epicycle motions , deviations in particle trajectories due to turbulent fluctuations in the gas can easily be isolated . under these assumptions , the equations of motion for each particle become [ e : eomp ] @xmath46 the vector @xmath47 is the position of the particle in the shearing box , while @xmath48 is the velocity of the particle relative to the background shear flow . the scalar variable @xmath49 is the gravitational potential of the gas , which is the solution of the poisson equation @xcite : @xmath50\phi = 4\pi g\rho,\ ] ] where @xmath51 is the gravitational constant . sheared , periodic boundary conditions @xcite are adopted for the solution of equation ( [ e : poisson ] ) . the system is strictly periodic in the @xmath8- and @xmath52-directions while the @xmath7-direction requires special treatment . since the @xmath53-plane at any given @xmath7 moves with the keplerian shear flow , the lower @xmath7-boundary plane should be imaged by the upper @xmath7-boundary plane shifted by @xmath54 in the @xmath8-direction , where @xmath55 is the time - step and @xmath56 is the @xmath7-dimension of the computational domain . in mathematical notation , @xmath57 . rather than interpolating @xmath58 in real space to obtain sheared periodicity , we use fourier interpolation when solving equation ( [ e : poisson ] ) in fourier space ( see * ? ? ? * supplementary information ) . the position @xmath47 and velocity @xmath48 of each particle is updated by solving the equations of motion ( [ e : eomp ] ) simultaneously with the third - order runge - kutta steps for the mhd equations ( [ e : mhd_cont])([e : mhd_ind ] ) . in addition to the courant conditions set by the mhd equations , the time - step is limited by the absolute maximum of equation ( [ e : eomp1 ] ) such that no particles can cross more than half the zone size in one time - step . we compute the gradient of the potential @xmath59 on the grid after solving equation ( [ e : poisson ] ) and then quadratically interpolate it to the position of each particle in the calculation of equation ( [ e : eomp2 ] ) . we define the length and the time units as the vertical scale height @xmath60 and the orbital period @xmath61 , respectively , at the center of our local shearing box located at an arbitrary distance to the host star @xmath62 . since vertical hydrostatic equilibrium of isothermal gas requires that @xmath63 , the speed of sound is fixed at @xmath64 . note that this choice makes the system invariant with temperature . we adopt two different mass units such that @xmath65 and @xmath66 for a low - mass and a high - mass disk , respectively , where @xmath67 is the uniform initial gas density . for these two disk models , the toomre @xmath68 parameter for the gas is @xmath69 and 5.0 , respectively , where @xmath70 is the column density . the gas disks in our models are gravitationally stable and thus we ignore gas self - gravity . for convenience , we define a dimensionless parameter @xmath71 as a measure of the strength of disk gravity . for our low - mass and high - mass disks , @xmath72 and @xmath73 , respectively . in physical units , @xmath67 is given by the following scaling relation : @xmath74 where @xmath75 is the mass of the host star . the corresponding column density is @xmath76 these scaling relations describe families of disk models to which our results apply . in particular , at 1 au around a solar - type star , the column density of our low - mass disk is roughly consistent with that of the classical minimum mass solar nebula ( mmsn ; * ? ? ? . finally , the units of magnetic field and vector potential are @xmath77 and @xmath78 , respectively . we arbitrarily set the permeability @xmath79 . the magnetic energy density associated with @xmath80 is then @xmath81 of the initial pressure @xmath82 . the initial conditions for our models are the following . the gas density is uniform ( @xmath83 ) while the magnetic vector potential is set to zero ( @xmath84 ) . an external vertical magnetic field is imposed , ranging from @xmath85 to 0.64 . the corresponding plasma @xmath86 ranges from @xmath87 to 96 . gaussian noise in gas velocity of amplitude @xmath88 is imposed to seed the mri . as noted in [ ss : pd ] , the boundary conditions for all dynamical variables are sheared periodic and we find values for the ghost zones using fourier interpolation . our fiducial model has a computational domain of @xmath89 , but we also study domains with sizes up to @xmath90 . the highest resolution we use is 64 grid points per disk scale height @xmath60 . the coefficient @xmath32 of the hyper - diffusive terms discussed in [ ss : mhd ] needs to be fine - tuned such that the mesh reynolds number @xmath91 is as close to unity as possible during the course of the simulation ( eq . [ [ e : remesh ] ] ) . we adopt an iterative approach to determine the optimal value of @xmath32 , using @xmath92 . for the case of @xmath93 ( @xmath94 ) with a @xmath89 box at a resolution of 64 points per scale height , we choose @xmath95 for which @xmath96 at saturation level , where the deviation of @xmath39 is given by @xmath97 in its time variation . we uniformly distribute 32@xmath98 particles in the entire computational domain . we do not allow them to move until time @xmath99 after which the hydromagnetic turbulence has saturated and approached a statistically steady state . for the case of @xmath93 ( @xmath94 ) , we choose @xmath100 ( see [ ss : conv ] ) . then the particles are set to initially move relative to the background shear flow such that they have an initial eccentricity of @xmath101 and start at the apogee of their orbits , i.e. , @xmath102 ( see appendix [ s : vpao ] ) . we wrap a particle around when it moves beyond any of the six boundary planes . we remark that each model presented in the following section is just one realization of the stochastic nature of the turbulence , corresponding to one set of initial velocity perturbations of the gas . the similarity in particle orbital evolutions found across several models are due to closeness of the random number sequences used to generate the velocity perturbations and thus similar initial conditions for the gas . we first present a study of the convergence with increasing numerical resolution of the properties of the turbulence important to our work . we work on a @xmath89 grid for this study to reach maximum resolution . figure [ fi : mrit ] plots density perturbation @xmath103 , inverse plasma @xmath104 , and the @xcite @xmath105-parameter as a function of time @xmath106 for disks with an external magnetic field of @xmath93 ( @xmath94 ) at resolutions up to 64 grid points per disk scale height @xmath60 , where @xmath107 . the density perturbation @xmath103 shown is the root - mean - square value over the computational domain while the inverse plasma @xmath104 shown is the volume - averaged value . the @xmath105-parameter is calculated from the combined effects due to the reynolds and maxwell shear stresses ( e.g. , * ? ? ? * ) : @xmath108 where the bracket @xmath109 denotes the volume average over the entire computational domain . as shown in figure [ fi : mrit ] , the mri saturates and remains roughly steady after about @xmath110 . after saturation , all three properties exhibit only small changes with increasing resolution , aside from a slight trend of increasing @xmath105 . the properties of the saturated turbulence appear to converge to a nonzero level , as opposed to disks without net magnetic flux ( e.g. , * ? ? ? we also examine how the same averaged quantities depend on the size of our local simulation box by studying three runs done with increasing horizontal size , up to @xmath90 , at our medium resolution of 32 points per scale height . @xcite ran high - resolution ( with @xmath1137 points per scale hight ) , unstratified models without mean field and found roughly linear growth in the effective viscosity @xmath105 with box size . in figure [ fi : mrit_box ] we show that the plasma @xmath104 and the effective @xmath105-parameter appear almost independent of box size in our models , aside from a trend toward reduced temporal fluctuations when averaged over larger boxes . the root - mean - square density perturbation @xmath103 shows a weak trend towards increasing at larger box size , though , with the average over the time period @xmath111 increasing by 26% from the smallest to the largest box , a scale change of a factor of four . this probably occurs because of the inclusion of larger - scale instability modes in the larger boxes ; it is not a particularly dramatic effect , though , because the smallest box size that we study already captures the fastest growing modes . nevertheless , this small effect seems to strongly affect particle orbital properties , as we will discuss below . we next turn to the effect of varying external vertical magnetic field . figure [ fi : mrib ] plots the same properties of the saturated turbulence as a function of the external vertical magnetic field , represented by the inverse plasma @xmath104 , for our smallest box . they are volume averaged as described above , and then time - averaged over a period of at least @xmath112 after saturation . also included in the figure are the time variation of these properties , as indicated by the error bars . we confirm the general trend of increasing turbulence activity with increasing uniform vertical field ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? numerical convergence can be seen over the range of the field strengths we have explored . in addition to the turbulent transport often discussed in the literature , we also report the dependency between density perturbation and external field in figure [ fi : mrib ] , which may be more relevant to the orbital dynamics of particles moving in these disks . we emphasize that by varying the net vertical magnetic flux through a disk , a wide range of turbulent viscosity values can be obtained , as suggested by numerous previous works as well as figure [ fi : mrib ] . to best represent typical protoplanetary accretion disks , we adopt a fiducial disk model with @xmath93 ( @xmath94 ) , which we run at a resolution of 64 points per scale height on a @xmath89 grid . as shown in figures [ fi : mrit ] and [ fi : mrib ] , this model gives a turbulent accretion of @xmath113 , which is consistent with current estimates for disks around typical t tauri stars ( e.g. , * ? ? ? * ; * ? ? ? note that in our fiducial model , the root - mean - square density perturbation of the gas is on the order of @xmath110% . using our fiducial model in the context of a protoplanetary disk , we now study the orbital dynamics of zero - mass particles moving in this turbulent environment . as demonstrated in figure [ fi : rd ] , a particle moving under gravity of the turbulent gas undergoes epicycle motion horizontally as well as continuous change in its mean radius . we define the radial drift of each particle as @xmath114 , where @xmath115 is the mean radial position over one orbital period ( as exemplified by the red line in fig . [ fi : rd ] ) and @xmath116 is the initial radial position . given that @xmath117 , the eccentricity of each particle can be approximated by @xmath118 , where @xmath119 and @xmath120 are the maximum and the minimum radial positions in one epicycle , respectively . with these two quantities , we can measure the orbital migration and eccentricity change of planetesimals induced by hydromagnetic turbulence . figure [ fi : dx - e ] shows the change of radial drift and eccentricity with time for four randomly selected particles . it is evidently a stochastic process and the final outcome can be quite different with slightly different initial conditions . nevertheless , statistical methods can be employed to quantify the process . we discuss the statistical evolution of these orbital properties in the following subsections . histograms of the distribution of radial drifts at three different times in the low - mass disk version of our fiducial model are plotted in figure [ fi : dx_dist ] . the distribution of particles in radial drift resembles a normal distribution with its center located at approximately zero . this is not surprising since there is no preferred direction locally for the turbulence to generate a net torque . more interestingly , the width of the distribution increases with time . although the hydromagnetic turbulence has no net effect on the orbital radius of the particles , it becomes more and more likely for any single particle to drift away from its original orbit as time increases . this could help a subset of particles to survive type i migration , as suggested by jgm06 and @xcite . figure [ fi : dxt ] shows the standard deviation of radial drift @xmath121 as a function of elapsed time @xmath122 for particles with different initial eccentricity @xmath101 moving in different strengths of disk gravity @xmath123 in our fiducial model . the standard deviation steadily increases with time , with little difference between particles of different initial eccentricities . power - law fitting results in time indices of about 0.520.58 , just slightly larger than 1/2 . this confirms the proposition that gravitational influence of the hydromagnetic turbulence makes particles undergo random walks ( lsa04 ; @xcite ; n05 ) and the resulting orbital evolution can be described as a diffusion process ( jgm06 ; oim07 ; * ? ? ? * ; * ? ? ? we measure the dependence of radial drift on disk gravity , as quantified by the dimensionless parameter @xmath123 , by comparing the results from our low - mass and high - mass disk models ( see [ ss : cusr ] ) . as demonstrated in figure [ fi : dxt ] , radial drifts in these models roughly coincide after being scaled with @xmath123 , indicating a dependence close to linear . by assuming that @xmath121 scales with @xmath124 , our best fit to the results shown in figure [ fi : dxt ] is @xmath125 the size of the computational domain of a local shearing box does have a rather substantial effect on the magnitude of the random walk , and thus the diffusion derived from this model , as shown in figure [ fi : dxt_box ] . increasing the horizontal size of the box by a factor of four results in almost an order of magnitude increase in the standard deviation of the radial drift at each time . in contrast to gas properties discussed in [ ss : conv ] , we have not seen convergence of the magnitude of the orbital random walk with box size in our study . our largest box shows an amplitude of the random walk roughly a factor of three smaller than seen in the global model described by n05 . we make this estimate by examining his figure 4 . this shows the semi - major axis for six zero - mass particles at different radii @xmath62 over a period of time of roughly 100 orbits in the relevant region of 23 times the inner edge of his grid , at @xmath126 , in a disk with @xmath127 . the standard deviation of @xmath128 of the particles at @xmath129 is roughly 0.06 , where @xmath130 is the orbital period at the respective initial radii of the particles and the relevant disk - gravity parameter @xmath131 ( richard p. nelson 2009 , private communication ) . by comparison , the result for our @xmath90 box shown in figure [ fi : dxt_box ] gives @xmath132 at @xmath129 . on the other hand , oim07 found results roughly consistent with our fiducial disk model . these authors used orbital integrations of particles influenced by torques given by a heuristic , stochastic formula for hydromagnetic turbulence , and the formula was suggested by lsa04 based on zero net flux , global disk , mhd simulations . the disk models oim07 studied were about 10100 times less massive than the mmsn , but they reported their scaling with varying disk mass . by extrapolating their results to values appropriate for our low - mass disk model with @xmath72 , and considering their fiducial magnitudes for the stochastic torques , we find that our measured spread of radial drift ( eq . [ [ e : dx ] ] ) is roughly consistent with theirs at 1 au . as discussed by these authors , large uncertainty in thier results might be involved , mostly due to the uncertainty in the magnitude of the stochastic torques and their neglecting the power given by lsa04 in the @xmath133 mode ( where the integer @xmath134 represents the fourier decomposition of density structure in azimuthal angle rather than the spiral mode used in density wave theories ) . figure [ fi : de_dist]a shows the histograms of eccentricity at three different times for particles with initial eccentricity @xmath135 moving in the low - mass version of our fiducial disk model . is about @xmath136 and @xmath137 at @xmath138 for the low - mass and the high - mass disk models , respectively . these eccentricities correspond to epicycle motions covering about 1.5 and 20 grid zones in the radial direction , enough to resolve the gravitational forces experienced by the particles . ] the distributions appear close to a rayleigh distribution : @xmath139 where @xmath140 is a constant proportional to both the peak and the width of the distribution . the standard deviation of this distribution is given by @xmath141 . as shown in figure [ fi : de_dist]a , both the eccentricity at the peak value and the width of the distribution increase with time , so it at first appears that eccentricity is excited by hydromagnetic turbulence . such eccentricity growth was also reported by n05 and oim07 . + however , we find a different distribution for particles with nonzero initial eccentricity in the same model . figure [ fi : de_dist]b shows histograms of eccentricity deviation @xmath142 at three different times for particles with initial eccentricity @xmath143 . they are similar to a normal distribution with a constant mean , implying that the average eccentricity of these particles remains constant at the initial eccentricity ( see also oim07 ) . the width of the distribution does increase with time . therefore , hydromagnetic turbulence does not just excite the eccentricity of particles ; it can also act to damp the existing eccentricity of some particles . the distribution found for particles with @xmath135 is just a special case of this general behavior : since eccentricity is a positive definite quantity and the initial eccentricity is zero , it is no surprise that a normal distribution for the eccentricity deviation , @xmath144 , manifests as a rayleigh distribution for the eccentricity itself ( eq . [ [ e : rayleigh ] ] ) . figure [ fi : det ] shows the standard deviation of eccentricity deviation @xmath145 as a function of elapsed time @xmath146 measured for our fiducial model . note that to be consistent with a normal distribution as discussed above , we have multiplied the standard deviation measured for particles with @xmath135 by a factor of @xmath147 . as in the case of radial drift discussed in [ ss : rd ] , little difference exists between particles with different initial eccentricities and the results scale linearly with the dimensionless parameter @xmath123 , which measures the strength of the disk gravity . chi - square fitting with a @xmath124 dependence to the growth in eccentricity deviation in all six models leads to ( fig . [ fi : det ] ) @xmath148 note that at 1 au in an mmsn disk , @xmath149 , @xmath150 , and @xmath151 yr , and thus the increase in eccentricity deviation due to hydromagnetic turbulence only amounts to about 0.04 in 1 myr . as with the case of radial drift discussed in [ ss : rd ] , our measured spread of eccentricity in our fiducial model is in approximate agreement with oim07 . on the other hand , n05 reported a typical eccentricity growth of @xmath152 for @xmath153 . with @xmath154 at radius @xmath155 in the model studied by n05 ( richard p. nelson 2009 , private communication ) and @xmath150 , the eccentricity deviation given by equation ( [ e : de ] ) is about one order of magnitude less than what was reported by n05 . one possible explanation for this inconsistency could be the presence of large - scale structures , particularly @xmath156 modes , in global , but not in local models . oim07 reported that the inclusion of an @xmath133 mode in their torque formula induces a ten times greater impact of hydromagnetic turbulence on particle orbits , using the calibration with global mhd simulations provided by lsa04 . inspection of lsa04 , as well as n05 , shows that the density structures in their global models often extend more than @xmath157 in azimuthal angle , leading to the @xmath133 mode having the largest amplitude . such large - scale modes indeed can be excited in self - gravitating disks , and they could also be excited by local turbulence . this idea is offered some support by the modest growth in density perturbations in larger boxes that we find ( fig . [ fi : mrit_box ] ) , and the growth in @xmath105 reported in larger boxes by @xcite . in figure [ fi : det_box ] we examine the growth in eccentricity deviation as a function of box size in our local models . increasing the horizontal box size by a factor of four indeed increases the eccentricity deviation by a factor of four , though this still does not account for the order of magnitude higher value found by n05 in his global model . if @xmath133 modes indeed can be similarly excited by well resolved turbulence , though , this could offer an explanation for the discrepancy . however , using local models with mean azimuthal fields , @xcite reported that the coherent structures induced by the mri are localized , with correlation lengths of about @xmath158 , @xmath159 , and @xmath158 in radial , azimuthal , and vertical directions , respectively . therefore , it is possible that current global models might not have enough resolution to model such fine structures , which were then spuriously connected into extended structures resembling @xmath133 modes . to determine the physical reality of large - scale structure in turbulent disks , global models capable of resolving localized structures will be needed . another important quantity in the study of planetesimal dynamics is the velocity dispersion of the particles . we calculate the radial and the azimuthal components of velocity dispersion by taking the standard deviations of radial and azimuthal velocities for all particles , i.e. , @xmath160 and @xmath161 , respectively . since all the dynamical equations are linearized in terms of @xmath162 in the local shearing box approximation , the background shear flow is uniform irrespective of position , so the velocity dispersion for all particles in the computational domain is a well - defined local quantity . figure [ fi : uil0 ] plots @xmath160 and @xmath161 measured for particles with zero initial eccentricity in the low - mass disk version of our fiducial model as a function of time @xmath106 . the velocity dispersion monotonically increases with time , and thus hydromagnetic turbulence tends to steadily heat up a planetesimal disk . note that @xmath163 , a sanity check that our results are consistent with a swarm of non - interacting particles moving epicyclically in a keplerian disk . figure [ fi : ux ] compiles the radial velocity dispersions @xmath160 as a function of elapsed time @xmath146 measured in our fiducial model for particles with different initial eccentricity @xmath101 moving in disks of different disk gravity . as is the case with the radial drift and eccentricity deviation discussed in [ ss : rd ] and [ ss : ecc ] , the results depend linearly on @xmath123 , the strength of disk gravity , though there seems to be a slightly enhanced effect for particles with @xmath164 . given the uncertainty involved in the numerical simulations , we assume it is a secondary effect as a first approximation . the best fit to all six models is then given by @xmath165 the corresponding timescale @xmath166 for turbulent excitation of velocity dispersion can be estimated by @xmath167 , and we find from equation ( [ e : rvd ] ) @xmath168 ^ 2.\ ] ] increasing the box size increases the magnitude of this effect , as shown in figure [ fi : ux_box ] , possibly even non - linearly . as noted in [ ss : ecc ] , hydromagnetic turbulence can act either to excite the eccentricities of planetesimals or to circularize their eccentric orbits . however , a perfectly cold disk of planetesimals with nonzero initial eccentricity but vanishing velocity dispersion will be monotonically heated by the turbulence , as shown above . the velocity dispersion increases with time while the mean eccentricity may remain unchanged unless a significant fraction of particles are circularized . therefore , the eccentricity may not necessarily be proportional to the velocity dispersion for a swarm of planetesimals moving through hydromagnetic turbulence . the velocity dispersion of a planetesimal disk also grows with time due to mutual gravitational scattering . the corresponding timescale for a swarm of identical particles of mass @xmath169 can be estimated by ( e.g. , * ? ? ? * ) @xmath170^{-1},\ ] ] where @xmath171 is the number density of planetesimals and @xmath172 , in which @xmath173 is the scale height of the planetesimal disk determined by the vertical velocity dispersion @xmath174 . to find @xmath175 in physical units , we assume for simplicity that most of the solid material in a protoplanetary disk is concentrated in planetesimals , and thus @xmath176 where @xmath177 is the solid - to - gas ratio . we also assume @xmath178 , so that equation ( [ e : gs1 ] ) becomes @xmath179^{-1}\ ] ] with @xmath180 we further focus our discussion on a velocity scale of order @xmath181 , the escape velocity at the surface of a planetesimal : @xmath182 where @xmath183 is the material density of the planetesimal . this scale is of critical interest for planetary cores to accrete solid material ; particles with relative velocities of order @xmath181 are more likely to coalesce into larger bodies than to be eroded into smaller pieces . by assuming @xmath184 , the timescales for heating a planetesimal disk by hydromagnetic turbulence and gravitational scattering become @xmath185 and @xmath186 with @xmath187 respectively . with the scales assumed above and at 1 au in an mmsn disk , @xmath188 yr while measurement from our high - resolution fiducial model described by equation ( [ e : t1 ] ) gives @xmath189 yr . for larger objects approaching the planetary mass regime , with @xmath190 , @xmath191 yr . therefore , hydromagnetic turbulence probably dominates the heating of a disk of kilometer - sized planetesimals , while gravitational scattering may be more important for objects approaching earth size . models with larger boxes yield smaller values of @xmath166 , strengthening this conclusion . note that @xmath175 increases more steeply with @xmath160 and @xmath130 but decreases less rapidly with @xmath123 than @xmath166 ( eqs . [ [ e : t1 ] ] and [ [ e : gs2 ] ] ) , and thus hydromagnetic turbulence gains dominance over gravitational scattering for larger velocity dispersion , larger distance to the host star , and more massive gas disks than assumed here . in this section , we apply our results on the orbital evolution of zero - mass particles to two specific problems in planet formation . first , we estimate the strength of diffusive migration of protoplanets due to hydromagnetic turbulence and discuss their survivability under type i migration following the analytical framework established by jgm06 . secondly , we revisit the proposition of igm08 that planetesimals may suffer from collisional destruction as a result of hydromagnetic turbulence excitation of velocity dispersion among them . using a fokker - planck formalism , jgm06 derived an advection - diffusion equation to describe the evolution of the distribution of protoplanets under the influence of both type i migration and hydromagnetic turbulence . @xcite further consolidated the analysis by studying more realistic disk density structure with both spatial and time dependence . these authors found that turbulence tends to reduce the lifetimes of most protoplanets while allowing some of them to linger long enough to survive rapid inward type i migration . the likelihood of producing a planetary system with a specific configuration sensitively depends on the strength of the diffusive migration induced by the turbulence , however . jgm06 and @xcite calibrated the turbulence strength with the global disk models computed by lsa04 , @xcite , and n05 . in contrast , using a local disk model , omm07 found that the strength might be several orders of magnitude less than what was estimated by jgm06 . in this section , we provide a new assessment based on the disk models studied in this work . as shown in [ ss : rd ] , an initial delta function in the distribution of mean orbital radii of zero - mass particles is spread with time into a normal distribution of constant mean . a @xmath192 time dependence for the standard deviation of the distribution suggests that this process can be described by a diffusion equation of the form @xmath193 where @xmath194 is the diffusion coefficient and @xmath195 is the distribution function : @xmath196 is the probability of finding a particle with a radial displacement in @xmath197 at time @xmath106 . let us write , @xmath198,\ ] ] @xmath199 where @xmath200 is a proportionality constant . substituting equation ( [ e : normal ] ) into equation ( [ e : diffus ] ) , we find that @xmath201 and thus with @xmath202 , @xmath203 by comparing equations ( [ e : sigma1 ] ) and ( [ e : sigma2 ] ) , the diffusion coefficient @xmath194 is related to @xmath200 and @xmath130 by @xmath204 the best - fit to our fiducial high resolution , small box model , given by equation ( [ e : dx ] ) , can be substituted here to find @xmath205 by identifying @xmath106 with @xmath146 . in this derivation , we have assumed that the stochastic torque exerted by hydromagnetic turbulence is a local process such that the diffusion coefficient @xmath194 is sufficiently constant near @xmath206 . we are now in a position to estimate the diffusion coefficient @xmath207 of jgm06 in comparison to @xmath208 , where @xmath209 is the orbital angular momentum of a protoplanet of mass @xmath169 orbiting a star of mass @xmath75 on a quasi - circular orbit at a radial distance @xmath62 . since @xmath207 and @xmath208 have dimensions of @xmath210 $ ] and @xmath211 $ ] , respectively , they may be related by @xmath212 . using dimensional arguments , jgm06 defined a dimensionless parameter @xmath213 to describe the uncertainties associated with hydromagnetic turbulence : @xmath214 by comparing equations ( [ e : dcr ] ) and ( [ e : dcj ] ) , we find that @xmath215 for our fiducial model . note that @xmath213 is a constant independent of @xmath62 given our scalings , in agreement with the assumption of constant @xmath213 made by jgm06 . the value of @xmath213 estimated in equation ( [ e : eps ] ) is about an order of magnitude smaller than what was reported by omm07 for a stratified disk model with zero net flux on a @xmath216 grid at the same resolution as our fiducial model with 64 points per scale height . to identify the reason for this discrepancy , we further evaluate the magnitude and the correlation time of the torques exerted by the turbulent gas on the particles in our model . firstly , the root - mean - square of the @xmath8-component of the gravitational force per unit mass exerted by the gas over all time and particles is @xmath217 . we find negligible difference between torques calculated following the particles along their orbits and those calculated at the fixed center of the box . the magnitude we obtained is reasonably consistent with the value of @xmath218 reported by omm07 at the same numerical resolution . secondly , we plot in figure [ fi : acf ] the autocorrelation functions ( acf ) of @xmath219 for several randomly selected particles as well as at the center of the box . the results are again similar to what was reported by omm07 , indicating a similar estimate for the correlation time , @xmath220 . the source of the discrepancy appears to be neither of these factors . we notice , though , that omm07 could have overestimated the correlation time by equating it to the value of the second zero - crossing of the acf . strictly speaking , the correlation time should instead be computed by integrating an ensemble average of the acf over all possible realizations , as motivated by the definitions of the diffusion coefficient and the correlation time in jgm06 : @xmath221 and @xmath222 where @xmath223 is the fluctuating part of the torque and the overline denotes ensemble average . since we distribute numerous particles uniformly over the entire computational domain , the acf obtained for each particle can be considered as one realization , and the average of the acfs over all particles may resemble the true ensemble average . this averaged acf is shown by the solid black curve in figure [ fi : acf ] . note that the oscillation occurring at time lag longer than the second crossing for each particle is much reduced , indicating the noise nature of the autocorrelation at long time lag . however , the negative value of the acf between the first two zero - crossings remains significant . this interval represents the anti - diffusion nature of the stochastic torques that we believe could be responsible for reducing the diffusion coefficient . therefore , we suggest that a better approximation for the correlation time in accordance with equations ( [ e : jgmd ] ) and ( [ e : jgmt ] ) be @xmath224 where @xmath225 is the ensemble - averaged acf of the torque per unit mass @xmath219 as a function of time lag @xmath226 . using equation ( [ e : ct ] ) , we find that in our fiducial model @xmath227 , about one order of magnitude less than the value of @xmath228 reported by omm07 . with the same approximation @xmath229 used by omm07 , we find that @xmath230 , in good agreement with the estimate of @xmath231 we derived from our direct measurement of particle radial drifts . therefore , we have achieved consistent results using two independent approaches to estimating the diffusion coefficient , one by direct measurement as in equation ( [ e : dcr ] ) and the other by the definition of correlation time given by jgm06 ( eq . [ [ e : jgmt ] ] ) . in principle , our direct measurement should be robust while using @xmath232 can only be considered as an approximation . to use the latter approach , one should refer to equation ( [ e : ct ] ) to measure the correlation time of the stochastic torques , instead of conventional methods like using the zero - crossing of the acf or the timescale of the peak of the temporal power spectrum , which probably give about one order of magnitude larger values . it will be enlightening for studies based on global models to conduct the same exercise described in this section , since this will likely explain part of the orders of magnitude discrepancy in diffusion coefficients derived from local versus global models . ( although the box size effects we have identified must also contribute to this discrepancy , they appear unable to increase the derived value of @xmath213 by more than one order of magnitude . ) according to figures 6 and 7 of jgm06 , the value of @xmath213 we inferred from our simulations indicates that advective ( type i ) migration dominates over diffusive ( stochastic ) migration for the parameter space jgm06 have investigated . for an earth - mass protoplanet at a radial distance up to 100 au in the mmsn disk and in a viscous disk with @xmath233 , advection dominates when @xmath234 and @xmath235 , respectively . for a protoplanet of mass as low as 0.01 @xmath236 at @xmath237 au in the same disk models , advection dominates when @xmath238 and @xmath239 , respectively . the critical distance and mass for the transition between dominance of advection and diffusion given our small estimate of @xmath213 for our fiducial model is outside of the parameter space explored by jgm06 , and even our largest box has a value of @xmath213 less than an order of magnitude larger . by inspection of figure 7 in jgm06 , though , the transition masses for an object at 10 au in the mmsn disk and in the viscous disk probably lies at about @xmath88 and @xmath240 , respectively . therefore , our results suggest that hydromagnetic turbulence does not significantly affect the secular migration of earth - sized protoplanets in regimes of current astrophysical interest . nevertheless , torques exerted by turbulent density perturbations seem to be a dominant agent determining the orbital dynamics of kilometer - sized planetesimals . igm08 suggested that hydromagnetic turbulence may inhibit the growth of kilometer - sized planetesimals . they argued that the velocity dispersion excited by the turbulence could be so large that collisions between planetesimals exceed their material strength or self - gravity , leading to destruction . their conclusion , however , relies on orbital integrations incorporating the heuristic , stochastic formulas for the time history of gravitational torques provided by lsa04 , which in turn were calibrated using mhd simulations of a global disk model . as pointed out in [ ss : ecc ] , a possible inconsistency exists between global and local models . since the latter shows a significantly lower effect on orbital dynamics of planetesimals , it is worthwhile revisiting the planetesimal growth problem in light of the results highlighted in this work . for comparison purposes , we adopt the same scalable mmsn disk model as used by igm08 . the gas density and the speed of sound in the mid - plane are given by @xmath241 and @xmath242 respectively , where a solar - type host star ( @xmath243 ) is assumed and @xmath244 is a scale factor . when @xmath245 , the disk mass is about 1.4 times that of an mmsn disk . the corresponding @xmath123-parameter and ratio of disk scale height to radial distance then become @xmath246 and @xmath247 respectively . substituting equations ( [ e : xi_mmsn ] ) and ( [ e : hor_mmsn ] ) into equation ( [ e : de ] ) , which is derived from our fiducial high - resolution model , we arrive at @xmath248 comparing equation ( [ e : de_mmsn ] ) with equation ( 13 ) of igm08 with the understanding that @xmath249 for particles with zero initial eccentricity ( see [ ss : ecc ] ) , we find the value of the dimensionless parameter @xmath250 a measure of the strength of hydromagnetic turbulence used by igm08 in our orbital integrations to be @xmath251 . the rest of the analysis performed by igm08 remains unchanged since the effects induced by hydromagnetic turbulence are all incorporated in the parameter @xmath250 . as noted in [ ss : ecc ] , enlarging the horizontal size of our shearing box by a factor of four at our medium resolution increases the amplitude of the eccentricity deviation by about a factor of four . nevertheless , the largest box we have studied gives @xmath252 , which remains somewhat smaller than the @xmath253@xmath239 estimated by igm08 . the rather small values of @xmath250 we obtained indicate that hydromagnetic turbulence might not pose as serious a threat to the growth of kilometer - sized planetesimals as suggested by igm08 . these authors compared the critical radii of planetesimals for accretive and erosive regimes due to different turbulence strengths @xmath254 , and @xmath255 in their figures 3 , 4 , and 5 , respectively . therefore , the values of @xmath250 we measured point to a scenario in between what is predicted by figures 4 and 5 of igm08 . in this scenario , the erosive regime only appears in the outer regions of a young protoplanetary disk and it disappears rapidly with decreasing disk mass . kilometer - sized planetesimals may be able to evade collisional destruction in the inner regions of the disk . we reiterate that the value of @xmath250 measured here pertains to a local region with turbulent stresses such that @xmath113 and @xmath256 . as discussed in [ ss : ecc ] , the validity of our results in a global context remains to be demonstrated by numerical experiments on a global disk model with a resolution capable of resolving the characteristic scales of coherent turbulence structures . in this work , we have used local , shearing - box simulations to study the dynamics of massless planetesimals in a turbulent , isothermal , unstratified , gas disk driven by the mri . with a uniform , vertical magnetic field but without explicit physical dissipation , the saturated turbulence is maintained at a roughly constant level , showing convergence with increasing resolution . by adopting a suitable magnitude for the net magnetic flux , we produce a fiducial disk model with turbulent accretion at the level of @xmath0 and with root - mean - square density perturbations @xmath257% . as discussed in [ ss : cusr ] , this model can be scaled to other physical systems of interest , as long as the assumption of negligible self - gravity of the gas remains valid . after the hydromagnetic turbulence in our fiducial model reaches saturation , we distribute numerous particles of zero mass and integrate their orbital motion under the gravitational influence of the turbulent gas . the stochastic nature of the orbital evolution of these particles is evident , so we characterize their orbital dynamics with statistical distributions , finding three major results . first , although the mean orbital radius does not change , particles slowly drift away from their original radii , so that the distribution of radii grows with time . second , gravitational force from density perturbations produced in hydromagnetic turbulence can both excite and damp the eccentricities of particle orbits , with again no change in the mean value , but a growing width of distribution if the particles possess non - negligible initial eccentricities . finally , the planetesimal disk is heated up by the turbulence , a process dominating over gravitational scattering between particles in most physical conditions relevant to protoplanetary gas disks and planetesimal sizes . a corollary of these results is that eccentricity does not serve as a good indicator of the velocity dispersion of the particles . the amplitude of orbital changes driven by the turbulence in our local models is significantly smaller than what was reported in recent global models ( lsa04 ; n05 ; igm08 ) . two possible explanations for this discrepancy suggest themselves : either insufficient resolution in the global models or the lack of convergence with box size in our local shearing box model , as discussed in [ ss : ecc ] . if our local results are valid , they indicate that although hydromagnetic turbulence can drive radial diffusion , eccentricity variations , and relative velocities of planetesimals and protoplanets , these effects may not be dominant in determining their evolution . in particular , it appears that type i migration dominates over turbulent radial drift for objects well above @xmath255 m@xmath258 . in addition , hydromagnetic turbulence might not be exciting sufficient velocity dispersion to drive planetesimals into an erosive regime that would inhibit their further growth . before these results can be considered robust , however , it will be necessary to elucidate , and hopefully reconcile , the differences that have appeared between global and local models . we thank jeffrey s. oishi and richard p. nelson for the clarification of their works and useful discussions . we thank the anonymous referee for urging us to explore models with larger box sizes . the computations reported here were performed on the columbia and pleiades systems of the nasa advanced supercomputing ( nas ) division . this research is supported by the nasa origins of solar systems program under grant nnx07ai74 g . in this section , we ( re-)derive the velocity of a particle at the apogee of its elliptical orbit in the local shearing box approximation of a keplerian disk . we repeat the equation of motion ( [ e : eomp2 ] ) for a single particle without the gravity of the gas here : @xmath259 where we have dropped the subscript @xmath13 for clarity . eliminating @xmath260 in equations ( [ e : eompax ] ) and ( [ e : eompay ] ) leads to @xmath261 by assuming the particle is at the apogee at @xmath262 , the solution for @xmath263 is@xmath264 where @xmath265 is the amplitude of the radial velocity . since @xmath266 ( eq . [ [ e : eomp1 ] ] ) , the radial oscillation is then @xmath267 where @xmath116 is the radial position of the center of the orbit . from equation ( [ e : eompay ] ) , the corresponding azimuthal velocity relative to the background shear flow is @xmath268 since the eccentricity @xmath269 of the orbit is related with the amplitude of the radial oscillation by @xmath270 , where @xmath62 is the distance to the central object , @xmath271 where @xmath60 is the disk scale height . this is just the initial condition ( [ e : icp ] ) we set out to prove . note that we have normalized @xmath269 by the ratio @xmath272 .

the dynamics of planetesimals and planetary cores may be strongly influenced by density perturbations driven by magneto - rotational turbulence in their natal protoplanetary gas disks . using the local shearing box approximation , we perform numerical simulations of planetesimals moving as massless particles in a turbulent , magnetized , unstratified gas disk . our fiducial disk model shows turbulent accretion characterized by a shakura - sunyaev viscosity parameter of @xmath0 , with root - mean - square density perturbations of @xmath110% . we measure the statistical evolution of particle orbital properties in our simulations including mean radius , eccentricity , and velocity dispersion . we confirm random walk growth in time of all three properties , the first time that this has been done with direct orbital integration in a local model . we find that the growth rate increases with the box size used at least up to boxes of eight scale heights in horizontal size . however , even our largest boxes show velocity dispersions sufficiently low that collisional destruction of planetesimals should be unimportant in the inner disk throughout its lifetime . our direct integrations agree with earlier torque measurements showing that type i migration dominates over diffusive migration by stochastic torques for most objects in the planetary core and terrestrial planet mass range . diffusive migration remains important for objects in the mass range of kilometer - sized planetesimals . discrepancies in the derived magnitude of turbulence between local and global simulations of magneto - rotationally unstable disks remains an open issue , with important consequences for planet formation scenarios .

<s>[INST]the core accretion scenario is a key ingredient of our current theory for planet formation ( see reviews by * ? ? ? * ; * ? ? ? * and references therein ) . in this model , solid bodies ranging from micron - sized dust grains to kilometer - sized planetesimals are the building blocks from which planetary cores assemble and ultimately form giant planets orbiting stars . the dynamics of planetesimals and planetary cores may be strongly influenced by their natal protoplanetary gas disks . in particular , type i migration due to angular momentum exchange with the gas disk could drive a planetary core into the host star in a short timescale ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) compared to a typical disk lifetime of @xmath210 myr ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? this remains one of the major obstacles to planet formation in the core accretion scenario unless recent models of the countervailing effects of type iii migration in non - adiabatic disks are confirmed @xcite . turbulent transport in young protoplanetary disks seems required for mass accretion to occur at observed rates . the most likely cause of this turbulence is that disks are unstable to linear perturbations if they are weakly magnetized @xcite . although this magneto - rotational instability ( mri ) is the most promising mechanism to drive turbulence in protoplanetary disks , the numerical convergence of simulations with increasing resolution continues to be an open issue . it has been shown that mri - driven turbulence in ideal , magnetized , unstratified disks without mean magnetic fields decreases with increasing resolution and might be negligible when resolution is high and numerical dissipation is small @xcite . to maintain a nonzero , convergent level of turbulent accretion , it has been argued that simulated disks might require stratification @xcite , explicit dissipation ( e.g. , * ? ? ? * ; * ? ? ? * ) , or nonzero magnetic flux ( e.g. , * ? ? ? * ; * ? ? ? furthermore , the conductivity near the mid - plane of a protoplanetary disk may be too low for the mri to operate , at least over some range of radii , resulting in a quiescent region known as a dead zone ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? disks containing dead zones will , nevertheless , be stirred by turbulent regions near the disk surface @xcite . the turbulent nature of protoplanetary disks might lead to scenarios for the formation and migration of planetesimals and planetary cores that are rather different from those suggested for the better - studied case of a laminar disk . the turbulence driven by the mri causes density enhancements significant enough to exert gravitational torques that turn the orbital motion of low - mass objects into a random walk ( ( * ? ? ? * hereafter lsa04 ) ; @xcite ) . it has been shown that radial excursions and eccentricities of planetesimals or protoplanets could be excited through such a process ( ( * ? ? ? * hereafter n05 ) ; ( * ? ? ? * hereafter oim07 ) ) . since some protoplanets could diffuse their way radially outward in the process , type i migration might be effectively delayed and some objects might more easily survive past the gas disk depletion ( ( * ? ? ? * hereafter jgm06 ) ; @xcite ) . even if the disk contains a dead zone , ( * ? ? ? * hereafter omm07 ) have shown that low - mass objects within the dead zone still experience some of the turbulent torques generated by the active layers . * hereafter igm08 ) suggest , on the other hand , that the velocity dispersion of planetesimals excited by hydromagnetic turbulence might be so strong that kilometer - sized objects suffer from collisional destruction . the survivability of planetesimals or protoplanets under type i migration or collisional destruction sensitively depends on their orbital dynamics in a turbulent gas disk . previous direct orbital integrations of planetesimals or protoplanets embedded in a turbulent gas disk were conducted in global disk models ( lsa04 ; n05 ; oim07 ; igm08 ) . in contrast to global disk models , it can be advantageous to employ the local shearing box approximation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) because of its high resolving power on turbulence structures and the possibility of integrating for long times . @xcite and omm07 first measured the stochastic torques generated by hydromagnetic turbulence at the center of a local shearing box . in this paper , we pursue this topic further by using direct orbital integration of planetesimals moving as massless particles under the gravitational influence of mri - driven turbulence in a local shearing box . we focus our attention on unstratified disks in the context of ideal magnetohydrodynamics ( mhd ) . to maintain a nonzero , numerically convergent level of stochastic perturbations driven by the mri , we impose a constant vertical magnetic flux . we describe our numerical models in [ s : nm ] and present the simulations in [ s : sr ] , along with statistical analyses of the disk properties and the planetesimal orbits . in [ s : ipf ] , we use our results to revisit the issue of survivability of planetesimals and planetary cores , before reaching our conclusions in [ s : conc ] . we use the parallelized , cache - efficient , pencil code described by @xcite . it solves the non - ideal mhd equations by sixth - order finite differences in space and third - order runge - kutta steps in time . the induction equation is solved using the magnetic vector potential @xmath3 so that zero divergence of magnetic field @xmath4 is guaranteed at all time . to save memory usage , the runge - kutta time integration is performed using the @xmath5-method @xcite . the scheme is not written in conservative form . instead , conserved quantities like total mass are monitored to evaluate the quality of the solution . in the following subsections , we describe the equations assumed in our models as well as the numerical constructs . we use the local shearing box approximation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) to simulate a small cartesian box carved out of a keplerian disk at a large distance from the host star . the center of the box co - rotates with the disk at keplerian angular speed @xmath6 , the @xmath7-axis is directed radially , and the @xmath8-axis is directed azimuthally . the vertical component of gravity from the host star is ignored and thus the disk is unstratified . we impose a vertical , external magnetic field @xmath9 to maintain a finite magnetic flux . the mhd equations then become @xmath10 in which @xmath11 is gas density , @xmath12 is gas velocity relative to the background shear flow , @xmath13 is gas pressure , @xmath14 is the electric current density , @xmath15 , and @xmath16 is permeability . the terms @xmath17 , @xmath18 , and @xmath19 , and those containing scalar variables @xmath20 and @xmath21 are numerical dissipation terms needed to stabilize the scheme , which are described below . they are needed to resolve shocks , and because the difference scheme formally has vanishing dissipation . we assume an isothermal equation of state , @xmath22 , where @xmath23 is the isothermal speed of sound . the mass diffusion term @xmath24 in the continuity equation ( [ e : mhd_cont ] ) and the bulk viscosity term @xmath25 in the momentum equation ( [ e : mhd_mom ] ) are implemented to broaden shocks . the artificial kinematic viscosity @xmath20 is of von neumann type ( c.f . * ; * ? ? ? * ) : @xmath26 where @xmath27 is grid spacing . it is smoothed by taking a maximum over nearest neighbors and then convolved with a gaussian kernel having a standard deviation of @xmath27 . note that the threshold for the velocity divergence is set for eliminating artificial diffusion where hydrodynamic shocks are unlikely to be present . we also include the ohmic term @xmath28 in the induction equation ( [ e : mhd_ind ] ) to broaden strong current sheets . the artificial resistivity @xmath21 assumes the same form used by @xcite but with a lower cutoff : @xmath29 where @xmath30 is the alvn speed . although simple , this form may perform better to resolve sharp magnetic structures than a resistivity proportional to the magnitude of current density itself @xcite . we apply a lower cutoff in equation ( [ e : nr ] ) to only treat regions where fast magnetic reconnection may occur . in addition to applying artificial diffusions addressing shocks and current sheets , we also implement hyper - diffusion @xmath17 , hyper - viscosity @xmath18 , and hyper - resistivity @xmath19 in the respective mhd equations ( [ e : mhd_cont])([e : mhd_ind ] ) ( e.g. , * ? ? ? * ; * ? ? ? * ) : @xmath31 where @xmath32 is a constant , the tensor @xmath33 is defined by @xmath34 , and the sixth - order differential operator @xmath35 . these terms are included in order to stabilize the high - order finite - difference scheme implemented by the pencil code . the corresponding diffusivity is proportional to @xmath36 , where @xmath37 is the wavenumber of a signal in the simulation , so features at small scales dissipate at a much higher rate than those at larger scales . therefore , by adjusting the coefficient @xmath32 , we can maintain numerical stability by damping oscillations near the grid scale while still preserving much of the inertial range of the modeled turbulence resolved in the simulation . in our models , we choose @xmath32 such that the mesh reynolds number @xmath38 where @xmath39 is the absolute maximum of @xmath40 over the computational domain . this criterion states that dissipation at the nyquist frequency should be comparable to or stronger than gas advection . notice that since all the adopted hyper - diffusive terms have the same coefficient @xmath32 , the effective magnetic prandtl number @xmath41 in our simulations should be reasonably close to unity , where @xmath42 and @xmath43 are the effective viscosity and resistivity in the simulations , respectively . in this work , we consider particles of zero mass to study the effect of hydromagnetic turbulence on the orbital properties of planetesimals . although simple , this offers a good approximation for kilometer - sized planetesimals as they are large enough that gaseous drag force can be neglected , but small enough that type i migration does not dominate . for the approximation to be valid , the mass of a particle must lie between roughly @xmath44 g and @xmath45 g , corresponding to a size range of about 0.11000 km ( omm07 ) . furthermore , if the action of hydromagnetic turbulence on the particles is separable from effects due to other interactions , our measurements can be applied to all stages of planet formation . in our models , therefore , we consider particles moving under only the gravitational influence of the host star and that of the protoplanetary gas disk . we ignore drag forces between the particles and the gas and the gravity of the particles . because the particles exert no force on the gas or themselves , no migration torques act . given deterministic keplerian shear flow and epicycle motions , deviations in particle trajectories due to turbulent fluctuations in the gas can easily be isolated . under these assumptions , the equations of motion for each particle become [ e : eomp ] @xmath46 the vector @xmath47 is the position of the particle in the shearing box , while @xmath48 is the velocity of the particle relative to the background shear flow . the scalar variable @xmath49 is the gravitational potential of the gas , which is the solution of the poisson equation @xcite : @xmath50\phi = 4\pi g\rho,\ ] ] where @xmath51 is the gravitational constant . sheared , periodic boundary conditions @xcite are adopted for the solution of equation ( [ e : poisson ] ) . the system is strictly periodic in the @xmath8- and @xmath52-directions while the @xmath7-direction requires special treatment . since the @xmath53-plane at any given @xmath7 moves with the keplerian shear flow , the lower @xmath7-boundary plane should be imaged by the upper @xmath7-boundary plane shifted by @xmath54 in the @xmath8-direction , where @xmath55 is the time - step and @xmath56 is the @xmath7-dimension of the computational domain . in mathematical notation , @xmath57 . rather than interpolating @xmath58 in real space to obtain sheared periodicity , we use fourier interpolation when solving equation ( [ e : poisson ] ) in fourier space ( see * ? ? ? * supplementary information ) . the position @xmath47 and velocity @xmath48 of each particle is updated by solving the equations of motion ( [ e : eomp ] ) simultaneously with the third - order runge - kutta steps for the mhd equations ( [ e : mhd_cont])([e : mhd_ind ] ) . in addition to the courant conditions set by the mhd equations , the time - step is limited by the absolute maximum of equation ( [ e : eomp1 ] ) such that no particles can cross more than half the zone size in one time - step . we compute the gradient of the potential @xmath59 on the grid after solving equation ( [ e : poisson ] ) and then quadratically interpolate it to the position of each particle in the calculation of equation ( [ e : eomp2 ] ) . we define the length and the time units as the vertical scale height @xmath60 and the orbital period @xmath61 , respectively , at the center of our local shearing box located at an arbitrary distance to the host star @xmath62 . since vertical hydrostatic equilibrium of isothermal gas requires that @xmath63 , the speed of sound is fixed at @xmath64 . note that this choice makes the system invariant with temperature . we adopt two different mass units such that @xmath65 and @xmath66 for a low - mass and a high - mass disk , respectively , where @xmath67 is the uniform initial gas density . for these two disk models , the toomre @xmath68 parameter for the gas is @xmath69 and 5.0 , respectively , where @xmath70 is the column density . the gas disks in our models are gravitationally stable and thus we ignore gas self - gravity . for convenience , we define a dimensionless parameter @xmath71 as a measure of the strength of disk gravity . for our low - mass and high - mass disks , @xmath72 and @xmath73 , respectively . in physical units , @xmath67 is given by the following scaling relation : @xmath74 where @xmath75 is the mass of the host star . the corresponding column density is @xmath76 these scaling relations describe families of disk models to which our results apply . in particular , at 1 au around a solar - type star , the column density of our low - mass disk is roughly consistent with that of the classical minimum mass solar nebula ( mmsn ; * ? ? ? . finally , the units of magnetic field and vector potential are @xmath77 and @xmath78 , respectively . we arbitrarily set the permeability @xmath79 . the magnetic energy density associated with @xmath80 is then @xmath81 of the initial pressure @xmath82 . the initial conditions for our models are the following . the gas density is uniform ( @xmath83 ) while the magnetic vector potential is set to zero ( @xmath84 ) . an external vertical magnetic field is imposed , ranging from @xmath85 to 0.64 . the corresponding plasma @xmath86 ranges from @xmath87 to 96 . gaussian noise in gas velocity of amplitude @xmath88 is imposed to seed the mri . as noted in [ ss : pd ] , the boundary conditions for all dynamical variables are sheared periodic and we find values for the ghost zones using fourier interpolation . our fiducial model has a computational domain of @xmath89 , but we also study domains with sizes up to @xmath90 . the highest resolution we use is 64 grid points per disk scale height @xmath60 . the coefficient @xmath32 of the hyper - diffusive terms discussed in [ ss : mhd ] needs to be fine - tuned such that the mesh reynolds number @xmath91 is as close to unity as possible during the course of the simulation ( eq . [ [ e : remesh ] ] ) . we adopt an iterative approach to determine the optimal value of @xmath32 , using @xmath92 . for the case of @xmath93 ( @xmath94 ) with a @xmath89 box at a resolution of 64 points per scale height , we choose @xmath95 for which @xmath96 at saturation level , where the deviation of @xmath39 is given by @xmath97 in its time variation . we uniformly distribute 32@xmath98 particles in the entire computational domain . we do not allow them to move until time @xmath99 after which the hydromagnetic turbulence has saturated and approached a statistically steady state . for the case of @xmath93 ( @xmath94 ) , we choose @xmath100 ( see [ ss : conv ] ) . then the particles are set to initially move relative to the background shear flow such that they have an initial eccentricity of @xmath101 and start at the apogee of their orbits , i.e. , @xmath102 ( see appendix [ s : vpao ] ) . we wrap a particle around when it moves beyond any of the six boundary planes . we remark that each model presented in the following section is just one realization of the stochastic nature of the turbulence , corresponding to one set of initial velocity perturbations of the gas . the similarity in particle orbital evolutions found across several models are due to closeness of the random number sequences used to generate the velocity perturbations and thus similar initial conditions for the gas . we first present a study of the convergence with increasing numerical resolution of the properties of the turbulence important to our work . we work on a @xmath89 grid for this study to reach maximum resolution . figure [ fi : mrit ] plots density perturbation @xmath103 , inverse plasma @xmath104 , and the @xcite @xmath105-parameter as a function of time @xmath106 for disks with an external magnetic field of @xmath93 ( @xmath94 ) at resolutions up to 64 grid points per disk scale height @xmath60 , where @xmath107 . the density perturbation @xmath103 shown is the root - mean - square value over the computational domain while the inverse plasma @xmath104 shown is the volume - averaged value . the @xmath105-parameter is calculated from the combined effects due to the reynolds and maxwell shear stresses ( e.g. , * ? ? ? * ) : @xmath108 where the bracket @xmath109 denotes the volume average over the entire computational domain . as shown in figure [ fi : mrit ] , the mri saturates and remains roughly steady after about @xmath110 . after saturation , all three properties exhibit only small changes with increasing resolution , aside from a slight trend of increasing @xmath105 . the properties of the saturated turbulence appear to converge to a nonzero level , as opposed to disks without net magnetic flux ( e.g. , * ? ? ? we also examine how the same averaged quantities depend on the size of our local simulation box by studying three runs done with increasing horizontal size , up to @xmath90 , at our medium resolution of 32 points per scale height . @xcite ran high - resolution ( with @xmath1137 points per scale hight ) , unstratified models without mean field and found roughly linear growth in the effective viscosity @xmath105 with box size . in figure [ fi : mrit_box ] we show that the plasma @xmath104 and the effective @xmath105-parameter appear almost independent of box size in our models , aside from a trend toward reduced temporal fluctuations when averaged over larger boxes . the root - mean - square density perturbation @xmath103 shows a weak trend towards increasing at larger box size , though , with the average over the time period @xmath111 increasing by 26% from the smallest to the largest box , a scale change of a factor of four . this probably occurs because of the inclusion of larger - scale instability modes in the larger boxes ; it is not a particularly dramatic effect , though , because the smallest box size that we study already captures the fastest growing modes . nevertheless , this small effect seems to strongly affect particle orbital properties , as we will discuss below . we next turn to the effect of varying external vertical magnetic field . figure [ fi : mrib ] plots the same properties of the saturated turbulence as a function of the external vertical magnetic field , represented by the inverse plasma @xmath104 , for our smallest box . they are volume averaged as described above , and then time - averaged over a period of at least @xmath112 after saturation . also included in the figure are the time variation of these properties , as indicated by the error bars . we confirm the general trend of increasing turbulence activity with increasing uniform vertical field ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? numerical convergence can be seen over the range of the field strengths we have explored . in addition to the turbulent transport often discussed in the literature , we also report the dependency between density perturbation and external field in figure [ fi : mrib ] , which may be more relevant to the orbital dynamics of particles moving in these disks . we emphasize that by varying the net vertical magnetic flux through a disk , a wide range of turbulent viscosity values can be obtained , as suggested by numerous previous works as well as figure [ fi : mrib ] . to best represent typical protoplanetary accretion disks , we adopt a fiducial disk model with @xmath93 ( @xmath94 ) , which we run at a resolution of 64 points per scale height on a @xmath89 grid . as shown in figures [ fi : mrit ] and [ fi : mrib ] , this model gives a turbulent accretion of @xmath113 , which is consistent with current estimates for disks around typical t tauri stars ( e.g. , * ? ? ? * ; * ? ? ? note that in our fiducial model , the root - mean - square density perturbation of the gas is on the order of @xmath110% . using our fiducial model in the context of a protoplanetary disk , we now study the orbital dynamics of zero - mass particles moving in this turbulent environment . as demonstrated in figure [ fi : rd ] , a particle moving under gravity of the turbulent gas undergoes epicycle motion horizontally as well as continuous change in its mean radius . we define the radial drift of each particle as @xmath114 , where @xmath115 is the mean radial position over one orbital period ( as exemplified by the red line in fig . [ fi : rd ] ) and @xmath116 is the initial radial position . given that @xmath117 , the eccentricity of each particle can be approximated by @xmath118 , where @xmath119 and @xmath120 are the maximum and the minimum radial positions in one epicycle , respectively . with these two quantities , we can measure the orbital migration and eccentricity change of planetesimals induced by hydromagnetic turbulence . figure [ fi : dx - e ] shows the change of radial drift and eccentricity with time for four randomly selected particles . it is evidently a stochastic process and the final outcome can be quite different with slightly different initial conditions . nevertheless , statistical methods can be employed to quantify the process . we discuss the statistical evolution of these orbital properties in the following subsections . histograms of the distribution of radial drifts at three different times in the low - mass disk version of our fiducial model are plotted in figure [ fi : dx_dist ] . the distribution of particles in radial drift resembles a normal distribution with its center located at approximately zero . this is not surprising since there is no preferred direction locally for the turbulence to generate a net torque . more interestingly , the width of the distribution increases with time . although the hydromagnetic turbulence has no net effect on the orbital radius of the particles , it becomes more and more likely for any single particle to drift away from its original orbit as time increases . this could help a subset of particles to survive type i migration , as suggested by jgm06 and @xcite . figure [ fi : dxt ] shows the standard deviation of radial drift @xmath121 as a function of elapsed time @xmath122 for particles with different initial eccentricity @xmath101 moving in different strengths of disk gravity @xmath123 in our fiducial model . the standard deviation steadily increases with time , with little difference between particles of different initial eccentricities . power - law fitting results in time indices of about 0.520.58 , just slightly larger than 1/2 . this confirms the proposition that gravitational influence of the hydromagnetic turbulence makes particles undergo random walks ( lsa04 ; @xcite ; n05 ) and the resulting orbital evolution can be described as a diffusion process ( jgm06 ; oim07 ; * ? ? ? * ; * ? ? ? we measure the dependence of radial drift on disk gravity , as quantified by the dimensionless parameter @xmath123 , by comparing the results from our low - mass and high - mass disk models ( see [ ss : cusr ] ) . as demonstrated in figure [ fi : dxt ] , radial drifts in these models roughly coincide after being scaled with @xmath123 , indicating a dependence close to linear . by assuming that @xmath121 scales with @xmath124 , our best fit to the results shown in figure [ fi : dxt ] is @xmath125 the size of the computational domain of a local shearing box does have a rather substantial effect on the magnitude of the random walk , and thus the diffusion derived from this model , as shown in figure [ fi : dxt_box ] . increasing the horizontal size of the box by a factor of four results in almost an order of magnitude increase in the standard deviation of the radial drift at each time . in contrast to gas properties discussed in [ ss : conv ] , we have not seen convergence of the magnitude of the orbital random walk with box size in our study . our largest box shows an amplitude of the random walk roughly a factor of three smaller than seen in the global model described by n05 . we make this estimate by examining his figure 4 . this shows the semi - major axis for six zero - mass particles at different radii @xmath62 over a period of time of roughly 100 orbits in the relevant region of 23 times the inner edge of his grid , at @xmath126 , in a disk with @xmath127 . the standard deviation of @xmath128 of the particles at @xmath129 is roughly 0.06 , where @xmath130 is the orbital period at the respective initial radii of the particles and the relevant disk - gravity parameter @xmath131 ( richard p. nelson 2009 , private communication ) . by comparison , the result for our @xmath90 box shown in figure [ fi : dxt_box ] gives @xmath132 at @xmath129 . on the other hand , oim07 found results roughly consistent with our fiducial disk model . these authors used orbital integrations of particles influenced by torques given by a heuristic , stochastic formula for hydromagnetic turbulence , and the formula was suggested by lsa04 based on zero net flux , global disk , mhd simulations . the disk models oim07 studied were about 10100 times less massive than the mmsn , but they reported their scaling with varying disk mass . by extrapolating their results to values appropriate for our low - mass disk model with @xmath72 , and considering their fiducial magnitudes for the stochastic torques , we find that our measured spread of radial drift ( eq . [ [ e : dx ] ] ) is roughly consistent with theirs at 1 au . as discussed by these authors , large uncertainty in thier results might be involved , mostly due to the uncertainty in the magnitude of the stochastic torques and their neglecting the power given by lsa04 in the @xmath133 mode ( where the integer @xmath134 represents the fourier decomposition of density structure in azimuthal angle rather than the spiral mode used in density wave theories ) . figure [ fi : de_dist]a shows the histograms of eccentricity at three different times for particles with initial eccentricity @xmath135 moving in the low - mass version of our fiducial disk model . is about @xmath136 and @xmath137 at @xmath138 for the low - mass and the high - mass disk models , respectively . these eccentricities correspond to epicycle motions covering about 1.5 and 20 grid zones in the radial direction , enough to resolve the gravitational forces experienced by the particles . ] the distributions appear close to a rayleigh distribution : @xmath139 where @xmath140 is a constant proportional to both the peak and the width of the distribution . the standard deviation of this distribution is given by @xmath141 . as shown in figure [ fi : de_dist]a , both the eccentricity at the peak value and the width of the distribution increase with time , so it at first appears that eccentricity is excited by hydromagnetic turbulence . such eccentricity growth was also reported by n05 and oim07 . + however , we find a different distribution for particles with nonzero initial eccentricity in the same model . figure [ fi : de_dist]b shows histograms of eccentricity deviation @xmath142 at three different times for particles with initial eccentricity @xmath143 . they are similar to a normal distribution with a constant mean , implying that the average eccentricity of these particles remains constant at the initial eccentricity ( see also oim07 ) . the width of the distribution does increase with time . therefore , hydromagnetic turbulence does not just excite the eccentricity of particles ; it can also act to damp the existing eccentricity of some particles . the distribution found for particles with @xmath135 is just a special case of this general behavior : since eccentricity is a positive definite quantity and the initial eccentricity is zero , it is no surprise that a normal distribution for the eccentricity deviation , @xmath144 , manifests as a rayleigh distribution for the eccentricity itself ( eq . [ [ e : rayleigh ] ] ) . figure [ fi : det ] shows the standard deviation of eccentricity deviation @xmath145 as a function of elapsed time @xmath146 measured for our fiducial model . note that to be consistent with a normal distribution as discussed above , we have multiplied the standard deviation measured for particles with @xmath135 by a factor of @xmath147 . as in the case of radial drift discussed in [ ss : rd ] , little difference exists between particles with different initial eccentricities and the results scale linearly with the dimensionless parameter @xmath123 , which measures the strength of the disk gravity . chi - square fitting with a @xmath124 dependence to the growth in eccentricity deviation in all six models leads to ( fig . [ fi : det ] ) @xmath148 note that at 1 au in an mmsn disk , @xmath149 , @xmath150 , and @xmath151 yr , and thus the increase in eccentricity deviation due to hydromagnetic turbulence only amounts to about 0.04 in 1 myr . as with the case of radial drift discussed in [ ss : rd ] , our measured spread of eccentricity in our fiducial model is in approximate agreement with oim07 . on the other hand , n05 reported a typical eccentricity growth of @xmath152 for @xmath153 . with @xmath154 at radius @xmath155 in the model studied by n05 ( richard p. nelson 2009 , private communication ) and @xmath150 , the eccentricity deviation given by equation ( [ e : de ] ) is about one order of magnitude less than what was reported by n05 . one possible explanation for this inconsistency could be the presence of large - scale structures , particularly @xmath156 modes , in global , but not in local models . oim07 reported that the inclusion of an @xmath133 mode in their torque formula induces a ten times greater impact of hydromagnetic turbulence on particle orbits , using the calibration with global mhd simulations provided by lsa04 . inspection of lsa04 , as well as n05 , shows that the density structures in their global models often extend more than @xmath157 in azimuthal angle , leading to the @xmath133 mode having the largest amplitude . such large - scale modes indeed can be excited in self - gravitating disks , and they could also be excited by local turbulence . this idea is offered some support by the modest growth in density perturbations in larger boxes that we find ( fig . [ fi : mrit_box ] ) , and the growth in @xmath105 reported in larger boxes by @xcite . in figure [ fi : det_box ] we examine the growth in eccentricity deviation as a function of box size in our local models . increasing the horizontal box size by a factor of four indeed increases the eccentricity deviation by a factor of four , though this still does not account for the order of magnitude higher value found by n05 in his global model . if @xmath133 modes indeed can be similarly excited by well resolved turbulence , though , this could offer an explanation for the discrepancy . however , using local models with mean azimuthal fields , @xcite reported that the coherent structures induced by the mri are localized , with correlation lengths of about @xmath158 , @xmath159 , and @xmath158 in radial , azimuthal , and vertical directions , respectively . therefore , it is possible that current global models might not have enough resolution to model such fine structures , which were then spuriously connected into extended structures resembling @xmath133 modes . to determine the physical reality of large - scale structure in turbulent disks , global models capable of resolving localized structures will be needed . another important quantity in the study of planetesimal dynamics is the velocity dispersion of the particles . we calculate the radial and the azimuthal components of velocity dispersion by taking the standard deviations of radial and azimuthal velocities for all particles , i.e. , @xmath160 and @xmath161 , respectively . since all the dynamical equations are linearized in terms of @xmath162 in the local shearing box approximation , the background shear flow is uniform irrespective of position , so the velocity dispersion for all particles in the computational domain is a well - defined local quantity . figure [ fi : uil0 ] plots @xmath160 and @xmath161 measured for particles with zero initial eccentricity in the low - mass disk version of our fiducial model as a function of time @xmath106 . the velocity dispersion monotonically increases with time , and thus hydromagnetic turbulence tends to steadily heat up a planetesimal disk . note that @xmath163 , a sanity check that our results are consistent with a swarm of non - interacting particles moving epicyclically in a keplerian disk . figure [ fi : ux ] compiles the radial velocity dispersions @xmath160 as a function of elapsed time @xmath146 measured in our fiducial model for particles with different initial eccentricity @xmath101 moving in disks of different disk gravity . as is the case with the radial drift and eccentricity deviation discussed in [ ss : rd ] and [ ss : ecc ] , the results depend linearly on @xmath123 , the strength of disk gravity , though there seems to be a slightly enhanced effect for particles with @xmath164 . given the uncertainty involved in the numerical simulations , we assume it is a secondary effect as a first approximation . the best fit to all six models is then given by @xmath165 the corresponding timescale @xmath166 for turbulent excitation of velocity dispersion can be estimated by @xmath167 , and we find from equation ( [ e : rvd ] ) @xmath168 ^ 2.\ ] ] increasing the box size increases the magnitude of this effect , as shown in figure [ fi : ux_box ] , possibly even non - linearly . as noted in [ ss : ecc ] , hydromagnetic turbulence can act either to excite the eccentricities of planetesimals or to circularize their eccentric orbits . however , a perfectly cold disk of planetesimals with nonzero initial eccentricity but vanishing velocity dispersion will be monotonically heated by the turbulence , as shown above . the velocity dispersion increases with time while the mean eccentricity may remain unchanged unless a significant fraction of particles are circularized . therefore , the eccentricity may not necessarily be proportional to the velocity dispersion for a swarm of planetesimals moving through hydromagnetic turbulence . the velocity dispersion of a planetesimal disk also grows with time due to mutual gravitational scattering . the corresponding timescale for a swarm of identical particles of mass @xmath169 can be estimated by ( e.g. , * ? ? ? * ) @xmath170^{-1},\ ] ] where @xmath171 is the number density of planetesimals and @xmath172 , in which @xmath173 is the scale height of the planetesimal disk determined by the vertical velocity dispersion @xmath174 . to find @xmath175 in physical units , we assume for simplicity that most of the solid material in a protoplanetary disk is concentrated in planetesimals , and thus @xmath176 where @xmath177 is the solid - to - gas ratio . we also assume @xmath178 , so that equation ( [ e : gs1 ] ) becomes @xmath179^{-1}\ ] ] with @xmath180 we further focus our discussion on a velocity scale of order @xmath181 , the escape velocity at the surface of a planetesimal : @xmath182 where @xmath183 is the material density of the planetesimal . this scale is of critical interest for planetary cores to accrete solid material ; particles with relative velocities of order @xmath181 are more likely to coalesce into larger bodies than to be eroded into smaller pieces . by assuming @xmath184 , the timescales for heating a planetesimal disk by hydromagnetic turbulence and gravitational scattering become @xmath185 and @xmath186 with @xmath187 respectively . with the scales assumed above and at 1 au in an mmsn disk , @xmath188 yr while measurement from our high - resolution fiducial model described by equation ( [ e : t1 ] ) gives @xmath189 yr . for larger objects approaching the planetary mass regime , with @xmath190 , @xmath191 yr . therefore , hydromagnetic turbulence probably dominates the heating of a disk of kilometer - sized planetesimals , while gravitational scattering may be more important for objects approaching earth size . models with larger boxes yield smaller values of @xmath166 , strengthening this conclusion . note that @xmath175 increases more steeply with @xmath160 and @xmath130 but decreases less rapidly with @xmath123 than @xmath166 ( eqs . [ [ e : t1 ] ] and [ [ e : gs2 ] ] ) , and thus hydromagnetic turbulence gains dominance over gravitational scattering for larger velocity dispersion , larger distance to the host star , and more massive gas disks than assumed here . in this section , we apply our results on the orbital evolution of zero - mass particles to two specific problems in planet formation . first , we estimate the strength of diffusive migration of protoplanets due to hydromagnetic turbulence and discuss their survivability under type i migration following the analytical framework established by jgm06 . secondly , we revisit the proposition of igm08 that planetesimals may suffer from collisional destruction as a result of hydromagnetic turbulence excitation of velocity dispersion among them . using a fokker - planck formalism , jgm06 derived an advection - diffusion equation to describe the evolution of the distribution of protoplanets under the influence of both type i migration and hydromagnetic turbulence . @xcite further consolidated the analysis by studying more realistic disk density structure with both spatial and time dependence . these authors found that turbulence tends to reduce the lifetimes of most protoplanets while allowing some of them to linger long enough to survive rapid inward type i migration . the likelihood of producing a planetary system with a specific configuration sensitively depends on the strength of the diffusive migration induced by the turbulence , however . jgm06 and @xcite calibrated the turbulence strength with the global disk models computed by lsa04 , @xcite , and n05 . in contrast , using a local disk model , omm07 found that the strength might be several orders of magnitude less than what was estimated by jgm06 . in this section , we provide a new assessment based on the disk models studied in this work . as shown in [ ss : rd ] , an initial delta function in the distribution of mean orbital radii of zero - mass particles is spread with time into a normal distribution of constant mean . a @xmath192 time dependence for the standard deviation of the distribution suggests that this process can be described by a diffusion equation of the form @xmath193 where @xmath194 is the diffusion coefficient and @xmath195 is the distribution function : @xmath196 is the probability of finding a particle with a radial displacement in @xmath197 at time @xmath106 . let us write , @xmath198,\ ] ] @xmath199 where @xmath200 is a proportionality constant . substituting equation ( [ e : normal ] ) into equation ( [ e : diffus ] ) , we find that @xmath201 and thus with @xmath202 , @xmath203 by comparing equations ( [ e : sigma1 ] ) and ( [ e : sigma2 ] ) , the diffusion coefficient @xmath194 is related to @xmath200 and @xmath130 by @xmath204 the best - fit to our fiducial high resolution , small box model , given by equation ( [ e : dx ] ) , can be substituted here to find @xmath205 by identifying @xmath106 with @xmath146 . in this derivation , we have assumed that the stochastic torque exerted by hydromagnetic turbulence is a local process such that the diffusion coefficient @xmath194 is sufficiently constant near @xmath206 . we are now in a position to estimate the diffusion coefficient @xmath207 of jgm06 in comparison to @xmath208 , where @xmath209 is the orbital angular momentum of a protoplanet of mass @xmath169 orbiting a star of mass @xmath75 on a quasi - circular orbit at a radial distance @xmath62 . since @xmath207 and @xmath208 have dimensions of @xmath210 $ ] and @xmath211 $ ] , respectively , they may be related by @xmath212 . using dimensional arguments , jgm06 defined a dimensionless parameter @xmath213 to describe the uncertainties associated with hydromagnetic turbulence : @xmath214 by comparing equations ( [ e : dcr ] ) and ( [ e : dcj ] ) , we find that @xmath215 for our fiducial model . note that @xmath213 is a constant independent of @xmath62 given our scalings , in agreement with the assumption of constant @xmath213 made by jgm06 . the value of @xmath213 estimated in equation ( [ e : eps ] ) is about an order of magnitude smaller than what was reported by omm07 for a stratified disk model with zero net flux on a @xmath216 grid at the same resolution as our fiducial model with 64 points per scale height . to identify the reason for this discrepancy , we further evaluate the magnitude and the correlation time of the torques exerted by the turbulent gas on the particles in our model . firstly , the root - mean - square of the @xmath8-component of the gravitational force per unit mass exerted by the gas over all time and particles is @xmath217 . we find negligible difference between torques calculated following the particles along their orbits and those calculated at the fixed center of the box . the magnitude we obtained is reasonably consistent with the value of @xmath218 reported by omm07 at the same numerical resolution . secondly , we plot in figure [ fi : acf ] the autocorrelation functions ( acf ) of @xmath219 for several randomly selected particles as well as at the center of the box . the results are again similar to what was reported by omm07 , indicating a similar estimate for the correlation time , @xmath220 . the source of the discrepancy appears to be neither of these factors . we notice , though , that omm07 could have overestimated the correlation time by equating it to the value of the second zero - crossing of the acf . strictly speaking , the correlation time should instead be computed by integrating an ensemble average of the acf over all possible realizations , as motivated by the definitions of the diffusion coefficient and the correlation time in jgm06 : @xmath221 and @xmath222 where @xmath223 is the fluctuating part of the torque and the overline denotes ensemble average . since we distribute numerous particles uniformly over the entire computational domain , the acf obtained for each particle can be considered as one realization , and the average of the acfs over all particles may resemble the true ensemble average . this averaged acf is shown by the solid black curve in figure [ fi : acf ] . note that the oscillation occurring at time lag longer than the second crossing for each particle is much reduced , indicating the noise nature of the autocorrelation at long time lag . however , the negative value of the acf between the first two zero - crossings remains significant . this interval represents the anti - diffusion nature of the stochastic torques that we believe could be responsible for reducing the diffusion coefficient . therefore , we suggest that a better approximation for the correlation time in accordance with equations ( [ e : jgmd ] ) and ( [ e : jgmt ] ) be @xmath224 where @xmath225 is the ensemble - averaged acf of the torque per unit mass @xmath219 as a function of time lag @xmath226 . using equation ( [ e : ct ] ) , we find that in our fiducial model @xmath227 , about one order of magnitude less than the value of @xmath228 reported by omm07 . with the same approximation @xmath229 used by omm07 , we find that @xmath230 , in good agreement with the estimate of @xmath231 we derived from our direct measurement of particle radial drifts . therefore , we have achieved consistent results using two independent approaches to estimating the diffusion coefficient , one by direct measurement as in equation ( [ e : dcr ] ) and the other by the definition of correlation time given by jgm06 ( eq . [ [ e : jgmt ] ] ) . in principle , our direct measurement should be robust while using @xmath232 can only be considered as an approximation . to use the latter approach , one should refer to equation ( [ e : ct ] ) to measure the correlation time of the stochastic torques , instead of conventional methods like using the zero - crossing of the acf or the timescale of the peak of the temporal power spectrum , which probably give about one order of magnitude larger values . it will be enlightening for studies based on global models to conduct the same exercise described in this section , since this will likely explain part of the orders of magnitude discrepancy in diffusion coefficients derived from local versus global models . ( although the box size effects we have identified must also contribute to this discrepancy , they appear unable to increase the derived value of @xmath213 by more than one order of magnitude . ) according to figures 6 and 7 of jgm06 , the value of @xmath213 we inferred from our simulations indicates that advective ( type i ) migration dominates over diffusive ( stochastic ) migration for the parameter space jgm06 have investigated . for an earth - mass protoplanet at a radial distance up to 100 au in the mmsn disk and in a viscous disk with @xmath233 , advection dominates when @xmath234 and @xmath235 , respectively . for a protoplanet of mass as low as 0.01 @xmath236 at @xmath237 au in the same disk models , advection dominates when @xmath238 and @xmath239 , respectively . the critical distance and mass for the transition between dominance of advection and diffusion given our small estimate of @xmath213 for our fiducial model is outside of the parameter space explored by jgm06 , and even our largest box has a value of @xmath213 less than an order of magnitude larger . by inspection of figure 7 in jgm06 , though , the transition masses for an object at 10 au in the mmsn disk and in the viscous disk probably lies at about @xmath88 and @xmath240 , respectively . therefore , our results suggest that hydromagnetic turbulence does not significantly affect the secular migration of earth - sized protoplanets in regimes of current astrophysical interest . nevertheless , torques exerted by turbulent density perturbations seem to be a dominant agent determining the orbital dynamics of kilometer - sized planetesimals . igm08 suggested that hydromagnetic turbulence may inhibit the growth of kilometer - sized planetesimals . they argued that the velocity dispersion excited by the turbulence could be so large that collisions between planetesimals exceed their material strength or self - gravity , leading to destruction . their conclusion , however , relies on orbital integrations incorporating the heuristic , stochastic formulas for the time history of gravitational torques provided by lsa04 , which in turn were calibrated using mhd simulations of a global disk model . as pointed out in [ ss : ecc ] , a possible inconsistency exists between global and local models . since the latter shows a significantly lower effect on orbital dynamics of planetesimals , it is worthwhile revisiting the planetesimal growth problem in light of the results highlighted in this work . for comparison purposes , we adopt the same scalable mmsn disk model as used by igm08 . the gas density and the speed of sound in the mid - plane are given by @xmath241 and @xmath242 respectively , where a solar - type host star ( @xmath243 ) is assumed and @xmath244 is a scale factor . when @xmath245 , the disk mass is about 1.4 times that of an mmsn disk . the corresponding @xmath123-parameter and ratio of disk scale height to radial distance then become @xmath246 and @xmath247 respectively . substituting equations ( [ e : xi_mmsn ] ) and ( [ e : hor_mmsn ] ) into equation ( [ e : de ] ) , which is derived from our fiducial high - resolution model , we arrive at @xmath248 comparing equation ( [ e : de_mmsn ] ) with equation ( 13 ) of igm08 with the understanding that @xmath249 for particles with zero initial eccentricity ( see [ ss : ecc ] ) , we find the value of the dimensionless parameter @xmath250 a measure of the strength of hydromagnetic turbulence used by igm08 in our orbital integrations to be @xmath251 . the rest of the analysis performed by igm08 remains unchanged since the effects induced by hydromagnetic turbulence are all incorporated in the parameter @xmath250 . as noted in [ ss : ecc ] , enlarging the horizontal size of our shearing box by a factor of four at our medium resolution increases the amplitude of the eccentricity deviation by about a factor of four . nevertheless , the largest box we have studied gives @xmath252 , which remains somewhat smaller than the @xmath253@xmath239 estimated by igm08 . the rather small values of @xmath250 we obtained indicate that hydromagnetic turbulence might not pose as serious a threat to the growth of kilometer - sized planetesimals as suggested by igm08 . these authors compared the critical radii of planetesimals for accretive and erosive regimes due to different turbulence strengths @xmath254 , and @xmath255 in their figures 3 , 4 , and 5 , respectively . therefore , the values of @xmath250 we measured point to a scenario in between what is predicted by figures 4 and 5 of igm08 . in this scenario , the erosive regime only appears in the outer regions of a young protoplanetary disk and it disappears rapidly with decreasing disk mass . kilometer - sized planetesimals may be able to evade collisional destruction in the inner regions of the disk . we reiterate that the value of @xmath250 measured here pertains to a local region with turbulent stresses such that @xmath113 and @xmath256 . as discussed in [ ss : ecc ] , the validity of our results in a global context remains to be demonstrated by numerical experiments on a global disk model with a resolution capable of resolving the characteristic scales of coherent turbulence structures . in this work , we have used local , shearing - box simulations to study the dynamics of massless planetesimals in a turbulent , isothermal , unstratified , gas disk driven by the mri . with a uniform , vertical magnetic field but without explicit physical dissipation , the saturated turbulence is maintained at a roughly constant level , showing convergence with increasing resolution . by adopting a suitable magnitude for the net magnetic flux , we produce a fiducial disk model with turbulent accretion at the level of @xmath0 and with root - mean - square density perturbations @xmath257% . as discussed in [ ss : cusr ] , this model can be scaled to other physical systems of interest , as long as the assumption of negligible self - gravity of the gas remains valid . after the hydromagnetic turbulence in our fiducial model reaches saturation , we distribute numerous particles of zero mass and integrate their orbital motion under the gravitational influence of the turbulent gas . the stochastic nature of the orbital evolution of these particles is evident , so we characterize their orbital dynamics with statistical distributions , finding three major results . first , although the mean orbital radius does not change , particles slowly drift away from their original radii , so that the distribution of radii grows with time . second , gravitational force from density perturbations produced in hydromagnetic turbulence can both excite and damp the eccentricities of particle orbits , with again no change in the mean value , but a growing width of distribution if the particles possess non - negligible initial eccentricities . finally , the planetesimal disk is heated up by the turbulence , a process dominating over gravitational scattering between particles in most physical conditions relevant to protoplanetary gas disks and planetesimal sizes . a corollary of these results is that eccentricity does not serve as a good indicator of the velocity dispersion of the particles . the amplitude of orbital changes driven by the turbulence in our local models is significantly smaller than what was reported in recent global models ( lsa04 ; n05 ; igm08 ) . two possible explanations for this discrepancy suggest themselves : either insufficient resolution in the global models or the lack of convergence with box size in our local shearing box model , as discussed in [ ss : ecc ] . if our local results are valid , they indicate that although hydromagnetic turbulence can drive radial diffusion , eccentricity variations , and relative velocities of planetesimals and protoplanets , these effects may not be dominant in determining their evolution . in particular , it appears that type i migration dominates over turbulent radial drift for objects well above @xmath255 m@xmath258 . in addition , hydromagnetic turbulence might not be exciting sufficient velocity dispersion to drive planetesimals into an erosive regime that would inhibit their further growth . before these results can be considered robust , however , it will be necessary to elucidate , and hopefully reconcile , the differences that have appeared between global and local models . we thank jeffrey s. oishi and richard p. nelson for the clarification of their works and useful discussions . we thank the anonymous referee for urging us to explore models with larger box sizes . the computations reported here were performed on the columbia and pleiades systems of the nasa advanced supercomputing ( nas ) division . this research is supported by the nasa origins of solar systems program under grant nnx07ai74 g . in this section , we ( re-)derive the velocity of a particle at the apogee of its elliptical orbit in the local shearing box approximation of a keplerian disk . we repeat the equation of motion ( [ e : eomp2 ] ) for a single particle without the gravity of the gas here : @xmath259 where we have dropped the subscript @xmath13 for clarity . eliminating @xmath260 in equations ( [ e : eompax ] ) and ( [ e : eompay ] ) leads to @xmath261 by assuming the particle is at the apogee at @xmath262 , the solution for @xmath263 is@xmath264 where @xmath265 is the amplitude of the radial velocity . since @xmath266 ( eq . [ [ e : eomp1 ] ] ) , the radial oscillation is then @xmath267 where @xmath116 is the radial position of the center of the orbit . from equation ( [ e : eompay ] ) , the corresponding azimuthal velocity relative to the background shear flow is @xmath268 since the eccentricity @xmath269 of the orbit is related with the amplitude of the radial oscillation by @xmath270 , where @xmath62 is the distance to the central object , @xmath271 where @xmath60 is the disk scale height . this is just the initial condition ( [ e : icp ] ) we set out to prove . note that we have normalized @xmath269 by the ratio @xmath272 .[/INST] the dynamics of planetesimals and planetary cores may be strongly influenced by density perturbations driven by magneto - rotational turbulence in their natal protoplanetary gas disks . using the local shearing box approximation , we perform numerical simulations of planetesimals moving as massless particles in a turbulent , magnetized , unstratified gas disk . our fiducial disk model shows turbulent accretion characterized by a shakura - sunyaev viscosity parameter of @xmath0 , with root - mean - square density perturbations of @xmath110% . we measure the statistical evolution of particle orbital properties in our simulations including mean radius , eccentricity , and velocity dispersion . we confirm random walk growth in time of all three properties , the first time that this has been done with direct orbital integration in a local model . we find that the growth rate increases with the box size used at least up to boxes of eight scale heights in horizontal size . however , even our largest boxes show velocity dispersions sufficiently low that collisional destruction of planetesimals should be unimportant in the inner disk throughout its lifetime . our direct integrations agree with earlier torque measurements showing that type i migration dominates over diffusive migration by stochastic torques for most objects in the planetary core and terrestrial planet mass range . diffusive migration remains important for objects in the mass range of kilometer - sized planetesimals . discrepancies in the derived magnitude of turbulence between local and global simulations of magneto - rotationally unstable disks remains an open issue , with important consequences for planet formation scenarios . </s>

Fergie has a new lovely lady lump: the Black Eyed Peas singer and her husband, Josh Duhamel, announced on their respective Twitter and Facebook pages today that they are expecting their first child together. "Josh & Me & BABY makes three!!! #mylovelybabybump," wrote Fergie, while Duhamel wrote similarly, "Fergie and Me and BABY makes three. #MyLovelyBabyBump." Photos: Red Carpet Fashion at the 2012 Grammys – Fergie In their posts, both parents-to-be included a manipulated picture of themselves as children along with a cat. Fergie and Duhamel married in 2009. ||||| Tweet with a location You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more ||||| Oh, that lying little Fergie. Liar, liar, big stretchy XL pants on fire! It was only a couple of weeks ago that Black Eyed Peas singer Fergie vehemently denied that she was pregnant. But guess what folks? She was just doing what any new mama would do -- try to keep her pregnancy secret until she was good and ready to reveal it to the world. And now she's ready! Fergie has confirmed that she's expecting her first child with actor husband Josh Duhamel. And they announced it in the cutest way. Fergie confirmed the news via Twitter, writing: Josh & Me & BABY makes three!!! #mylovelybabybump Josh wrote the same thing, but with her name first. And then they added a twist, posting a picture of themselves as children. In the Photoshopped pic of them together as kids, they look eerily like brother and sister -- possibly even twins! (I'm pretty sure Fergie is the one with the cat.) Anyway, it gives us a good idea of what their baby might look like. More from The Stir: Fergie Shares Her Naughty Bedroom Secrets (VIDEO) Congrats poured in from all over Twitter and Instragram. (In other bun-in-the-oven news, Saturday Night Live alum and Up All Night star Maya Rudolph announced she's pregnant with her fourth child.) Fergie has been open about she and Josh, who have been married for three years, wanting children. She said that the trying part was loads of fun (I bet -- have you seen Josh?): "We'll be happy when it happens. It's not really in our hands but trying is great for our relationship." And reportedly though the couple lost a beloved dog last year, they decided not to get another one, and concentrate instead on trying for their "human family." Looks like it worked. Congrats to both of them. Are you happy to hear about Fergie's news? Image via SplashNews

– Not only did that whole affair scandal strengthen Fergie's marriage to Josh Duhamel—it apparently strengthened it so much that now they're having a baby. The couple, married since 2009, announced the pregnancy on Twitter and Facebook, Rolling Stone reports. "Josh & Me & BABY makes three!!! #mylovelybabybump," wrote Fergie, with Duhamel posting a similar message. They also included a Photoshopped picture showing the two of them as babies together, and they look a bit disturbingly like siblings, notes Kiri Blakeley on The Stir.

<s>[INST]Fergie has a new lovely lady lump: the Black Eyed Peas singer and her husband, Josh Duhamel, announced on their respective Twitter and Facebook pages today that they are expecting their first child together. "Josh & Me & BABY makes three!!! #mylovelybabybump," wrote Fergie, while Duhamel wrote similarly, "Fergie and Me and BABY makes three. #MyLovelyBabyBump." Photos: Red Carpet Fashion at the 2012 Grammys – Fergie In their posts, both parents-to-be included a manipulated picture of themselves as children along with a cat. Fergie and Duhamel married in 2009. ||||| Tweet with a location You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more ||||| Oh, that lying little Fergie. Liar, liar, big stretchy XL pants on fire! It was only a couple of weeks ago that Black Eyed Peas singer Fergie vehemently denied that she was pregnant. But guess what folks? She was just doing what any new mama would do -- try to keep her pregnancy secret until she was good and ready to reveal it to the world. And now she's ready! Fergie has confirmed that she's expecting her first child with actor husband Josh Duhamel. And they announced it in the cutest way. Fergie confirmed the news via Twitter, writing: Josh & Me & BABY makes three!!! #mylovelybabybump Josh wrote the same thing, but with her name first. And then they added a twist, posting a picture of themselves as children. In the Photoshopped pic of them together as kids, they look eerily like brother and sister -- possibly even twins! (I'm pretty sure Fergie is the one with the cat.) Anyway, it gives us a good idea of what their baby might look like. More from The Stir: Fergie Shares Her Naughty Bedroom Secrets (VIDEO) Congrats poured in from all over Twitter and Instragram. (In other bun-in-the-oven news, Saturday Night Live alum and Up All Night star Maya Rudolph announced she's pregnant with her fourth child.) Fergie has been open about she and Josh, who have been married for three years, wanting children. She said that the trying part was loads of fun (I bet -- have you seen Josh?): "We'll be happy when it happens. It's not really in our hands but trying is great for our relationship." And reportedly though the couple lost a beloved dog last year, they decided not to get another one, and concentrate instead on trying for their "human family." Looks like it worked. Congrats to both of them. Are you happy to hear about Fergie's news? Image via SplashNews [/INST]– Not only did that whole affair scandal strengthen Fergie's marriage to Josh Duhamel—it apparently strengthened it so much that now they're having a baby. The couple, married since 2009, announced the pregnancy on Twitter and Facebook, Rolling Stone reports. "Josh & Me & BABY makes three!!! #mylovelybabybump," wrote Fergie, with Duhamel posting a similar message. They also included a Photoshopped picture showing the two of them as babies together, and they look a bit disturbingly like siblings, notes Kiri Blakeley on The Stir.</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Community Disaster Loan Equity Act of 2005''. SEC. 2. FINDINGS. Congress finds the following: (1) Major disasters, including natural disasters and disasters caused by terrorist acts, often result in a decline in economic activity in areas affected by the disaster and a reduction in tax collections by State and local governments serving those areas. (2) A report of the Government Accountability Office entitled ``September 11: Recent Estimates of Fiscal Impact of 2001 Terrorist Attack on New York'', dated March 2005, confirmed prior estimates that-- (A) New York City lost between $2,500,000,000 and $2,900,000,000 in tax revenues for fiscal years 2002 and 2003; and (B) the State of New York lost $2,900,000,000 for fiscal years 2002 and 2003. (3) The impact of Hurricane Katrina on State and local tax revenues is not yet known, but the impact is believed to be extensive. (4) Under the community disaster loan program (in this section referred to as the ``CDL program''), as authorized by the Robert T. Stafford Disaster Relief and Emergency Assistance Act, the President may make loans to a local government suffering a substantial loss of tax and other revenues as a result of a major disaster, if the local government demonstrates a need for financial assistance in order to preform its governmental function. (5) The President may cancel the repayment of all or any part of a loan made to a local government under the CDL program if revenues following the disaster are insufficient to meet the operating budget of that local government as a result of disaster-related revenue losses and additional unreimbursed disaster-related municipal operating expenses. In the case of a major disaster designated as an incident of national significance, including natural disasters and disasters caused by terrorist acts, repayment of any interest or principal on a loan made under the CDL program should not be required. (6) Assistance made available under the CDL program is often instrumental in aiding the full recovery of a local government following a major disaster. (7) The Disaster Mitigation Act of 2000 established a $5,000,000 limitation on loans made to a local government under the CDL program in connection with a major disaster. Before the date of enactment of such Act, there was not any limitation on the amount of such loans. (8) The $5,000,000 limitation is inequitable when applied to a local government serving a largely populated area, such as New York City, and when applied to an area that is completely devastated by a major disaster (such as Orleans, St. Bernard, and Plaquemines parishes in the State of Louisiana following Hurricane Katrina), and is inconsistent with the objective of the CDL program to provide meaningful assistance to a local government recovering from a major disaster. (9) On October 4, 2005, the Mayor of New Orleans announced that the city was laying off 3,000 city employees as a result of reduced tax revenues following Hurricane Katrina. SEC. 3. COMMUNITY DISASTER LOANS. (a) Eligibility of States.--Section 417 of the Robert T. Stafford Disaster Relief and Emergency Assistance Act (42 U.S.C. 5184) is amended by striking ``local government'' each place it appears and inserting ``State or local government''. (b) Amount.--Section 417(b) of such Act (42 U.S.C. 5184(b)) is amended-- (1) by striking ``based on need, shall'' and inserting ``based on need and shall''; and (2) by striking ``, and shall not exceed $5,000,000''. (c) Incidents of National Significance.--Section 417 of such Act (42 U.S.C. 5184) is amended by adding at the end the following: ``(e) Incidents of National Significance.-- ``(1) Loan terms.--In the case a loan made under this section to a State or local government which may suffer a substantial loss of tax and other revenues as a result of a major disaster that the President determines to be an incident of national significance-- ``(A) the amount of the loan shall not be subject to the per centum limitation in subsection (b); and ``(B) the President shall not require the payment of any interest or principal on a loan. ``(2) Incident of national significance defined.--In this subsection, the term `incident of national significance' has the meaning such term has in the national response plan established pursuant to section 502(6) of the Homeland Security Act of 2002 (6 U.S.C. 312(6)).''. (d) Applicability.--The amendments made by this section shall apply with respect to any major disaster occurring on or after August 24, 2005.

Community Disaster Loan Equity Act of 2005 - Amends the Robert T. Stafford Disaster Relief and Emergency Assistance Act to authorize the President to make community disaster loans to state governments. Eliminates the $5 million limit on such a loan, and prohibits the President from requiring its repayment, if the state or local government receiving it may suffer a substantial loss of tax and other revenues as a result of a major disaster determined to be an incident of national significance. Applies this Act to any major disaster occurring on or after August 24, 2005.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Community Disaster Loan Equity Act of 2005''. SEC. 2. FINDINGS. Congress finds the following: (1) Major disasters, including natural disasters and disasters caused by terrorist acts, often result in a decline in economic activity in areas affected by the disaster and a reduction in tax collections by State and local governments serving those areas. (2) A report of the Government Accountability Office entitled ``September 11: Recent Estimates of Fiscal Impact of 2001 Terrorist Attack on New York'', dated March 2005, confirmed prior estimates that-- (A) New York City lost between $2,500,000,000 and $2,900,000,000 in tax revenues for fiscal years 2002 and 2003; and (B) the State of New York lost $2,900,000,000 for fiscal years 2002 and 2003. (3) The impact of Hurricane Katrina on State and local tax revenues is not yet known, but the impact is believed to be extensive. (4) Under the community disaster loan program (in this section referred to as the ``CDL program''), as authorized by the Robert T. Stafford Disaster Relief and Emergency Assistance Act, the President may make loans to a local government suffering a substantial loss of tax and other revenues as a result of a major disaster, if the local government demonstrates a need for financial assistance in order to preform its governmental function. (5) The President may cancel the repayment of all or any part of a loan made to a local government under the CDL program if revenues following the disaster are insufficient to meet the operating budget of that local government as a result of disaster-related revenue losses and additional unreimbursed disaster-related municipal operating expenses. In the case of a major disaster designated as an incident of national significance, including natural disasters and disasters caused by terrorist acts, repayment of any interest or principal on a loan made under the CDL program should not be required. (6) Assistance made available under the CDL program is often instrumental in aiding the full recovery of a local government following a major disaster. (7) The Disaster Mitigation Act of 2000 established a $5,000,000 limitation on loans made to a local government under the CDL program in connection with a major disaster. Before the date of enactment of such Act, there was not any limitation on the amount of such loans. (8) The $5,000,000 limitation is inequitable when applied to a local government serving a largely populated area, such as New York City, and when applied to an area that is completely devastated by a major disaster (such as Orleans, St. Bernard, and Plaquemines parishes in the State of Louisiana following Hurricane Katrina), and is inconsistent with the objective of the CDL program to provide meaningful assistance to a local government recovering from a major disaster. (9) On October 4, 2005, the Mayor of New Orleans announced that the city was laying off 3,000 city employees as a result of reduced tax revenues following Hurricane Katrina. SEC. 3. COMMUNITY DISASTER LOANS. (a) Eligibility of States.--Section 417 of the Robert T. Stafford Disaster Relief and Emergency Assistance Act (42 U.S.C. 5184) is amended by striking ``local government'' each place it appears and inserting ``State or local government''. (b) Amount.--Section 417(b) of such Act (42 U.S.C. 5184(b)) is amended-- (1) by striking ``based on need, shall'' and inserting ``based on need and shall''; and (2) by striking ``, and shall not exceed $5,000,000''. (c) Incidents of National Significance.--Section 417 of such Act (42 U.S.C. 5184) is amended by adding at the end the following: ``(e) Incidents of National Significance.-- ``(1) Loan terms.--In the case a loan made under this section to a State or local government which may suffer a substantial loss of tax and other revenues as a result of a major disaster that the President determines to be an incident of national significance-- ``(A) the amount of the loan shall not be subject to the per centum limitation in subsection (b); and ``(B) the President shall not require the payment of any interest or principal on a loan. ``(2) Incident of national significance defined.--In this subsection, the term `incident of national significance' has the meaning such term has in the national response plan established pursuant to section 502(6) of the Homeland Security Act of 2002 (6 U.S.C. 312(6)).''. (d) Applicability.--The amendments made by this section shall apply with respect to any major disaster occurring on or after August 24, 2005.[/INST]Community Disaster Loan Equity Act of 2005 - Amends the Robert T. Stafford Disaster Relief and Emergency Assistance Act to authorize the President to make community disaster loans to state governments. Eliminates the $5 million limit on such a loan, and prohibits the President from requiring its repayment, if the state or local government receiving it may suffer a substantial loss of tax and other revenues as a result of a major disaster determined to be an incident of national significance. Applies this Act to any major disaster occurring on or after August 24, 2005.</s>

Celestino Moras, 25, is charged in a shooting that happened at the Bartow County rodeo Sunday night. An Austell man remains in custody after deputies said he opened fire into a crowd and wounded three people attending a Memorial Day Weekend rodeo in Bartow County. Celestino Moras, 25, is charged with aggravated assault in the shootings. According to deputies, Moras was drunk while attending an annual church picnic and rodeo at a property off Fossetts Cove in Cassville. The property owner told Channel 2 Action News that Moras was not one of the invited guests. He said when other guests asked him to leave, Moras stood up, pulled out a pistol and started shooting. Deputies said as many as 300 guests took off running. The property owner said when Moras ran out of bullets, one of the rodeo cowboys lassoed him. Other guests beat him and tied him up until deputies could arrive. Doctors treated Moras for facial injuries before deputies took him to jail. Lucikly, the three wounded guests suffered only minor injuries and were treated and released from local hospitals. The Garcia family lives right next door and heard the gun shots. The father, Ronaldo Garcia, ordered his children inside when he heard the shots. "My dad said we had to move in the house," said Isai Garcia. "He said, we've got to come back inside. He just wanted to know of there were any people over there with a gun." Garcia said deputies brought a K9 onto his property as they searched for another man they thought might have been involved in the shooting. ||||| Just One More Thing... We have sent you a verification email. Please check your email and click on the link to activate your profile. If you do not receive the verification message within a few minutes of signing up, please check your Spam or Junk folder. Close

– Things got rowdy at a rodeo in Bartow County, Georgia, over the weekend when guests asked a drunk man to leave. Instead, police say Celestino Moras, 25, stood up and started shooting, reports the Atlanta Journal Constitution. One other unidentified person also started firing, and four people ended up with minor injuries by the time the dust had cleared. But the absolute best detail comes from WSB-TV, which reports that when Moras finally ran out of bullets, a rodeo cowboy lassoed him. The crowd then held him until police arrived to charge him with aggravated assault.

<s>[INST]Celestino Moras, 25, is charged in a shooting that happened at the Bartow County rodeo Sunday night. An Austell man remains in custody after deputies said he opened fire into a crowd and wounded three people attending a Memorial Day Weekend rodeo in Bartow County. Celestino Moras, 25, is charged with aggravated assault in the shootings. According to deputies, Moras was drunk while attending an annual church picnic and rodeo at a property off Fossetts Cove in Cassville. The property owner told Channel 2 Action News that Moras was not one of the invited guests. He said when other guests asked him to leave, Moras stood up, pulled out a pistol and started shooting. Deputies said as many as 300 guests took off running. The property owner said when Moras ran out of bullets, one of the rodeo cowboys lassoed him. Other guests beat him and tied him up until deputies could arrive. Doctors treated Moras for facial injuries before deputies took him to jail. Lucikly, the three wounded guests suffered only minor injuries and were treated and released from local hospitals. The Garcia family lives right next door and heard the gun shots. The father, Ronaldo Garcia, ordered his children inside when he heard the shots. "My dad said we had to move in the house," said Isai Garcia. "He said, we've got to come back inside. He just wanted to know of there were any people over there with a gun." Garcia said deputies brought a K9 onto his property as they searched for another man they thought might have been involved in the shooting. ||||| Just One More Thing... We have sent you a verification email. Please check your email and click on the link to activate your profile. If you do not receive the verification message within a few minutes of signing up, please check your Spam or Junk folder. Close[/INST]– Things got rowdy at a rodeo in Bartow County, Georgia, over the weekend when guests asked a drunk man to leave. Instead, police say Celestino Moras, 25, stood up and started shooting, reports the Atlanta Journal Constitution. One other unidentified person also started firing, and four people ended up with minor injuries by the time the dust had cleared. But the absolute best detail comes from WSB-TV, which reports that when Moras finally ran out of bullets, a rodeo cowboy lassoed him. The crowd then held him until police arrived to charge him with aggravated assault.</s>

virt1 ( 100,80 ) ( 100,80 ) ( 100,80 ) + virt2 ( 100,80 ) ( 100,80 ) ( 100,80 ) + second ( 100,80 ) ( 100,80 ) ( 100,80 ) + for corrections due to virtual photons see figure [ fig : virt ] , for corrections due to real photons see figure [ fig : real ] . the @xmath11 decay is important since it is the cleanest way to measure the @xmath2 matrix element of the ckm matrix . if one uses the current values for @xmath12 , @xmath2 , and @xmath13 taken from the pdg then @xmath14 misses unity by @xmath15 standard deviations which contradicts the unitarity of the ckm matrix and might indicate physics beyond the standard model . the uncertainty brought to the above expression by @xmath2 is about the same as uncertainty that comes from @xmath12 . therefore reducing the error in the @xmath2 matrix element would reduce substantially the error in the whole unitarity equation . reliable radiative corrections , potentially of the order of a few percent are necessary to extract the @xmath2 matrix element from the @xmath11 decay width with high precision . calculations of the radiative corrections to the @xmath11 decay were performed independently by e.s.ginsberg and t.becherrawy in the late 60 s @xcite . their results for corrections to the decay rate , dalitz plot , pion and positron spectra disagree , in some places quite sharply ; for example ginsberg s correction to the decay rate is @xmath16 while that of becherrawy is @xmath17 ( corresponding to corrections to the total width @xmath18 of 0.45 and 2 respectively ) . we have decided to perform a new calculation since results of the experiments will become available soon and to explore the causes of the discrepancies in the previous calculations . recently a revision of e. ginsberg s paper , with numerical estimation of the radiation corrections @xcite was published . our paper is organized as follows . the introduction ( section 2 ) is devoted to the short review of kinematics of the elastic decay process ( without emission of real photon ) . in section 3 we put the results concerning the virtual and soft real photons emission contribution to the differential width . in section 4 we consider the hard photon emission including both the inner bremsstrahlung ( ib ) and the structure - dependent ( sd ) contributions and derive an expression for the differential width by starting with the born width and adding the known structure functions in the leading logarithmical approximation ( the so - called drell - yan picture of the process ) . we give the explicit expressions for the non - leading contributions . in section 5 , we summarize our results and compare them with those in the previously published papers . appendix a contains the details of calculations of virtual and real soft photons emission . appendix b contains the details of description of hard photon emission both by ib and sd mechanisms . our approach to study the hard photon emission differs technically from the ones used in papers @xcite . appendix c contains the explicit formulae for description of sd emission including the interference of ib and sd amplitudes . appendix d is devoted to analysis of dalitz - plot distribution and the properties of drell - yan conversion mentioned above . appendix e contains the list of the formulae used for the numerical integration . appendix f contains the details of kinematics of radiative kaon decay and , besides the analysis of relations of our and paper @xcite technical approaches . in tables 1,2 and graphics ( fig . ( 3,4,5,6 ) ) the result of numerical estimation of born values and the correction to dalitz - plot distribution and pion and positron spectra are given . the lowest order perturbation theory ( pt ) matrix element of the process @xmath19 has the form @xmath20 where @xmath21 . dalitz plot density which takes into account the radiative corrections ( rc ) of the lowest order pt is @xmath22 where the momentum transfer squared between kaon and pion is : @xmath23 we accept here the following form for the strong interactions induced form factor @xmath24 : @xmath25 according to pdg @xmath26 . from now on we ll use @xmath27 instead of @xmath28 . we define @xmath29 and @xmath30 here we follow the notation of @xcite : @xmath31 where @xmath32 , @xmath33 , and @xmath34 are the masses of electron , pion , and kaon ; two convenient kinematical variables are @xmath35 in the kaon s rest frame , which we ll imply throughout the paper , @xmath36 and @xmath37 are the energy fractions of the positron and pion : @xmath38 the region of @xmath39-plane where @xmath40 we will named as a region @xmath41 . later , when dealing with real photons we ll also use @xmath42 with @xmath43-real photon energy . the physical region for @xmath36 and @xmath37 ( further called @xmath41 -region ) is @xcite @xmath44 \ , \nonumber \\ f_2(y)=\sqrt{y^2 - 4r_e}(1+r_e - r_\pi - y)/\left[2(1+r_e - y)\right ] \ ; \end{aligned}\ ] ] or , equivalently , @xmath45 \ , \nonumber \\ f_4(z)=\sqrt{z^2 - 4r_\pi}(1+r_\pi - r_e - z)/[2(1+r_\pi - z ) ] \ .\end{aligned}\ ] ] for our aims we use the simplified form of physical region ( omitting the terms of the order of @xmath46 ) : @xmath47 with @xmath48 or , @xmath49 with @xmath50 @xmath51 for definiteness we give here the numerical value for born total width . it is : @xmath52 comparing this value with pdg result : @xmath53 we conclude @xmath54 taking into account the accuracy level of 0.1% for determination of @xmath55 we will drop terms of order @xmath46 . we will distinguish 3 kinds of contributions to @xmath56 : from emission of virtual , soft real , and hard real photons in the rest frame of kaon : @xmath57 . standard calculation ( see appendix a for details ) allows one to obtain the following contributions : + from the soft real photons @xmath58 from the virtual photons @xmath59 that make up charged fermion s renormalization , @xmath60 ( throughout this paper we use feynman gauge ) : @xmath61 + \left[l_\lambda+ \ln \frac{m^2 } { \lambda^2}- \frac{3}{4 } \right ] \right\ } \ , \ ] ] here @xmath62 , @xmath63 is ultraviolet momentum cutoff , the first term in the curly braces comes from positron , the second one from kaon ; and for the diagram in fig1(f ) in the point like meson ( plm ) approximation , @xmath64 : @xmath65 when these contributions are grouped all together the dependence on @xmath66 ( fictitious `` photon mass '' ) disappears . according to sirlin s prescription @xcite we set @xmath67 . the result can be written in the form : @xmath68 , \qquad s_w=1+\frac{3\alpha}{4\pi } l_w.\end{gathered}\ ] ] in the above equations @xmath69 , and @xmath70 ; @xmath71 is the mass of @xmath72 , @xmath73 , and @xmath74 is the maximal energy ( in the rest frame of kaon ) of a real soft photon . we imply @xmath75 . for the details of eqs ( [ ds ] ) , ( [ dc ] ) , ( [ plm ] ) , and ( [ scplm ] ) see appendix a. contribution from soft photon emission from structure dependent part ( such as for example , interaction with resonances and intermediate @xmath72 ) is small , of the order @xmath76 and thus is also neglected . next we need to calculate contributions from hard photons . we have to distinguish between inner bremsstrahlung ( ib ) and the structure - dependent ( sd ) contributions : @xmath77 , where @xmath78 is the interference term between the two . the terms @xmath78 and @xmath79 are considered in the framework of the chiral perturbation theory ( chpt ) to the orders of @xmath80 and @xmath81 and find their contribution to be at the level of @xmath82 ( see appendix c ) . @xmath83 with @xmath84 given below . extracting the short - distances contributions in form of replacement @xmath85 it is useful to split @xmath56 ( see eq.(2))in the form @xmath86 where @xmath87 is the leading order contribution , it contains the large logarithm @xmath88 and @xmath89 is the non leading contribution , it contains the rest of the terms . @xmath87 contains terms from @xmath60 , @xmath90 , @xmath64 , and the contribution from the collinear configuration of hard ib emission ( in the collinear configuration the angle between the positron and the emitted photon is small ) . @xmath87 turns out to be @xmath91 first we note that the kinematics of hard photon emission does not coincide with the elastic process ( region d , the strictly allowed boundaries of the dalitz plot ) . in hard photon emission an additional region in the @xmath39 plane , namely @xmath92 appears . the nature of this phenomenon is the same as the known phenomenon of the radiative tail in the process of hadron production at colliding @xmath93 beams . the quantity @xmath94 has a different form for region @xmath41 and outside it : @xmath95 and @xmath96 @xmath97 when @xmath98 . functions @xmath99 are studied in appendix d. @xmath89 contains contributions from @xmath60 , @xmath64 , from sd part of hard photons and from the interference term of sd and ib parts of hard radiation . @xmath100 where @xmath101 \ , \ ] ] and for the case when the variables @xmath39 are inside @xmath41 region : @xmath102 @xmath103 explicit expressions for @xmath104 and @xmath105 are given in appendix b. the born value and the correction to dalitz - plot distribution @xmath106 is illustrated in tables 1,2 . we see that the leading contribution from virtual and soft photon emission is associated with the so called @xmath56part of the evolution equation kernel : @xmath107 where @xmath108 the contribution of hard photon kinematics in the leading order can be found with the method of quasireal electrons @xcite as a convolution of the born approximation with the @xmath109part of evolution equation kernel @xmath110 : @xmath111 where @xmath112 in such a way the whole leading order contribution can be expressed in terms of convolution of the width in the born approximation with the whole kernel of the evolution equation : @xmath113 this approach can be extended to use nonsinglet structure functions @xmath114 @xcite : @xmath115}^{b(z ) } \frac{dt}{t } \ d\gamma_0 \left ( t , z \right ) d \left ( \frac{y}{t } , \ l_e \right ) , \ t = x+y \ , \\ \nonumber % \end{equation } % % \begin{equation } \label{d } d(z , l)=\delta(1-z)+\frac{\alpha}{2\pi } l p^{(1)}(z)+ \frac{1}{2 ! } \left ( \frac{\alpha l } { 2\pi } \right)^2p^{(2)}(z)+ ... \ , \\ \nonumber % \end{equation } % % \begin{equation } % p^{(1)}(z)=\left [ \frac{1+z^2}{1-z}\theta \left ( 1-z-\delta \right ) % + \delta \left ( 1-z \right ) \left(2\ln\delta+ % \frac{3}{2 } \right ) \right]_{\delta\to 0 } \ , \nonumber % \end{equation } % % \begin{equation } \label{pi } p^{(i)}(z)=\int\limits_z^1\frac{dx}{x}p^{(1)}(x)p^{(i-1)}(\frac{z}{x } ) \ , \ i=2,3 , ... \ .\end{aligned}\ ] ] one can check the validity of the useful relation : @xmath116 the above makes it easy to see that in the limit @xmath117 terms that contain @xmath32 do not contribute to the total width in correspondence with kinoshita lee nauenberg ( kln ) theorem @xcite as well as with results of e.ginsberg @xcite . keeping in mind the representation @xmath118}^{b(z ) } \frac{dt}{t } \ a_0(t , z ) p^{(1 ) } \left ( \frac{y}{t } \right ) \ , \ ] ] one can get convinced ( see appendix d ) that the leading logarithmical contribution to the total width as well as one to the pion spectrum is zero due to : @xmath119 using the general properties of the evolution equations kernels , eq([d ] ) one can see that kln cancellation will take place in all orders of the perturbation theory . the spectra in born approximation are ( we omit terms @xmath120 ) : + for pion @xmath121 and for positron @xmath122 \ , \\ f_0(y)=\frac{y^2(1-r_\pi - y)^2}{2(1-y)}.\end{gathered}\ ] ] the corrected pion spectrum in the inclusive set - up of experiment when integrating over the whole region for @xmath36 ( @xmath123 ) have a form @xmath124 with @xmath125 + \int\limits_{b_-(z)}^{b(z)}dy [ \psi_>(y , z)\ln y+a_0(y , z)z_1(y , z)+ \frac{1}{2}z_2(y , z ) ] \biggr],%\left.\end{gathered}\ ] ] the quantities @xmath126 explained in appendix e. this function do not depend on @xmath127 . pion spectrum in the exclusive set - up ( @xmath39 in the region @xmath41 ) will depend on @xmath88 . it s expression is given in the appendix e. numerical estimation of pion spectrum is illustrated in figure ( 3,5 ) . the inclusive positron spectrum with the correction of the lowest order is @xmath128 with @xmath129 given above and : @xmath130 , \end{gathered}\ ] ] with @xmath131 @xmath132 \ ; \end{gathered}\ ] ] explicit expressions for @xmath133 and @xmath134 are given in appendix d. numerical estimation of positron spectrum is illustrated in figure ( 4,6 ) . one can check the fulfillment of kln cancellation of singular in the limit @xmath117 terms for the total width correction:@xmath135 . the expression for @xmath136 agree with a(2 ) from the 1966 year paper of eduard ginsberg @xcite . we put here the general expression for differential width of hard photon emission which might be useful for construction of monte carlo simulation of real photon emission in @xmath11 : @xmath137 with @xmath138 and @xmath139 is an element of photon s solid angle . the quantity @xmath140 is explained in appendix b. for soft photon emission we have @xmath141 , \ x < y\frac{\delta\epsilon}{e_e } \ .\ ] ] integrating over angles within phase volume of hard photon we obtain the spectral distribution of radiative kaon decay : @xmath142 , \\ y\delta < x < b(z)-y , \qquad \delta=\frac{\delta \epsilon}{e_e } \ll 1.\end{gathered}\ ] ] structure dependent contribution to emission of virtual photons ( see fig 1 d ) , e ) ) can be interpreted as a correction to the strong formfactor of @xmath143 transition , @xmath24 . we assume that this formfactor can be extracted from experiment and thus do not consider it . the problem of calculation of rc to @xmath11 and especially the formfactors in the framework of chpt with virtual photons was considered in a recent paper @xcite . as in paper @xcite we assume a phenomenological form for the hadronic contribution to the @xmath144 vertex , but here we use explicitly the dependence of the form factor in the form @xmath145 we assume that the effect of higher order chpt as well as rc to the formfactors can be taken as a multiplicative scaling factor for @xmath146 , which we take from of a recent paper @xcite . we assume such an experiment in which only one positron in the final state is present , but place no limits on the number of photons . the ratio of the lo contributions in the first order to the born contribution is a few percent , and for the second order it is about @xmath147 due to non - definite sign structure of the leading logarithm contribution ( see eq([dlp ] ) ) there are regions in the kinematically allowed area where @xmath148 is close to zero . in these regions the non - leading contributions become dominant . the contribution of the channels with more than 1 charged lepton in the final state as well as the vacuum polarization effects in higher orders may be taken into account by introducing the singlet contribution to the structure functions . the effect will be at the level of 0.03% and we omit them within the precision of our calculation . the contribution of the @xmath149 terms @xcite turns out to be small . indeed , one can see that they are of the order @xmath150 , @xmath151 ( @xmath152 is the pion life time constant ) , where @xmath153 is the characteristic momentum of a final particle in the given reaction , @xmath154 . so the terms of the orders @xmath149 and @xmath155 can be omitted within the accuracy of @xmath156 . our main results are given in formulae ( 2,21,22,26 - 28 ) for dalitz plot distribution ; ( 38 - 41 ) for pion and positron spectra;(47 ) for hard photon emission;(53 ) for the value @xmath157 , in the tables and figures . the accuracy of these formulas is determined by the following : 1 . we do nt account higher order terms in pt , the ones of the order of @xmath158 which is smaller than @xmath159 2 . structure dependent real hard photon emission contribution to rc we estimate to be at the level of @xmath160 . higher order chpt contributions to the structure dependent part are of the order @xmath161 @xcite all the percentages are taken with respect to the born width . all together we believe the accuracy of the results to be at the level of @xmath162 . so the final result of our calculation may be written in the form @xmath163 the terms on the rhs are given in ( [ split ] , [ dlp ] , [ nl ] ) . here is the list of improvements comparing with the older calculations @xcite : 1 . we eliminate the ultra violet cutoff dependence by choosing @xmath67 , 2 . we describe the dependence on the lepton mass logarithm @xmath88 in all orders of the perturbation theory and explain why the correction to the total width does not depend on @xmath32 , 3 . we treat the strong interaction effects by the means of chpt in its lowest order @xmath164 and show that the next order contribution is small , 4 . we give an explicit formulas for the total differential cross section and explicit results for corrections to the dalitz plot and particle spectra that might be used in experimental analysis . in the papers of e.ginsberg the structure - dependent emission was not considered . t.becherrawy , on the other hand , did include it , and this will give rise to differences in the dalitz plot . in addition , ginsberg used the proton mass as the momentum cutoff parameter . we do not consider the evolution of coupling constant effects in the regions of virtual photon momentum modulo square from the quantities of order @xmath165 up to @xmath166,which can be taken into account @xcite ( and for details see @xcite ) by replacing the quantity @xmath167 by the @xmath168 . taking this replacement into account our result for the correction to the total width is @xmath169 which results in @xmath170 so the correction to the total width is @xmath171 while ginsberg s result is @xmath172 and becherrawy s is @xmath173 . neither ginsberg nor becherrawy used the factor @xmath174 , and this factor ( 1.023 ) accounts for most of the difference between ginsberg s and our result . electromagnetic corrections become negative and have an order of @xmath175 . the effect of the sd part , which e.ginsberg did not consider , is small , of the order of 0.1% . we use the value of formfactor @xmath176 calculated in the paper @xcite in the framework of chpt , including virtual photonic loops and terms of order @xmath155 of chpt . to avoid double counting we use the mesonic contribution to @xmath177 and the @xmath178 terms one @xmath179 ) . our final result is : @xmath180 in estimating the uncertainty we take into account the uncertainties arising from structure - dependent emission @xmath181 , theoretical errors of order @xmath182 , experimental error @xmath183 and the chpt error in @xmath178 terms @xmath184 . in tables 1,2 we give corrections to the distributions in the dalitz - plot @xmath185 . in figures ( 3 - 6 ) we illustrate the corrections to the pion and positron spectra . here we see qualitative agreement for the positron spectrum and disagreement with the pion spectrum obtained by e.ginsberg . we are grateful to s.i.eidelman for interest to this problem , and to e. swanson for constructive critical discussions . one of us ( e.k . ) is grateful to the department of physics and astronomy of the university of pittsburgh for the warm hospitality during the last stages of this work , a.ali for valuable discussion and v.n.samoilov for support . the work was supported partly by grants rffi 01 - 02 - 17437 and intas 00366 and by usdoe de fg02 91er40646 . [ cols="^,^,^,^,^,^,^,^,^,^",options="header " , ] table 2 . dalitz plot distribution in born approximation @xmath186 . [ fig3 ] [ fig4 ] [ fig5 ] [ fig6 ] here we explain how to calculate @xmath90 , @xmath60 , @xmath64 and how to group them into eq([scplm ] ) . contribution from emission of a soft real photon can be written in a standard form in terms of the classical currents : @xmath187 where @xmath66 is fictitious mass of photon . we use the following formulas : @xmath188 @xmath189 @xmath190 from them we obtain the eq([ds ] ) . consider now radiative corrections that arise from emission of virtual photons ( excluding sd virtual photons ) . feynman graphs containing self energy insertion to positron and kaon green functions ( fig.1,b , c ) can be taken into account by introducing the wave function renormalization constants @xmath191 and @xmath192 : @xmath193 . we use the expression for @xmath191 given in the textbooks @xcite ; the expression for @xmath192 is given in the paper @xcite . the result is eq([dc ] ) . now consider the feynman graph in which a virtual photon is emitted by kaon and absorbed by positron or by @xmath3boson in the intermediate state ( fig.1,d , e , f ) . this long distance contribution is calculated using a phenomenological model with point like mesons as a relevant degrees of freedom . to calculate the contribution from the region @xmath194 ( @xmath63 is the ultra violet cutoff ) we use the following expressions for loop momenta scalar , vector , and tensor integrals : @xmath195 a standard calculation yields : @xmath196 where @xmath62 and we omitted terms of the order of @xmath197 . as a result we obtain @xmath198 in a series of papers @xcite a.sirlin has conducted a detailed analysis of uv behaviour of amplitudes of processes with hadrons in 1loop level . he showed that they are uv finite ( if considered on the quark level ) , but the effective cutoff scale on loop momenta is of the order @xmath71 . for this reason we choose @xmath199 the sum @xmath200 yields eq([scplm ] ) the matrix element of the radiative @xmath11 decay @xmath201 with terms up to @xmath202 in chpt @xcite has the form @xmath203 where @xmath204 \ ; \\ \nonumber % \end{equation } % \begin{equation } q_\mu^{sd}=\gamma_\nu r_{\mu\nu } \ .\end{aligned}\ ] ] where tensor @xmath205 describes ( see eq(4.17 ) in @xcite ) the structure dependent emission ( fig 2(c ) ) . @xmath206 singular at @xmath207 terms which provide contribution containing large logarithm @xmath88 arises only from @xmath208 . to extract the corresponding terms we introduce four vector @xmath209 , and @xmath210 is the energy fraction of the photon ( 9 ) . note that @xmath211 when @xmath212 . separating leading and non leading terms and letting @xmath213 , i.e. neglecting form factor s momentum dependence , we obtain : @xmath214 where @xmath215- \frac{ya_0(x+y , z)}{x+y}+ \mathcal{p } \ .\end{gathered}\ ] ] the quantity @xmath216 contains some non leading contributions from the ib part and the ones that arise from the structure dependent part : @xmath217 with @xmath218 @xmath219 @xmath220 @xmath221 \hat{p}_e\gamma_\lambda \ .\ ] ] to calculate these traces we use the following expressions for the scalar products of the 4momenta ( in units @xmath222 ) : @xmath223 @xmath224 @xmath225 @xmath226 @xmath227 @xmath228 @xmath229 @xmath230 three terms in the rhs of ( [ t ] ) have a completely different behavior . the first one corresponds to the kinematic region of collinear emission , when photon is emitted along positron s momentum . the relevant phase volume has essentially 3particles form : @xmath231 the limits of photon s energy fraction variation are @xmath232 . the upper limit is imposed by the born structure of the width in this kinematical region . the second term corresponds to the contribution from emission by kaon . the relevant kinematics is isotropic . the kinematics of radiative kaon decay and the comparison of our and e.ginsbergs approaches is given in appendix f. the third term corresponds to the rest of the contributions which contain neither collinear nor infrared singularities . performing the integration over photon s phase volume provided @xmath39 are in the @xmath41 region we obtain : @xmath233 \ \\ -2\int\limits_{y\delta}^{b(z)-y}\frac{dx}{x}[a_0(y , z)+x(\frac{r(z)}{x+y}-y)]+ \int\limits_0^{b(z)-y } dx\mathcal{j},\end{gathered}\ ] ] we obtain ( [ deltahard ] ) with @xmath234 @xmath235 and @xmath236 one can check that the sum of rc arising from hard , soft and virtual photons do not depend on the auxiliary parameter @xmath237 . we note that the leading contribution from hard part of photon spectra can be reproduced using the method of quasi real electrons @xcite . ] ] now we concentrate on the contribution of the third term in the rhs of ( [ t ] ) . to perform the integration over the phase volume of final states it is convenient to use the following parameterization ( see appendix f ) : @xmath238 with @xmath239 the neutrino on mass shell ( nms ) condition provides the relation @xmath240 \ .\ ] ] for the aim of further integration of @xmath216 over angular variables we put it in the form : @xmath241 % \ [ a_e=\frac{xy}{2}\left(1-c_e \right ) \ , \\ \nonumber % \ ] % \ [ a_\nu = x - a_e-\frac{xz}{2}\left(1-\beta_\pi c_\pi \right ) \ . % \]\end{aligned}\ ] ] and @xmath242 angular integration can be performed explicitly , we have @xmath243 \ , \ ] ] with @xmath244 performing the integration over @xmath245 we have : @xmath246 the following integrals are helpful in integrating the above expression . we define @xmath247 then @xmath248 where @xmath249 and @xmath250 . the first term in @xmath251 together with the leading contributions from virtual and soft real photons was given in the form required by rg approach eq([psii ] ) . the non leading contributions , @xmath84 from hard photon emission , include sd emission , ib of point like mesons as well as the interference terms . it is free from infrared and mass singularities and given above ( [ deltahard ] ) with @xmath252 and @xmath253 the contribution to @xmath84 from sd emission have the form : @xmath254 where @xmath255 with @xmath256 given in appendix b and @xmath257 \ , \nonumber \\ q_3=-\frac{1}{8 } \left[-8+(z+y)(4 + 3x)-2x+3x^2 \right ] \ , \nonumber \\ q_4= \frac{1}{8 } \left [ 4y+4x+3xy \right ] , \qquad q_5=-\frac{3}{4 } \ .\end{aligned}\ ] ] the contribution to the total width have a form : @xmath258 numerical estimation gives : @xmath259 the function @xmath260 , defined as @xmath261 contains a restriction on the domain of integration , namely @xmath262 exceed @xmath36 or equal to it , which is implied by the kernel @xmath263 . explicit calculations give : @xmath264\ln\frac{b(z)}{b_-(z)}+ \\ 2a_0(y , z)\ln\frac{b(z)-y}{b_-(z)-y}+ \frac{1}{2}(b(z)^2-b_-(z)^2 ) \ , \\ 2\sqrt{r_e}<y<1-\sqrt{r_\pi},\qquad \psi_<(y , z)=0 , y>1-\sqrt{r_\pi } \ .\end{gathered}\ ] ] and @xmath265- \\ \frac{1}{2}(b(z)^2-y^2)+ ( b(z)-y)(2-y - z+b_-(z))+[r(z)-y(2-z)]\ln\frac{b(z)}{y}.\end{gathered}\ ] ] one can convince the validity of the relations : @xmath266 and @xmath267 the last relation demonstrates the kln cancellation for the pion spectrum obtained by integration of the corrections over @xmath36 in the interval @xmath123 . the explicit expressions for @xmath133 and @xmath134 are:(for @xmath136 see ( [ fulli ] ) ) . @xmath268 \ln \frac{1-y}{r_\pi } - \\ \frac{1-r_\pi - y}{36(1-y)^2 } \left [ ( 1-y)^2 \left(43 y^3 -15 y^2 -3y-1 \right . + r_\pi(83y^2 + 26y+11 ) + 3r_\pi^3 \right ) + \\ r_\pi^2(31 y^3 -15y^2 - 39y+47 ) \left . \right ] \ , \end{gathered}\ ] ] @xmath269 + \frac{1-r_\pi - y}{720(1-y)^3 } \biggl[-(1-y)^3(247y^4 - 88y^3 - 28y^2 - 8y-3)- \\ % \right . r_\pi(1-y)^3(733y^3 + 341y^2 + 129y+57)-\\ r_\pi^2(1-y)(707y^4 - 808y^3 + 212y^2- 408y+717)\\ + r_\pi^3(173y^4 - 72y^3 - 492y^2 + 1048y-477 ) -12 r_\pi^4(1-y)^3 \biggr].\end{gathered}\ ] ] collection of the relevant formulae . the dalitz - plot distribution in the region @xmath41 : @xmath270\biggr),\\ z_1=\frac{3}{4}-\frac{\pi^2}{6}-\frac{3}{2}\ln y- \ln ( ( { b(z)-y})/y ) - li_2(1-y ) \ .\end{gathered}\ ] ] the function @xmath271 is defined in ( [ z2 ] ) . correction to the total width ( we include the contribution of the region outside the region @xmath41 ) , @xmath5 : @xmath272 + \\ \int\limits_{b_-(z)}^{b(z)}dy[a_0(y , z)z_1+(1/2)z_2]\biggr ] \ , \end{gathered}\ ] ] with @xmath273 the expression in big square brackets in right - hand side of ( 95 ) can be put in the form : @xmath274 which results in @xmath275 . for the aim of comparison with e. ginsberg result we must put here @xmath276 as was mentioned above we have reasonable agreement with e. ginsberg results . for the inclusive set - up of experiment ( energy fraction of positron is not measured ) we have for pion energy spectrum given above ( [ rcpions ] ) . when we restrict ourselves only by the region @xmath41 the spectrum becomes dependent on @xmath127 : @xmath277 \right\ } \left(1+\frac{\lambda_+}{r_\pi}r(z ) \right)^2 \ , \end{gathered}\ ] ] with @xmath278 our approach to study the radiative kaon decay has an advantage compared to the one used by e. ginsberg it has a simple interpretation of electron mass singularities based on drell - yan picture . the @xcite approach to study noncollinear kinematics is more transparent than ours one . we remind the reader of some some topics of @xcite paper . one can introduce the missing mass square variable @xmath279 the limits of this quantity variation at fixed @xmath39 are pu by the last term : for collinear or anticollinear kinematics of pion and positron 3-momenta . being expressed in terms of @xmath39 they are ( we consider the general point of dalitz - plot and omit positron mass dependence ) : @xmath280 for the @xmath39 in the @xmath41 region and @xmath281 for the case when they are in the region @xmath282 outside @xmath41 : @xmath283 for our approach with separating the case of soft and hard photon emission we must modify the lower bound for @xmath284 in the region @xmath41 . it can be done using another representation of @xmath284 : @xmath285,\ ] ] with @xmath286-the cosine of the angles between photon 3-momentum and positron and pion ones , @xmath287-is the pion velocity . maximum of this quantity is @xmath288 . taking this into account we obtain for the region oh hard photon @xmath289 for the region @xmath41 : @xmath290 and for region @xmath282 : @xmath291 in particular for the collinear case we must choice @xmath292 , which corresponds to @xmath293 . let infer this condition using the nms condition : @xmath294 in collinear case we have @xmath295.from nms condition we obtain @xmath296 . using this value we obtain @xmath297 . using further the relation @xmath298 we obtain again @xmath299 in the case of emission along positron . comparing the phase volumes in general case calculated in our approach with using nms condition with @xcite approach we obtain the relation : @xmath300 the non leading contribution arising from hard photon emission considered above : @xmath301 with @xmath302 ( note that @xmath303 , see appendix b and c ) can be transformed to the form : @xmath304i_{10}- \\ ( 1/2)i_{1 - 1}-((1/2)l+y+z)i_{2 - 1}+i_z].\end{gathered}\ ] ] here we use the list of integrals obtained in the paper of @xcite : @xmath305 besides we need two additional ones : @xmath306 one can see the cancellation of mass singularities ( terms containing @xmath127 ) in the expression @xmath307 . 99 t.becherrawy , phys . d1 ( 1970 ) , 1452 e.ginsberg , phys . 162(1967 ) , 1570 ; phys . rev . 142(1966 ) , 1035 ; phys . rev . 171(1968 ) , 1675 ; phys . rev . 187(1968 ) , 2280 j.gasser and h.leutwyller , nucl . phys . b250(1985 ) , 464 , 517 ; j.bijnens , g.colangelo , g.ecker , and j.gasser , the second da@xmath308ne physics handbook , vol.1 , 313 j.bijnens , g.ecker , and j.gasser , nucl . phys . b396(1993 ) , 81 ; b.holstein phys . rev . d41(1990 ) , 2829 ; a.sirlin , phys . rev . d5(1972 ) , 436 ; rev . 50(1978 ) , 573 ; nucl b196(1982 ) , 83 ; m.v.terentev , yad . fiz . 18(1973 ) , 870 ; sov . j. nucl . 18(1974 ) , 449 e.a.kuraev , v.s.fadin , yad . fiz . 41(1985 ) , 466 v.n.baier , v.s.fadin , v.a.khoze , nucl . phys . b65(1973 ) , 381 w.marciano and a.sirlin , phys . rev . 71(1993 ) , 3629 t.kinoshita , j. math . phys . 3(1972 ) , 650 ; + t.d.lee and m.nauenberg , phys . rev . b133(1964 ) , 1549 r.decker and m.finkemeier , nucl . phys . b438(1995 ) , 17 v.cirigliano , m.knecht , h.neufeld , h.rupertsbergen , p.talavera , + hep - ph/0110153 n - p . chang , phys . 131(1963),1272 a.i.akhiezer , v.b.berestetski , quantum electrodynamics , moscow , 1981 ; + v.b.berestetski , e.lifshitz , l.pitaevski,quantum electrodynamics , moscow , 1989 e.s . ginsberg , phys . d 1 , 229 ( 1970 )

we consider the lowest order radiative corrections for the decay @xmath0 , usually referred as @xmath1 decay . this decay is the best way to extract the value of the @xmath2 element of the ckm matrix . the radiative corrections become crucial if one wants a precise value of @xmath2 . the existing calculations were performed in the late 60 s @xcite and are in disagreement . the calculation in @xcite turns out to be ultraviolet cutoff sensitive . the necessity of precise knowledge of @xmath2 and the contradiction between the existing results constitute the motivation of our paper . we remove the ultraviolet cutoff dependence by using a.sirlins prescription ; we set it equal to the @xmath3 mass . we establish the whole character of small lepton mass dependence based on the renormalization group approach . in this way we can provide a simple explanation of kinoshita lee nauenberg cancellation of singularities in the lepton mass terms in the total width and pion spectrum . we give an explicit evaluation of the structure dependent photon emission based on chpt in the lowest order . we estimate the accuracy of our results to be at the level of @xmath4 . the corrected total width is @xmath5 with @xmath6 . using the formfactor value @xmath7 calculated in @xcite leads to @xmath8 . @xmath9 bogoliubov laboratory of theoretical physics , jinr , dubna , moscow region , 141980 , russia + @xmath10 department of physics and astronomy , university of pittsburgh , pa , u.s.a +

<s>[INST]virt1 ( 100,80 ) ( 100,80 ) ( 100,80 ) + virt2 ( 100,80 ) ( 100,80 ) ( 100,80 ) + second ( 100,80 ) ( 100,80 ) ( 100,80 ) + for corrections due to virtual photons see figure [ fig : virt ] , for corrections due to real photons see figure [ fig : real ] . the @xmath11 decay is important since it is the cleanest way to measure the @xmath2 matrix element of the ckm matrix . if one uses the current values for @xmath12 , @xmath2 , and @xmath13 taken from the pdg then @xmath14 misses unity by @xmath15 standard deviations which contradicts the unitarity of the ckm matrix and might indicate physics beyond the standard model . the uncertainty brought to the above expression by @xmath2 is about the same as uncertainty that comes from @xmath12 . therefore reducing the error in the @xmath2 matrix element would reduce substantially the error in the whole unitarity equation . reliable radiative corrections , potentially of the order of a few percent are necessary to extract the @xmath2 matrix element from the @xmath11 decay width with high precision . calculations of the radiative corrections to the @xmath11 decay were performed independently by e.s.ginsberg and t.becherrawy in the late 60 s @xcite . their results for corrections to the decay rate , dalitz plot , pion and positron spectra disagree , in some places quite sharply ; for example ginsberg s correction to the decay rate is @xmath16 while that of becherrawy is @xmath17 ( corresponding to corrections to the total width @xmath18 of 0.45 and 2 respectively ) . we have decided to perform a new calculation since results of the experiments will become available soon and to explore the causes of the discrepancies in the previous calculations . recently a revision of e. ginsberg s paper , with numerical estimation of the radiation corrections @xcite was published . our paper is organized as follows . the introduction ( section 2 ) is devoted to the short review of kinematics of the elastic decay process ( without emission of real photon ) . in section 3 we put the results concerning the virtual and soft real photons emission contribution to the differential width . in section 4 we consider the hard photon emission including both the inner bremsstrahlung ( ib ) and the structure - dependent ( sd ) contributions and derive an expression for the differential width by starting with the born width and adding the known structure functions in the leading logarithmical approximation ( the so - called drell - yan picture of the process ) . we give the explicit expressions for the non - leading contributions . in section 5 , we summarize our results and compare them with those in the previously published papers . appendix a contains the details of calculations of virtual and real soft photons emission . appendix b contains the details of description of hard photon emission both by ib and sd mechanisms . our approach to study the hard photon emission differs technically from the ones used in papers @xcite . appendix c contains the explicit formulae for description of sd emission including the interference of ib and sd amplitudes . appendix d is devoted to analysis of dalitz - plot distribution and the properties of drell - yan conversion mentioned above . appendix e contains the list of the formulae used for the numerical integration . appendix f contains the details of kinematics of radiative kaon decay and , besides the analysis of relations of our and paper @xcite technical approaches . in tables 1,2 and graphics ( fig . ( 3,4,5,6 ) ) the result of numerical estimation of born values and the correction to dalitz - plot distribution and pion and positron spectra are given . the lowest order perturbation theory ( pt ) matrix element of the process @xmath19 has the form @xmath20 where @xmath21 . dalitz plot density which takes into account the radiative corrections ( rc ) of the lowest order pt is @xmath22 where the momentum transfer squared between kaon and pion is : @xmath23 we accept here the following form for the strong interactions induced form factor @xmath24 : @xmath25 according to pdg @xmath26 . from now on we ll use @xmath27 instead of @xmath28 . we define @xmath29 and @xmath30 here we follow the notation of @xcite : @xmath31 where @xmath32 , @xmath33 , and @xmath34 are the masses of electron , pion , and kaon ; two convenient kinematical variables are @xmath35 in the kaon s rest frame , which we ll imply throughout the paper , @xmath36 and @xmath37 are the energy fractions of the positron and pion : @xmath38 the region of @xmath39-plane where @xmath40 we will named as a region @xmath41 . later , when dealing with real photons we ll also use @xmath42 with @xmath43-real photon energy . the physical region for @xmath36 and @xmath37 ( further called @xmath41 -region ) is @xcite @xmath44 \ , \nonumber \\ f_2(y)=\sqrt{y^2 - 4r_e}(1+r_e - r_\pi - y)/\left[2(1+r_e - y)\right ] \ ; \end{aligned}\ ] ] or , equivalently , @xmath45 \ , \nonumber \\ f_4(z)=\sqrt{z^2 - 4r_\pi}(1+r_\pi - r_e - z)/[2(1+r_\pi - z ) ] \ .\end{aligned}\ ] ] for our aims we use the simplified form of physical region ( omitting the terms of the order of @xmath46 ) : @xmath47 with @xmath48 or , @xmath49 with @xmath50 @xmath51 for definiteness we give here the numerical value for born total width . it is : @xmath52 comparing this value with pdg result : @xmath53 we conclude @xmath54 taking into account the accuracy level of 0.1% for determination of @xmath55 we will drop terms of order @xmath46 . we will distinguish 3 kinds of contributions to @xmath56 : from emission of virtual , soft real , and hard real photons in the rest frame of kaon : @xmath57 . standard calculation ( see appendix a for details ) allows one to obtain the following contributions : + from the soft real photons @xmath58 from the virtual photons @xmath59 that make up charged fermion s renormalization , @xmath60 ( throughout this paper we use feynman gauge ) : @xmath61 + \left[l_\lambda+ \ln \frac{m^2 } { \lambda^2}- \frac{3}{4 } \right ] \right\ } \ , \ ] ] here @xmath62 , @xmath63 is ultraviolet momentum cutoff , the first term in the curly braces comes from positron , the second one from kaon ; and for the diagram in fig1(f ) in the point like meson ( plm ) approximation , @xmath64 : @xmath65 when these contributions are grouped all together the dependence on @xmath66 ( fictitious `` photon mass '' ) disappears . according to sirlin s prescription @xcite we set @xmath67 . the result can be written in the form : @xmath68 , \qquad s_w=1+\frac{3\alpha}{4\pi } l_w.\end{gathered}\ ] ] in the above equations @xmath69 , and @xmath70 ; @xmath71 is the mass of @xmath72 , @xmath73 , and @xmath74 is the maximal energy ( in the rest frame of kaon ) of a real soft photon . we imply @xmath75 . for the details of eqs ( [ ds ] ) , ( [ dc ] ) , ( [ plm ] ) , and ( [ scplm ] ) see appendix a. contribution from soft photon emission from structure dependent part ( such as for example , interaction with resonances and intermediate @xmath72 ) is small , of the order @xmath76 and thus is also neglected . next we need to calculate contributions from hard photons . we have to distinguish between inner bremsstrahlung ( ib ) and the structure - dependent ( sd ) contributions : @xmath77 , where @xmath78 is the interference term between the two . the terms @xmath78 and @xmath79 are considered in the framework of the chiral perturbation theory ( chpt ) to the orders of @xmath80 and @xmath81 and find their contribution to be at the level of @xmath82 ( see appendix c ) . @xmath83 with @xmath84 given below . extracting the short - distances contributions in form of replacement @xmath85 it is useful to split @xmath56 ( see eq.(2))in the form @xmath86 where @xmath87 is the leading order contribution , it contains the large logarithm @xmath88 and @xmath89 is the non leading contribution , it contains the rest of the terms . @xmath87 contains terms from @xmath60 , @xmath90 , @xmath64 , and the contribution from the collinear configuration of hard ib emission ( in the collinear configuration the angle between the positron and the emitted photon is small ) . @xmath87 turns out to be @xmath91 first we note that the kinematics of hard photon emission does not coincide with the elastic process ( region d , the strictly allowed boundaries of the dalitz plot ) . in hard photon emission an additional region in the @xmath39 plane , namely @xmath92 appears . the nature of this phenomenon is the same as the known phenomenon of the radiative tail in the process of hadron production at colliding @xmath93 beams . the quantity @xmath94 has a different form for region @xmath41 and outside it : @xmath95 and @xmath96 @xmath97 when @xmath98 . functions @xmath99 are studied in appendix d. @xmath89 contains contributions from @xmath60 , @xmath64 , from sd part of hard photons and from the interference term of sd and ib parts of hard radiation . @xmath100 where @xmath101 \ , \ ] ] and for the case when the variables @xmath39 are inside @xmath41 region : @xmath102 @xmath103 explicit expressions for @xmath104 and @xmath105 are given in appendix b. the born value and the correction to dalitz - plot distribution @xmath106 is illustrated in tables 1,2 . we see that the leading contribution from virtual and soft photon emission is associated with the so called @xmath56part of the evolution equation kernel : @xmath107 where @xmath108 the contribution of hard photon kinematics in the leading order can be found with the method of quasireal electrons @xcite as a convolution of the born approximation with the @xmath109part of evolution equation kernel @xmath110 : @xmath111 where @xmath112 in such a way the whole leading order contribution can be expressed in terms of convolution of the width in the born approximation with the whole kernel of the evolution equation : @xmath113 this approach can be extended to use nonsinglet structure functions @xmath114 @xcite : @xmath115}^{b(z ) } \frac{dt}{t } \ d\gamma_0 \left ( t , z \right ) d \left ( \frac{y}{t } , \ l_e \right ) , \ t = x+y \ , \\ \nonumber % \end{equation } % % \begin{equation } \label{d } d(z , l)=\delta(1-z)+\frac{\alpha}{2\pi } l p^{(1)}(z)+ \frac{1}{2 ! } \left ( \frac{\alpha l } { 2\pi } \right)^2p^{(2)}(z)+ ... \ , \\ \nonumber % \end{equation } % % \begin{equation } % p^{(1)}(z)=\left [ \frac{1+z^2}{1-z}\theta \left ( 1-z-\delta \right ) % + \delta \left ( 1-z \right ) \left(2\ln\delta+ % \frac{3}{2 } \right ) \right]_{\delta\to 0 } \ , \nonumber % \end{equation } % % \begin{equation } \label{pi } p^{(i)}(z)=\int\limits_z^1\frac{dx}{x}p^{(1)}(x)p^{(i-1)}(\frac{z}{x } ) \ , \ i=2,3 , ... \ .\end{aligned}\ ] ] one can check the validity of the useful relation : @xmath116 the above makes it easy to see that in the limit @xmath117 terms that contain @xmath32 do not contribute to the total width in correspondence with kinoshita lee nauenberg ( kln ) theorem @xcite as well as with results of e.ginsberg @xcite . keeping in mind the representation @xmath118}^{b(z ) } \frac{dt}{t } \ a_0(t , z ) p^{(1 ) } \left ( \frac{y}{t } \right ) \ , \ ] ] one can get convinced ( see appendix d ) that the leading logarithmical contribution to the total width as well as one to the pion spectrum is zero due to : @xmath119 using the general properties of the evolution equations kernels , eq([d ] ) one can see that kln cancellation will take place in all orders of the perturbation theory . the spectra in born approximation are ( we omit terms @xmath120 ) : + for pion @xmath121 and for positron @xmath122 \ , \\ f_0(y)=\frac{y^2(1-r_\pi - y)^2}{2(1-y)}.\end{gathered}\ ] ] the corrected pion spectrum in the inclusive set - up of experiment when integrating over the whole region for @xmath36 ( @xmath123 ) have a form @xmath124 with @xmath125 + \int\limits_{b_-(z)}^{b(z)}dy [ \psi_>(y , z)\ln y+a_0(y , z)z_1(y , z)+ \frac{1}{2}z_2(y , z ) ] \biggr],%\left.\end{gathered}\ ] ] the quantities @xmath126 explained in appendix e. this function do not depend on @xmath127 . pion spectrum in the exclusive set - up ( @xmath39 in the region @xmath41 ) will depend on @xmath88 . it s expression is given in the appendix e. numerical estimation of pion spectrum is illustrated in figure ( 3,5 ) . the inclusive positron spectrum with the correction of the lowest order is @xmath128 with @xmath129 given above and : @xmath130 , \end{gathered}\ ] ] with @xmath131 @xmath132 \ ; \end{gathered}\ ] ] explicit expressions for @xmath133 and @xmath134 are given in appendix d. numerical estimation of positron spectrum is illustrated in figure ( 4,6 ) . one can check the fulfillment of kln cancellation of singular in the limit @xmath117 terms for the total width correction:@xmath135 . the expression for @xmath136 agree with a(2 ) from the 1966 year paper of eduard ginsberg @xcite . we put here the general expression for differential width of hard photon emission which might be useful for construction of monte carlo simulation of real photon emission in @xmath11 : @xmath137 with @xmath138 and @xmath139 is an element of photon s solid angle . the quantity @xmath140 is explained in appendix b. for soft photon emission we have @xmath141 , \ x < y\frac{\delta\epsilon}{e_e } \ .\ ] ] integrating over angles within phase volume of hard photon we obtain the spectral distribution of radiative kaon decay : @xmath142 , \\ y\delta < x < b(z)-y , \qquad \delta=\frac{\delta \epsilon}{e_e } \ll 1.\end{gathered}\ ] ] structure dependent contribution to emission of virtual photons ( see fig 1 d ) , e ) ) can be interpreted as a correction to the strong formfactor of @xmath143 transition , @xmath24 . we assume that this formfactor can be extracted from experiment and thus do not consider it . the problem of calculation of rc to @xmath11 and especially the formfactors in the framework of chpt with virtual photons was considered in a recent paper @xcite . as in paper @xcite we assume a phenomenological form for the hadronic contribution to the @xmath144 vertex , but here we use explicitly the dependence of the form factor in the form @xmath145 we assume that the effect of higher order chpt as well as rc to the formfactors can be taken as a multiplicative scaling factor for @xmath146 , which we take from of a recent paper @xcite . we assume such an experiment in which only one positron in the final state is present , but place no limits on the number of photons . the ratio of the lo contributions in the first order to the born contribution is a few percent , and for the second order it is about @xmath147 due to non - definite sign structure of the leading logarithm contribution ( see eq([dlp ] ) ) there are regions in the kinematically allowed area where @xmath148 is close to zero . in these regions the non - leading contributions become dominant . the contribution of the channels with more than 1 charged lepton in the final state as well as the vacuum polarization effects in higher orders may be taken into account by introducing the singlet contribution to the structure functions . the effect will be at the level of 0.03% and we omit them within the precision of our calculation . the contribution of the @xmath149 terms @xcite turns out to be small . indeed , one can see that they are of the order @xmath150 , @xmath151 ( @xmath152 is the pion life time constant ) , where @xmath153 is the characteristic momentum of a final particle in the given reaction , @xmath154 . so the terms of the orders @xmath149 and @xmath155 can be omitted within the accuracy of @xmath156 . our main results are given in formulae ( 2,21,22,26 - 28 ) for dalitz plot distribution ; ( 38 - 41 ) for pion and positron spectra;(47 ) for hard photon emission;(53 ) for the value @xmath157 , in the tables and figures . the accuracy of these formulas is determined by the following : 1 . we do nt account higher order terms in pt , the ones of the order of @xmath158 which is smaller than @xmath159 2 . structure dependent real hard photon emission contribution to rc we estimate to be at the level of @xmath160 . higher order chpt contributions to the structure dependent part are of the order @xmath161 @xcite all the percentages are taken with respect to the born width . all together we believe the accuracy of the results to be at the level of @xmath162 . so the final result of our calculation may be written in the form @xmath163 the terms on the rhs are given in ( [ split ] , [ dlp ] , [ nl ] ) . here is the list of improvements comparing with the older calculations @xcite : 1 . we eliminate the ultra violet cutoff dependence by choosing @xmath67 , 2 . we describe the dependence on the lepton mass logarithm @xmath88 in all orders of the perturbation theory and explain why the correction to the total width does not depend on @xmath32 , 3 . we treat the strong interaction effects by the means of chpt in its lowest order @xmath164 and show that the next order contribution is small , 4 . we give an explicit formulas for the total differential cross section and explicit results for corrections to the dalitz plot and particle spectra that might be used in experimental analysis . in the papers of e.ginsberg the structure - dependent emission was not considered . t.becherrawy , on the other hand , did include it , and this will give rise to differences in the dalitz plot . in addition , ginsberg used the proton mass as the momentum cutoff parameter . we do not consider the evolution of coupling constant effects in the regions of virtual photon momentum modulo square from the quantities of order @xmath165 up to @xmath166,which can be taken into account @xcite ( and for details see @xcite ) by replacing the quantity @xmath167 by the @xmath168 . taking this replacement into account our result for the correction to the total width is @xmath169 which results in @xmath170 so the correction to the total width is @xmath171 while ginsberg s result is @xmath172 and becherrawy s is @xmath173 . neither ginsberg nor becherrawy used the factor @xmath174 , and this factor ( 1.023 ) accounts for most of the difference between ginsberg s and our result . electromagnetic corrections become negative and have an order of @xmath175 . the effect of the sd part , which e.ginsberg did not consider , is small , of the order of 0.1% . we use the value of formfactor @xmath176 calculated in the paper @xcite in the framework of chpt , including virtual photonic loops and terms of order @xmath155 of chpt . to avoid double counting we use the mesonic contribution to @xmath177 and the @xmath178 terms one @xmath179 ) . our final result is : @xmath180 in estimating the uncertainty we take into account the uncertainties arising from structure - dependent emission @xmath181 , theoretical errors of order @xmath182 , experimental error @xmath183 and the chpt error in @xmath178 terms @xmath184 . in tables 1,2 we give corrections to the distributions in the dalitz - plot @xmath185 . in figures ( 3 - 6 ) we illustrate the corrections to the pion and positron spectra . here we see qualitative agreement for the positron spectrum and disagreement with the pion spectrum obtained by e.ginsberg . we are grateful to s.i.eidelman for interest to this problem , and to e. swanson for constructive critical discussions . one of us ( e.k . ) is grateful to the department of physics and astronomy of the university of pittsburgh for the warm hospitality during the last stages of this work , a.ali for valuable discussion and v.n.samoilov for support . the work was supported partly by grants rffi 01 - 02 - 17437 and intas 00366 and by usdoe de fg02 91er40646 . [ cols="^,^,^,^,^,^,^,^,^,^",options="header " , ] table 2 . dalitz plot distribution in born approximation @xmath186 . [ fig3 ] [ fig4 ] [ fig5 ] [ fig6 ] here we explain how to calculate @xmath90 , @xmath60 , @xmath64 and how to group them into eq([scplm ] ) . contribution from emission of a soft real photon can be written in a standard form in terms of the classical currents : @xmath187 where @xmath66 is fictitious mass of photon . we use the following formulas : @xmath188 @xmath189 @xmath190 from them we obtain the eq([ds ] ) . consider now radiative corrections that arise from emission of virtual photons ( excluding sd virtual photons ) . feynman graphs containing self energy insertion to positron and kaon green functions ( fig.1,b , c ) can be taken into account by introducing the wave function renormalization constants @xmath191 and @xmath192 : @xmath193 . we use the expression for @xmath191 given in the textbooks @xcite ; the expression for @xmath192 is given in the paper @xcite . the result is eq([dc ] ) . now consider the feynman graph in which a virtual photon is emitted by kaon and absorbed by positron or by @xmath3boson in the intermediate state ( fig.1,d , e , f ) . this long distance contribution is calculated using a phenomenological model with point like mesons as a relevant degrees of freedom . to calculate the contribution from the region @xmath194 ( @xmath63 is the ultra violet cutoff ) we use the following expressions for loop momenta scalar , vector , and tensor integrals : @xmath195 a standard calculation yields : @xmath196 where @xmath62 and we omitted terms of the order of @xmath197 . as a result we obtain @xmath198 in a series of papers @xcite a.sirlin has conducted a detailed analysis of uv behaviour of amplitudes of processes with hadrons in 1loop level . he showed that they are uv finite ( if considered on the quark level ) , but the effective cutoff scale on loop momenta is of the order @xmath71 . for this reason we choose @xmath199 the sum @xmath200 yields eq([scplm ] ) the matrix element of the radiative @xmath11 decay @xmath201 with terms up to @xmath202 in chpt @xcite has the form @xmath203 where @xmath204 \ ; \\ \nonumber % \end{equation } % \begin{equation } q_\mu^{sd}=\gamma_\nu r_{\mu\nu } \ .\end{aligned}\ ] ] where tensor @xmath205 describes ( see eq(4.17 ) in @xcite ) the structure dependent emission ( fig 2(c ) ) . @xmath206 singular at @xmath207 terms which provide contribution containing large logarithm @xmath88 arises only from @xmath208 . to extract the corresponding terms we introduce four vector @xmath209 , and @xmath210 is the energy fraction of the photon ( 9 ) . note that @xmath211 when @xmath212 . separating leading and non leading terms and letting @xmath213 , i.e. neglecting form factor s momentum dependence , we obtain : @xmath214 where @xmath215- \frac{ya_0(x+y , z)}{x+y}+ \mathcal{p } \ .\end{gathered}\ ] ] the quantity @xmath216 contains some non leading contributions from the ib part and the ones that arise from the structure dependent part : @xmath217 with @xmath218 @xmath219 @xmath220 @xmath221 \hat{p}_e\gamma_\lambda \ .\ ] ] to calculate these traces we use the following expressions for the scalar products of the 4momenta ( in units @xmath222 ) : @xmath223 @xmath224 @xmath225 @xmath226 @xmath227 @xmath228 @xmath229 @xmath230 three terms in the rhs of ( [ t ] ) have a completely different behavior . the first one corresponds to the kinematic region of collinear emission , when photon is emitted along positron s momentum . the relevant phase volume has essentially 3particles form : @xmath231 the limits of photon s energy fraction variation are @xmath232 . the upper limit is imposed by the born structure of the width in this kinematical region . the second term corresponds to the contribution from emission by kaon . the relevant kinematics is isotropic . the kinematics of radiative kaon decay and the comparison of our and e.ginsbergs approaches is given in appendix f. the third term corresponds to the rest of the contributions which contain neither collinear nor infrared singularities . performing the integration over photon s phase volume provided @xmath39 are in the @xmath41 region we obtain : @xmath233 \ \\ -2\int\limits_{y\delta}^{b(z)-y}\frac{dx}{x}[a_0(y , z)+x(\frac{r(z)}{x+y}-y)]+ \int\limits_0^{b(z)-y } dx\mathcal{j},\end{gathered}\ ] ] we obtain ( [ deltahard ] ) with @xmath234 @xmath235 and @xmath236 one can check that the sum of rc arising from hard , soft and virtual photons do not depend on the auxiliary parameter @xmath237 . we note that the leading contribution from hard part of photon spectra can be reproduced using the method of quasi real electrons @xcite . ] ] now we concentrate on the contribution of the third term in the rhs of ( [ t ] ) . to perform the integration over the phase volume of final states it is convenient to use the following parameterization ( see appendix f ) : @xmath238 with @xmath239 the neutrino on mass shell ( nms ) condition provides the relation @xmath240 \ .\ ] ] for the aim of further integration of @xmath216 over angular variables we put it in the form : @xmath241 % \ [ a_e=\frac{xy}{2}\left(1-c_e \right ) \ , \\ \nonumber % \ ] % \ [ a_\nu = x - a_e-\frac{xz}{2}\left(1-\beta_\pi c_\pi \right ) \ . % \]\end{aligned}\ ] ] and @xmath242 angular integration can be performed explicitly , we have @xmath243 \ , \ ] ] with @xmath244 performing the integration over @xmath245 we have : @xmath246 the following integrals are helpful in integrating the above expression . we define @xmath247 then @xmath248 where @xmath249 and @xmath250 . the first term in @xmath251 together with the leading contributions from virtual and soft real photons was given in the form required by rg approach eq([psii ] ) . the non leading contributions , @xmath84 from hard photon emission , include sd emission , ib of point like mesons as well as the interference terms . it is free from infrared and mass singularities and given above ( [ deltahard ] ) with @xmath252 and @xmath253 the contribution to @xmath84 from sd emission have the form : @xmath254 where @xmath255 with @xmath256 given in appendix b and @xmath257 \ , \nonumber \\ q_3=-\frac{1}{8 } \left[-8+(z+y)(4 + 3x)-2x+3x^2 \right ] \ , \nonumber \\ q_4= \frac{1}{8 } \left [ 4y+4x+3xy \right ] , \qquad q_5=-\frac{3}{4 } \ .\end{aligned}\ ] ] the contribution to the total width have a form : @xmath258 numerical estimation gives : @xmath259 the function @xmath260 , defined as @xmath261 contains a restriction on the domain of integration , namely @xmath262 exceed @xmath36 or equal to it , which is implied by the kernel @xmath263 . explicit calculations give : @xmath264\ln\frac{b(z)}{b_-(z)}+ \\ 2a_0(y , z)\ln\frac{b(z)-y}{b_-(z)-y}+ \frac{1}{2}(b(z)^2-b_-(z)^2 ) \ , \\ 2\sqrt{r_e}<y<1-\sqrt{r_\pi},\qquad \psi_<(y , z)=0 , y>1-\sqrt{r_\pi } \ .\end{gathered}\ ] ] and @xmath265- \\ \frac{1}{2}(b(z)^2-y^2)+ ( b(z)-y)(2-y - z+b_-(z))+[r(z)-y(2-z)]\ln\frac{b(z)}{y}.\end{gathered}\ ] ] one can convince the validity of the relations : @xmath266 and @xmath267 the last relation demonstrates the kln cancellation for the pion spectrum obtained by integration of the corrections over @xmath36 in the interval @xmath123 . the explicit expressions for @xmath133 and @xmath134 are:(for @xmath136 see ( [ fulli ] ) ) . @xmath268 \ln \frac{1-y}{r_\pi } - \\ \frac{1-r_\pi - y}{36(1-y)^2 } \left [ ( 1-y)^2 \left(43 y^3 -15 y^2 -3y-1 \right . + r_\pi(83y^2 + 26y+11 ) + 3r_\pi^3 \right ) + \\ r_\pi^2(31 y^3 -15y^2 - 39y+47 ) \left . \right ] \ , \end{gathered}\ ] ] @xmath269 + \frac{1-r_\pi - y}{720(1-y)^3 } \biggl[-(1-y)^3(247y^4 - 88y^3 - 28y^2 - 8y-3)- \\ % \right . r_\pi(1-y)^3(733y^3 + 341y^2 + 129y+57)-\\ r_\pi^2(1-y)(707y^4 - 808y^3 + 212y^2- 408y+717)\\ + r_\pi^3(173y^4 - 72y^3 - 492y^2 + 1048y-477 ) -12 r_\pi^4(1-y)^3 \biggr].\end{gathered}\ ] ] collection of the relevant formulae . the dalitz - plot distribution in the region @xmath41 : @xmath270\biggr),\\ z_1=\frac{3}{4}-\frac{\pi^2}{6}-\frac{3}{2}\ln y- \ln ( ( { b(z)-y})/y ) - li_2(1-y ) \ .\end{gathered}\ ] ] the function @xmath271 is defined in ( [ z2 ] ) . correction to the total width ( we include the contribution of the region outside the region @xmath41 ) , @xmath5 : @xmath272 + \\ \int\limits_{b_-(z)}^{b(z)}dy[a_0(y , z)z_1+(1/2)z_2]\biggr ] \ , \end{gathered}\ ] ] with @xmath273 the expression in big square brackets in right - hand side of ( 95 ) can be put in the form : @xmath274 which results in @xmath275 . for the aim of comparison with e. ginsberg result we must put here @xmath276 as was mentioned above we have reasonable agreement with e. ginsberg results . for the inclusive set - up of experiment ( energy fraction of positron is not measured ) we have for pion energy spectrum given above ( [ rcpions ] ) . when we restrict ourselves only by the region @xmath41 the spectrum becomes dependent on @xmath127 : @xmath277 \right\ } \left(1+\frac{\lambda_+}{r_\pi}r(z ) \right)^2 \ , \end{gathered}\ ] ] with @xmath278 our approach to study the radiative kaon decay has an advantage compared to the one used by e. ginsberg it has a simple interpretation of electron mass singularities based on drell - yan picture . the @xcite approach to study noncollinear kinematics is more transparent than ours one . we remind the reader of some some topics of @xcite paper . one can introduce the missing mass square variable @xmath279 the limits of this quantity variation at fixed @xmath39 are pu by the last term : for collinear or anticollinear kinematics of pion and positron 3-momenta . being expressed in terms of @xmath39 they are ( we consider the general point of dalitz - plot and omit positron mass dependence ) : @xmath280 for the @xmath39 in the @xmath41 region and @xmath281 for the case when they are in the region @xmath282 outside @xmath41 : @xmath283 for our approach with separating the case of soft and hard photon emission we must modify the lower bound for @xmath284 in the region @xmath41 . it can be done using another representation of @xmath284 : @xmath285,\ ] ] with @xmath286-the cosine of the angles between photon 3-momentum and positron and pion ones , @xmath287-is the pion velocity . maximum of this quantity is @xmath288 . taking this into account we obtain for the region oh hard photon @xmath289 for the region @xmath41 : @xmath290 and for region @xmath282 : @xmath291 in particular for the collinear case we must choice @xmath292 , which corresponds to @xmath293 . let infer this condition using the nms condition : @xmath294 in collinear case we have @xmath295.from nms condition we obtain @xmath296 . using this value we obtain @xmath297 . using further the relation @xmath298 we obtain again @xmath299 in the case of emission along positron . comparing the phase volumes in general case calculated in our approach with using nms condition with @xcite approach we obtain the relation : @xmath300 the non leading contribution arising from hard photon emission considered above : @xmath301 with @xmath302 ( note that @xmath303 , see appendix b and c ) can be transformed to the form : @xmath304i_{10}- \\ ( 1/2)i_{1 - 1}-((1/2)l+y+z)i_{2 - 1}+i_z].\end{gathered}\ ] ] here we use the list of integrals obtained in the paper of @xcite : @xmath305 besides we need two additional ones : @xmath306 one can see the cancellation of mass singularities ( terms containing @xmath127 ) in the expression @xmath307 . 99 t.becherrawy , phys . d1 ( 1970 ) , 1452 e.ginsberg , phys . 162(1967 ) , 1570 ; phys . rev . 142(1966 ) , 1035 ; phys . rev . 171(1968 ) , 1675 ; phys . rev . 187(1968 ) , 2280 j.gasser and h.leutwyller , nucl . phys . b250(1985 ) , 464 , 517 ; j.bijnens , g.colangelo , g.ecker , and j.gasser , the second da@xmath308ne physics handbook , vol.1 , 313 j.bijnens , g.ecker , and j.gasser , nucl . phys . b396(1993 ) , 81 ; b.holstein phys . rev . d41(1990 ) , 2829 ; a.sirlin , phys . rev . d5(1972 ) , 436 ; rev . 50(1978 ) , 573 ; nucl b196(1982 ) , 83 ; m.v.terentev , yad . fiz . 18(1973 ) , 870 ; sov . j. nucl . 18(1974 ) , 449 e.a.kuraev , v.s.fadin , yad . fiz . 41(1985 ) , 466 v.n.baier , v.s.fadin , v.a.khoze , nucl . phys . b65(1973 ) , 381 w.marciano and a.sirlin , phys . rev . 71(1993 ) , 3629 t.kinoshita , j. math . phys . 3(1972 ) , 650 ; + t.d.lee and m.nauenberg , phys . rev . b133(1964 ) , 1549 r.decker and m.finkemeier , nucl . phys . b438(1995 ) , 17 v.cirigliano , m.knecht , h.neufeld , h.rupertsbergen , p.talavera , + hep - ph/0110153 n - p . chang , phys . 131(1963),1272 a.i.akhiezer , v.b.berestetski , quantum electrodynamics , moscow , 1981 ; + v.b.berestetski , e.lifshitz , l.pitaevski,quantum electrodynamics , moscow , 1989 e.s . ginsberg , phys . d 1 , 229 ( 1970 )[/INST] we consider the lowest order radiative corrections for the decay @xmath0 , usually referred as @xmath1 decay . this decay is the best way to extract the value of the @xmath2 element of the ckm matrix . the radiative corrections become crucial if one wants a precise value of @xmath2 . the existing calculations were performed in the late 60 s @xcite and are in disagreement . the calculation in @xcite turns out to be ultraviolet cutoff sensitive . the necessity of precise knowledge of @xmath2 and the contradiction between the existing results constitute the motivation of our paper . we remove the ultraviolet cutoff dependence by using a.sirlins prescription ; we set it equal to the @xmath3 mass . we establish the whole character of small lepton mass dependence based on the renormalization group approach . in this way we can provide a simple explanation of kinoshita lee nauenberg cancellation of singularities in the lepton mass terms in the total width and pion spectrum . we give an explicit evaluation of the structure dependent photon emission based on chpt in the lowest order . we estimate the accuracy of our results to be at the level of @xmath4 . the corrected total width is @xmath5 with @xmath6 . using the formfactor value @xmath7 calculated in @xcite leads to @xmath8 . @xmath9 bogoliubov laboratory of theoretical physics , jinr , dubna , moscow region , 141980 , russia + @xmath10 department of physics and astronomy , university of pittsburgh , pa , u.s.a + </s>

mouse embryonic stem cells ( mescs ) ( r1 and r1/e ) were maintained on a layer of mitomycin c - treated mouse embryonic fibroblast feeder cells in standard medium supplemented with 1000 u / ml mouse leukemia inhibitory factor ( lif ) . briefly , escs were dissociated into single cells after treatment with 0.05% trypsin edta at 37 c for 2 min and were seeded at a density of 1 10 cells / ml in petri dishes to form embryonic bodies ( ebs ) . eb cells are maintained in supplemented dmem containing 10% fbs ( gibco ) , 1% neaa , 1% sodium pyruvate , and 0.1 mm -mercaptoethanol ( both from gibco ) . on days 2 , 4 and 6 , wild - type cells and pou3f1 stable overexpressed ( pou3f1-oe ) cells were collected for rna - seq analysis , and pou3f1 chip - seq was performed on day 2 and day 4 with pou3f1-overexpression cells ( fig . chip assays were performed as described in the manufacturer 's manuals ( dynabeads protein a / g ( invitrogen ) and protein a / g agarose / salmon sperm dna ( upstate biotech ) ) , and modified as previously reported . briefly , differentiated eb cells were dissociated into single cells by trypsin and subjected to cross - linking . the cells were lysed and crude extracts were sonicated into dna fragments of an average size of 200 bp . cell lysate was cleared and subsequently incubated with antibodies against pou3f1 or directly used as chip input . the input dna and 1015 ng ip dna were used to construct sequencing library by chip - seq sample prep kit ( illumina ) . the high - throughput sequencing was performed by the computational biology omics core , picb , shanghai . the chip - seq reads were mapped into the mouse genome build mm9 using the soap version 2.20 . we then used findpeaks in homer package to call pou3f1 binding peaks , which required 4-fold greater normalized reads in chip sample comparing with the control . furthermore , the distance of peak center to the nearest transcription start site ( tss ) was calculated for all peaks , and most of them were distal to tss ( fig . 3 ) . tophat ( version 1.4.1 ) alignment tool was used to map raw reads to mm9 , and cufflinks ( version 1.3.0 ) was used to calculate fpkm ( fragment per kilo base per million ) as an expression value for each gene . then , we identified differentially expressed genes between treatment and control samples using cuffdiff software , and performed k - means clustering using euclidean distance as the distance between genes . mouse embryonic stem cells ( mescs ) ( r1 and r1/e ) were maintained on a layer of mitomycin c - treated mouse embryonic fibroblast feeder cells in standard medium supplemented with 1000 u / ml mouse leukemia inhibitory factor ( lif ) . briefly , escs were dissociated into single cells after treatment with 0.05% trypsin edta at 37 c for 2 min and were seeded at a density of 1 10 cells / ml in petri dishes to form embryonic bodies ( ebs ) . eb cells are maintained in supplemented dmem containing 10% fbs ( gibco ) , 1% neaa , 1% sodium pyruvate , and 0.1 mm -mercaptoethanol ( both from gibco ) . on days 2 , 4 and 6 , wild - type cells and pou3f1 stable overexpressed ( pou3f1-oe ) cells were collected for rna - seq analysis , and pou3f1 chip - seq was performed on day 2 and day 4 with pou3f1-overexpression cells ( fig . chip assays were performed as described in the manufacturer 's manuals ( dynabeads protein a / g ( invitrogen ) and protein a / g agarose / salmon sperm dna ( upstate biotech ) ) , and modified as previously reported . briefly , differentiated eb cells were dissociated into single cells by trypsin and subjected to cross - linking . the cells were lysed and crude extracts were sonicated into dna fragments of an average size of 200 bp . cell lysate was cleared and subsequently incubated with antibodies against pou3f1 or directly used as chip input . the input dna and 1015 ng ip dna were used to construct sequencing library by chip - seq sample prep kit ( illumina ) . the high - throughput sequencing was performed by the computational biology omics core , picb , shanghai . the chip - seq reads were mapped into the mouse genome build mm9 using the soap version 2.20 . we then used findpeaks in homer package to call pou3f1 binding peaks , which required 4-fold greater normalized reads in chip sample comparing with the control . furthermore , the distance of peak center to the nearest transcription start site ( tss ) was calculated for all peaks , and most of them were distal to tss ( fig . tophat ( version 1.4.1 ) alignment tool was used to map raw reads to mm9 , and cufflinks ( version 1.3.0 ) was used to calculate fpkm ( fragment per kilo base per million ) as an expression value for each gene . then , we identified differentially expressed genes between treatment and control samples using cuffdiff software , and performed k - means clustering using euclidean distance as the distance between genes .

appropriate neural initiation of the pluripotent stem cells in the early embryos is critical for the development of the central nervous system . this process is regulated by the coordination of extrinsic signals and intrinsic programs . however , how the coordination is achieved to ensure proper neural fate commitment is largely unknown . here , taking advantage of genome - wide chip - sequencing ( chip - seq ) and rna - sequencing ( rna - seq ) analyses , we demonstrate that the transcriptional factor pou3f1 is an upstream activator of neural - promoting genes , and it is able to repress neural - inhibitory signals as well . further studies revealed that pou3f1 could directly bind neural lineage genes like sox2 and downstream targets of neural inhibition signaling such as bmp and wnt . our results thus identify pou3f1 as a critical dual - regulator of the intrinsic transcription factors and the extrinsic cellular signals during neural fate commitment . data were deposited in gene expression omnibus ( geo ) datasets under reference number gse69865 .

<s>[INST] mouse embryonic stem cells ( mescs ) ( r1 and r1/e ) were maintained on a layer of mitomycin c - treated mouse embryonic fibroblast feeder cells in standard medium supplemented with 1000 u / ml mouse leukemia inhibitory factor ( lif ) . briefly , escs were dissociated into single cells after treatment with 0.05% trypsin edta at 37 c for 2 min and were seeded at a density of 1 10 cells / ml in petri dishes to form embryonic bodies ( ebs ) . eb cells are maintained in supplemented dmem containing 10% fbs ( gibco ) , 1% neaa , 1% sodium pyruvate , and 0.1 mm -mercaptoethanol ( both from gibco ) . on days 2 , 4 and 6 , wild - type cells and pou3f1 stable overexpressed ( pou3f1-oe ) cells were collected for rna - seq analysis , and pou3f1 chip - seq was performed on day 2 and day 4 with pou3f1-overexpression cells ( fig . chip assays were performed as described in the manufacturer 's manuals ( dynabeads protein a / g ( invitrogen ) and protein a / g agarose / salmon sperm dna ( upstate biotech ) ) , and modified as previously reported . briefly , differentiated eb cells were dissociated into single cells by trypsin and subjected to cross - linking . the cells were lysed and crude extracts were sonicated into dna fragments of an average size of 200 bp . cell lysate was cleared and subsequently incubated with antibodies against pou3f1 or directly used as chip input . the input dna and 1015 ng ip dna were used to construct sequencing library by chip - seq sample prep kit ( illumina ) . the high - throughput sequencing was performed by the computational biology omics core , picb , shanghai . the chip - seq reads were mapped into the mouse genome build mm9 using the soap version 2.20 . we then used findpeaks in homer package to call pou3f1 binding peaks , which required 4-fold greater normalized reads in chip sample comparing with the control . furthermore , the distance of peak center to the nearest transcription start site ( tss ) was calculated for all peaks , and most of them were distal to tss ( fig . 3 ) . tophat ( version 1.4.1 ) alignment tool was used to map raw reads to mm9 , and cufflinks ( version 1.3.0 ) was used to calculate fpkm ( fragment per kilo base per million ) as an expression value for each gene . then , we identified differentially expressed genes between treatment and control samples using cuffdiff software , and performed k - means clustering using euclidean distance as the distance between genes . mouse embryonic stem cells ( mescs ) ( r1 and r1/e ) were maintained on a layer of mitomycin c - treated mouse embryonic fibroblast feeder cells in standard medium supplemented with 1000 u / ml mouse leukemia inhibitory factor ( lif ) . briefly , escs were dissociated into single cells after treatment with 0.05% trypsin edta at 37 c for 2 min and were seeded at a density of 1 10 cells / ml in petri dishes to form embryonic bodies ( ebs ) . eb cells are maintained in supplemented dmem containing 10% fbs ( gibco ) , 1% neaa , 1% sodium pyruvate , and 0.1 mm -mercaptoethanol ( both from gibco ) . on days 2 , 4 and 6 , wild - type cells and pou3f1 stable overexpressed ( pou3f1-oe ) cells were collected for rna - seq analysis , and pou3f1 chip - seq was performed on day 2 and day 4 with pou3f1-overexpression cells ( fig . chip assays were performed as described in the manufacturer 's manuals ( dynabeads protein a / g ( invitrogen ) and protein a / g agarose / salmon sperm dna ( upstate biotech ) ) , and modified as previously reported . briefly , differentiated eb cells were dissociated into single cells by trypsin and subjected to cross - linking . the cells were lysed and crude extracts were sonicated into dna fragments of an average size of 200 bp . cell lysate was cleared and subsequently incubated with antibodies against pou3f1 or directly used as chip input . the input dna and 1015 ng ip dna were used to construct sequencing library by chip - seq sample prep kit ( illumina ) . the high - throughput sequencing was performed by the computational biology omics core , picb , shanghai . the chip - seq reads were mapped into the mouse genome build mm9 using the soap version 2.20 . we then used findpeaks in homer package to call pou3f1 binding peaks , which required 4-fold greater normalized reads in chip sample comparing with the control . furthermore , the distance of peak center to the nearest transcription start site ( tss ) was calculated for all peaks , and most of them were distal to tss ( fig . tophat ( version 1.4.1 ) alignment tool was used to map raw reads to mm9 , and cufflinks ( version 1.3.0 ) was used to calculate fpkm ( fragment per kilo base per million ) as an expression value for each gene . then , we identified differentially expressed genes between treatment and control samples using cuffdiff software , and performed k - means clustering using euclidean distance as the distance between genes .[/INST]appropriate neural initiation of the pluripotent stem cells in the early embryos is critical for the development of the central nervous system . this process is regulated by the coordination of extrinsic signals and intrinsic programs . however , how the coordination is achieved to ensure proper neural fate commitment is largely unknown . here , taking advantage of genome - wide chip - sequencing ( chip - seq ) and rna - sequencing ( rna - seq ) analyses , we demonstrate that the transcriptional factor pou3f1 is an upstream activator of neural - promoting genes , and it is able to repress neural - inhibitory signals as well . further studies revealed that pou3f1 could directly bind neural lineage genes like sox2 and downstream targets of neural inhibition signaling such as bmp and wnt . our results thus identify pou3f1 as a critical dual - regulator of the intrinsic transcription factors and the extrinsic cellular signals during neural fate commitment . data were deposited in gene expression omnibus ( geo ) datasets under reference number gse69865 .</s>

ngc 2110 , an s0/e galaxy at a distance of @xmath1 30 mpc , is host to one of the most extensively studied active galactic nuclei ( agns ) in the local universe . the nuclear activity in this object was originally recognized because of its intense x - ray emission ( bradt et al . 1978 ) , and it has been a popular target for x - ray investigations ever since ( mushotzky 1982 ; turner & pounds 1989 ; weaver et al . 1995 ; hayashi et al . 1996 ; malaguti et al . 1999 ) . ngc 2110 is classified as a type 2 seyfert galaxy based on its nuclear optical spectrum , which is dominated by narrow emission lines ( mcclintock et al . observations of the the circumnuclear environment of ngc 2110 have revealed peculiar kinematics and complex structure at all wavelengths ( ulvestad & wilson 1983 ; wilson et al . 1985 ; pogge 1989 ; haniff et al . 1991 ; mulchaey et al . 1994 ; ferruit et al . 1999 , 2004 ; quillen et al . 1999 ; gonzlez delgado et al . 2002 ; evans et al . 2006 ) as a result , ngc 2110 has emerged as an important laboratory for studying the interaction between an active nucleus and its surroundings . ngc 2110 has been frequently considered in the context of agn unification ( e.g. , antonucci 1993 ) . the presence of a hidden type 1 nucleus is implied by x - ray observations , which indicate heavy absorption of the soft x - ray spectrum and a seyfert 1-like intrinsic luminosity at hard x - ray energies ( mushotzky 1982 ; turner & pounds 1989 ; malaguti et al . similarly , if the extended narrow - line region is powered by photoionization from the nucleus , the morphology of this region and the strength of the balmer recombination lines relative to the observed ionizing flux would suggest that the nuclear continuum source is obscured from our view ( wilson et al.1985 ; mulchaey et al . yet despite a number of direct searches for broad emission lines in both the optical ( shuder 1980 ; veilleux 1991 ) and near - infrared ( veilleux et al . 1997 ; storchi - bergmann et al . 1999 ; knop et al . 2001 ; lutz et al . 2004 ) , conclusive evidence that ngc 2110 harbors a hidden broad - line region ( blr ) has been elusive . in this _ letter _ , we report the discovery of a spectacular broad h@xmath0 emission line in the polarized flux spectrum of this object . we observed ngc 2110 on 30 december 2005 ( ut ) with the lris spectropolarimeter ( cohen et al . 1997 ) on the keck i 10 m telescope . both beams of the instrument were employed in conjunction with the d560 dichroic beam splitter . on the blue side , a 400 l mm@xmath2 grism blazed at 3400 was used , providing coverage of the 32005700 range at @xmath3 resolution ( fwhm ) . the red side data , obtained with a 600 l mm@xmath2 grating blazed at 7500 , span 55207990 at @xmath1 4.5 resolution . a 900 s exposure was acquired at each of the four waveplate positions using a 10 slit , which was oriented at the mid - observation parallactic angle of 16@xmath4 . the observations were obtained under photometric conditions at an average airmass of 1.13 . we extracted one - dimensional spectra from the reduced images within a 315 region centered on the galaxy s nucleus . spectropolarimetric processing and measurements were performed following the methods described by miller et al . ( 1988 ) and barth et al . ( 1999 ) . because of the proximity of ngc 2110 to the galactic plane ( @xmath5 , @xmath6 = 0.375 mag ) , we explored whether transmission through galactic dust might affect the observed polarization . a search of the heiles ( 2000 ) catalog of stellar polarizations reveals two stars within @xmath7 of ngc 2110 with linear polarization data . the stars have nearly identical polarization levels and position angles ; using the average values of these ( @xmath8% , @xmath9 ) , we made synthetic @xmath10 and @xmath11 spectra assuming a serkowski et al . ( 1975 ) curve for @xmath12 . these were then subtracted from the normalized stokes parameters for ngc 2110 to correct the galaxy s polarization and position - angle spectra . as discussed below , these corrections prove to be relatively minor . our spectropolarimetry results are displayed in figure 1 . the total - flux spectrum of ngc 2110 ( _ top panel _ ) is clearly dominated by narrow emission lines . the small but significant amount of continuum polarization observed ( _ middle panel _ ) is approximately constant with wavelength , suggesting that it is caused by electron scattering . in the 52006200 range the polarization and polarization angle are @xmath13% and @xmath14 , respectively . after correction for interstellar effects , the value of @xmath15 is virtually unchanged , while the polarization angle rotates a modest amount to @xmath16 . the corrected value of @xmath17 is nearly orthogonal to the arcsecond - scale radio and optical emission - line structures observed along p.a . @xmath18 in ngc 2110 ( gonzlez delgado et al . 2002 , and references therein ) . this is consistent with expectations based on the unified agn model , whereby scattering of the nuclear continuum occurs along a direction parallel to the axis of the obscuring torus ( antonucci 1984 ) . a dramatic increase in polarization ( peaking at @xmath19% ) is observed on either side of the h@xmath0 + [ ] narrow - line blend in figure 1 . as a result , the polarized flux spectrum of ngc 2110 ( _ bottom panel _ ) exhibits an extremely broad , double - peaked h@xmath0 line . the full - width at zero - intensity of the broad h@xmath0 line is roughly @xmath20 km s@xmath2 . a similar feature is not observed at h@xmath21 , although the h@xmath21 line is broader ( @xmath22 km s@xmath2 fwhm ) than the forbidden lines in the polarized flux spectrum . previous studies have shown that the polarized h@xmath0 lines of hidden seyfert 1s can be asymmetric and broad ( e.g. , schmidt et al . 2002 ) , but because of the structure observed in its h@xmath0 profile , ngc 2110 is perhaps the most extreme example discovered to date . the broad h@xmath0 line shown in figure 1 closely resembles those exhibited by double - peaked emission - line agns , a small but important class of active nuclei ( eracleous & halpern 1994 , 2003 ; strateva et al . in fact , ngc 2110 s broad h@xmath0 profile is nearly identical to that of the prototypical double - peaked agn arp 102b ( cf . fig . 2 of halpern et al . an important secondary characteristic of double - peaked emitters is that they often display strong low - ionization forbidden lines , such as [ ] @xmath23 , [ ] @xmath24 , and [ ] @xmath25 . similar to many radio - selected double - peakers , the emission - line flux ratios in ngc 2110 suggest a liner classification ( heckman 1980 ; veilleux & osterbrock 1987 ) : log ( [ ] /h@xmath0 ) = 0.17 , log ( [ ] /h@xmath0 ) = @xmath260.23 , and log ( [ ] /h@xmath0 ) = 0.00 . the seyfert - like [ ] @xmath27/h@xmath21 flux ratio of @xmath28 in ngc 2110 is common among optically selected double - peaked emitters ( strateva et al . thus , on spectroscopic grounds , ngc 2110 appears to be a genuine double - peaked emission - line agn . this marks the first time that this type of object has been discovered via spectropolarimetry in a seyfert 2 galaxy . although at one time the origin of broad , double - peaked emission lines in agns was a matter of considerable debate ( see gaskell et al . 1999 ) , the prevailing interpretation today is that such lines are produced in blrs that have a disk geometry ( eracleous & halpern 2003 ) . we have thus fitted relativistic keplerian disk models to the h@xmath0 profile in the polarized flux spectrum of ngc 2110 . a circular disk model ( chen & halpern 1989 ) provides a rather poor fit , so we have instead fitted the line profile with an elliptical disk model ( following eracleous et al . 1995 ) under the assumption that the emissivity of the disk scales with radius as @xmath29 ( collin - souffrin & dumont 1989 ; eracleous & halpern 2003 ; strateva et al . as illustrated in figure 2 , this model provides a very good fit to the polarized h@xmath0 line profile . the best - fitting model is described by the following parameters : the inner and outer pericenter distances of the line - emitting portion of the disk ( in units of the gravitational radius , @xmath30 , where @xmath31 is the black - hole mass ) are @xmath32 and @xmath33 ; the inclination of the disk axis is @xmath34 ; the eccentricity of the disk is @xmath35 ; the orientation of the major axis relative to the line of sight ( see fig . 2 of eracleous et al . 1995 ) is @xmath36 ; and the broadening parameter ( representing turbulent motions in the line - emitting `` skin '' of the disk ) is @xmath37 . these parameters are consistent with those obtained for arp 102b by chen & halpern ( 1989 ) , i.e. , @xmath38 , @xmath39 , @xmath40 , and @xmath41 . ( note that because the broad h@xmath0 line in ngc 2110 is reflected , the angles @xmath42 and @xmath43 describe the orientation of the disk to the scattering medium , not the observer . ) the residuals of the fit , also shown in figure 2 , show a weak , broad , bell - shaped pedestal underlying the h@xmath0 + [ ] complex . such a kinematic component is also observed in the h@xmath0 and ly@xmath0 profiles of arp 102b ( it is in fact the dominant component of the ly@xmath0 line ; halpern et al . 1996 ) . based on a four - component gaussian fit to the h@xmath0 + [ ] lines in the residuals spectrum , we estimate the width of the bell - shaped broad component to be @xmath44 ( fwhm ) , similar to the widths of the ly@xmath0 and h@xmath0 lines of arp 102b ( halpern et al . 1996 ) . for a final comparison to other double - peaked agns , we have estimated the bolometric - to - eddington luminosity ratio @xmath45 of ngc 2110 . using the tremaine et al . ( 2002 ) @xmath46 relation , the observed stellar velocity dispersion of @xmath47 km s@xmath2 ( nelson & whittle 1995 ) indicates a black - hole mass of @xmath48 @xmath49 , which implies @xmath50 ergs s@xmath2 . the intrinsic 210 kev x - ray luminosity of @xmath51 ergs s@xmath2 ( malaguti et al . 1999 ) , combined with a bolometric correction factor of @xmath52 ( typical of radio - quiet quasars ; elvis et al . 1994 ) , yields @xmath53 ergs s@xmath2 . we note that the extinction - corrected [ ] @xmath27 luminosity of @xmath54 ergs s@xmath2 derived from our keck data , combined with a bolometric correction of @xmath55 ( heckman et al . 2004 ) , yields @xmath56 ergs s@xmath2 . thus , for ngc 2110 we estimate that @xmath57 . despite the rough numbers used here , this is in close agreement with the value of @xmath58 obtained by lewis & eracleous ( 2006 ) for arp 102b , which further strengthens the case that ngc 2110 is an obscured twin of arp 102b . close inspection of the top panel of figure 1 reveals that the blue peak of the broad h@xmath0 line is faintly visible in the total - flux spectrum of ngc 2110 . this is perhaps not too surprising , given the high polarization of the feature and the unconfused nature of the spectrum in its vicinity . to investigate whether the double - peaked line was present in previous years , we have combed the literature for published nuclear spectra of ngc 2110 . the most recent spectrum we were able to find was one obtained on 30 december 2000 ( ut ) with the stis instrument on board the _ hubble space telescope _ ( ferruit et al . 2004 ) , which we have retrieved from the _ hst _ archive . a total exposure of 4445 s was obtained using a 02 slit . our extraction of the spectrum covers a 5-pixel ( 025 ) region centered on the nucleus . before comparing the keck and stis data , we removed the continuum from each spectrum . to model the keck continuum , we combined a spiral galaxy bulge template ( that of m31 ) with a power - law component . the continuum in the stis spectrum , which contains little or no starlight because of the small effective aperture , was removed by subtracting a constant . we rescaled the continuum - subtracted stis spectrum to match the strength of the narrow h@xmath0 line in the keck spectrum . the results of our comparison are displayed in figure 3 . the narrow emission lines exhibit somewhat different velocity widths and flux ratios in the keck and stis data ; this is a reflection of density stratification in the narrow - line region of ngc 2110 ( e.g. , filippenko & halpern 1984 ) , which has been sampled by different apertures . the blue peak of the broad h@xmath0 line , clearly visible in the keck spectrum near 6425 , is completely absent in the high signal - to - noise ratio stis spectrum . given the lower amount of diluting starlight in the small 02 @xmath59 025 stis aperture , the blue peak would be at least as prominent in the stis spectrum if it were present . we conclude , therefore , that the double - peaked h@xmath0 line in the nucleus of ngc 2110 has appeared rather recently . moreover , additional spectropolarimetric observations in 2007 february by h. tran have shown that the line profile has varied significantly over an interval of 14 months . the transient nature of this feature and its subsequent variations are not without precendent ; the emergence of double - peaked lines has been noted in other agns ( e.g. , pictor a ; halpern & eracleous 1994 ; eracleous & halpern 1998 ) , and numerous other objects exhibit variability of the double - peaked line profile ( e.g. , storchi - bergmann et al . 1995 ; gezari et al . beginning with observations of ngc 1068 ( antonucci & miller 1985 ) , spectropolarimetry has played a crucial role in our understanding of the physical nature of agns , and it continues to provide valuable insight . our results establish that ngc 2110 possesses a disk - like blr , which expands the range of properties exhibited by seyfert 2s . in addition , ngc 2110 presents some opportunities for interesting follow - up study . as noted above , the double - peaked feature is transient and variable , and it would be worthwhile to monitor its behavior . the observed variations may trace changes in the structure of the blr or in the properties of the scattering medium . also , the similarity of ngc 2110 s broad h@xmath0 profile to that of arp 102b suggests that the line has not been distorted significantly in the scattering process . this has implications for the scattering geometry , e.g. , the scattering medium may only see the line - emitting disk over a narrow range of inclination angles . high - resolution imaging polarimetry and detailed spectropolarimetric modeling ( e.g. , smith et al . 2004 , 2005 ) would clarify this issue . in the bigger picture , by demonstrating that at least one double - peaked emitter contains the type of nuclear obscuration believed to be present in most ( if not all ) classical seyfert galaxies , we can now extend the concept of unification to the disk - emitting class of agns . on parsec scales , double - peaked agns may be structurally similar to other types of seyfert nuclei . if so , this underscores the need to understand how physical differences might originate in their broad - line regions . the data presented herein were obtained at the w. m. keck observatory , which is operated as a scientific partnership among the california institute of technology , the university of california , and nasa . the observatory was made possible by the generous financial support of the w. m. keck foundation . the work of a. j. b. was supported in part by the national science foundation through grant ast-0548198 . m. e. acknowledges the warm hospitality of the department of astrophysics at the american museum of natural history . antonucci , r. r. j. 1984 , apj , 278 , 499 antonucci , r. 1993 , , 31 , 473 antonucci , r. r. j. , & miller , j. s. 1985 , , 297 , 621 barth , a. j. , filippenko , a. v. , & moran , e. c. 1999 , , 525 , 673 bradt , h. v. , burke , b. f. , canizares , c. r. , greenfield , p. e. , kelley , r. l. , mcclintock , j. e. , koski , a. t. , & van paradijs , j. 1978 , , 226 , 111 chen , k. , & halpern , j. p. 1989 , , 344 , 115 cohen , m. h. , vermeulen , r. c. , ogle , p. m. , tran , h. d. , & goodrich , r. w. 1997 , , , 484 , 193 collin - souffrin , s. , & dumont , a. m. 1989 , , 213 , 29 elvis , m. , et al . 1994 , apjs , 95 , 1 eracleous , m. , & halpern , j. p. 1994 , , 90 , 1 eracleous , m. , & halpern , j. p. 1998 , , 505 , 577 eracleous , m. , & halpern , j. p. 2003 , , 599 , 886 eracleous , m. , livio , m. , halpern , j. p. , & storchi - bergmann , t. 1995 , apj , 438 , 610 evans , d. a. , lee , j. c. , kamenetska , m. , gallagher , s. c. , kraft , r. p. , hardcastle , m. j. , & weaver , k. a. 2006 , , 653 , 1121 ferruit , p. , mundell , c. g. , nagar , n. m. , emsellem , e. , pcontal , e. , wilson , a. s. , & schinnerer , e. 2004 , , 352 , 1180 ferruit , p. , wilson , a. s. , whittle , m. , simpson , c. , mulchaey , j. s. , & ferland , g. j. 1999 , , 523 , 147 filippenko , a. v. , & halpern , j. p. 1984 , , 285 , 475 gaskell , c. m. , brandt , w. n. , dietrich , m. , dultzin - hacyan , d. , & eracleous , m. 1999 , structure and kinematics of quasar broad line regions , asp conf . ser . , 175 ( san fransisco : asp ) gezari , s. , halpern , j. p. , & eracleous , m. 2007 , , 169 , 167 gonzlez delgado , r. m. , arribas , s. , perez , e. , & heckman , t. 2002 , , 579 , 188 halpern , j. p. , & eracleous , m. 1994 , , 433 , 17 halpern , j. p. , eracleous , m. , filippenko , a. v. , & chen , k. 1996 , , 464 , 704 haniff , c. a. , ward , m. j. , & wilson , a. s. 1991 , , 368 , 167 hayashi , i. , koyama , k. , awaki , h. , & yamauchi , s. 1996 , , 48 , 219 heckman , t. m. 1980 , a&a , 87 , 152 heckman , t. m. , kauffmann , g. , brinchmann , j. , charlot , s. , tremonti , c. , & white , s. d. m. 2004 , apj , 613 , 109 heiles , c. 2000 , , 119 , 939 knop , r. a. , armus , l. , matthews , k. , murphy , t. w. , & soifer , b. t. 2001 , , 122 , 764 lewis , k. t. , & eracleous , m. 2006 , , 642 , 711 lutz , d. , maiolino , r. , moorwood , a. f. m. , netzer , h. , wagner , s. j. , sturm , e. , & genzel , r. 2002 , , 396 , 439 malaguti , g. , et al . 1999 , , 342 , l41 mcclintock , j. e. , remillard , r. a. , canizares , c. r. , veron , p. , & van paradijs , j. 1979 , , 233 , 809 miller , j. s. , robinson , l. b. , & goodrich , r. w. 1988 , in instrumentation for ground - based astronomy , ed . l. b. robinson ( new york : springer ) , 157 mulchaey , j. s. , wilson , a. s. , bower , g. a. , heckman , t. m. , krolik , j. h. , miley , g. k. 1994 , , 433 , 625 mushotsky , r. f. 1982 , , 256 , 92 nelson , c. h. , & whittle , m. 1995 , apjs , 99 , 67 pogge , r. w. 1989 , , 345 , 730 quillen , a. c. , alonso - herrero , a. , rieke , m. j. , mcdonald , c. , falcke , h. , & rieke , g. h. 1999 , , 525 , 685 schmidt , g. d. , smith , p. s. , foltz , c. b. , & hines , d. c. 2002 , , 578 , l99 serkowski , k. , mathewson , d. l. , & ford , v. l. 1975 , , 196 , 261 shuder , j. m. 1980 , , 240 , 32 smith , j. e. , robinson , a. , alexander , d. m. , young , s. , axon , d. j. , & corbett , e. a. 2004 , , 350 , 140 smith , j. e. , robinson , a. , young , s. , axon , d. j. , & corbett , e. a. 2005 , , 359 , 846 storchi - bergmann , t. , eracleous , m. , livio , m. , wilson , a. s. , filippenko , a. v. , & halpern , j. p. 1995 , , 443 , 617 storchi - bergmann , t. , winge , c. , ward , m. j. , & wilson , a. s. 1999 , , 304 , 35 strateva , i. v. , et al . 2003 , , 126 , 1720 strateva , i. v. , brandt , w. n. , eracleous , m. , schneider , d. p. , & chartas , g. 2006 , , 651 , 749 tremaine , s. , et al . 2002 , apj , 574 , 740 turner , t. j. , & pounds , k. a. 1989 , , 240 , 833 ulvestad , j. s. , & wilson , a. s. 1983 , , 264 , l7 veilleux , s. 1991 , 369 , 331 veilleux , s. , goodrich , r. w. , & hill , g. j. 1997 , , 477 , 631 veilleux , s. , & osterbrock , d. e. 1987 , apjs , 63 , 295 weaver , k. a. , mushotzky , r. f. , serlemitsos , p. j. , wilson , a. s. , elvis , m. , & briel , u. 1995 , , 442 , 597 wilson , a. s. , baldwin , j. a. , & ulvestad , j. s. 1985 , , 291 , 627 erg @xmath60 s@xmath2 @xmath2 . _ middle _ : degree of linear polarization , given as the rotated stokes parameter . _ bottom _ : polarized flux , or `` stokes flux , '' which is the product of the total flux and rotated stokes parameter.,title="fig:",scaledwidth=75.0% ] 0.1truein

we have discovered an extremely broad , double - peaked h@xmath0 emission line in the polarized flux spectrum of ngc 2110 , establishing that this well - studied seyfert 2 galaxy contains a disk - like hidden broad - line region ( blr ) . several properties of ngc 2110 suggest that it is an obscured twin of arp 102b , the prototypical double - peaked emission - line active galactic nucleus ( agn ) . a comparison between our data and previous spectra of ngc 2110 indicates that the double - peaked h@xmath0 feature is transient . the presence of a disk - like blr in ngc 2110 has important implications for agns : it expands the range of properties exhibited by seyfert 2 galaxies , and the fact that the blr is obscured by a torus - like structure provides the first evidence that double - peaked emitters and classical seyfert nuclei may have the same basic parsec - scale geometry .

<s>[INST]ngc 2110 , an s0/e galaxy at a distance of @xmath1 30 mpc , is host to one of the most extensively studied active galactic nuclei ( agns ) in the local universe . the nuclear activity in this object was originally recognized because of its intense x - ray emission ( bradt et al . 1978 ) , and it has been a popular target for x - ray investigations ever since ( mushotzky 1982 ; turner & pounds 1989 ; weaver et al . 1995 ; hayashi et al . 1996 ; malaguti et al . 1999 ) . ngc 2110 is classified as a type 2 seyfert galaxy based on its nuclear optical spectrum , which is dominated by narrow emission lines ( mcclintock et al . observations of the the circumnuclear environment of ngc 2110 have revealed peculiar kinematics and complex structure at all wavelengths ( ulvestad & wilson 1983 ; wilson et al . 1985 ; pogge 1989 ; haniff et al . 1991 ; mulchaey et al . 1994 ; ferruit et al . 1999 , 2004 ; quillen et al . 1999 ; gonzlez delgado et al . 2002 ; evans et al . 2006 ) as a result , ngc 2110 has emerged as an important laboratory for studying the interaction between an active nucleus and its surroundings . ngc 2110 has been frequently considered in the context of agn unification ( e.g. , antonucci 1993 ) . the presence of a hidden type 1 nucleus is implied by x - ray observations , which indicate heavy absorption of the soft x - ray spectrum and a seyfert 1-like intrinsic luminosity at hard x - ray energies ( mushotzky 1982 ; turner & pounds 1989 ; malaguti et al . similarly , if the extended narrow - line region is powered by photoionization from the nucleus , the morphology of this region and the strength of the balmer recombination lines relative to the observed ionizing flux would suggest that the nuclear continuum source is obscured from our view ( wilson et al.1985 ; mulchaey et al . yet despite a number of direct searches for broad emission lines in both the optical ( shuder 1980 ; veilleux 1991 ) and near - infrared ( veilleux et al . 1997 ; storchi - bergmann et al . 1999 ; knop et al . 2001 ; lutz et al . 2004 ) , conclusive evidence that ngc 2110 harbors a hidden broad - line region ( blr ) has been elusive . in this _ letter _ , we report the discovery of a spectacular broad h@xmath0 emission line in the polarized flux spectrum of this object . we observed ngc 2110 on 30 december 2005 ( ut ) with the lris spectropolarimeter ( cohen et al . 1997 ) on the keck i 10 m telescope . both beams of the instrument were employed in conjunction with the d560 dichroic beam splitter . on the blue side , a 400 l mm@xmath2 grism blazed at 3400 was used , providing coverage of the 32005700 range at @xmath3 resolution ( fwhm ) . the red side data , obtained with a 600 l mm@xmath2 grating blazed at 7500 , span 55207990 at @xmath1 4.5 resolution . a 900 s exposure was acquired at each of the four waveplate positions using a 10 slit , which was oriented at the mid - observation parallactic angle of 16@xmath4 . the observations were obtained under photometric conditions at an average airmass of 1.13 . we extracted one - dimensional spectra from the reduced images within a 315 region centered on the galaxy s nucleus . spectropolarimetric processing and measurements were performed following the methods described by miller et al . ( 1988 ) and barth et al . ( 1999 ) . because of the proximity of ngc 2110 to the galactic plane ( @xmath5 , @xmath6 = 0.375 mag ) , we explored whether transmission through galactic dust might affect the observed polarization . a search of the heiles ( 2000 ) catalog of stellar polarizations reveals two stars within @xmath7 of ngc 2110 with linear polarization data . the stars have nearly identical polarization levels and position angles ; using the average values of these ( @xmath8% , @xmath9 ) , we made synthetic @xmath10 and @xmath11 spectra assuming a serkowski et al . ( 1975 ) curve for @xmath12 . these were then subtracted from the normalized stokes parameters for ngc 2110 to correct the galaxy s polarization and position - angle spectra . as discussed below , these corrections prove to be relatively minor . our spectropolarimetry results are displayed in figure 1 . the total - flux spectrum of ngc 2110 ( _ top panel _ ) is clearly dominated by narrow emission lines . the small but significant amount of continuum polarization observed ( _ middle panel _ ) is approximately constant with wavelength , suggesting that it is caused by electron scattering . in the 52006200 range the polarization and polarization angle are @xmath13% and @xmath14 , respectively . after correction for interstellar effects , the value of @xmath15 is virtually unchanged , while the polarization angle rotates a modest amount to @xmath16 . the corrected value of @xmath17 is nearly orthogonal to the arcsecond - scale radio and optical emission - line structures observed along p.a . @xmath18 in ngc 2110 ( gonzlez delgado et al . 2002 , and references therein ) . this is consistent with expectations based on the unified agn model , whereby scattering of the nuclear continuum occurs along a direction parallel to the axis of the obscuring torus ( antonucci 1984 ) . a dramatic increase in polarization ( peaking at @xmath19% ) is observed on either side of the h@xmath0 + [ ] narrow - line blend in figure 1 . as a result , the polarized flux spectrum of ngc 2110 ( _ bottom panel _ ) exhibits an extremely broad , double - peaked h@xmath0 line . the full - width at zero - intensity of the broad h@xmath0 line is roughly @xmath20 km s@xmath2 . a similar feature is not observed at h@xmath21 , although the h@xmath21 line is broader ( @xmath22 km s@xmath2 fwhm ) than the forbidden lines in the polarized flux spectrum . previous studies have shown that the polarized h@xmath0 lines of hidden seyfert 1s can be asymmetric and broad ( e.g. , schmidt et al . 2002 ) , but because of the structure observed in its h@xmath0 profile , ngc 2110 is perhaps the most extreme example discovered to date . the broad h@xmath0 line shown in figure 1 closely resembles those exhibited by double - peaked emission - line agns , a small but important class of active nuclei ( eracleous & halpern 1994 , 2003 ; strateva et al . in fact , ngc 2110 s broad h@xmath0 profile is nearly identical to that of the prototypical double - peaked agn arp 102b ( cf . fig . 2 of halpern et al . an important secondary characteristic of double - peaked emitters is that they often display strong low - ionization forbidden lines , such as [ ] @xmath23 , [ ] @xmath24 , and [ ] @xmath25 . similar to many radio - selected double - peakers , the emission - line flux ratios in ngc 2110 suggest a liner classification ( heckman 1980 ; veilleux & osterbrock 1987 ) : log ( [ ] /h@xmath0 ) = 0.17 , log ( [ ] /h@xmath0 ) = @xmath260.23 , and log ( [ ] /h@xmath0 ) = 0.00 . the seyfert - like [ ] @xmath27/h@xmath21 flux ratio of @xmath28 in ngc 2110 is common among optically selected double - peaked emitters ( strateva et al . thus , on spectroscopic grounds , ngc 2110 appears to be a genuine double - peaked emission - line agn . this marks the first time that this type of object has been discovered via spectropolarimetry in a seyfert 2 galaxy . although at one time the origin of broad , double - peaked emission lines in agns was a matter of considerable debate ( see gaskell et al . 1999 ) , the prevailing interpretation today is that such lines are produced in blrs that have a disk geometry ( eracleous & halpern 2003 ) . we have thus fitted relativistic keplerian disk models to the h@xmath0 profile in the polarized flux spectrum of ngc 2110 . a circular disk model ( chen & halpern 1989 ) provides a rather poor fit , so we have instead fitted the line profile with an elliptical disk model ( following eracleous et al . 1995 ) under the assumption that the emissivity of the disk scales with radius as @xmath29 ( collin - souffrin & dumont 1989 ; eracleous & halpern 2003 ; strateva et al . as illustrated in figure 2 , this model provides a very good fit to the polarized h@xmath0 line profile . the best - fitting model is described by the following parameters : the inner and outer pericenter distances of the line - emitting portion of the disk ( in units of the gravitational radius , @xmath30 , where @xmath31 is the black - hole mass ) are @xmath32 and @xmath33 ; the inclination of the disk axis is @xmath34 ; the eccentricity of the disk is @xmath35 ; the orientation of the major axis relative to the line of sight ( see fig . 2 of eracleous et al . 1995 ) is @xmath36 ; and the broadening parameter ( representing turbulent motions in the line - emitting `` skin '' of the disk ) is @xmath37 . these parameters are consistent with those obtained for arp 102b by chen & halpern ( 1989 ) , i.e. , @xmath38 , @xmath39 , @xmath40 , and @xmath41 . ( note that because the broad h@xmath0 line in ngc 2110 is reflected , the angles @xmath42 and @xmath43 describe the orientation of the disk to the scattering medium , not the observer . ) the residuals of the fit , also shown in figure 2 , show a weak , broad , bell - shaped pedestal underlying the h@xmath0 + [ ] complex . such a kinematic component is also observed in the h@xmath0 and ly@xmath0 profiles of arp 102b ( it is in fact the dominant component of the ly@xmath0 line ; halpern et al . 1996 ) . based on a four - component gaussian fit to the h@xmath0 + [ ] lines in the residuals spectrum , we estimate the width of the bell - shaped broad component to be @xmath44 ( fwhm ) , similar to the widths of the ly@xmath0 and h@xmath0 lines of arp 102b ( halpern et al . 1996 ) . for a final comparison to other double - peaked agns , we have estimated the bolometric - to - eddington luminosity ratio @xmath45 of ngc 2110 . using the tremaine et al . ( 2002 ) @xmath46 relation , the observed stellar velocity dispersion of @xmath47 km s@xmath2 ( nelson & whittle 1995 ) indicates a black - hole mass of @xmath48 @xmath49 , which implies @xmath50 ergs s@xmath2 . the intrinsic 210 kev x - ray luminosity of @xmath51 ergs s@xmath2 ( malaguti et al . 1999 ) , combined with a bolometric correction factor of @xmath52 ( typical of radio - quiet quasars ; elvis et al . 1994 ) , yields @xmath53 ergs s@xmath2 . we note that the extinction - corrected [ ] @xmath27 luminosity of @xmath54 ergs s@xmath2 derived from our keck data , combined with a bolometric correction of @xmath55 ( heckman et al . 2004 ) , yields @xmath56 ergs s@xmath2 . thus , for ngc 2110 we estimate that @xmath57 . despite the rough numbers used here , this is in close agreement with the value of @xmath58 obtained by lewis & eracleous ( 2006 ) for arp 102b , which further strengthens the case that ngc 2110 is an obscured twin of arp 102b . close inspection of the top panel of figure 1 reveals that the blue peak of the broad h@xmath0 line is faintly visible in the total - flux spectrum of ngc 2110 . this is perhaps not too surprising , given the high polarization of the feature and the unconfused nature of the spectrum in its vicinity . to investigate whether the double - peaked line was present in previous years , we have combed the literature for published nuclear spectra of ngc 2110 . the most recent spectrum we were able to find was one obtained on 30 december 2000 ( ut ) with the stis instrument on board the _ hubble space telescope _ ( ferruit et al . 2004 ) , which we have retrieved from the _ hst _ archive . a total exposure of 4445 s was obtained using a 02 slit . our extraction of the spectrum covers a 5-pixel ( 025 ) region centered on the nucleus . before comparing the keck and stis data , we removed the continuum from each spectrum . to model the keck continuum , we combined a spiral galaxy bulge template ( that of m31 ) with a power - law component . the continuum in the stis spectrum , which contains little or no starlight because of the small effective aperture , was removed by subtracting a constant . we rescaled the continuum - subtracted stis spectrum to match the strength of the narrow h@xmath0 line in the keck spectrum . the results of our comparison are displayed in figure 3 . the narrow emission lines exhibit somewhat different velocity widths and flux ratios in the keck and stis data ; this is a reflection of density stratification in the narrow - line region of ngc 2110 ( e.g. , filippenko & halpern 1984 ) , which has been sampled by different apertures . the blue peak of the broad h@xmath0 line , clearly visible in the keck spectrum near 6425 , is completely absent in the high signal - to - noise ratio stis spectrum . given the lower amount of diluting starlight in the small 02 @xmath59 025 stis aperture , the blue peak would be at least as prominent in the stis spectrum if it were present . we conclude , therefore , that the double - peaked h@xmath0 line in the nucleus of ngc 2110 has appeared rather recently . moreover , additional spectropolarimetric observations in 2007 february by h. tran have shown that the line profile has varied significantly over an interval of 14 months . the transient nature of this feature and its subsequent variations are not without precendent ; the emergence of double - peaked lines has been noted in other agns ( e.g. , pictor a ; halpern & eracleous 1994 ; eracleous & halpern 1998 ) , and numerous other objects exhibit variability of the double - peaked line profile ( e.g. , storchi - bergmann et al . 1995 ; gezari et al . beginning with observations of ngc 1068 ( antonucci & miller 1985 ) , spectropolarimetry has played a crucial role in our understanding of the physical nature of agns , and it continues to provide valuable insight . our results establish that ngc 2110 possesses a disk - like blr , which expands the range of properties exhibited by seyfert 2s . in addition , ngc 2110 presents some opportunities for interesting follow - up study . as noted above , the double - peaked feature is transient and variable , and it would be worthwhile to monitor its behavior . the observed variations may trace changes in the structure of the blr or in the properties of the scattering medium . also , the similarity of ngc 2110 s broad h@xmath0 profile to that of arp 102b suggests that the line has not been distorted significantly in the scattering process . this has implications for the scattering geometry , e.g. , the scattering medium may only see the line - emitting disk over a narrow range of inclination angles . high - resolution imaging polarimetry and detailed spectropolarimetric modeling ( e.g. , smith et al . 2004 , 2005 ) would clarify this issue . in the bigger picture , by demonstrating that at least one double - peaked emitter contains the type of nuclear obscuration believed to be present in most ( if not all ) classical seyfert galaxies , we can now extend the concept of unification to the disk - emitting class of agns . on parsec scales , double - peaked agns may be structurally similar to other types of seyfert nuclei . if so , this underscores the need to understand how physical differences might originate in their broad - line regions . the data presented herein were obtained at the w. m. keck observatory , which is operated as a scientific partnership among the california institute of technology , the university of california , and nasa . the observatory was made possible by the generous financial support of the w. m. keck foundation . the work of a. j. b. was supported in part by the national science foundation through grant ast-0548198 . m. e. acknowledges the warm hospitality of the department of astrophysics at the american museum of natural history . antonucci , r. r. j. 1984 , apj , 278 , 499 antonucci , r. 1993 , , 31 , 473 antonucci , r. r. j. , & miller , j. s. 1985 , , 297 , 621 barth , a. j. , filippenko , a. v. , & moran , e. c. 1999 , , 525 , 673 bradt , h. v. , burke , b. f. , canizares , c. r. , greenfield , p. e. , kelley , r. l. , mcclintock , j. e. , koski , a. t. , & van paradijs , j. 1978 , , 226 , 111 chen , k. , & halpern , j. p. 1989 , , 344 , 115 cohen , m. h. , vermeulen , r. c. , ogle , p. m. , tran , h. d. , & goodrich , r. w. 1997 , , , 484 , 193 collin - souffrin , s. , & dumont , a. m. 1989 , , 213 , 29 elvis , m. , et al . 1994 , apjs , 95 , 1 eracleous , m. , & halpern , j. p. 1994 , , 90 , 1 eracleous , m. , & halpern , j. p. 1998 , , 505 , 577 eracleous , m. , & halpern , j. p. 2003 , , 599 , 886 eracleous , m. , livio , m. , halpern , j. p. , & storchi - bergmann , t. 1995 , apj , 438 , 610 evans , d. a. , lee , j. c. , kamenetska , m. , gallagher , s. c. , kraft , r. p. , hardcastle , m. j. , & weaver , k. a. 2006 , , 653 , 1121 ferruit , p. , mundell , c. g. , nagar , n. m. , emsellem , e. , pcontal , e. , wilson , a. s. , & schinnerer , e. 2004 , , 352 , 1180 ferruit , p. , wilson , a. s. , whittle , m. , simpson , c. , mulchaey , j. s. , & ferland , g. j. 1999 , , 523 , 147 filippenko , a. v. , & halpern , j. p. 1984 , , 285 , 475 gaskell , c. m. , brandt , w. n. , dietrich , m. , dultzin - hacyan , d. , & eracleous , m. 1999 , structure and kinematics of quasar broad line regions , asp conf . ser . , 175 ( san fransisco : asp ) gezari , s. , halpern , j. p. , & eracleous , m. 2007 , , 169 , 167 gonzlez delgado , r. m. , arribas , s. , perez , e. , & heckman , t. 2002 , , 579 , 188 halpern , j. p. , & eracleous , m. 1994 , , 433 , 17 halpern , j. p. , eracleous , m. , filippenko , a. v. , & chen , k. 1996 , , 464 , 704 haniff , c. a. , ward , m. j. , & wilson , a. s. 1991 , , 368 , 167 hayashi , i. , koyama , k. , awaki , h. , & yamauchi , s. 1996 , , 48 , 219 heckman , t. m. 1980 , a&a , 87 , 152 heckman , t. m. , kauffmann , g. , brinchmann , j. , charlot , s. , tremonti , c. , & white , s. d. m. 2004 , apj , 613 , 109 heiles , c. 2000 , , 119 , 939 knop , r. a. , armus , l. , matthews , k. , murphy , t. w. , & soifer , b. t. 2001 , , 122 , 764 lewis , k. t. , & eracleous , m. 2006 , , 642 , 711 lutz , d. , maiolino , r. , moorwood , a. f. m. , netzer , h. , wagner , s. j. , sturm , e. , & genzel , r. 2002 , , 396 , 439 malaguti , g. , et al . 1999 , , 342 , l41 mcclintock , j. e. , remillard , r. a. , canizares , c. r. , veron , p. , & van paradijs , j. 1979 , , 233 , 809 miller , j. s. , robinson , l. b. , & goodrich , r. w. 1988 , in instrumentation for ground - based astronomy , ed . l. b. robinson ( new york : springer ) , 157 mulchaey , j. s. , wilson , a. s. , bower , g. a. , heckman , t. m. , krolik , j. h. , miley , g. k. 1994 , , 433 , 625 mushotsky , r. f. 1982 , , 256 , 92 nelson , c. h. , & whittle , m. 1995 , apjs , 99 , 67 pogge , r. w. 1989 , , 345 , 730 quillen , a. c. , alonso - herrero , a. , rieke , m. j. , mcdonald , c. , falcke , h. , & rieke , g. h. 1999 , , 525 , 685 schmidt , g. d. , smith , p. s. , foltz , c. b. , & hines , d. c. 2002 , , 578 , l99 serkowski , k. , mathewson , d. l. , & ford , v. l. 1975 , , 196 , 261 shuder , j. m. 1980 , , 240 , 32 smith , j. e. , robinson , a. , alexander , d. m. , young , s. , axon , d. j. , & corbett , e. a. 2004 , , 350 , 140 smith , j. e. , robinson , a. , young , s. , axon , d. j. , & corbett , e. a. 2005 , , 359 , 846 storchi - bergmann , t. , eracleous , m. , livio , m. , wilson , a. s. , filippenko , a. v. , & halpern , j. p. 1995 , , 443 , 617 storchi - bergmann , t. , winge , c. , ward , m. j. , & wilson , a. s. 1999 , , 304 , 35 strateva , i. v. , et al . 2003 , , 126 , 1720 strateva , i. v. , brandt , w. n. , eracleous , m. , schneider , d. p. , & chartas , g. 2006 , , 651 , 749 tremaine , s. , et al . 2002 , apj , 574 , 740 turner , t. j. , & pounds , k. a. 1989 , , 240 , 833 ulvestad , j. s. , & wilson , a. s. 1983 , , 264 , l7 veilleux , s. 1991 , 369 , 331 veilleux , s. , goodrich , r. w. , & hill , g. j. 1997 , , 477 , 631 veilleux , s. , & osterbrock , d. e. 1987 , apjs , 63 , 295 weaver , k. a. , mushotzky , r. f. , serlemitsos , p. j. , wilson , a. s. , elvis , m. , & briel , u. 1995 , , 442 , 597 wilson , a. s. , baldwin , j. a. , & ulvestad , j. s. 1985 , , 291 , 627 erg @xmath60 s@xmath2 @xmath2 . _ middle _ : degree of linear polarization , given as the rotated stokes parameter . _ bottom _ : polarized flux , or `` stokes flux , '' which is the product of the total flux and rotated stokes parameter.,title="fig:",scaledwidth=75.0% ] 0.1truein[/INST] we have discovered an extremely broad , double - peaked h@xmath0 emission line in the polarized flux spectrum of ngc 2110 , establishing that this well - studied seyfert 2 galaxy contains a disk - like hidden broad - line region ( blr ) . several properties of ngc 2110 suggest that it is an obscured twin of arp 102b , the prototypical double - peaked emission - line active galactic nucleus ( agn ) . a comparison between our data and previous spectra of ngc 2110 indicates that the double - peaked h@xmath0 feature is transient . the presence of a disk - like blr in ngc 2110 has important implications for agns : it expands the range of properties exhibited by seyfert 2 galaxies , and the fact that the blr is obscured by a torus - like structure provides the first evidence that double - peaked emitters and classical seyfert nuclei may have the same basic parsec - scale geometry . </s>

the transmission risk of foot - and - mouth disease ( fmd ) in japan was evaluated using a mathematical fmd transmission model . the distance - based transmission rate between farms , which was parameterized using the fmd epidemic data in 2010 in japan , was used to calculate the local - level reproduction numbers expected numbers of secondary infections caused by one infected farm for all cattle and pig farms in the country , which were then visualized as a risk map . the risk map demonstrated the spatial heterogeneity of transmission risk in the country and identified risk areas with higher possibility of disease spread . this result suggests that , particularly in high - risk areas , it is important to prepare for the smooth and efficient implementation of control measures against fmd outbreaks .

<s>[INST]None[/INST]the transmission risk of foot - and - mouth disease ( fmd ) in japan was evaluated using a mathematical fmd transmission model . the distance - based transmission rate between farms , which was parameterized using the fmd epidemic data in 2010 in japan , was used to calculate the local - level reproduction numbers expected numbers of secondary infections caused by one infected farm for all cattle and pig farms in the country , which were then visualized as a risk map . the risk map demonstrated the spatial heterogeneity of transmission risk in the country and identified risk areas with higher possibility of disease spread . this result suggests that , particularly in high - risk areas , it is important to prepare for the smooth and efficient implementation of control measures against fmd outbreaks .</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Forbidding Advertisement Through Child Exploitation Act of 2013'', or the ``FACE Act of 2013''. SEC. 2. PROHIBITION ON COMMERCIAL USE BY SOCIAL MEDIA SERVICES OF UPLOADED SELF-IMAGES OF MINORS. (a) In General.--A provider of a social media service may not intentionally or knowingly use for a commercial purpose a self-image uploaded to such service by a minor. (b) Regulations.--The Federal Trade Commission may promulgate regulations under section 553 of title 5, United States Code, to implement this section. SEC. 3. APPLICATION AND ENFORCEMENT. (a) General Application.--The requirements of section 2 and the regulations promulgated under such section apply, according to their terms, to those persons, partnerships, and corporations over which the Federal Trade Commission has authority pursuant to section 5(a)(2) of the Federal Trade Commission Act (15 U.S.C. 45(a)(2)). (b) Enforcement by Federal Trade Commission.-- (1) Unfair or deceptive acts or practices.--A violation of section 2 or a regulation promulgated under such section shall be treated as an unfair or deceptive act or practice in violation of a regulation under section 18(a)(1)(B) of the Federal Trade Commission Act (15 U.S.C. 57a(a)(1)(B)) regarding unfair or deceptive acts or practices. (2) Powers of commission.--The Federal Trade Commission shall enforce section 2 and the regulations promulgated under such section in the same manner, by the same means, and with the same jurisdiction, powers, and duties as though all applicable terms and provisions of the Federal Trade Commission Act (15 U.S.C. 41 et seq.) were incorporated into and made a part of this Act. Any person who violates section 2 or a regulation promulgated under such section shall be subject to the penalties and entitled to the privileges and immunities provided in the Federal Trade Commission Act. (c) Enforcement by State Attorneys General.-- (1) In general.--In any case in which the attorney general of a State, or an official or agency of a State, has reason to believe that an interest of the residents of such State has been or is threatened or adversely affected by an act or practice in violation of section 2 or a regulation promulgated under such section, the State, as parens patriae, may bring a civil action on behalf of the residents of the State in an appropriate State court or an appropriate district court of the United States to-- (A) enjoin such act or practice; (B) enforce compliance with such section or such regulation; (C) obtain damages, restitution, or other compensation on behalf of residents of the State; or (D) obtain such other legal and equitable relief as the court may consider to be appropriate. (2) Notice.--Before filing an action under this subsection, the attorney general, official, or agency of the State involved shall provide to the Federal Trade Commission a written notice of such action and a copy of the complaint for such action. If the attorney general, official, or agency determines that it is not feasible to provide the notice described in this paragraph before the filing of the action, the attorney general, official, or agency shall provide written notice of the action and a copy of the complaint to the Federal Trade Commission immediately upon the filing of the action. (3) Authority of federal trade commission.--On receiving notice under paragraph (2) of an action under this subsection, the Federal Trade Commission shall have the right-- (A) to intervene in the action; (B) upon so intervening, to be heard on all matters arising therein; and (C) to file petitions for appeal. (4) Rule of construction.--For purposes of bringing a civil action under this subsection, nothing in this Act shall be construed to prevent an attorney general, official, or agency of a State from exercising the powers conferred on the attorney general, official, or agency by the laws of such State to conduct investigations, administer oaths and affirmations, or compel the attendance of witnesses or the production of documentary and other evidence. SEC. 4. EFFECT ON STATE LAW. Nothing in this Act preempts any provision of law of a State or a political subdivision of a State that is more protective with respect to commercial use of self-images uploaded by minors to social media services. SEC. 5. DEFINITIONS. In this Act: (1) Self-image.--The term ``self-image'' means, with respect to an individual, an image that depicts the individual. (2) Social media service.--The term ``social media service'' means any online service that allows an individual to upload, store, and manage personal content in order to share the content with other individuals. SEC. 6. EFFECTIVE DATE. This Act shall take effect on the date that is 6 months after the date of the enactment of this Act.

Forbidding Advertisement Through Child Exploitation Act of 2013 or the FACE Act of 2013 - Prohibits social media service providers from intentionally or knowingly using for a commercial purpose a self-image uploaded by a minor. Defines &quot;social media service&quot; as any online service that allows an individual to upload, store, and manage personal content to share with other individuals. Requires violations to be treated as an unfair or deceptive act or practice under the Federal Trade Commission Act. Sets forth the enforcement authority of the Federal Trade Commission (FTC) and state attorneys general.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Forbidding Advertisement Through Child Exploitation Act of 2013'', or the ``FACE Act of 2013''. SEC. 2. PROHIBITION ON COMMERCIAL USE BY SOCIAL MEDIA SERVICES OF UPLOADED SELF-IMAGES OF MINORS. (a) In General.--A provider of a social media service may not intentionally or knowingly use for a commercial purpose a self-image uploaded to such service by a minor. (b) Regulations.--The Federal Trade Commission may promulgate regulations under section 553 of title 5, United States Code, to implement this section. SEC. 3. APPLICATION AND ENFORCEMENT. (a) General Application.--The requirements of section 2 and the regulations promulgated under such section apply, according to their terms, to those persons, partnerships, and corporations over which the Federal Trade Commission has authority pursuant to section 5(a)(2) of the Federal Trade Commission Act (15 U.S.C. 45(a)(2)). (b) Enforcement by Federal Trade Commission.-- (1) Unfair or deceptive acts or practices.--A violation of section 2 or a regulation promulgated under such section shall be treated as an unfair or deceptive act or practice in violation of a regulation under section 18(a)(1)(B) of the Federal Trade Commission Act (15 U.S.C. 57a(a)(1)(B)) regarding unfair or deceptive acts or practices. (2) Powers of commission.--The Federal Trade Commission shall enforce section 2 and the regulations promulgated under such section in the same manner, by the same means, and with the same jurisdiction, powers, and duties as though all applicable terms and provisions of the Federal Trade Commission Act (15 U.S.C. 41 et seq.) were incorporated into and made a part of this Act. Any person who violates section 2 or a regulation promulgated under such section shall be subject to the penalties and entitled to the privileges and immunities provided in the Federal Trade Commission Act. (c) Enforcement by State Attorneys General.-- (1) In general.--In any case in which the attorney general of a State, or an official or agency of a State, has reason to believe that an interest of the residents of such State has been or is threatened or adversely affected by an act or practice in violation of section 2 or a regulation promulgated under such section, the State, as parens patriae, may bring a civil action on behalf of the residents of the State in an appropriate State court or an appropriate district court of the United States to-- (A) enjoin such act or practice; (B) enforce compliance with such section or such regulation; (C) obtain damages, restitution, or other compensation on behalf of residents of the State; or (D) obtain such other legal and equitable relief as the court may consider to be appropriate. (2) Notice.--Before filing an action under this subsection, the attorney general, official, or agency of the State involved shall provide to the Federal Trade Commission a written notice of such action and a copy of the complaint for such action. If the attorney general, official, or agency determines that it is not feasible to provide the notice described in this paragraph before the filing of the action, the attorney general, official, or agency shall provide written notice of the action and a copy of the complaint to the Federal Trade Commission immediately upon the filing of the action. (3) Authority of federal trade commission.--On receiving notice under paragraph (2) of an action under this subsection, the Federal Trade Commission shall have the right-- (A) to intervene in the action; (B) upon so intervening, to be heard on all matters arising therein; and (C) to file petitions for appeal. (4) Rule of construction.--For purposes of bringing a civil action under this subsection, nothing in this Act shall be construed to prevent an attorney general, official, or agency of a State from exercising the powers conferred on the attorney general, official, or agency by the laws of such State to conduct investigations, administer oaths and affirmations, or compel the attendance of witnesses or the production of documentary and other evidence. SEC. 4. EFFECT ON STATE LAW. Nothing in this Act preempts any provision of law of a State or a political subdivision of a State that is more protective with respect to commercial use of self-images uploaded by minors to social media services. SEC. 5. DEFINITIONS. In this Act: (1) Self-image.--The term ``self-image'' means, with respect to an individual, an image that depicts the individual. (2) Social media service.--The term ``social media service'' means any online service that allows an individual to upload, store, and manage personal content in order to share the content with other individuals. SEC. 6. EFFECTIVE DATE. This Act shall take effect on the date that is 6 months after the date of the enactment of this Act.[/INST]Forbidding Advertisement Through Child Exploitation Act of 2013 or the FACE Act of 2013 - Prohibits social media service providers from intentionally or knowingly using for a commercial purpose a self-image uploaded by a minor. Defines &quot;social media service&quot; as any online service that allows an individual to upload, store, and manage personal content to share with other individuals. Requires violations to be treated as an unfair or deceptive act or practice under the Federal Trade Commission Act. Sets forth the enforcement authority of the Federal Trade Commission (FTC) and state attorneys general.</s>

the nemo 3 has been taking data since 2003 in the modane underground laboratory located in the frejus tunnel at the depth of 4800 m w.e . its method of @xmath5-decay study is based on the detection of the electron tracks in a tracking device and the energy measurement in a calorimeter . the detector @xcite has a cylindrical shape . thin source foils ( @xmath6 ) are located in the middle of the tracking volume surrounded by the calorimeter . almost 10 kg of enriched @xmath5 isotopes ( listed in table [ tab : t12 ] ) were used to produce the source foils . the tracking chamber contains 6180 open drift cells operating in the geiger mode . it provides a vertex resolution of about 1 cm . the calorimeter consists of 1940 plastic scintillator blocks with photomultiplier readout . the energy resolution is 14 - 17%/@xmath7 fwhm . the time resolution of 250 ps allows excellect suppression of the crossing electron background . a 25 g magnetic field is used for charge identification . the detector is capable of identifying e@xmath8 , e@xmath9 , @xmath10 and @xmath11 particles and allows good discrimination between signal and background events . measurements of the @xmath13 decay half - lives were performed for 7 isotopes available in nemo 3 ( see table [ tab : t12 ] ) . new preliminary results based on higher statistics than previously are presented here for two of these isotopes : @xmath14 and @xmath15 . .nemo 3 results of half - life measurement.[tab : t12 ] [ cols="^,^,^,^,^",options="header " , ] a possible design for the supernemo detector @xcite could be planar and modular : the 100 kg of enriched isotopes could be placed in 20 modules each containing 5 kg of isotopes . each source could have a thickness of 40 @xmath16 and a surface of 4 x 3 @xmath17 . for each module , the tracking device could be a drift chamber made of around 3000 cells , operating in geiger mode . for each module , the calorimeter could either be made of around 1000 scintillators blocks coupled to low - radioactivity pmts , or of scintillators bars , coupled to around 100 pmts ( see figure [ module ] ) . the best sensitivity for the high - purity germanium detectors used for nemo-3 is 60 @xmath18bq / kg for @xmath19 and 200 @xmath18bq / kg for @xmath20 . the goal of the r@xmath4d phase is to improve the sensitivity by developping 800 @xmath21 high purity germaniun ( with canberra - eurisys ) with shields improvment and a new ultra - pure cryostat . a new planar germanium detector with a resolution of 0.5 kev at 40 kev is also in development . the bipo detector @xcite has been developped to measure the radiopurity in @xmath19 and in @xmath20 of the source foils before their installation in the supernemo detector . the goal is to measure 5 kg of foils in 1 month with a sensitivity of 2 @xmath18bq / kg in @xmath19 and of 10 @xmath18bq / kg in @xmath20 . the principle is to tag the electron emitted by the beta desintegration of @xmath22 or of @xmath20 , then to tag the alpha emitted by the desintegration of @xmath23 or of @xmath24 ( with a decay half - time of 300 ns or of 164 @xmath18s ) . the thin source can be put in a sandwich of scintillators . for the measurement of the source contained in one module of the supernemo detector ( 12 @xmath17 ) , the background has to be very low , less than 1 event per month . already , a prototype using 20 cm x 20 cm x 3 mm plastic scintillators has been developped and installed in the frejus underground laboratory ; with the measured background , the expected sensitivity extrapolated for the full bipo detector is of the order of 5 @xmath18bq / kg in @xmath19 . the goal of the calorimeter r@xmath4d is to reach a fwhm energy resolution of 4@xmath25 for 3 mev electrons ( 7@xmath25 for 1 mev electrons ) and to optimize the number of channels and the detector geometry . the goal of the r@xmath4d for scintillators is to improve the light yield and the homogeneity . plastic scintillators are developped in collaboration with kharkhov and dubna , trying to improve the performances of polystyrene and to develop polyvinylxylene . already , a fwhm of ( 8.2 @xmath26 0.1 ) @xmath25 for 1 mev electrons has been obtained for 10 cm thick plastic scintillator coupled to a @xmath27 pmt . tests with different wrappings of the scintillators are also proceeded in kharkhov . liquid scintillators are also studied : their advantages are the high light yield , the very good uniformity and transparency ; the challenge is to satisfy the mechanical constraints , especially for the entrance window , which has to be as thin as possible , in order not to degrade the electron energy . the aim of the r@xmath4d for pmts is to improve the quantum efficiency , the collection efficiency and to develop low radioactivity pmts : an agreement between photonis and in2p3 has been signed , tests are also done with hamamatsu and etl . already , pmts with very high quantum efficiencies ( 43@xmath25 for 3 inches and 35@xmath25 for 8 inches ) have been developped . slow and fast pmts are also studied . the goal is also to have a higher compacity by reducing the number of channels , without reducing too much the light collection . the energy measurement with scintillator bars with 2 pmts or with optical fibers is also studied . the bipo detector for ultralow radioactivity measurements , m. bongrand ( on behalf of the supernemo collaboration ) , topical workshop on low radioactivity techniques , lrt 2006 , aussois , france , 1 - 4 october 2006

the nemo experiment is investigating the neutrinoless double beta decay . the nemo-3 detector is taking data in the frejus underground laboratory . the goal of the supernemo detector is to reach a sensitivity on the order of @xmath0 year on the half - life of the @xmath1 process . the chosen isotopes for the future detector are @xmath2 and @xmath3 , because of the reduced background . the collaboration has started a 3-year r@xmath4d developpement on all components : tracking detector , calorimeter , source enrichment and purification , radiopurity measurements .

<s>[INST]the nemo 3 has been taking data since 2003 in the modane underground laboratory located in the frejus tunnel at the depth of 4800 m w.e . its method of @xmath5-decay study is based on the detection of the electron tracks in a tracking device and the energy measurement in a calorimeter . the detector @xcite has a cylindrical shape . thin source foils ( @xmath6 ) are located in the middle of the tracking volume surrounded by the calorimeter . almost 10 kg of enriched @xmath5 isotopes ( listed in table [ tab : t12 ] ) were used to produce the source foils . the tracking chamber contains 6180 open drift cells operating in the geiger mode . it provides a vertex resolution of about 1 cm . the calorimeter consists of 1940 plastic scintillator blocks with photomultiplier readout . the energy resolution is 14 - 17%/@xmath7 fwhm . the time resolution of 250 ps allows excellect suppression of the crossing electron background . a 25 g magnetic field is used for charge identification . the detector is capable of identifying e@xmath8 , e@xmath9 , @xmath10 and @xmath11 particles and allows good discrimination between signal and background events . measurements of the @xmath13 decay half - lives were performed for 7 isotopes available in nemo 3 ( see table [ tab : t12 ] ) . new preliminary results based on higher statistics than previously are presented here for two of these isotopes : @xmath14 and @xmath15 . .nemo 3 results of half - life measurement.[tab : t12 ] [ cols="^,^,^,^,^",options="header " , ] a possible design for the supernemo detector @xcite could be planar and modular : the 100 kg of enriched isotopes could be placed in 20 modules each containing 5 kg of isotopes . each source could have a thickness of 40 @xmath16 and a surface of 4 x 3 @xmath17 . for each module , the tracking device could be a drift chamber made of around 3000 cells , operating in geiger mode . for each module , the calorimeter could either be made of around 1000 scintillators blocks coupled to low - radioactivity pmts , or of scintillators bars , coupled to around 100 pmts ( see figure [ module ] ) . the best sensitivity for the high - purity germanium detectors used for nemo-3 is 60 @xmath18bq / kg for @xmath19 and 200 @xmath18bq / kg for @xmath20 . the goal of the r@xmath4d phase is to improve the sensitivity by developping 800 @xmath21 high purity germaniun ( with canberra - eurisys ) with shields improvment and a new ultra - pure cryostat . a new planar germanium detector with a resolution of 0.5 kev at 40 kev is also in development . the bipo detector @xcite has been developped to measure the radiopurity in @xmath19 and in @xmath20 of the source foils before their installation in the supernemo detector . the goal is to measure 5 kg of foils in 1 month with a sensitivity of 2 @xmath18bq / kg in @xmath19 and of 10 @xmath18bq / kg in @xmath20 . the principle is to tag the electron emitted by the beta desintegration of @xmath22 or of @xmath20 , then to tag the alpha emitted by the desintegration of @xmath23 or of @xmath24 ( with a decay half - time of 300 ns or of 164 @xmath18s ) . the thin source can be put in a sandwich of scintillators . for the measurement of the source contained in one module of the supernemo detector ( 12 @xmath17 ) , the background has to be very low , less than 1 event per month . already , a prototype using 20 cm x 20 cm x 3 mm plastic scintillators has been developped and installed in the frejus underground laboratory ; with the measured background , the expected sensitivity extrapolated for the full bipo detector is of the order of 5 @xmath18bq / kg in @xmath19 . the goal of the calorimeter r@xmath4d is to reach a fwhm energy resolution of 4@xmath25 for 3 mev electrons ( 7@xmath25 for 1 mev electrons ) and to optimize the number of channels and the detector geometry . the goal of the r@xmath4d for scintillators is to improve the light yield and the homogeneity . plastic scintillators are developped in collaboration with kharkhov and dubna , trying to improve the performances of polystyrene and to develop polyvinylxylene . already , a fwhm of ( 8.2 @xmath26 0.1 ) @xmath25 for 1 mev electrons has been obtained for 10 cm thick plastic scintillator coupled to a @xmath27 pmt . tests with different wrappings of the scintillators are also proceeded in kharkhov . liquid scintillators are also studied : their advantages are the high light yield , the very good uniformity and transparency ; the challenge is to satisfy the mechanical constraints , especially for the entrance window , which has to be as thin as possible , in order not to degrade the electron energy . the aim of the r@xmath4d for pmts is to improve the quantum efficiency , the collection efficiency and to develop low radioactivity pmts : an agreement between photonis and in2p3 has been signed , tests are also done with hamamatsu and etl . already , pmts with very high quantum efficiencies ( 43@xmath25 for 3 inches and 35@xmath25 for 8 inches ) have been developped . slow and fast pmts are also studied . the goal is also to have a higher compacity by reducing the number of channels , without reducing too much the light collection . the energy measurement with scintillator bars with 2 pmts or with optical fibers is also studied . the bipo detector for ultralow radioactivity measurements , m. bongrand ( on behalf of the supernemo collaboration ) , topical workshop on low radioactivity techniques , lrt 2006 , aussois , france , 1 - 4 october 2006[/INST] the nemo experiment is investigating the neutrinoless double beta decay . the nemo-3 detector is taking data in the frejus underground laboratory . the goal of the supernemo detector is to reach a sensitivity on the order of @xmath0 year on the half - life of the @xmath1 process . the chosen isotopes for the future detector are @xmath2 and @xmath3 , because of the reduced background . the collaboration has started a 3-year r@xmath4d developpement on all components : tracking detector , calorimeter , source enrichment and purification , radiopurity measurements . </s>

it is generally assumed that our galaxy is embedded in a halo of dark matter particles ( wimps ) with energy density @xmath1 gev/@xmath2 and velocities distributed according to a maxwellian distribution with parameter @xmath3 ( defined as @xmath4 ) and cut - off velocity equal to the escape velocity in the galaxy ( @xmath5 km / s ) . the recoil spectrum produced by wimp - nucleus scattering in a target detector is expected to show the so - called annual modulation effect , due to the earth s motion around the sun @xcite . along the year , the earth s velocity with respect to the galactic reference frame ( @xmath6 ) varies according to a cosinus law . it is customary to express the earth s velocity in units of the parameter @xmath3 defined above . the adimensional quantity @xmath7 shows the following time - dependence : @xmath8 where the amplitude of the modulated component ( @xmath9 is small compared to the annual average @xmath10 . the period and phase of the cosinus function are known to be @xmath11/t ( t= 1 year ) and @xmath12 june . in this framework , the expected countrate of wimp interactions can be written ( first order taylor approximation ) : @xmath13 where @xmath14 $ ] is the time - independent part and @xmath15 is the amplitude of the modulated signal . both @xmath16 and @xmath17 depend on the wimp mass @xmath18 and on the wimp cross section on proton @xmath19 , as well as on many astrophysical parameters ( @xmath3 , @xmath20 , @xmath21 ) and some properties of the target material . a calculation of the expected count rate r from wimp interactions in a germanium detector as a function of the recoil energy @xmath22 can be performed following the formula given in ref.@xcite : @xmath23 where : @xmath24 and the variables @xmath25 , @xmath26 and @xmath27 are listed in table [ tab1 ] together with the values of the parameters used in the calculation . the wimp cross section on germanium @xmath28 can be easily related to the correspondant cross section on proton ; in the case of spin - independent interaction ( si ) , the conversion formula is ( see @xcite and @xcite ) : @xmath29 where @xmath30 is the reduced mass and @xmath31 . .relevant astrophysical and detector parameters : their expressions and the values used in the present work . [ cols="^,^,^,^ " , ] the distribution of @xmath32 for the modulated data - set shows no substantial variation when we move the left limit of the energy interval where we integrate the signal ( @xmath33 ) from 4 kev to 8 kev . increasing @xmath33 above 8 kev , the mean value of the distribution slowly decreases ; this is an indication that we are missing part of the signal that , as we recall here , is concentrated in the lower energy bins . for this reason is of primary importance to have a low experimental threshold . we have repeated the same simulation for different wimp masses and the same cross section ; in tab . ( [ tab2 ] ) we report , for different measuring times , the mean value of the @xmath32 distribution ( for the modulated data - set ) together with the corresponding confidence level @xmath34 . calculating the value of the above mentioned estimators @xmath32 and @xmath35 is not the only way to discover the modulation hidden in the data . given our set of experimental data , we can try to extract directly the value of @xmath17 , the amplitude of the modulated signal , as a function of the energy . following @xcite , we can write : @xmath36 ^ 2 s_i}}{n } \end{aligned}\ ] ] where n is the running time of the experiment and @xmath37 is no more integrated over a broad energy region but in small energy bins ( 1 or 2 kev ) . in this way it is possible to measure the amplitude of the modulated signal and its error for each energy bin ( of the given size ) and moreover , taking small energy bins we avoid the problem of the cross - over energy . in picture ( [ sm_picture ] ) we report a tipical result for the amplitude of the modulated signal @xmath17 as calculated using ( [ sm ] ) on the simulated data without and with modulation ( @xmath18 = 40 gev and @xmath38 pb ) . the energy region between 4 and 50 kev has been divided in 2 kev energy bins and for each one the value of @xmath17 and the corresponding error have been calculated . by looking at the two pictures ( note the different scales on the @xmath39 axis ) , we see how the distribution b represents an indication of an annual modulation amplitude @xmath40 . in the case with modulation ( b ) all the data points are compatible within the error with the theoretical signal while in the case where no modulation is present ( a ) the same points are distributed around zero . the big errors are due to the low statistic and become smaller if we increase the measuring time . averaging the signal in the region from 4 to 16 kev , we obtain in the case of modulation : @xmath41 counts / kev day , while in the case of no modulation we have : @xmath42 counts / kev day , compatible with the hypothesis @xmath43 . one of the general procedures to treat experimental data when searching for the annual modulation effect is to use the maximum - likelihood method . the likelihood function @xmath44 for a set of experimental rates @xmath45 , assuming that they are poisson - distributed , is : @xmath46 since @xmath47 depends on the parameters of interest @xmath18 and @xmath48 , through the expressions of @xmath49 and @xmath50 , it is possible to obtain the best - fit value for the parameters minimizing @xmath51 , or better the function : @xmath52 where the constant contains the components that do not depend on @xmath18 and @xmath48 . the minimization of @xmath53 is not an easy operation : if we want to keep as a free parameter the number of background counts in each energy bin ( and here we consider as background the number of counts due to the time - independent component of the signal ( @xmath16 + @xmath54 ) ) we have to deal with many parameters . the usual procedure is to carry out the minimization in two steps . as a first step we minimize with respect to the time - independent component @xmath55 . during this minimization the condition @xmath56 , @xmath57 is imposed . as a second step we minimize with respect to @xmath48 and @xmath18 requiring , as is usual done : @xmath58 we did not impose limits or conditions on the parameters @xmath48 and @xmath18 except that both have to be greater than zero . we have carried out the minimization procedure on the data set simulated under the mentioned hypothesis @xmath18 = 40 gev and @xmath38 pb , in the energy range from 5 to 40 gev . after the first step we obtain the values of the quantity @xmath55 for each energy bin : we have plotted that result in fig . ( [ f_k ] ) and this reproduces exactly the curve @xmath59 that we have used in the simulation . in the second step we obtain the best - fit values for the parameters of interest . the minimization procedure converged for the selected energy window , giving the following best - fit values for the fit parameters : @xmath60 the value of the wimp mass is in excellent agreement with the real one used in the sumulation ; the value of the cross section , though compatible within 1 @xmath61 with the true value , shows a lower agreement : this can be due to the fact that @xmath18 influences the shape of the wimp spectrum while @xmath48 appears only as a multiplying factor . we repeated the fitting procedure assuming different values of the energy threshold of the experiment ( 3 and 4 kev ) , finding very little difference from the given best - fit . the set of best - fit values ( [ best - fit ] ) corresponds to the 2 @xmath61 allowed region shown in fig . ( [ region ] ) . this region of the plane @xmath62 has been calculated using : @xmath63 with @xmath64 and @xmath65 being the result of the fitting procedure . [ region ] should be interpreted in this way : if a wimp exists with the properties assumed so far , we can point out its presence within two years of measurement ( 80 kg y significance ) and give the result in fig . [ region ] for the 2 @xmath61 allowed region for the relevant parameters . the annual modulation , due to the motion of the earth with respect to the galactic halo , is the main signature of a possible wimp signal . the effect is supposed to be small , only a few percent of the total dark matter signal , and therefore very difficult to extract . a positive indication of this modulation has been found over the past five years by the dama experiment and it would be of great importance to look for the same effect with another experiment , expecially in the region of the wimp parameter s space indicated by the dama results . the genius - tf experiment @xcite , born as a prototype for the genius project , is at present under installation at the gran sasso national laboratory . with a mass of 40 kg and a background of 4 counts/(kg y kev ) , genius - tf can be used to look for dark matter , not only through the direct detection of wimp - induced nuclear recoils , but also through the annual modulation of the experimental rate . genius - tf will be - in addition to dama @xcite - the _ only _ experiment which will be able to probe the annual modulation signature in a foreseeable future . the at present much discussed cryo detector experiments , such as cdms @xcite , cresst @xcite , edelweiss @xcite have no chance to do this because the mass projected to be in operation in these experiments is by far too low ( see also @xcite ) . we have developed a set of routines and tools to look for the annual modulation effect with our genius - tf experiment using different analysis methods discussed in the literature . we have analysed data simulated under the hypothesis of modulation , using three different approaches ( modulation significance , direct calculation of the modulation amplitude @xmath66 and maximum likelihood fit of the data ) and we have shown that the mass and the low background level of genius - tf will allow us test , within few years of measurements , low wimp masses and wimp cross sections in the region of interest indicated by the dama experiment . a digital multi - channel spectroscopy system with 100mhz flash adc s for the genius - tf project has been recently developed @xcite . klapdor - kleingrothaus , j. hellmig and m hirsch , j.phys.g : nucl . ( 1998 ) 483 - 516 ; h.v . klapdor - kleingrothaus , l. baudis , g. heusser , b. majorovits and h. ps , `` genius : a supersensitive germanium detector system for rare events '' , proposal mpi - h - v26 - 1999 , hep - ph/9910205 and in proceedings of the second international conference on particle physics beyond the standard model , beyond the desert 1999 , castle ringberg , germany 6 - 12 june 1999 , ed . klapdor - kleingrothaus , i. krivosheina ( iop bristol 2000 ) , 915 . r. bernabei et al . , in _ proc . of intern . conf . on physics beyond the standard model : beyond the desert 02 , beyond02 _ , oulu , finland , 2 - 7 jun 2002 , _ iop , bristol _ , 2003 , ed . klapdor - kleingrothaus .

the annual modulation of the recoil spectrum observed in an underground detector is well known as the main signature of a possible wimp signal . the genius - tf experiment , under construction in the gran sasso national laboratory , can search for the annual modulation of the dark matter signal using 40 kg of naked - ge detectors in liquid nitrogen . starting from a set of data simulated under the hypothesis of modulation and using different methods , we show the potential of genius - tf for extracting the modulated signal and the expected wimp mass and wimp cross section . + prof . dr . h.v . klapdor - kleingrothaus + max - planck - institut fr kernphysik + saupfercheckweg 1 + d-69117 heidelberg + germany + phone office : + 49-(0)6221 - 516 - 262 + fax : + 49-(0)6221 - 516 - 540 + email : @xmath0 +

<s>[INST]it is generally assumed that our galaxy is embedded in a halo of dark matter particles ( wimps ) with energy density @xmath1 gev/@xmath2 and velocities distributed according to a maxwellian distribution with parameter @xmath3 ( defined as @xmath4 ) and cut - off velocity equal to the escape velocity in the galaxy ( @xmath5 km / s ) . the recoil spectrum produced by wimp - nucleus scattering in a target detector is expected to show the so - called annual modulation effect , due to the earth s motion around the sun @xcite . along the year , the earth s velocity with respect to the galactic reference frame ( @xmath6 ) varies according to a cosinus law . it is customary to express the earth s velocity in units of the parameter @xmath3 defined above . the adimensional quantity @xmath7 shows the following time - dependence : @xmath8 where the amplitude of the modulated component ( @xmath9 is small compared to the annual average @xmath10 . the period and phase of the cosinus function are known to be @xmath11/t ( t= 1 year ) and @xmath12 june . in this framework , the expected countrate of wimp interactions can be written ( first order taylor approximation ) : @xmath13 where @xmath14 $ ] is the time - independent part and @xmath15 is the amplitude of the modulated signal . both @xmath16 and @xmath17 depend on the wimp mass @xmath18 and on the wimp cross section on proton @xmath19 , as well as on many astrophysical parameters ( @xmath3 , @xmath20 , @xmath21 ) and some properties of the target material . a calculation of the expected count rate r from wimp interactions in a germanium detector as a function of the recoil energy @xmath22 can be performed following the formula given in ref.@xcite : @xmath23 where : @xmath24 and the variables @xmath25 , @xmath26 and @xmath27 are listed in table [ tab1 ] together with the values of the parameters used in the calculation . the wimp cross section on germanium @xmath28 can be easily related to the correspondant cross section on proton ; in the case of spin - independent interaction ( si ) , the conversion formula is ( see @xcite and @xcite ) : @xmath29 where @xmath30 is the reduced mass and @xmath31 . .relevant astrophysical and detector parameters : their expressions and the values used in the present work . [ cols="^,^,^,^ " , ] the distribution of @xmath32 for the modulated data - set shows no substantial variation when we move the left limit of the energy interval where we integrate the signal ( @xmath33 ) from 4 kev to 8 kev . increasing @xmath33 above 8 kev , the mean value of the distribution slowly decreases ; this is an indication that we are missing part of the signal that , as we recall here , is concentrated in the lower energy bins . for this reason is of primary importance to have a low experimental threshold . we have repeated the same simulation for different wimp masses and the same cross section ; in tab . ( [ tab2 ] ) we report , for different measuring times , the mean value of the @xmath32 distribution ( for the modulated data - set ) together with the corresponding confidence level @xmath34 . calculating the value of the above mentioned estimators @xmath32 and @xmath35 is not the only way to discover the modulation hidden in the data . given our set of experimental data , we can try to extract directly the value of @xmath17 , the amplitude of the modulated signal , as a function of the energy . following @xcite , we can write : @xmath36 ^ 2 s_i}}{n } \end{aligned}\ ] ] where n is the running time of the experiment and @xmath37 is no more integrated over a broad energy region but in small energy bins ( 1 or 2 kev ) . in this way it is possible to measure the amplitude of the modulated signal and its error for each energy bin ( of the given size ) and moreover , taking small energy bins we avoid the problem of the cross - over energy . in picture ( [ sm_picture ] ) we report a tipical result for the amplitude of the modulated signal @xmath17 as calculated using ( [ sm ] ) on the simulated data without and with modulation ( @xmath18 = 40 gev and @xmath38 pb ) . the energy region between 4 and 50 kev has been divided in 2 kev energy bins and for each one the value of @xmath17 and the corresponding error have been calculated . by looking at the two pictures ( note the different scales on the @xmath39 axis ) , we see how the distribution b represents an indication of an annual modulation amplitude @xmath40 . in the case with modulation ( b ) all the data points are compatible within the error with the theoretical signal while in the case where no modulation is present ( a ) the same points are distributed around zero . the big errors are due to the low statistic and become smaller if we increase the measuring time . averaging the signal in the region from 4 to 16 kev , we obtain in the case of modulation : @xmath41 counts / kev day , while in the case of no modulation we have : @xmath42 counts / kev day , compatible with the hypothesis @xmath43 . one of the general procedures to treat experimental data when searching for the annual modulation effect is to use the maximum - likelihood method . the likelihood function @xmath44 for a set of experimental rates @xmath45 , assuming that they are poisson - distributed , is : @xmath46 since @xmath47 depends on the parameters of interest @xmath18 and @xmath48 , through the expressions of @xmath49 and @xmath50 , it is possible to obtain the best - fit value for the parameters minimizing @xmath51 , or better the function : @xmath52 where the constant contains the components that do not depend on @xmath18 and @xmath48 . the minimization of @xmath53 is not an easy operation : if we want to keep as a free parameter the number of background counts in each energy bin ( and here we consider as background the number of counts due to the time - independent component of the signal ( @xmath16 + @xmath54 ) ) we have to deal with many parameters . the usual procedure is to carry out the minimization in two steps . as a first step we minimize with respect to the time - independent component @xmath55 . during this minimization the condition @xmath56 , @xmath57 is imposed . as a second step we minimize with respect to @xmath48 and @xmath18 requiring , as is usual done : @xmath58 we did not impose limits or conditions on the parameters @xmath48 and @xmath18 except that both have to be greater than zero . we have carried out the minimization procedure on the data set simulated under the mentioned hypothesis @xmath18 = 40 gev and @xmath38 pb , in the energy range from 5 to 40 gev . after the first step we obtain the values of the quantity @xmath55 for each energy bin : we have plotted that result in fig . ( [ f_k ] ) and this reproduces exactly the curve @xmath59 that we have used in the simulation . in the second step we obtain the best - fit values for the parameters of interest . the minimization procedure converged for the selected energy window , giving the following best - fit values for the fit parameters : @xmath60 the value of the wimp mass is in excellent agreement with the real one used in the sumulation ; the value of the cross section , though compatible within 1 @xmath61 with the true value , shows a lower agreement : this can be due to the fact that @xmath18 influences the shape of the wimp spectrum while @xmath48 appears only as a multiplying factor . we repeated the fitting procedure assuming different values of the energy threshold of the experiment ( 3 and 4 kev ) , finding very little difference from the given best - fit . the set of best - fit values ( [ best - fit ] ) corresponds to the 2 @xmath61 allowed region shown in fig . ( [ region ] ) . this region of the plane @xmath62 has been calculated using : @xmath63 with @xmath64 and @xmath65 being the result of the fitting procedure . [ region ] should be interpreted in this way : if a wimp exists with the properties assumed so far , we can point out its presence within two years of measurement ( 80 kg y significance ) and give the result in fig . [ region ] for the 2 @xmath61 allowed region for the relevant parameters . the annual modulation , due to the motion of the earth with respect to the galactic halo , is the main signature of a possible wimp signal . the effect is supposed to be small , only a few percent of the total dark matter signal , and therefore very difficult to extract . a positive indication of this modulation has been found over the past five years by the dama experiment and it would be of great importance to look for the same effect with another experiment , expecially in the region of the wimp parameter s space indicated by the dama results . the genius - tf experiment @xcite , born as a prototype for the genius project , is at present under installation at the gran sasso national laboratory . with a mass of 40 kg and a background of 4 counts/(kg y kev ) , genius - tf can be used to look for dark matter , not only through the direct detection of wimp - induced nuclear recoils , but also through the annual modulation of the experimental rate . genius - tf will be - in addition to dama @xcite - the _ only _ experiment which will be able to probe the annual modulation signature in a foreseeable future . the at present much discussed cryo detector experiments , such as cdms @xcite , cresst @xcite , edelweiss @xcite have no chance to do this because the mass projected to be in operation in these experiments is by far too low ( see also @xcite ) . we have developed a set of routines and tools to look for the annual modulation effect with our genius - tf experiment using different analysis methods discussed in the literature . we have analysed data simulated under the hypothesis of modulation , using three different approaches ( modulation significance , direct calculation of the modulation amplitude @xmath66 and maximum likelihood fit of the data ) and we have shown that the mass and the low background level of genius - tf will allow us test , within few years of measurements , low wimp masses and wimp cross sections in the region of interest indicated by the dama experiment . a digital multi - channel spectroscopy system with 100mhz flash adc s for the genius - tf project has been recently developed @xcite . klapdor - kleingrothaus , j. hellmig and m hirsch , j.phys.g : nucl . ( 1998 ) 483 - 516 ; h.v . klapdor - kleingrothaus , l. baudis , g. heusser , b. majorovits and h. ps , `` genius : a supersensitive germanium detector system for rare events '' , proposal mpi - h - v26 - 1999 , hep - ph/9910205 and in proceedings of the second international conference on particle physics beyond the standard model , beyond the desert 1999 , castle ringberg , germany 6 - 12 june 1999 , ed . klapdor - kleingrothaus , i. krivosheina ( iop bristol 2000 ) , 915 . r. bernabei et al . , in _ proc . of intern . conf . on physics beyond the standard model : beyond the desert 02 , beyond02 _ , oulu , finland , 2 - 7 jun 2002 , _ iop , bristol _ , 2003 , ed . klapdor - kleingrothaus .[/INST] the annual modulation of the recoil spectrum observed in an underground detector is well known as the main signature of a possible wimp signal . the genius - tf experiment , under construction in the gran sasso national laboratory , can search for the annual modulation of the dark matter signal using 40 kg of naked - ge detectors in liquid nitrogen . starting from a set of data simulated under the hypothesis of modulation and using different methods , we show the potential of genius - tf for extracting the modulated signal and the expected wimp mass and wimp cross section . + prof . dr . h.v . klapdor - kleingrothaus + max - planck - institut fr kernphysik + saupfercheckweg 1 + d-69117 heidelberg + germany + phone office : + 49-(0)6221 - 516 - 262 + fax : + 49-(0)6221 - 516 - 540 + email : @xmath0 + </s>

MONROVIA, Liberia -- Amid the deadliest Ebola outbreak in history, it's easier to get help if you are dead than if you are alive. Interested in ? Add as an interest to stay up to date on the latest news, video, and analysis from ABC News. Add Interest My producer and I were driving back from an assignment in Monrovia, where we filmed this morning's "Good Morning America" segment, when we saw a burial team working along the roadway surrounded by crowds of angry locals. A community leader said they had been trying to get help for the dead man for days, but no ambulance ever came. When the man died, a burial team came in an hour. Get the Latest News on the Ebola Outbreak The Experimental Treatments That Could Stop Ebola New Details on First U.S. Ebola Patient Richard Besser/ABC News We watched as the burial team suited up and approached the body lying against a wall. They sprayed it down with bleach and moved it to a black, plastic sheet and began to wrap it up. "We couldn't get him help when he was alive," a community leader told me. "They only come when you die." Just then, the dead man moved his arm -- just a little, but clearly a sign of life. "He's alive," someone yelled. The burial team unwrapped him and put him back on the ground. The man was alive but looked like he would only last a few more hours. About ten minutes later, an ambulance pulled up and a separate team of health workers loaded him into the back. The crowd went wild cheering. ||||| They carry photos, bags of food -- and hope. But what the families idling at the gate of this Ebola centre in Monrovia lack is news of the fate of their sick loved ones inside. George Williams brought his wife and daughter to the Island Clinic on Tuesday and since then has had "no news, no contact with my family". "I trust the doctors and the government," he says. But his faith draws hoots of laughter from the 40-odd others also waiting. For days, they say, no news of their family has ventured beyond the clinic's barbed-wire and high walls -- only cadavers. The keeper of the clinic gate, in protective white gear from head to toe, looks like he is transported from outer space to this sweltering, misery-infected African city. The crowd's noisy complaints fall silent as the gates open, and two Red Cross trucks, each carrying a dozen body bags, emerge. A woman cries out, then two -- and then anger surges again. "I want to see my son!" Janjay Geleplay, hard-faced, demands. She brought 12-year-old Joshua on Sunday from the "72nd" district of Liberia's capital, where "there is a lot of Ebola". "We get no record from the authorities. They always say we should wait. I come here every day. I want to see my son! Maybe he is already dead," she says, dry-eyed. The Island clinic opened on Sunday. By the next day its 120 beds were full. "As of Friday, we had 206 patients," a spokesman for the UN's World Health Organization, which runs the centre, told AFP. Like all the NGO-run Ebola centres in Liberia, the Island is under-resourced and overrun by demand, forced to fill in for a public health infrastructure that has been decimated by 14 years of civil war and grinding poverty. "There is supposed to be a system to allow the patients to talk to their families while keeping a distance of several metres (yards) -- but apparently it's not up and running yet," a clearly embarrassed WHO official there says. Of the four west African nations affected by the Ebola outbreak, Liberia has been hit the hardest, with 3,458 people infected, and 1,830 of killed by the disease. A total of more than 6,500 infections, almost all in Guinea, Liberia and Sierra Leone, have been recorded since the beginning of the year according to a WHO count as of Saturday. Of those, 3,091 people have died so far. - More beds, few aid workers - On the other side of Monrovia, a 160-bed Ebola clinic run by Doctors Without Borders (Medecins Sans Frontieres, MSF) had to turn away patients for days. A Belgian aid worker, forced to act as a "bouncer" there, quit and returned home, traumatised by the need to turn away the sick and dying. "A lot of people are saying this is the hardest mission they've ever had," an MSF colleague says, requesting anonymity. But the colleague also pointed to progress, saying that "slightly fewer arrivals" since Thursday has meant no one needed to be turned away -- "perhaps because new centres have been opened". International efforts are finally building speed to get critical supplies and staff to stricken nations, following a call for fresh aid by US President Barack Obama, and along with fast-track funding from the International Monetary Fund. The UN has estimated that nearly one billion dollars will be required to effectively fight the disease. "In the next two to three weeks, we'll have over a thousand beds available in Monrovia," Frank Mahoney, the representative of the US health body Centers for Disease Control and Prevention, says. The WHO is planning on creating 500 new beds within the month, and MSF plans to have a total of 400 beds, while Obama has also charged the US army with setting up beds. Jean-Pierre Veyrenche, in charge of the construction of clinics in Monrovia for the WHO, says the task is especially complicated in the dense Liberian capital. "You need 5,000 square metres (5,400 square feet) for a 100-bed clinic -- not easy to find in a big city like Monrovia, with marshy terrain. And the heavy rains are an enormous obstacle, as is the high water table which makes it impossible to dig latrines and is forcing us to build septic tanks out of concrete." Like all NGOs and political leaders, he appeals for more aid workers on the ground. "I think people are scared," Veyrenche says, "No one knows how to deal with Ebola in an urban zone, and in such numbers.... But the international humanitarian community must act. There are ways of working here. You can't get Ebola from stepping down onto the runway." A group of aid workers in Monrovia noted the same problem. "Supplies are coming in, but what we're still missing are healthcare personnel," one of them tells AFP. After a devastating earthquake in Haiti in 2010, 820 NGOs mobilised with on-the-ground efforts, he says. In Liberia, there are fewer than 10. Outside the Island clinic, 32-year-old Finley Freeman handed his homemade meals over to the gatekeeper to deliver to his mother. He has not seen her for days but gets his news directly. "I talked to her on the phone last night. She keeps praying," he says. mba/sst/mkh/rmb

– At the heart of the Ebola outbreak in Liberia, it's difficult to find aid for those who contract the virus. As ABC News' chief medical editor Dr. Richard Besser puts it, it's easier to get help dead than alive. Case in point: Locals crowded onto a Monrovia street yesterday to watch a burial team recover the body of a man thought to have died from Ebola alongside a sidewalk, with Besser reporting live on the scene. He explained that locals had tried to get help for the 37-year-old the previous day. No one came. But following the news of his death, the burial team arrived on the scene within an hour. The team was in for quite a shock, however. After spraying the man's body down with bleach and moving him to a black plastic sheet for wrapping, the man suddenly moved. "He's not dead. He's not dead," said Besser, as ABC's cameras captured the victim's arm moving slightly. The man was able to hitch a ride on a passing ambulance, but "I don't know where they could take him," Besser said. "There are no hospitals to treat him" in Monrovia, where free beds are scarce. AFP took a look at the lack of beds earlier this week, noting that one clinic had its 120 beds full within 24 hours of opening; a Belgian aid worker who functioned as a "bouncer" at a 160-bed Doctors Without Borders clinic quit, unable to deal with the stress of turning away the sick and dying. (Meanwhile, an NBC cameraman is the fourth American hit with Ebola in Liberia.)

<s>[INST]MONROVIA, Liberia -- Amid the deadliest Ebola outbreak in history, it's easier to get help if you are dead than if you are alive. Interested in ? Add as an interest to stay up to date on the latest news, video, and analysis from ABC News. Add Interest My producer and I were driving back from an assignment in Monrovia, where we filmed this morning's "Good Morning America" segment, when we saw a burial team working along the roadway surrounded by crowds of angry locals. A community leader said they had been trying to get help for the dead man for days, but no ambulance ever came. When the man died, a burial team came in an hour. Get the Latest News on the Ebola Outbreak The Experimental Treatments That Could Stop Ebola New Details on First U.S. Ebola Patient Richard Besser/ABC News We watched as the burial team suited up and approached the body lying against a wall. They sprayed it down with bleach and moved it to a black, plastic sheet and began to wrap it up. "We couldn't get him help when he was alive," a community leader told me. "They only come when you die." Just then, the dead man moved his arm -- just a little, but clearly a sign of life. "He's alive," someone yelled. The burial team unwrapped him and put him back on the ground. The man was alive but looked like he would only last a few more hours. About ten minutes later, an ambulance pulled up and a separate team of health workers loaded him into the back. The crowd went wild cheering. ||||| They carry photos, bags of food -- and hope. But what the families idling at the gate of this Ebola centre in Monrovia lack is news of the fate of their sick loved ones inside. George Williams brought his wife and daughter to the Island Clinic on Tuesday and since then has had "no news, no contact with my family". "I trust the doctors and the government," he says. But his faith draws hoots of laughter from the 40-odd others also waiting. For days, they say, no news of their family has ventured beyond the clinic's barbed-wire and high walls -- only cadavers. The keeper of the clinic gate, in protective white gear from head to toe, looks like he is transported from outer space to this sweltering, misery-infected African city. The crowd's noisy complaints fall silent as the gates open, and two Red Cross trucks, each carrying a dozen body bags, emerge. A woman cries out, then two -- and then anger surges again. "I want to see my son!" Janjay Geleplay, hard-faced, demands. She brought 12-year-old Joshua on Sunday from the "72nd" district of Liberia's capital, where "there is a lot of Ebola". "We get no record from the authorities. They always say we should wait. I come here every day. I want to see my son! Maybe he is already dead," she says, dry-eyed. The Island clinic opened on Sunday. By the next day its 120 beds were full. "As of Friday, we had 206 patients," a spokesman for the UN's World Health Organization, which runs the centre, told AFP. Like all the NGO-run Ebola centres in Liberia, the Island is under-resourced and overrun by demand, forced to fill in for a public health infrastructure that has been decimated by 14 years of civil war and grinding poverty. "There is supposed to be a system to allow the patients to talk to their families while keeping a distance of several metres (yards) -- but apparently it's not up and running yet," a clearly embarrassed WHO official there says. Of the four west African nations affected by the Ebola outbreak, Liberia has been hit the hardest, with 3,458 people infected, and 1,830 of killed by the disease. A total of more than 6,500 infections, almost all in Guinea, Liberia and Sierra Leone, have been recorded since the beginning of the year according to a WHO count as of Saturday. Of those, 3,091 people have died so far. - More beds, few aid workers - On the other side of Monrovia, a 160-bed Ebola clinic run by Doctors Without Borders (Medecins Sans Frontieres, MSF) had to turn away patients for days. A Belgian aid worker, forced to act as a "bouncer" there, quit and returned home, traumatised by the need to turn away the sick and dying. "A lot of people are saying this is the hardest mission they've ever had," an MSF colleague says, requesting anonymity. But the colleague also pointed to progress, saying that "slightly fewer arrivals" since Thursday has meant no one needed to be turned away -- "perhaps because new centres have been opened". International efforts are finally building speed to get critical supplies and staff to stricken nations, following a call for fresh aid by US President Barack Obama, and along with fast-track funding from the International Monetary Fund. The UN has estimated that nearly one billion dollars will be required to effectively fight the disease. "In the next two to three weeks, we'll have over a thousand beds available in Monrovia," Frank Mahoney, the representative of the US health body Centers for Disease Control and Prevention, says. The WHO is planning on creating 500 new beds within the month, and MSF plans to have a total of 400 beds, while Obama has also charged the US army with setting up beds. Jean-Pierre Veyrenche, in charge of the construction of clinics in Monrovia for the WHO, says the task is especially complicated in the dense Liberian capital. "You need 5,000 square metres (5,400 square feet) for a 100-bed clinic -- not easy to find in a big city like Monrovia, with marshy terrain. And the heavy rains are an enormous obstacle, as is the high water table which makes it impossible to dig latrines and is forcing us to build septic tanks out of concrete." Like all NGOs and political leaders, he appeals for more aid workers on the ground. "I think people are scared," Veyrenche says, "No one knows how to deal with Ebola in an urban zone, and in such numbers.... But the international humanitarian community must act. There are ways of working here. You can't get Ebola from stepping down onto the runway." A group of aid workers in Monrovia noted the same problem. "Supplies are coming in, but what we're still missing are healthcare personnel," one of them tells AFP. After a devastating earthquake in Haiti in 2010, 820 NGOs mobilised with on-the-ground efforts, he says. In Liberia, there are fewer than 10. Outside the Island clinic, 32-year-old Finley Freeman handed his homemade meals over to the gatekeeper to deliver to his mother. He has not seen her for days but gets his news directly. "I talked to her on the phone last night. She keeps praying," he says. mba/sst/mkh/rmb[/INST]– At the heart of the Ebola outbreak in Liberia, it's difficult to find aid for those who contract the virus. As ABC News' chief medical editor Dr. Richard Besser puts it, it's easier to get help dead than alive. Case in point: Locals crowded onto a Monrovia street yesterday to watch a burial team recover the body of a man thought to have died from Ebola alongside a sidewalk, with Besser reporting live on the scene. He explained that locals had tried to get help for the 37-year-old the previous day. No one came. But following the news of his death, the burial team arrived on the scene within an hour. The team was in for quite a shock, however. After spraying the man's body down with bleach and moving him to a black plastic sheet for wrapping, the man suddenly moved. "He's not dead. He's not dead," said Besser, as ABC's cameras captured the victim's arm moving slightly. The man was able to hitch a ride on a passing ambulance, but "I don't know where they could take him," Besser said. "There are no hospitals to treat him" in Monrovia, where free beds are scarce. AFP took a look at the lack of beds earlier this week, noting that one clinic had its 120 beds full within 24 hours of opening; a Belgian aid worker who functioned as a "bouncer" at a 160-bed Doctors Without Borders clinic quit, unable to deal with the stress of turning away the sick and dying. (Meanwhile, an NBC cameraman is the fourth American hit with Ebola in Liberia.)</s>

therefore , androgen deprivation therapy ( adt ) is one of most effective systemic palliative treatments for such carcinomas . although adt is initially extremely effective , serum prostate - specific antigen ( psa ) levels increase over time , and the disease eventually becomes characteristic of hormone - refractory prostate cancer ( hrpc ) . several types of treatment have been applied to treat hrpc , including antiandrogen alternation , supplemental steroid therapy , and generalized chemotherapy with docetaxel hydrate ( dtx ) [ 3 , 4 ] . however , these therapeutic modalities have only a short - term effect . in addition , hrpc is occasionally encountered with locally recurring carcinoma and uncontrolled gross hematuria , dysuria , and scalding . treatment with intra - arterial infusion chemotherapy using cisplatin ( cddp ) and ifosfamide ( ifm ) removed the symptom for a considerable period . a 64-year - old japanese man was admitted to hospital with lower urinary tract symptom ( luts ) and a high psa level ( 180 ng / ml ) in april 1997 . he was diagnosed with prostate cancer ( moderately differentiated adenocarcinoma , t3bn1m0 , stage d1 ) and was started on combined androgen blockade ( cab ) with leuprorelin acetate ( 11.25 mg/3 months ) and flutamide ( 375 mg / day ) . two months later , flutamide was discontinued because of liver damage , and treatment was switched to estramustine phosphate ( emp ) sodium ( 626.8 mg / day ) . six months after starting hormonal therapy , metastatic lymph node lesion and seminal vessel invasion was no longer visible on computed tomography ( ct ) . therefore , we performed radical prostatectomy ( moderately differentiated adenocarcinoma , gleason score 4 + 3 = 7 , ly , v , pn , sv , pw , dw , cap , n ) and obturator lymph node excision to completely remove the cancerous lesion . the patient received adjuvant radiation therapy ( 60 gy ) to the pelvic cavity postoperatively because pathological findings showed the prostatic carcinoma had extended beyond the prostate capsule . additionally , a course of chemotherapy with cyclophosphamide ( cpm ) , doxorubicin hydrochloride ( adm ) , and cddp ( cpm 500 mg , adm 50 mg , cddp 100 thereafter , the patient was followed up with hormonal therapy consisting of leuprorelin acetate ( 11.25 mg/3 months ) and emp ( 626.8 mg / day ) . in june 2002 , however , psa value continued to increase ( 13.74 ng / ml ) in december 2004 ; magnetic resonance imaging ( mri , fig . 1 ) and transrectal biopsy was performed , and we diagnosed a recurrence of prostatic carcinoma ( moderately differentiated adenocarcinoma , gleasen score , 4 + 4 = 8) . whole - body ct and bone scintigraphy showed no abnormal findings . as a result , 1magnetic resonance imaging ( mri ) shows anastomotic recurrence after radical prostatectomy and radiation therapy magnetic resonance imaging ( mri ) shows anastomotic recurrence after radical prostatectomy and radiation therapy we then decided to attempt intra - arterial infusion chemotherapy to treat the local recurrence . an indwelling catheter was placed in the bilateral internal iliac artery , and the pump was placed in a subcutaneous pocket in february 2005 . the combination chemotherapy consisted of cddp ( 20 mg / m ) ( days 15 ) and ifm ( 1.2 mg / m ) ( days 13 ) , and its regimen cycle was every 21 days . the patient received two courses of chemotherapy , after which his psa value decreased to 1.94 ng / ml , the tumor showed a remarkable reduction in size ( fig . 2 ) , and the symptom improved . in this case , grade 3 neutropenia ( which was improved by granulocyte - colony stimulating factor ) , vomiting , general fatigue , and grade 3 alopecia were observed . however , other serious side effects that could pose a risk to continued intra - arterial infusion chemotherapy were not observed . . however , psa value gradually increased to 4.61 ng / ml in april 2006 . we once again attempted intra - arterial infusion chemotherapy of cddp and ifm with the same dose as previously used ( fig . at a later time , the psa value once again rose from the value in may 2007 . however , the patient had no symptoms of luts for 45 months after the first chemotherapy treatment.fig . 2magnetic resonance imaging ( mri shows disappearance of the anastomotic tumor after intra - arterial infusion chemotherapyfig . 3progress of psa treatment and transition values magnetic resonance imaging ( mri shows disappearance of the anastomotic tumor after intra - arterial infusion chemotherapy progress of psa treatment and transition values treating hrpc is troublesome for a urologist because the standard treatment has not yet been established . in addition , hrpc patients occasionally have luts , such as urinary retention and dysuria accompanied with gross hematuria , which adversely affects quality of life . here , we reported a case of urinary retention due to locally recurrent hrpc in which retention was improved by intra - arterial infusion of cddp and ifm . according to the established criteria for evaluating outcomes of nonsurgical therapy for prostate cancer , the prostatic lesions of the case showed a partial response ( pr ) . however , on the basis of psa responses , the patient showed complete response ( cr ) . at present , hrpc treatments , such as antiandrogen alteration , systemic chemotherapy with dtx [ 3 , 4 ] , and low - dose steroids , are effective in the short term , but their effectiveness decreases over time . various generalized combination chemotherapies have been tried for hrpc , but no reports of their long - term efficacy are available [ 510 ] . in the 1990s , intra - arterial chemotherapies for hrpc were reported , which indicated that , whereas they were effective for local carcinostatics , they were not effective as a generalized treatment modality [ 1113 ] . in the study reported here , because we encountered locally recurring hrpc with luts , we thought it may be worthwhile to try intra - arterial chemotherapy for relieving luts caused by hrpc . our cases suggest that intra - arterial chemotherapy may be a good choice for treating hrpc with locally recurring hrpc only . however , the problem with this therapy is that it does not radically treat the cancer . in addition , it should not be administered in cases with poor performance status or prognosis . dtx could be used as a second - line intra - arterial chemotherapy treatment after cddp and ifm , because intra - arterial dtx accompanied with cddp for oropharyngeal cancer is reported to result in an excellent primary response rate and acceptable acute toxicity . in conclusion , intra - arterial chemotherapy with cddp and ifm can alleviate luts caused by locally recurrent hrpc . accordingly , this regimen should be seen as a treatment option for locally recurrent hrpc . as the number of prostate cancer cases increases , urologists are likely to encounter more patients who are suitable for such treatment .

although many treatments have been applied to treat hormone - refractory prostate cancer ( hrpc ) , therapeutic outcome is not altogether satisfactory . in the case of locally recurring hrpc , uncontrolled gross hematuria , dysuria , and scalding are often experienced . we report a patient who improved following intra - arterial infusion of cisplatin ( cddp ) and ifosfamide ( ifm ) to treat urinary retention caused by locally recurring hrpc . after chemotherapy , cancer volume was remarkably reduced and symptoms improved .

<s>[INST]therefore , androgen deprivation therapy ( adt ) is one of most effective systemic palliative treatments for such carcinomas . although adt is initially extremely effective , serum prostate - specific antigen ( psa ) levels increase over time , and the disease eventually becomes characteristic of hormone - refractory prostate cancer ( hrpc ) . several types of treatment have been applied to treat hrpc , including antiandrogen alternation , supplemental steroid therapy , and generalized chemotherapy with docetaxel hydrate ( dtx ) [ 3 , 4 ] . however , these therapeutic modalities have only a short - term effect . in addition , hrpc is occasionally encountered with locally recurring carcinoma and uncontrolled gross hematuria , dysuria , and scalding . treatment with intra - arterial infusion chemotherapy using cisplatin ( cddp ) and ifosfamide ( ifm ) removed the symptom for a considerable period . a 64-year - old japanese man was admitted to hospital with lower urinary tract symptom ( luts ) and a high psa level ( 180 ng / ml ) in april 1997 . he was diagnosed with prostate cancer ( moderately differentiated adenocarcinoma , t3bn1m0 , stage d1 ) and was started on combined androgen blockade ( cab ) with leuprorelin acetate ( 11.25 mg/3 months ) and flutamide ( 375 mg / day ) . two months later , flutamide was discontinued because of liver damage , and treatment was switched to estramustine phosphate ( emp ) sodium ( 626.8 mg / day ) . six months after starting hormonal therapy , metastatic lymph node lesion and seminal vessel invasion was no longer visible on computed tomography ( ct ) . therefore , we performed radical prostatectomy ( moderately differentiated adenocarcinoma , gleason score 4 + 3 = 7 , ly , v , pn , sv , pw , dw , cap , n ) and obturator lymph node excision to completely remove the cancerous lesion . the patient received adjuvant radiation therapy ( 60 gy ) to the pelvic cavity postoperatively because pathological findings showed the prostatic carcinoma had extended beyond the prostate capsule . additionally , a course of chemotherapy with cyclophosphamide ( cpm ) , doxorubicin hydrochloride ( adm ) , and cddp ( cpm 500 mg , adm 50 mg , cddp 100 thereafter , the patient was followed up with hormonal therapy consisting of leuprorelin acetate ( 11.25 mg/3 months ) and emp ( 626.8 mg / day ) . in june 2002 , however , psa value continued to increase ( 13.74 ng / ml ) in december 2004 ; magnetic resonance imaging ( mri , fig . 1 ) and transrectal biopsy was performed , and we diagnosed a recurrence of prostatic carcinoma ( moderately differentiated adenocarcinoma , gleasen score , 4 + 4 = 8) . whole - body ct and bone scintigraphy showed no abnormal findings . as a result , 1magnetic resonance imaging ( mri ) shows anastomotic recurrence after radical prostatectomy and radiation therapy magnetic resonance imaging ( mri ) shows anastomotic recurrence after radical prostatectomy and radiation therapy we then decided to attempt intra - arterial infusion chemotherapy to treat the local recurrence . an indwelling catheter was placed in the bilateral internal iliac artery , and the pump was placed in a subcutaneous pocket in february 2005 . the combination chemotherapy consisted of cddp ( 20 mg / m ) ( days 15 ) and ifm ( 1.2 mg / m ) ( days 13 ) , and its regimen cycle was every 21 days . the patient received two courses of chemotherapy , after which his psa value decreased to 1.94 ng / ml , the tumor showed a remarkable reduction in size ( fig . 2 ) , and the symptom improved . in this case , grade 3 neutropenia ( which was improved by granulocyte - colony stimulating factor ) , vomiting , general fatigue , and grade 3 alopecia were observed . however , other serious side effects that could pose a risk to continued intra - arterial infusion chemotherapy were not observed . . however , psa value gradually increased to 4.61 ng / ml in april 2006 . we once again attempted intra - arterial infusion chemotherapy of cddp and ifm with the same dose as previously used ( fig . at a later time , the psa value once again rose from the value in may 2007 . however , the patient had no symptoms of luts for 45 months after the first chemotherapy treatment.fig . 2magnetic resonance imaging ( mri shows disappearance of the anastomotic tumor after intra - arterial infusion chemotherapyfig . 3progress of psa treatment and transition values magnetic resonance imaging ( mri shows disappearance of the anastomotic tumor after intra - arterial infusion chemotherapy progress of psa treatment and transition values treating hrpc is troublesome for a urologist because the standard treatment has not yet been established . in addition , hrpc patients occasionally have luts , such as urinary retention and dysuria accompanied with gross hematuria , which adversely affects quality of life . here , we reported a case of urinary retention due to locally recurrent hrpc in which retention was improved by intra - arterial infusion of cddp and ifm . according to the established criteria for evaluating outcomes of nonsurgical therapy for prostate cancer , the prostatic lesions of the case showed a partial response ( pr ) . however , on the basis of psa responses , the patient showed complete response ( cr ) . at present , hrpc treatments , such as antiandrogen alteration , systemic chemotherapy with dtx [ 3 , 4 ] , and low - dose steroids , are effective in the short term , but their effectiveness decreases over time . various generalized combination chemotherapies have been tried for hrpc , but no reports of their long - term efficacy are available [ 510 ] . in the 1990s , intra - arterial chemotherapies for hrpc were reported , which indicated that , whereas they were effective for local carcinostatics , they were not effective as a generalized treatment modality [ 1113 ] . in the study reported here , because we encountered locally recurring hrpc with luts , we thought it may be worthwhile to try intra - arterial chemotherapy for relieving luts caused by hrpc . our cases suggest that intra - arterial chemotherapy may be a good choice for treating hrpc with locally recurring hrpc only . however , the problem with this therapy is that it does not radically treat the cancer . in addition , it should not be administered in cases with poor performance status or prognosis . dtx could be used as a second - line intra - arterial chemotherapy treatment after cddp and ifm , because intra - arterial dtx accompanied with cddp for oropharyngeal cancer is reported to result in an excellent primary response rate and acceptable acute toxicity . in conclusion , intra - arterial chemotherapy with cddp and ifm can alleviate luts caused by locally recurrent hrpc . accordingly , this regimen should be seen as a treatment option for locally recurrent hrpc . as the number of prostate cancer cases increases , urologists are likely to encounter more patients who are suitable for such treatment .[/INST]although many treatments have been applied to treat hormone - refractory prostate cancer ( hrpc ) , therapeutic outcome is not altogether satisfactory . in the case of locally recurring hrpc , uncontrolled gross hematuria , dysuria , and scalding are often experienced . we report a patient who improved following intra - arterial infusion of cisplatin ( cddp ) and ifosfamide ( ifm ) to treat urinary retention caused by locally recurring hrpc . after chemotherapy , cancer volume was remarkably reduced and symptoms improved .</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Free Burma Act of 1995''. SEC. 2. SANCTIONS AGAINST BURMA. Except as provided in section 4, the following sanctions shall apply to Burma, effective 90 days after the date of enactment of this Act (or on such other date as is specified in this section): (1) Investments.--No United States national may make any investment in Burma. (2) United states assistance.--United States assistance for Burma is prohibited. (3) Trade privileges.--The President shall continue the suspension of special trade privileges pursuant to the Generalized System of Preferences (GSP), and shall continue the suspension of nondiscriminatory trade treatment (most-favored- nation status), with respect to Burma. (4) Importation of goods.--No article which is produced, manufactured, grown, or extracted in Burma may be imported into the United States. (5) Trade and investment treaties.--The United States should continue to suspend carrying out obligations under bilateral trade and investment treaties with Burma. (6) Travel restrictions.--The Secretary of State shall prohibit the use of United States passports for travel to Burma except for travel by United States diplomatic personnel. (7) Diplomatic representation.--The President is urged not to accept diplomatic representation from Burma at a level greater than the level of diplomatic representation accorded the United States in Burma. (8) Foreign assistance.--The United States shall suspend assistance under the Foreign Assistance Act of 1961 and the Arms Export Control Act to any foreign government which sells or otherwise transfers arms to the Government of Burma. (9) International organizations contributions.--The United States shall withhold from each international organization that funds activities in Burma other than humanitarian activities an amount equal to the United States proportionate share of that funding. (10) Multilateral assistance.--The Secretary of the Treasury shall instruct the United States executive director of each financial institution to vote against any loan or other utilization of the funds of the respective bank to or for Burma. (11) Eminent persons group.--The President, acting through the United States Permanent Representative to the United Nations, should urge the United Nations to establish an eminent persons group to report on compliance by the Government of Burma with United Nations resolutions. (12) International arms embargo.--The President, acting through the United States Permanent Representative to the United Nations, should urge the establishment by the United Nations of an international arms embargo of Burma. SEC. 3. AGREEMENTS TO IMPOSE SANCTIONS ON BURMA. (a) Negotiations With Trading Partners.-- (1) In general.--Not later than 15 days after the date of the enactment of this Act, the President shall initiate negotiations with all foreign countries with which the United States trades for the purpose of entering into agreements with the countries-- (A) to support United States sanctions against Burma, and (B) to cease trade with and investment in Burma. (2) Certification of negotiations and agreements.--Not later than 90 days after the date of the enactment of this Act, the President shall certify to the Congress each country that-- (A) has failed to enter into an agreement described in paragraph (1), or (B) has entered into such an agreement but is not enforcing it. (3) Action by the president.--Notwithstanding any other provision of law, if a certification is made with respect to any country under paragraph (2) the President shall withdraw-- (A) any designation of such country-- (i) as a beneficiary developing country for purposes of title V of the Trade Act of 1974 (19 U.S.C. 2461 et seq.), (ii) as a beneficiary country for purposes of the Caribbean Basin Economic Recovery Act (19 U.S.C. 2701 et seq.), or (iii) as a beneficiary country for purposes of the Andean Trade Preference Act (19 U.S.C. 3201 et seq.), (B) from such countries the benefits of any other special tariff treatment program under which the special rates of duty apply under column 1 of the Harmonized Tariff Schedule of the United States, and (C) most-favored-nation trade treatment with respect to any such country. (b) Applicability.-- (1) In general.--The provisions of this section apply to goods entered, or withdrawn from warehouse for consumption, originating in or imported from a country with respect to which an action described in subsection (a)(3) has been taken, during the period beginning on the date that is 15 days after the date of the certification described in subsection (a)(2) and ending on the date that is 15 days after the earlier of-- (A) the date the President certifies to the Congress that such country has entered into an agreement described in subsection (a)(1) and is enforcing the agreement, or (B) the date a certification described in section 4 is made. (2) Rate of duty during period designation is withdrawn.-- During the period described in paragraph (1), goods entered, or withdrawn from warehouse for consumption, originating in or imported from a country described in subsection (a)(3) shall be subject to duty at the rates of duty specified for such goods under column 2 of the Harmonized Tariff Schedule of the United States. SEC. 4. CERTIFICATION. The sanctions of section 2 shall not apply upon the determination and certification by the President to the appropriate congressional committees that the following conditions are met: (1) The Government of Burma has unconditionally released all political prisoners, including Aung San Suu Kyi. (2) The Government of Burma has fully implemented the results of the 1990 elections in Burma, including the transfer of power to civilian authority, the protection of basic human rights, and guaranteeing the right of Burmese citizens to participate freely in the political process, assuring freedom of speech and the right of association and assembly. (3) The Government of Burma has implemented an effective counternarcotics effort. SEC. 5. SANCTIONS AGAINST THE PEOPLE'S REPUBLIC OF CHINA. The Secretary of the Treasury shall instruct the United States executive director of each multilateral financial institution to vote against any loan or other utilization of the facilities of the respective institution to or for the People's Republic of China until the President determines and certifies to the appropriate congressional committees that the People's Republic of China has terminated arms sales and other arms transfers to Burma. SEC. 6. SANCTIONS AGAINST THE GOVERNMENT OF THAILAND. The President shall withhold all United States assistance to the Government of Thailand until the President determines and certifies to the appropriate congressional committees that the Government of Thailand is fully cooperating in providing support and relief for Burmese exiles and refugees. SEC. 7. REPORT. Not later than 45 days after the date of enactment of this Act, the President shall submit a report to the appropriate congressional committees on-- (1) the chemical and biological weapons capability of Burma; (2) a plan to provide United States assistance in support of the democracy movement active inside Burma; (3) the treatment by the Government of Thailand of Burmese students, refugees, and exiles resident in Thailand; and (4) the status of arms sales and other arms transfers to the Government of Burma, including the amount of expenditures by the Government of Burma in the acquisition of arms. SEC. 8. DEFINITIONS. As used in this Act: (1) Appropriate congressional committees.--The term ``appropriate congressional committees'' means the Committee on Appropriations and the Committee on Foreign Relations of the Senate and the Committee on Appropriations and the Committee on International Relations of the House of Representatives. (2) Investment.--The term ``investment'' includes any contribution or commitment of funds, commodities, services, patents, processes, or techniques, in the form of-- (A) a loan or loans; (B) the purchase of a share of ownership; (C) participation in royalties, earnings, or profits; and (D) the furnishing of commodities or services pursuant to a lease or other contract. (3) Humanitarian activities.--The term ``humanitarian activities'' means the provision of food, medicine, medical supplies, or clothing and does not include cash transfers. (4) Financial institutions.--The term ``financial institutions'' includes the International Bank for Reconstruction and Development, the International Development Association, the Asian Development Bank, and the International Monetary Fund. (5) United states assistance.--The term ``United States assistance'' means assistance of any kind which is provided by grant, sale, loan, lease, credit, guaranty, or insurance, or by any other means, by any agency or instrumentality of the United States Government to any foreign country, including-- (A) assistance under the Foreign Assistance Act of 1961 (including programs under title IV of chapter 2 of part I of the Act); (B) sales, credits, and guaranties under the Arms Export Control Act (22 U.S.C. 2751 et seq.); (C) sales under title I (7 U.S.C.A. 1701 et seq.) or III (17 U.S.C.A. 1727 et seq.) and donations under title II (17 U.S.C.A. 1721 et seq.) of the Agricultural Trade Development and Assistance Act of 1954 of nonfood commodities; (D) other financing programs of the Commodity Credit Corporation for export sales of nonfood commodities; and (E) financing under the Export-Import Bank Act of 1945 (12 U.S.C.A. 635 et seq.).

Free Burma Act of 1995 - Imposes specified sanctions against Burma, unless the President certifies to appropriate congressional committees that Burma has: (1) unconditionally released all political prisoners, including Aung San Suu Kyi; (2) implemented the results of the 1990 elections, including the transfer of power to civilian authority and the protection of basic human rights; and (3) implemented an effective counternarcotics effort. (Sec. 3) Directs the President to initiate negotiations with foreign countries the United States trades with for the purpose of entering into agreements to: (1) support U.S. sanctions against Burma; and (2) cease trade with and investment in Burma. Directs the President, if he certifies to the Congress that a country has failed to enter into an agreement, or has entered into an agreement but is not enforcing it, to withdraw: (1) any designation of such country as a beneficiary developing country or beneficiary country under specified Acts; (2) special duty rate status under column one of the Harmonized Tariff Schedule of the United States; and (3) most-favored-nation treatment status. (Sec. 5) Requires the Secretary of the Treasury to instruct the U.S. executive director of each multilateral financial institution to vote against any loan for China until the President certifies to the appropriate congressional committees it has terminated arms sales and other arms transfers to Burma. (Sec. 6) Directs the President to withhold all U.S. assistance to Thailand until he certifies to the appropriate congressional committees that it is cooperating in providing support and relief for Burmese exiles and refugees. (Sec. 7) Requires the President to report to the appropriate congressional committees on: (1) the chemical and biological weapons capability of Burma; (2) a plan to provide U.S. assistance in support of the democracy movement in Burma; (3) the treatment by Thailand of Burmese students, refugees, and exiles resident there; and (4) the status of arms sales and other arms transfers to Burma, including the amount of expenditures by it in the acquisition of arms.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Free Burma Act of 1995''. SEC. 2. SANCTIONS AGAINST BURMA. Except as provided in section 4, the following sanctions shall apply to Burma, effective 90 days after the date of enactment of this Act (or on such other date as is specified in this section): (1) Investments.--No United States national may make any investment in Burma. (2) United states assistance.--United States assistance for Burma is prohibited. (3) Trade privileges.--The President shall continue the suspension of special trade privileges pursuant to the Generalized System of Preferences (GSP), and shall continue the suspension of nondiscriminatory trade treatment (most-favored- nation status), with respect to Burma. (4) Importation of goods.--No article which is produced, manufactured, grown, or extracted in Burma may be imported into the United States. (5) Trade and investment treaties.--The United States should continue to suspend carrying out obligations under bilateral trade and investment treaties with Burma. (6) Travel restrictions.--The Secretary of State shall prohibit the use of United States passports for travel to Burma except for travel by United States diplomatic personnel. (7) Diplomatic representation.--The President is urged not to accept diplomatic representation from Burma at a level greater than the level of diplomatic representation accorded the United States in Burma. (8) Foreign assistance.--The United States shall suspend assistance under the Foreign Assistance Act of 1961 and the Arms Export Control Act to any foreign government which sells or otherwise transfers arms to the Government of Burma. (9) International organizations contributions.--The United States shall withhold from each international organization that funds activities in Burma other than humanitarian activities an amount equal to the United States proportionate share of that funding. (10) Multilateral assistance.--The Secretary of the Treasury shall instruct the United States executive director of each financial institution to vote against any loan or other utilization of the funds of the respective bank to or for Burma. (11) Eminent persons group.--The President, acting through the United States Permanent Representative to the United Nations, should urge the United Nations to establish an eminent persons group to report on compliance by the Government of Burma with United Nations resolutions. (12) International arms embargo.--The President, acting through the United States Permanent Representative to the United Nations, should urge the establishment by the United Nations of an international arms embargo of Burma. SEC. 3. AGREEMENTS TO IMPOSE SANCTIONS ON BURMA. (a) Negotiations With Trading Partners.-- (1) In general.--Not later than 15 days after the date of the enactment of this Act, the President shall initiate negotiations with all foreign countries with which the United States trades for the purpose of entering into agreements with the countries-- (A) to support United States sanctions against Burma, and (B) to cease trade with and investment in Burma. (2) Certification of negotiations and agreements.--Not later than 90 days after the date of the enactment of this Act, the President shall certify to the Congress each country that-- (A) has failed to enter into an agreement described in paragraph (1), or (B) has entered into such an agreement but is not enforcing it. (3) Action by the president.--Notwithstanding any other provision of law, if a certification is made with respect to any country under paragraph (2) the President shall withdraw-- (A) any designation of such country-- (i) as a beneficiary developing country for purposes of title V of the Trade Act of 1974 (19 U.S.C. 2461 et seq.), (ii) as a beneficiary country for purposes of the Caribbean Basin Economic Recovery Act (19 U.S.C. 2701 et seq.), or (iii) as a beneficiary country for purposes of the Andean Trade Preference Act (19 U.S.C. 3201 et seq.), (B) from such countries the benefits of any other special tariff treatment program under which the special rates of duty apply under column 1 of the Harmonized Tariff Schedule of the United States, and (C) most-favored-nation trade treatment with respect to any such country. (b) Applicability.-- (1) In general.--The provisions of this section apply to goods entered, or withdrawn from warehouse for consumption, originating in or imported from a country with respect to which an action described in subsection (a)(3) has been taken, during the period beginning on the date that is 15 days after the date of the certification described in subsection (a)(2) and ending on the date that is 15 days after the earlier of-- (A) the date the President certifies to the Congress that such country has entered into an agreement described in subsection (a)(1) and is enforcing the agreement, or (B) the date a certification described in section 4 is made. (2) Rate of duty during period designation is withdrawn.-- During the period described in paragraph (1), goods entered, or withdrawn from warehouse for consumption, originating in or imported from a country described in subsection (a)(3) shall be subject to duty at the rates of duty specified for such goods under column 2 of the Harmonized Tariff Schedule of the United States. SEC. 4. CERTIFICATION. The sanctions of section 2 shall not apply upon the determination and certification by the President to the appropriate congressional committees that the following conditions are met: (1) The Government of Burma has unconditionally released all political prisoners, including Aung San Suu Kyi. (2) The Government of Burma has fully implemented the results of the 1990 elections in Burma, including the transfer of power to civilian authority, the protection of basic human rights, and guaranteeing the right of Burmese citizens to participate freely in the political process, assuring freedom of speech and the right of association and assembly. (3) The Government of Burma has implemented an effective counternarcotics effort. SEC. 5. SANCTIONS AGAINST THE PEOPLE'S REPUBLIC OF CHINA. The Secretary of the Treasury shall instruct the United States executive director of each multilateral financial institution to vote against any loan or other utilization of the facilities of the respective institution to or for the People's Republic of China until the President determines and certifies to the appropriate congressional committees that the People's Republic of China has terminated arms sales and other arms transfers to Burma. SEC. 6. SANCTIONS AGAINST THE GOVERNMENT OF THAILAND. The President shall withhold all United States assistance to the Government of Thailand until the President determines and certifies to the appropriate congressional committees that the Government of Thailand is fully cooperating in providing support and relief for Burmese exiles and refugees. SEC. 7. REPORT. Not later than 45 days after the date of enactment of this Act, the President shall submit a report to the appropriate congressional committees on-- (1) the chemical and biological weapons capability of Burma; (2) a plan to provide United States assistance in support of the democracy movement active inside Burma; (3) the treatment by the Government of Thailand of Burmese students, refugees, and exiles resident in Thailand; and (4) the status of arms sales and other arms transfers to the Government of Burma, including the amount of expenditures by the Government of Burma in the acquisition of arms. SEC. 8. DEFINITIONS. As used in this Act: (1) Appropriate congressional committees.--The term ``appropriate congressional committees'' means the Committee on Appropriations and the Committee on Foreign Relations of the Senate and the Committee on Appropriations and the Committee on International Relations of the House of Representatives. (2) Investment.--The term ``investment'' includes any contribution or commitment of funds, commodities, services, patents, processes, or techniques, in the form of-- (A) a loan or loans; (B) the purchase of a share of ownership; (C) participation in royalties, earnings, or profits; and (D) the furnishing of commodities or services pursuant to a lease or other contract. (3) Humanitarian activities.--The term ``humanitarian activities'' means the provision of food, medicine, medical supplies, or clothing and does not include cash transfers. (4) Financial institutions.--The term ``financial institutions'' includes the International Bank for Reconstruction and Development, the International Development Association, the Asian Development Bank, and the International Monetary Fund. (5) United states assistance.--The term ``United States assistance'' means assistance of any kind which is provided by grant, sale, loan, lease, credit, guaranty, or insurance, or by any other means, by any agency or instrumentality of the United States Government to any foreign country, including-- (A) assistance under the Foreign Assistance Act of 1961 (including programs under title IV of chapter 2 of part I of the Act); (B) sales, credits, and guaranties under the Arms Export Control Act (22 U.S.C. 2751 et seq.); (C) sales under title I (7 U.S.C.A. 1701 et seq.) or III (17 U.S.C.A. 1727 et seq.) and donations under title II (17 U.S.C.A. 1721 et seq.) of the Agricultural Trade Development and Assistance Act of 1954 of nonfood commodities; (D) other financing programs of the Commodity Credit Corporation for export sales of nonfood commodities; and (E) financing under the Export-Import Bank Act of 1945 (12 U.S.C.A. 635 et seq.).[/INST]Free Burma Act of 1995 - Imposes specified sanctions against Burma, unless the President certifies to appropriate congressional committees that Burma has: (1) unconditionally released all political prisoners, including Aung San Suu Kyi; (2) implemented the results of the 1990 elections, including the transfer of power to civilian authority and the protection of basic human rights; and (3) implemented an effective counternarcotics effort. (Sec. 3) Directs the President to initiate negotiations with foreign countries the United States trades with for the purpose of entering into agreements to: (1) support U.S. sanctions against Burma; and (2) cease trade with and investment in Burma. Directs the President, if he certifies to the Congress that a country has failed to enter into an agreement, or has entered into an agreement but is not enforcing it, to withdraw: (1) any designation of such country as a beneficiary developing country or beneficiary country under specified Acts; (2) special duty rate status under column one of the Harmonized Tariff Schedule of the United States; and (3) most-favored-nation treatment status. (Sec. 5) Requires the Secretary of the Treasury to instruct the U.S. executive director of each multilateral financial institution to vote against any loan for China until the President certifies to the appropriate congressional committees it has terminated arms sales and other arms transfers to Burma. (Sec. 6) Directs the President to withhold all U.S. assistance to Thailand until he certifies to the appropriate congressional committees that it is cooperating in providing support and relief for Burmese exiles and refugees. (Sec. 7) Requires the President to report to the appropriate congressional committees on: (1) the chemical and biological weapons capability of Burma; (2) a plan to provide U.S. assistance in support of the democracy movement in Burma; (3) the treatment by Thailand of Burmese students, refugees, and exiles resident there; and (4) the status of arms sales and other arms transfers to Burma, including the amount of expenditures by it in the acquisition of arms.</s>

the grb afterglow as perceived in the x - ray , optical and radio wavelengths is now understood to be the result of the collision between relativistic ejecta from the gamma - ray bursts and the interstellar medium ( ism ) . a comparison of afterglow lightcurves obtained at different wavelengths gives important information about the surrounding ism environment and the interaction processes . such analyses can also provide essential input for theoretical models . recently , the pace of this type of activity has quickened significantly , stimulated by the capabilities of the quick response and accurate localization of the grb by the _ swift _ satellite ( gehrels et al . this has meant that the number of grb optical afterglow detections in the first several hours by ground - based telescopes has recently increased significantly . it is interesting to note that the observations by _ swift _ of the early x - ray emissions from a number of grbs reveal a canonical behavior . the x - ray lightcurves can be divided into three distinct power law segments ( nousek et al . 2006 ) . some x - ray and optical observations show that the evolution of both lightcurves changes at the same time ( blustin et al . 2006 ; rykoff et al . 2006 ) , however chromatic breaks were also found in some cases ( fan & piran 2006 ; panaitescu et al . the nature of the afterglow early breaks in the lightcurves is thus uncertain . a detailed comparison of changes in the evolution of the optical , radio and x - ray lightcurves should therefore be very interesting . this kind of physical study demands both a well - coordinated observational program and careful data analysis . we use grb050319 which has comprehensive observational coverage in both the x - ray and optical wavelengths may be used as just such an example . grb050319 was detected by the burst alert telescope ( bat ) instrument onboard the _ swift _ satellite on march 19 , 2005 at 09:31:18.44 ut ( krimm et al . 2005 ) . however , a re - analysis of the bat data showed two flares , which indicated that grb050319 had already started 137 sec before the trigger . the 15350 kev fluence for the entire burst duration of @xmath8 sec has been estimated to be 1.6 @xmath9 ( cusumano et al . the x - ray emission of grb050319 after the burst was monitored by the xrt from 225 sec to 28 days . two breaks in the emission curves were found ( cusumano et al . the initial sharp decline can be described by a power - law with an index of @xmath10 to be followed by @xmath11 after 0.004 days since the burst . the unusually flat decline in the second part might have been caused by continuous energy injection ( cusumano et al . 2006 ) . at about 0.313 days after the burst , the power - law index changed to @xmath12 which can be readily explained as a jet break or a reduction in the energy injection ( cusumano et al . 2006 ; zhang et al . 2006 ) . the early optical afterglow emission at 230 s was observed by the uvot telescope on _ swift _ ( mason et al . 2006 ) and by two ground - based robotic telescopes , _ rotse - iii _ ( quimby et al . , 2006 ) and _ raptor _ ( woniak et al . 2005 ) . the best single power - law fit of unfiltered data from _ rotse - iii _ and _ raptor _ indicates that @xmath13 . a number of optical observatories have joined the follow - up observations ( see yoshioka et al . 2005 ; torii et al . 2005 ; sharapov et al . 2005a , b ; george et al . 2006 ; misra et al . 2005 ; kiziloglu et al . 2005 ; greco et al . 2005 ) . the spectral measurements of the afterglow by the nordic optical telescope ( not ) indicate that was redshift @xmath14 of this event ( fynbo et al . after receiving the grb alert message from _ swift _ and the afterglow position was reported by rykoff et al . ( 2005 ) , the target - of - opportunity procedures of the east - asia grb follow - up observation network ( eafon , urata et al . 2005 ) were immediately carried out . a series of multi - band follow - up observations were successfully performed by the 1.05-m schmidt telescope of the kiso observatory in japan and the lulin one - meter telescope ( lot ) in taiwan . photometric @xmath0 and @xmath2 images were obtained at the kiso site with a 2k @xmath15 2k ccd camera ( urata et al . 2005 ) between 0.055 and 0.326 days after the burst . a number of parallel @xmath0 , @xmath1 , @xmath2 and @xmath3 images were obtained by lot with a pi1300 ccd camera ( kinoshita et al . 2005 ) from 0.080 to 0.413 days after the burst . the standard routine including bias subtraction and dark subtraction ; flat - field corrections were employed with the appropriate calibration data needed to process the data using iraf . the afterglow can be clearly seen in the images . the signal - to - noise ratio was improved by combing the lot @xmath0 band data with median filtering . the daophot package ( stetson 1989 ) was then used to perform point - spread function ( psf ) fitting for the grb images . four field stars were used to create a psf model which was applied to the optical afterglow of each grb image . for absolute photometric calibration , we used calibrated data of the grb field obtained by the usnofs 1.0-m telescope ( henden 2005 ) . the photometric error and the systematic calibration error were included in the magnitude error estimation . figure1 shows the multi - band lightcurves of the grb050319 afterglow . besides our @xmath0 , @xmath1 , @xmath2 and @xmath3 band data ( table1 ) we also included the @xmath2 band measurements from _ rotse - iii _ ( quimby et al . 2006 ) , _ raptor _ ( woniak et al . 2005 ) and several gcn reports ( greco et al . 2005 ; kiziloglu et al . 2005 ; misra et al . 2005 ; sharapov et al . 2005a , b ) . in addition , we also made use of several @xmath0 and @xmath1 band measurements taken by the _ swift _ uvot ( mason et al . the gcn @xmath2 band points were re - calibrated using the grb050319 field stars reported by henden ( 2005 ) so they could be plotted on the same magnitude scale . the magnitude differences between photometric field stars in henden ( 2005 ) and in usno - a2.0 , usno - b1.0 stars are @xmath16 and @xmath17 mag , respectively . we re - measured the reference stars from greco et al . ( 2005 ) from the lot @xmath2 band images and obtained the average magnitudes and rms errors . after fitting the @xmath0 , @xmath1 , @xmath2 and @xmath3 band lightcurves to a single power - law expression @xmath18 , where @xmath19 is the index and @xmath20 is the time after the burst , we get @xmath21 ( @xmath22= 2.90 for @xmath23 ) for the @xmath0 band , @xmath24 ( @xmath22= 2.60 for @xmath25 ) for the @xmath1 band , @xmath26 ( @xmath22= 5.3 for @xmath27 ) for the @xmath2 band , and @xmath28 ( @xmath22= 7.7 for @xmath29 ) for the @xmath3 band . this single power - law fitting indicates that these lightcurves , obtained with different filters have similar power - law decay even though the reduced chi - square values are relatively large . since the data sets of the @xmath1 and @xmath2 measurements are more complete , it is possible with following expression to attempt the fitting of the corresponding lightcurves with a smoothly broken power - law function : @xmath30^{(1/k)}},\ ] ] where @xmath31 is the break time , @xmath4 and @xmath7 are the power - law indices before and after @xmath31 , @xmath32 is flux at break @xmath31 , and @xmath33 is a smoothness factor . for the @xmath1 band , we obtain @xmath34 , @xmath35 , @xmath31 = 0.042 @xmath6 0.058 days and @xmath36 ( @xmath22= 1.48 for @xmath37 ) . for the @xmath2 band , we obtain @xmath38 , @xmath39 , @xmath40 days , and @xmath41 ( @xmath22= 2.24 for @xmath42 ) . this result implies a mild break in both the @xmath1 and the @xmath2 band lightcurves at around 0.04 days after the occurrence of the grb . taking @xmath31 = 0.04 days , we fit the data in the @xmath0 and @xmath3 bands to a respective power - law before and after the break . in this manner , we find @xmath4 = @xmath50.79 @xmath6 0.09 ( @xmath43 for @xmath44 ; @xmath7 = @xmath50.36 @xmath6 0.05 ( @xmath45 for @xmath46 for the @xmath0 band and @xmath7 = @xmath50.52 @xmath6 0.15 ( @xmath47 for @xmath46 for the @xmath3 band . the best - fit parameters for the @xmath0 , @xmath1 , @xmath2 , and @xmath3 bands are summarized in table 2 . our results show not only the clear presence of mild breaks in the @xmath1 , @xmath2 band lightcurves but a flattening trend after the break . furthermore , our @xmath2 band slope before the break ( @xmath48 ) is in agreement with the corresponding value derived by quimby et al . ( 2006 ) for the interval between 0.0019 and 0.05 days after the burst . our multi - wavelength observations indicate that median colors between 0.07 and 0.35 days are @xmath49 , @xmath50 , and @xmath51 . these values have been corrected for foreground reddening of e(@xmath52 0.011 mag ( schlegel et al . the @xmath53 and @xmath54 colors so derived are consistent with those of the typical long grbs ( simon et al . 2001 ) , but the @xmath55 color is slightly redder than those of the typical long grbs ( @xmath56 ) . the larger @xmath55 value may imply a certain absorption effect because the redshift of grb050319 was determined to be 3.24 ( fynbo et al . 2005 ) . the @xmath0 , @xmath1 , @xmath2 and @xmath3 magnitudes have been further converted to fluxes using the effective wavelengths and normalizations of fukugita et al . the effect of the galactic interstellar extinction has been corrected . figure 2 shows two samples of spectral energy distribution obtained by lot at 0.13 and 0.21 days after the occurrence of grb050319 . a drop in the @xmath0 band flux at about @xmath57 can be clearly seen . we subsequently fitted the flux distribution of @xmath1 , @xmath2 and @xmath3 bands with a power - law function @xmath58 ; here @xmath59 is the flux at frequency @xmath60 with a certain @xmath20 and @xmath61 is the spectral index . we find that @xmath62 ( @xmath22= 0.05 for @xmath63 ) at 0.13 days and that @xmath64 ( @xmath22 = 2.3 for @xmath63 ) at 0.21 days . our result ( @xmath65 with a rms error 0.23 ) is consistent with the x - ray fitting value ( @xmath66 ) in a 3-@xmath67 level . with a redshift of 3.24 , the ly@xmath68 absorption feature would shift into the @xmath0 bandpass , causing reduction of the afterglow flux in the @xmath0 band . to correct for this absorption effect , we used the formulation derived by yoshii et al . ( 1994 ) , in which the optical depth is a function of the observed wavelength and source redshift . with the computed optical depth in the @xmath0 band , and a spectral slope of @xmath69 , we found the expected @xmath0 band magnitude after ly@xmath68 absorption to be @xmath70 at 0.13 days . this value compares very well with our observed value of @xmath0 = 21.26 @xmath6 0.17 at 0.13 days after correction for galactic extinction . the drop at the b band is hence fully produced by the ly@xmath68 absorption and no spectral breaks should have taken place during our observation . it is important to note that _ swift _ found two breaks at 0.004 and 0.313 days after the burst in the x - ray afterglow observations ( cusumano et al . 2006 ) , but we only found a single break in our @xmath1 and @xmath2 lightcurves ( see figure 1 ) . in the following since there are more data points available for the @xmath2 band data we will focus on this . it is useful to remember that @xmath4 = @xmath71 and @xmath72 at the break time of @xmath31 = 0.04 days . the slope @xmath4 ( = @xmath50.84 ) is consistent with the typical range of @xmath74 to @xmath75 for many well observed grbs . according to the standard afterglow model relating the power - law index ( @xmath19 ) to the power - law index ( @xmath76 ) of an electron spectrum ( zhang & mszros , 2004 ; dai & cheng , 2001 ) , the corresponding value for @xmath77 is @xmath76 = 2.1 , which is in agreement with the constant - density ism model with slow cooling in which @xmath78 2 for @xmath79 ( @xmath80 is the typical frequency ; @xmath81 is the optical frequency ; @xmath82 is the cooling frequency ) . in light of the xrt observations , the first break was likely caused by the transition from the tail end of the low energy prompt emission to the afterglow phase ( zhang et al . however , it is important to note that the x - ray break at 0.004 days ( where the steeper slope becomes shallow ) is not accompanied by an @xmath2 band break . at the same time , the power - law decay slope in the x - ray ( @xmath83 5.53 ) and the @xmath2 band ( @xmath83 0.84 ) are quite different . this is an indication not only that the behaviors of the x - ray afterglow and optical afterglow of the grb050319 event are different , but also suggested that the afterglow phase already dominated the optical bands when the optical emission was first detected . the power law index becomes shallow after the break ( @xmath31 = 0.04 days ) . neither the jet ( rhoads 1999 ) nor the break frequencies across the optical wavelength ( sari et al . , 1998 ) suitably explain the break they see in the grb050319 lightcurves . as discussed before , the x - ray lightcurve between the two breaks 0.004 and 0.313 days after the burst is also characterized by shallow decay . zhang et al . ( 2006 ) suggested that such behavior is related to continuous energy injection into the ism . for a long - lasting central engine , the energy injection rate is @xmath84 and with @xmath85 ( zhang & mszros 2001 ) . for slow cooling in the ism , the temporal index can be expressed as : @xmath86 / 4 = [ ( q-1 ) + { ( 2+q)\beta ] / 2},$ ] when @xmath87 . using this formulation , zhang et al . ( 2006 ) obtained @xmath88 = 0.6 and @xmath89 = 2.4 from the x - ray observations . with @xmath19 = @xmath50.48 and @xmath61 = @xmath51.08 from the @xmath2 band observations , we find that @xmath88 = 0.72 and @xmath89 = 2.12 . the results not only indicate that the electron spectrum power law index is the same before and after the break , they also compare well with the results of zhang et al . these results indicate that the shallow decays evidenced by both x - ray and optical afterglows could be of a similar origin , related to a continuous energy injection mechanism . according to the energy injection model , would also expect an x - ray break at the time of the optical flattening break , because the onset of the energy injection should also alter the x - ray temporal index . however , such an x - ray break is not observed , which suggests that some modifications to the injection model may be needed . as mentioned in @xmath90 4.1 , the x - ray break at 0.004 days was not accompanied by a break in the @xmath2 lightcurve . although a chromatic break in the x - ray was found at 0.004 days and in the optical region at 0.04 days , the lightcurves at both wavelengths indeed showed shallow decay after the breaks , which can be explained by the energy injection model . however , it is difficult for energy injection from 0.004 days to 0.04 days to affect only high energies . this difficulty indicates that energy injection is an imperfect mechanism for explaining the shallow optical or x - ray phase associated with the grb050319 event . several models have recently been proposed to explain the shallow decay effect . using the multiple - subjet model ( nakamura , 2000 ) , toma et al . ( 2006 ) invoked the superposition of afterglows from many off - axis subjets . eichler & granot ( 2006 ) favored a combination of the tail of prompt emission model with the afterglow emissions observed from a viewing angle outside the edge of the jet . these arguments hence suggest that the multiple - subjet model and the patchy - shell model ( kumar & piran , 2000 ) might provide a theoretical basis for explaining the observed shallow decays in the x - ray and optical lightcurves . it is interesting to note that in order to sustain the shallow decay process these models all require high gamma - ray efficiency ( 75 - 90@xmath91 ) ; additional mechanisms such as prior activity ( ioka et al . 2005 ) and time - dependent shock generation ( fan & piran , 2006 ) have been also proposed . comprehensive multi - wavelength observations , such as those reported here , provide important keys to improve these models . finally , the second break in the x - ray emissions ( @xmath92 0.313 days after the burst ) , has been interpreted as being due to an unusual flat jet break ( cusumano et al . 2006 ) , zhang et al . ( 2006 ) however provided an alternate explanation , a sudden cessation of the energy injection . in both interpretations , the corresponding break should appear in both the x - ray and optical lightcurves . this effect can not be clearly identified in our measurements until 0.413 days after the burst . the lack of data for the subsequent time interval could lead to uncertainty in the power - law fitting . we thus can not fully exclude the existence of a second break in the optical lightcurves . however , panaitescu et al . ( 2006 ) have studied several afterglows . they found the shallow power - law decay evidenced by the x - ray emissions to steepen about [email protected] days after the burst , although there was no accompanying break found in the optical range . they suggest that such chromatic x - ray breaks may be common . the chromatic breaks ( e.g. the shallow x - ray phase becomes steeper , with no accompanying optical break ) may be caused by differences in the x - ray and optical outflow ( panaitescu et al . 2006 ) , or by changes in the typical electron energy parameters ( the so - called microphysical parameters ) at the end of energy injection ( panaitescu 2006 ) . * the @xmath0 , @xmath1 , @xmath2 , and @xmath3 band lightcurves displayed unusual shallow decays . * the @xmath2 lightcurve can be described by a smooth broken power - law function . @xmath93 becomes shallow ( @xmath94 ) 0.04 days after the occurrence of the grb . * the shallow decay observed in the x - ray and optical lightcurves may have a similar origin related to energy injection . however , our observations indicate that there is still a major puzzle remaining concerning the chromatic breaks in the @xmath2 band lightcurve ( at 0.04 days ) and the x - ray lightcurve ( at 0.004 days ) . * our calculations revealed that the drop in spectral energy distribution was fully caused by a shift in the ly@xmath68 absorption to the @xmath0 bandpass at @xmath95 = 3.24 . we thank the referee for his / her valuable advice . this work is supported by nsc95 - 2752-m-008 - 001-pae , nsc95 - 2112-m-008 - 021 , the japan society for the promotion of science ( jsps ) grant - in - aid for young scientists ( b ) no.18740147 and jsps research fellowships for young scientists ( y.u . ) . blustin , e. et al . 2006 , 637 , 901 cusumano , g. et al . 2006 , , 639 , 316 dai , z. g. , & cheng , k. s. 2001 , , 558 , 109 eichler , d. , & granot , j. 2006 , , 641 , l5 fan , y. , & piran , t. 2006 , , 369 , 197 fynbo , j. p. u. et al . 2005 , gcn circ . 3136 fukugita , m. , shimasaku , k. , & ichikawa , t. 1995 , pasp , 107 , 945 gehrels , n. et al . 2004 , 611 , 1005 george , k. , banerjee , d. p. k. , chandrasekhar , t. , & ashok , n. m. 2006 , 640 , l13 greco , g. , bartolini , c. , guarnieri , a. , piccioni , a . , ferrero , p. & bruni , i. 2005 , gcn circ . 3142 henden , a. 2005 , gcn circ . 3454 ioka , k. , toma , k. , yamazaki , r. , & nakamura , t. 2005 , a&a in press ( astro - ph/0511749 ) kinoshita , d. , et al . 2005 , chjaa , 5 , 315 kiziloglu , u. et al . 2005 , gcn circ . 3139 krimm , h. et al . 2005 , gcn circ . 3119 kumar , p. & piran , t. 2000 , , 535 , 152 mason , k. o. et al . 2006 , , 639 , 311 misra , k. , kamble , a. p. & pandey , s.b . 2005 , gcn circ . 3130 nakamura , t. 2000 , , 534 , l159 nousek , j. a. et al . 2006 , , 642 , 389 panaitescu , a. , mszros , p. , burrows , d. , nousek , j. , obrien , p. & willingale , r. 2006 , mnras , 369 , 2059 panaitescu , a. , 2006 , preprint ( astro - ph/0607396 ) quimby , r. m. et al . 2006 , , 640 , 402 rhoads , j. e. 1999 , , 525 , 737 rykoff , e. , schaefer , b. , & quimby , r. 2005 , gcn cir . 3116 rykoff , e. et al . 2006 , , 638 , l5 sari , r. , piran , t. , & narayan , r. 1998 , , 497 , l17 schlegel , d. j. , finkbeiner , d. p. , & davis , m. 1998 , apj , 500 , 525 sharapov , d. et al . 2005a , gcn circ . 3124 sharapov , d. et al . 2005b , gcn circ . 3140 simon , v. , hudec , r. , pizzichini , g. , & masetti , n. 2001 , a&a , 377 , 450 stetson , p. b. 1987 , pasp , 99 , 191 toma , k. , ioka , k. , yamazaki , r. & nakamura , t. 2006 , 640 , l139 torii , k. 2005 , gcn circ . 3121 urata , y. et al . 2005 , nuovo cimento , 28 , 775 woniak , p. r. , vestrand , w. t. , wren , j. a. , white , r. r. , evans , s. m. , & casperson , d. 2005 , apj , 627 , l13 yoshii , y. & peterson , b. a. 1994 , , 436 , 551 yoshioka , t. et al . 2005 , gcn circ . 3120 zhang , b. , & mszros , p. 2001 , , 552 , l35 zhang , b. , & mszros , p. 2004 , int . j. mod . a. , 19 , 2385 zhang , b. et al . 2006 , , 642 , 354 cccc days after grb & filter & magnitude & site + 0.05443 & r & [email protected] & kiso + 0.06023 & b & [email protected] & kiso + 0.08037 & v & [email protected] & lulin + 0.10439 & i & [email protected] & lulin + 0.27821 & b & [email protected] & kiso + 0.33424 & i & [email protected] & lulin + 0.40097 & v & [email protected] & lulin + 0.41346 & r & [email protected] & lulin + .fitting results of the grb050319 lightcurves : the @xmath0 and @xmath3 band data were fitted by a respective power - law model [ @xmath96 before and after the break ( @xmath97 ) . on the other hand , the @xmath1 and @xmath2 data were fitted by a smoothly broken power - law [ equation ( 1 ) ] . [ cols="^,^,^,^ " , ] ] for the @xmath0 band ( @xmath98 ) and the @xmath3 band ( @xmath99 ) . the dashed line indicates the best fit by the smooth broken power - law [ equation ( 1 ) ] with the @xmath1 band ( @xmath100 , @xmath35 , @xmath31 = 0.042 @xmath6 0.058 days ) and the @xmath2 band ( @xmath101 , @xmath39 , @xmath31 = 0.046 @xmath6 0.008 days ) . these observations are based on our eafon data and quimby et al . ( 2006 ) , woniak et al . ( 2005 ) , mason et al . ( 2005 ) , greco et al . ( 2005 ) , kiziloglu et al . ( 2005 ) , misra et al . ( 2005 ) , and sharapov et al . ( 2005a , b ) . the dotted lines represent the break times of x - ray afterglows at 0.004 and 0.31 days after the burst . the two breaks were not found in x - ray observations , but a mild break seems to exist in the @xmath1 and @xmath2 band lightcurves . , scaledwidth=80.0% ] , @xmath2 and @xmath3 bands at 0.13 and 0.21 days after the burst ( corrected for galactic extinction ) . the solid and dashed lines indicate the best fit by the power - law model [ @xmath102 , where @xmath103 for 0.13 days and @xmath64 for 0.21 days , respectively.,scaledwidth=80.0% ]

multi - wavelength @xmath0 , @xmath1 , @xmath2 , @xmath3 observations of the optical afterglow of grb050319 were performed by the 1.05-m telescope at kiso observatory and the 1.0-m telescope at lulin observatory from 1.31 hours to 9.92 hours after the burst . our @xmath2 band lightcurves , combined with other published data , can be described by the smooth broken power - law function , with @xmath4 = @xmath50.84 @xmath60.02 to @xmath7 = @[email protected] , 0.04 days after the grb . the optical lightcurves are characterized by shallow decays as was also observed in the x - rays which may have a similar origin , related to energy injection . however , our observations indicate that there is still a puzzle concerning the chromatic breaks in the @xmath2 band lightcurve ( at 0.04 days ) and the x - ray lightcurve ( at 0.004 days ) that remains to be solved .

<s>[INST]the grb afterglow as perceived in the x - ray , optical and radio wavelengths is now understood to be the result of the collision between relativistic ejecta from the gamma - ray bursts and the interstellar medium ( ism ) . a comparison of afterglow lightcurves obtained at different wavelengths gives important information about the surrounding ism environment and the interaction processes . such analyses can also provide essential input for theoretical models . recently , the pace of this type of activity has quickened significantly , stimulated by the capabilities of the quick response and accurate localization of the grb by the _ swift _ satellite ( gehrels et al . this has meant that the number of grb optical afterglow detections in the first several hours by ground - based telescopes has recently increased significantly . it is interesting to note that the observations by _ swift _ of the early x - ray emissions from a number of grbs reveal a canonical behavior . the x - ray lightcurves can be divided into three distinct power law segments ( nousek et al . 2006 ) . some x - ray and optical observations show that the evolution of both lightcurves changes at the same time ( blustin et al . 2006 ; rykoff et al . 2006 ) , however chromatic breaks were also found in some cases ( fan & piran 2006 ; panaitescu et al . the nature of the afterglow early breaks in the lightcurves is thus uncertain . a detailed comparison of changes in the evolution of the optical , radio and x - ray lightcurves should therefore be very interesting . this kind of physical study demands both a well - coordinated observational program and careful data analysis . we use grb050319 which has comprehensive observational coverage in both the x - ray and optical wavelengths may be used as just such an example . grb050319 was detected by the burst alert telescope ( bat ) instrument onboard the _ swift _ satellite on march 19 , 2005 at 09:31:18.44 ut ( krimm et al . 2005 ) . however , a re - analysis of the bat data showed two flares , which indicated that grb050319 had already started 137 sec before the trigger . the 15350 kev fluence for the entire burst duration of @xmath8 sec has been estimated to be 1.6 @xmath9 ( cusumano et al . the x - ray emission of grb050319 after the burst was monitored by the xrt from 225 sec to 28 days . two breaks in the emission curves were found ( cusumano et al . the initial sharp decline can be described by a power - law with an index of @xmath10 to be followed by @xmath11 after 0.004 days since the burst . the unusually flat decline in the second part might have been caused by continuous energy injection ( cusumano et al . 2006 ) . at about 0.313 days after the burst , the power - law index changed to @xmath12 which can be readily explained as a jet break or a reduction in the energy injection ( cusumano et al . 2006 ; zhang et al . 2006 ) . the early optical afterglow emission at 230 s was observed by the uvot telescope on _ swift _ ( mason et al . 2006 ) and by two ground - based robotic telescopes , _ rotse - iii _ ( quimby et al . , 2006 ) and _ raptor _ ( woniak et al . 2005 ) . the best single power - law fit of unfiltered data from _ rotse - iii _ and _ raptor _ indicates that @xmath13 . a number of optical observatories have joined the follow - up observations ( see yoshioka et al . 2005 ; torii et al . 2005 ; sharapov et al . 2005a , b ; george et al . 2006 ; misra et al . 2005 ; kiziloglu et al . 2005 ; greco et al . 2005 ) . the spectral measurements of the afterglow by the nordic optical telescope ( not ) indicate that was redshift @xmath14 of this event ( fynbo et al . after receiving the grb alert message from _ swift _ and the afterglow position was reported by rykoff et al . ( 2005 ) , the target - of - opportunity procedures of the east - asia grb follow - up observation network ( eafon , urata et al . 2005 ) were immediately carried out . a series of multi - band follow - up observations were successfully performed by the 1.05-m schmidt telescope of the kiso observatory in japan and the lulin one - meter telescope ( lot ) in taiwan . photometric @xmath0 and @xmath2 images were obtained at the kiso site with a 2k @xmath15 2k ccd camera ( urata et al . 2005 ) between 0.055 and 0.326 days after the burst . a number of parallel @xmath0 , @xmath1 , @xmath2 and @xmath3 images were obtained by lot with a pi1300 ccd camera ( kinoshita et al . 2005 ) from 0.080 to 0.413 days after the burst . the standard routine including bias subtraction and dark subtraction ; flat - field corrections were employed with the appropriate calibration data needed to process the data using iraf . the afterglow can be clearly seen in the images . the signal - to - noise ratio was improved by combing the lot @xmath0 band data with median filtering . the daophot package ( stetson 1989 ) was then used to perform point - spread function ( psf ) fitting for the grb images . four field stars were used to create a psf model which was applied to the optical afterglow of each grb image . for absolute photometric calibration , we used calibrated data of the grb field obtained by the usnofs 1.0-m telescope ( henden 2005 ) . the photometric error and the systematic calibration error were included in the magnitude error estimation . figure1 shows the multi - band lightcurves of the grb050319 afterglow . besides our @xmath0 , @xmath1 , @xmath2 and @xmath3 band data ( table1 ) we also included the @xmath2 band measurements from _ rotse - iii _ ( quimby et al . 2006 ) , _ raptor _ ( woniak et al . 2005 ) and several gcn reports ( greco et al . 2005 ; kiziloglu et al . 2005 ; misra et al . 2005 ; sharapov et al . 2005a , b ) . in addition , we also made use of several @xmath0 and @xmath1 band measurements taken by the _ swift _ uvot ( mason et al . the gcn @xmath2 band points were re - calibrated using the grb050319 field stars reported by henden ( 2005 ) so they could be plotted on the same magnitude scale . the magnitude differences between photometric field stars in henden ( 2005 ) and in usno - a2.0 , usno - b1.0 stars are @xmath16 and @xmath17 mag , respectively . we re - measured the reference stars from greco et al . ( 2005 ) from the lot @xmath2 band images and obtained the average magnitudes and rms errors . after fitting the @xmath0 , @xmath1 , @xmath2 and @xmath3 band lightcurves to a single power - law expression @xmath18 , where @xmath19 is the index and @xmath20 is the time after the burst , we get @xmath21 ( @xmath22= 2.90 for @xmath23 ) for the @xmath0 band , @xmath24 ( @xmath22= 2.60 for @xmath25 ) for the @xmath1 band , @xmath26 ( @xmath22= 5.3 for @xmath27 ) for the @xmath2 band , and @xmath28 ( @xmath22= 7.7 for @xmath29 ) for the @xmath3 band . this single power - law fitting indicates that these lightcurves , obtained with different filters have similar power - law decay even though the reduced chi - square values are relatively large . since the data sets of the @xmath1 and @xmath2 measurements are more complete , it is possible with following expression to attempt the fitting of the corresponding lightcurves with a smoothly broken power - law function : @xmath30^{(1/k)}},\ ] ] where @xmath31 is the break time , @xmath4 and @xmath7 are the power - law indices before and after @xmath31 , @xmath32 is flux at break @xmath31 , and @xmath33 is a smoothness factor . for the @xmath1 band , we obtain @xmath34 , @xmath35 , @xmath31 = 0.042 @xmath6 0.058 days and @xmath36 ( @xmath22= 1.48 for @xmath37 ) . for the @xmath2 band , we obtain @xmath38 , @xmath39 , @xmath40 days , and @xmath41 ( @xmath22= 2.24 for @xmath42 ) . this result implies a mild break in both the @xmath1 and the @xmath2 band lightcurves at around 0.04 days after the occurrence of the grb . taking @xmath31 = 0.04 days , we fit the data in the @xmath0 and @xmath3 bands to a respective power - law before and after the break . in this manner , we find @xmath4 = @xmath50.79 @xmath6 0.09 ( @xmath43 for @xmath44 ; @xmath7 = @xmath50.36 @xmath6 0.05 ( @xmath45 for @xmath46 for the @xmath0 band and @xmath7 = @xmath50.52 @xmath6 0.15 ( @xmath47 for @xmath46 for the @xmath3 band . the best - fit parameters for the @xmath0 , @xmath1 , @xmath2 , and @xmath3 bands are summarized in table 2 . our results show not only the clear presence of mild breaks in the @xmath1 , @xmath2 band lightcurves but a flattening trend after the break . furthermore , our @xmath2 band slope before the break ( @xmath48 ) is in agreement with the corresponding value derived by quimby et al . ( 2006 ) for the interval between 0.0019 and 0.05 days after the burst . our multi - wavelength observations indicate that median colors between 0.07 and 0.35 days are @xmath49 , @xmath50 , and @xmath51 . these values have been corrected for foreground reddening of e(@xmath52 0.011 mag ( schlegel et al . the @xmath53 and @xmath54 colors so derived are consistent with those of the typical long grbs ( simon et al . 2001 ) , but the @xmath55 color is slightly redder than those of the typical long grbs ( @xmath56 ) . the larger @xmath55 value may imply a certain absorption effect because the redshift of grb050319 was determined to be 3.24 ( fynbo et al . 2005 ) . the @xmath0 , @xmath1 , @xmath2 and @xmath3 magnitudes have been further converted to fluxes using the effective wavelengths and normalizations of fukugita et al . the effect of the galactic interstellar extinction has been corrected . figure 2 shows two samples of spectral energy distribution obtained by lot at 0.13 and 0.21 days after the occurrence of grb050319 . a drop in the @xmath0 band flux at about @xmath57 can be clearly seen . we subsequently fitted the flux distribution of @xmath1 , @xmath2 and @xmath3 bands with a power - law function @xmath58 ; here @xmath59 is the flux at frequency @xmath60 with a certain @xmath20 and @xmath61 is the spectral index . we find that @xmath62 ( @xmath22= 0.05 for @xmath63 ) at 0.13 days and that @xmath64 ( @xmath22 = 2.3 for @xmath63 ) at 0.21 days . our result ( @xmath65 with a rms error 0.23 ) is consistent with the x - ray fitting value ( @xmath66 ) in a 3-@xmath67 level . with a redshift of 3.24 , the ly@xmath68 absorption feature would shift into the @xmath0 bandpass , causing reduction of the afterglow flux in the @xmath0 band . to correct for this absorption effect , we used the formulation derived by yoshii et al . ( 1994 ) , in which the optical depth is a function of the observed wavelength and source redshift . with the computed optical depth in the @xmath0 band , and a spectral slope of @xmath69 , we found the expected @xmath0 band magnitude after ly@xmath68 absorption to be @xmath70 at 0.13 days . this value compares very well with our observed value of @xmath0 = 21.26 @xmath6 0.17 at 0.13 days after correction for galactic extinction . the drop at the b band is hence fully produced by the ly@xmath68 absorption and no spectral breaks should have taken place during our observation . it is important to note that _ swift _ found two breaks at 0.004 and 0.313 days after the burst in the x - ray afterglow observations ( cusumano et al . 2006 ) , but we only found a single break in our @xmath1 and @xmath2 lightcurves ( see figure 1 ) . in the following since there are more data points available for the @xmath2 band data we will focus on this . it is useful to remember that @xmath4 = @xmath71 and @xmath72 at the break time of @xmath31 = 0.04 days . the slope @xmath4 ( = @xmath50.84 ) is consistent with the typical range of @xmath74 to @xmath75 for many well observed grbs . according to the standard afterglow model relating the power - law index ( @xmath19 ) to the power - law index ( @xmath76 ) of an electron spectrum ( zhang & mszros , 2004 ; dai & cheng , 2001 ) , the corresponding value for @xmath77 is @xmath76 = 2.1 , which is in agreement with the constant - density ism model with slow cooling in which @xmath78 2 for @xmath79 ( @xmath80 is the typical frequency ; @xmath81 is the optical frequency ; @xmath82 is the cooling frequency ) . in light of the xrt observations , the first break was likely caused by the transition from the tail end of the low energy prompt emission to the afterglow phase ( zhang et al . however , it is important to note that the x - ray break at 0.004 days ( where the steeper slope becomes shallow ) is not accompanied by an @xmath2 band break . at the same time , the power - law decay slope in the x - ray ( @xmath83 5.53 ) and the @xmath2 band ( @xmath83 0.84 ) are quite different . this is an indication not only that the behaviors of the x - ray afterglow and optical afterglow of the grb050319 event are different , but also suggested that the afterglow phase already dominated the optical bands when the optical emission was first detected . the power law index becomes shallow after the break ( @xmath31 = 0.04 days ) . neither the jet ( rhoads 1999 ) nor the break frequencies across the optical wavelength ( sari et al . , 1998 ) suitably explain the break they see in the grb050319 lightcurves . as discussed before , the x - ray lightcurve between the two breaks 0.004 and 0.313 days after the burst is also characterized by shallow decay . zhang et al . ( 2006 ) suggested that such behavior is related to continuous energy injection into the ism . for a long - lasting central engine , the energy injection rate is @xmath84 and with @xmath85 ( zhang & mszros 2001 ) . for slow cooling in the ism , the temporal index can be expressed as : @xmath86 / 4 = [ ( q-1 ) + { ( 2+q)\beta ] / 2},$ ] when @xmath87 . using this formulation , zhang et al . ( 2006 ) obtained @xmath88 = 0.6 and @xmath89 = 2.4 from the x - ray observations . with @xmath19 = @xmath50.48 and @xmath61 = @xmath51.08 from the @xmath2 band observations , we find that @xmath88 = 0.72 and @xmath89 = 2.12 . the results not only indicate that the electron spectrum power law index is the same before and after the break , they also compare well with the results of zhang et al . these results indicate that the shallow decays evidenced by both x - ray and optical afterglows could be of a similar origin , related to a continuous energy injection mechanism . according to the energy injection model , would also expect an x - ray break at the time of the optical flattening break , because the onset of the energy injection should also alter the x - ray temporal index . however , such an x - ray break is not observed , which suggests that some modifications to the injection model may be needed . as mentioned in @xmath90 4.1 , the x - ray break at 0.004 days was not accompanied by a break in the @xmath2 lightcurve . although a chromatic break in the x - ray was found at 0.004 days and in the optical region at 0.04 days , the lightcurves at both wavelengths indeed showed shallow decay after the breaks , which can be explained by the energy injection model . however , it is difficult for energy injection from 0.004 days to 0.04 days to affect only high energies . this difficulty indicates that energy injection is an imperfect mechanism for explaining the shallow optical or x - ray phase associated with the grb050319 event . several models have recently been proposed to explain the shallow decay effect . using the multiple - subjet model ( nakamura , 2000 ) , toma et al . ( 2006 ) invoked the superposition of afterglows from many off - axis subjets . eichler & granot ( 2006 ) favored a combination of the tail of prompt emission model with the afterglow emissions observed from a viewing angle outside the edge of the jet . these arguments hence suggest that the multiple - subjet model and the patchy - shell model ( kumar & piran , 2000 ) might provide a theoretical basis for explaining the observed shallow decays in the x - ray and optical lightcurves . it is interesting to note that in order to sustain the shallow decay process these models all require high gamma - ray efficiency ( 75 - 90@xmath91 ) ; additional mechanisms such as prior activity ( ioka et al . 2005 ) and time - dependent shock generation ( fan & piran , 2006 ) have been also proposed . comprehensive multi - wavelength observations , such as those reported here , provide important keys to improve these models . finally , the second break in the x - ray emissions ( @xmath92 0.313 days after the burst ) , has been interpreted as being due to an unusual flat jet break ( cusumano et al . 2006 ) , zhang et al . ( 2006 ) however provided an alternate explanation , a sudden cessation of the energy injection . in both interpretations , the corresponding break should appear in both the x - ray and optical lightcurves . this effect can not be clearly identified in our measurements until 0.413 days after the burst . the lack of data for the subsequent time interval could lead to uncertainty in the power - law fitting . we thus can not fully exclude the existence of a second break in the optical lightcurves . however , panaitescu et al . ( 2006 ) have studied several afterglows . they found the shallow power - law decay evidenced by the x - ray emissions to steepen about [email protected] days after the burst , although there was no accompanying break found in the optical range . they suggest that such chromatic x - ray breaks may be common . the chromatic breaks ( e.g. the shallow x - ray phase becomes steeper , with no accompanying optical break ) may be caused by differences in the x - ray and optical outflow ( panaitescu et al . 2006 ) , or by changes in the typical electron energy parameters ( the so - called microphysical parameters ) at the end of energy injection ( panaitescu 2006 ) . * the @xmath0 , @xmath1 , @xmath2 , and @xmath3 band lightcurves displayed unusual shallow decays . * the @xmath2 lightcurve can be described by a smooth broken power - law function . @xmath93 becomes shallow ( @xmath94 ) 0.04 days after the occurrence of the grb . * the shallow decay observed in the x - ray and optical lightcurves may have a similar origin related to energy injection . however , our observations indicate that there is still a major puzzle remaining concerning the chromatic breaks in the @xmath2 band lightcurve ( at 0.04 days ) and the x - ray lightcurve ( at 0.004 days ) . * our calculations revealed that the drop in spectral energy distribution was fully caused by a shift in the ly@xmath68 absorption to the @xmath0 bandpass at @xmath95 = 3.24 . we thank the referee for his / her valuable advice . this work is supported by nsc95 - 2752-m-008 - 001-pae , nsc95 - 2112-m-008 - 021 , the japan society for the promotion of science ( jsps ) grant - in - aid for young scientists ( b ) no.18740147 and jsps research fellowships for young scientists ( y.u . ) . blustin , e. et al . 2006 , 637 , 901 cusumano , g. et al . 2006 , , 639 , 316 dai , z. g. , & cheng , k. s. 2001 , , 558 , 109 eichler , d. , & granot , j. 2006 , , 641 , l5 fan , y. , & piran , t. 2006 , , 369 , 197 fynbo , j. p. u. et al . 2005 , gcn circ . 3136 fukugita , m. , shimasaku , k. , & ichikawa , t. 1995 , pasp , 107 , 945 gehrels , n. et al . 2004 , 611 , 1005 george , k. , banerjee , d. p. k. , chandrasekhar , t. , & ashok , n. m. 2006 , 640 , l13 greco , g. , bartolini , c. , guarnieri , a. , piccioni , a . , ferrero , p. & bruni , i. 2005 , gcn circ . 3142 henden , a. 2005 , gcn circ . 3454 ioka , k. , toma , k. , yamazaki , r. , & nakamura , t. 2005 , a&a in press ( astro - ph/0511749 ) kinoshita , d. , et al . 2005 , chjaa , 5 , 315 kiziloglu , u. et al . 2005 , gcn circ . 3139 krimm , h. et al . 2005 , gcn circ . 3119 kumar , p. & piran , t. 2000 , , 535 , 152 mason , k. o. et al . 2006 , , 639 , 311 misra , k. , kamble , a. p. & pandey , s.b . 2005 , gcn circ . 3130 nakamura , t. 2000 , , 534 , l159 nousek , j. a. et al . 2006 , , 642 , 389 panaitescu , a. , mszros , p. , burrows , d. , nousek , j. , obrien , p. & willingale , r. 2006 , mnras , 369 , 2059 panaitescu , a. , 2006 , preprint ( astro - ph/0607396 ) quimby , r. m. et al . 2006 , , 640 , 402 rhoads , j. e. 1999 , , 525 , 737 rykoff , e. , schaefer , b. , & quimby , r. 2005 , gcn cir . 3116 rykoff , e. et al . 2006 , , 638 , l5 sari , r. , piran , t. , & narayan , r. 1998 , , 497 , l17 schlegel , d. j. , finkbeiner , d. p. , & davis , m. 1998 , apj , 500 , 525 sharapov , d. et al . 2005a , gcn circ . 3124 sharapov , d. et al . 2005b , gcn circ . 3140 simon , v. , hudec , r. , pizzichini , g. , & masetti , n. 2001 , a&a , 377 , 450 stetson , p. b. 1987 , pasp , 99 , 191 toma , k. , ioka , k. , yamazaki , r. & nakamura , t. 2006 , 640 , l139 torii , k. 2005 , gcn circ . 3121 urata , y. et al . 2005 , nuovo cimento , 28 , 775 woniak , p. r. , vestrand , w. t. , wren , j. a. , white , r. r. , evans , s. m. , & casperson , d. 2005 , apj , 627 , l13 yoshii , y. & peterson , b. a. 1994 , , 436 , 551 yoshioka , t. et al . 2005 , gcn circ . 3120 zhang , b. , & mszros , p. 2001 , , 552 , l35 zhang , b. , & mszros , p. 2004 , int . j. mod . a. , 19 , 2385 zhang , b. et al . 2006 , , 642 , 354 cccc days after grb & filter & magnitude & site + 0.05443 & r & [email protected] & kiso + 0.06023 & b & [email protected] & kiso + 0.08037 & v & [email protected] & lulin + 0.10439 & i & [email protected] & lulin + 0.27821 & b & [email protected] & kiso + 0.33424 & i & [email protected] & lulin + 0.40097 & v & [email protected] & lulin + 0.41346 & r & [email protected] & lulin + .fitting results of the grb050319 lightcurves : the @xmath0 and @xmath3 band data were fitted by a respective power - law model [ @xmath96 before and after the break ( @xmath97 ) . on the other hand , the @xmath1 and @xmath2 data were fitted by a smoothly broken power - law [ equation ( 1 ) ] . [ cols="^,^,^,^ " , ] ] for the @xmath0 band ( @xmath98 ) and the @xmath3 band ( @xmath99 ) . the dashed line indicates the best fit by the smooth broken power - law [ equation ( 1 ) ] with the @xmath1 band ( @xmath100 , @xmath35 , @xmath31 = 0.042 @xmath6 0.058 days ) and the @xmath2 band ( @xmath101 , @xmath39 , @xmath31 = 0.046 @xmath6 0.008 days ) . these observations are based on our eafon data and quimby et al . ( 2006 ) , woniak et al . ( 2005 ) , mason et al . ( 2005 ) , greco et al . ( 2005 ) , kiziloglu et al . ( 2005 ) , misra et al . ( 2005 ) , and sharapov et al . ( 2005a , b ) . the dotted lines represent the break times of x - ray afterglows at 0.004 and 0.31 days after the burst . the two breaks were not found in x - ray observations , but a mild break seems to exist in the @xmath1 and @xmath2 band lightcurves . , scaledwidth=80.0% ] , @xmath2 and @xmath3 bands at 0.13 and 0.21 days after the burst ( corrected for galactic extinction ) . the solid and dashed lines indicate the best fit by the power - law model [ @xmath102 , where @xmath103 for 0.13 days and @xmath64 for 0.21 days , respectively.,scaledwidth=80.0% ][/INST] multi - wavelength @xmath0 , @xmath1 , @xmath2 , @xmath3 observations of the optical afterglow of grb050319 were performed by the 1.05-m telescope at kiso observatory and the 1.0-m telescope at lulin observatory from 1.31 hours to 9.92 hours after the burst . our @xmath2 band lightcurves , combined with other published data , can be described by the smooth broken power - law function , with @xmath4 = @xmath50.84 @xmath60.02 to @xmath7 = @[email protected] , 0.04 days after the grb . the optical lightcurves are characterized by shallow decays as was also observed in the x - rays which may have a similar origin , related to energy injection . however , our observations indicate that there is still a puzzle concerning the chromatic breaks in the @xmath2 band lightcurve ( at 0.04 days ) and the x - ray lightcurve ( at 0.004 days ) that remains to be solved . </s>

Cardinal Bernard Law, the disgraced former archbishop of Boston whose years of shielding sexually abusive priests caused generations of pain, has died at the age of 86, a source close to Law told the Herald. Law served as archbishop of Boston from 1984 until his resignation in December 13, 2002, after church documents revealed he was deeply involved in the process of shielding and moving priests who had been accused of sexually abusing children — stunning Catholics and community leaders who had known him as a relatively progressive archbishop, deeply concerned about racial issues, youth issues, and outreach to Cuba. Attorney Mitchell Garabedian, who represented the victims of priest sex abuse and won multi-million-dollar suits against archdioceses that sheltered priests, said last night that with news in recent days of Law’s impending death, “Many of my clients have expressed that Cardinal Law represents all that was wrong with the Catholic church in allowing children to be abused at the hands of priests. “He was a typical supervisor who allowed the victims and their families to be destroyed, by turning his back on children in need of protection,” Garabedian said. He said his clients voiced “disdain” for Law and “pain.” “This has reminded many of my clients of how painful child abuse is,” Garabedian said. Named archbishop of Boston Jan. 11, 1984, documents show he immediately became embroiled in the priest sex abuse scandal, when he received a letter from a bishop expressing concerns about Rev. John Geoghan — a priest later convicted of abusing children who was eventually murdered in prison. Barbara Dorris, executive director for SNAP — Survivors Network of those Abused by Priests — said of survivors’ reaction to Law’s death, “I don’t think there’s going to be any great sadness.” In the scandal that unfolded over the course of the decade and remain still unresolved, she said, “He was the first big name that got out there, where there were documents to prove what was done. We all hoped that church officials would do the right thing and he would be removed and live out the rest of his days in some out of the way place.” She noted instead he was recalled to the Vatican and given a new title and position in the church. Law would eventually say in apology: “With all my heart, I wish to apologize once again for the harm done to the victims of sexual abuse by priests. I do so in my own name, but also in the name of my brother priests. These days are particularly painful for the victims of John Geoghan. My apology to them and their families, and particularly to those who were abused in assignments which I made, comes from a grieving heart. I am indeed profoundly sorry. “The trust that was broken in the lives of those suffering the effects of abuse is a trust which was built upon the selfless lives of thousands of priests who have served faithfully and well in this archdiocese throughout its history,” Law said. “One of the sad consequences of these instances of abuse, a consequence which pales in comparison to the harm done to these most innocent of victims, is that they have placed under a cloud of suspicion the faithful priests who serve the mission of the Church with integrity.” ||||| Cardinal Bernard F. Law, whose 19-year tenure as head of the Archdiocese of Boston ended in his resignation after it was revealed he had failed to remove sexually abusive priests from the ministry, setting off a scandal that reached around the world, died Tuesday. He was 86. The Vatican’s newspaper confirmed his death early Wednesday. � morto a 86 anni il cardinale statunitense Bernard Francis Law. Dal 1984 al 2002 era stato arcivescovo di Boston — L'Osservatore Romano (@oss_romano) December 20, 2017 Cardinal Law will be buried in Rome, according to a statement from his successor, Cardinal Sean P. O’Malley. Advertisement O’Malley wrote that Cardinal Law’s passing “brings forth a wide range of emotions on the part of many people.” Get Today's Headlines in your inbox: The day's top stories delivered every morning. Sign Up Thank you for signing up! Sign up for more newsletters here “As Archbishop of Boston, Cardinal Law served at a time when the Church failed seriously in its responsibilities to provide pastoral care for her people, and with tragic outcomes failed to care for the children of our parish communities,” he said. Boston’s eighth bishop and fourth archbishop, Cardinal Law was the highest-ranking official in the history of the US church to leave office in public disgrace. Although he had not broken any laws in the Commonwealth — clergy were not required to report child sex abuse until 2002 — his actions led to a sense of betrayal among many Boston Catholics that the church is still dealing with today. The abuse scandal was “the greatest tragedy to befall children — ever” in the Commonwealth, the attorney general’s office said in 2003, and “as archbishop, and therefore chief executive of the archdiocese, Cardinal Bernard Law bears ultimate responsibility for the tragic treatment of children that occurred during his tenure. But by no means does he bear sole responsibility.” The attorney general’s office said the abuse extended over six decades and involved at least 237 priests and 789 children; of those, 48 priests and other archdiocesan employees were alleged to have abused children while Law was leader of the Boston archdiocese. Advertisement In 2004, after Cardinal Law’s resignation, Pope John Paul II appointed him archpriest of the Patriarchal Basilica of St. Mary Major, and he moved to Rome. The controversial appointment was a reminder of the regard in which the Vatican held Cardinal Law. Widely seen as a Vatican loyalist and champion of church orthodoxy, he had been a favorite of John Paul II and Cardinal Joseph Ratzinger, prefect of the Sacred Congregation for the Doctrine of the Faith, who later became Pope Benedict XVI. At a bishops synod in Rome in 1985, Cardinal Law proposed the publication of a new Catholic catechism. The result was the first universal catechism since the Council of Trent, in the 16th century. Cardinal Law was given responsibility for drafting the catechism’s English translation. Cardinal Law was just 41 when he was named bishop of Missouri’s Springfield-Cape Girardeau diocese. Few US priests become bishops before 45. Another sign of Vatican favor was Cardinal Law’s having served as archbishop for only a little more than a year before receiving his red hat. The archdiocese’s first cardinal, William H. O’Connell, had served four years, Cardinal Richard J. Cushing 14, and Cardinal Humberto J. Medeiros three. Harvard educated and the onetime editor of a diocesan newspaper, in Mississippi, Cardinal Law appeared to be a departure from a more insular, less media-attuned church, when he was named archbishop of Boston in 1984. Yet in a key respect, he was a throwback: Cardinal Law believed in being in charge and staying in touch. Whenever a priest in the archdiocese died, Cardinal Law would attend the funeral. He also would go to great lengths to visit hospitalized priests and their relatives. Cardinal Law’s former secretary once joked that the worst torture for his boss would be being bound up with a phone ringing just beyond his reach. For a time, he used a helicopter to get around the 2,500-square-mile archdiocese. He introduced a cabinet system to administer the archdiocese, as well as a fifth episcopal region, Merrimack. The other regions are South, West, Central, and North. Advertisement Cardinal Law had the solemn manner and stately bearing of one accustomed to deference. According to a parishioner of one of the most notorious sexually abusive priests, the Rev. Paul Shanley, Cardinal Law was dismissive when she warned him about Shanley’s behavior. “See my bishops,” he said. “That’s why I have them.” As a young man, he had thought of the Foreign Service as a career; and with his thatch of white hair, thick build, square jaw, and deliberate speech, he had the distinguished appearance and demeanor of a banker or diplomat. More than that, Cardinal Law conveyed the sense of being someone conscious of having such an appearance and manner. He may have lacked the colorfulness and common touch of Cardinal Cushing; but he shared Cushing’s comfort with being in the spotlight. This contrasted sharply with Cardinal Law’s immediate predecessor, Cardinal Medeiros, who had been ill at ease with the public aspects of being a prelate. Cardinal Law embraced those duties. Where Medeiros had suffered from comparisons with the much-beloved figure of Cushing, Cardinal Law benefited from comparisons with Medeiros. Medeiros, an immigrant from the Azores who grew up in Fall River, had never been fully accepted by his largely Irish flock. Cardinal Law did not face that problem. “I have a sense of being loved and accepted,” he said at the time of his elevation to cardinal. As the historian Thomas O’Connor put it in “Boston Catholics: A History of the Church and Its People,” “Law’s appointment was roundly greeted with enthusiasm by local residents as a welcome return to a more familiar Boston ecclesiastical tradition.” The clearest sign of that enthusiasm was financial. Donations to the archdiocese rose 50 percent after Cardinal Law’s arrival and within five years had doubled. The archdiocese had accumulated an enormous debt load as a result of Cushing’s extensive building program. One reason for Medeiros’s relative lack of popularity was his having to make budget cuts and focus on administrative matters at the expense of pastoral duties he would have preferred to focus on. By the time of his death, Medeiros had largely retired the debt. So Cardinal Law could take over the archdiocese under relatively happy financial circumstances. One consequence was his being able to institute the archdiocese’s first capital fund drive. Unlike Medeiros, Cardinal Law did not have to deal with the divisiveness of court-ordered school desegregation, which cast such a shadow over the city in the 1970s. Involvement in the controversy was thrust upon Medeiros. In contrast, Cardinal Law’s involvement in political issues could be of his own choosing. That involvement was considerable. “Boston Catholics” relates the response of an anonymous diocesan priest to the news of Cardinal Law’s appointment: “Oh God, we’re getting a Midwestern liberal!” That characterization wasn’t entirely wrong. Cardinal Law supported lifting the embargo on Cuba and favored forgiving Third World debt obligations. He opposed the death penalty, advocated for public housing, and vigorously reached out to the growing Hispanic, Haitian, and Southeast Asian immigrant communities in the archdiocese. He urged defeat of a referendum to make English the official language of Lowell. More often, Cardinal Law took conservative positions, both doctrinally and politically. In his first speech as archbishop, he called abortion a “national disgrace” and the “primordial evil of our time, the cloud that shrouds the conscience of our world.” A year later, he referred to abortion as “the critical issue of the moment” and criticized US Representative Geraldine Ferraro, the Democratic vice presidential nominee in 1984, for her support of abortion rights. Ferraro was also criticized by Cardinal John J. O’Connor of New York. Cardinal Law and O’Connor had been named archbishops within two weeks of each other. Their conservative political views and consistent support of church orthodoxy inspired a joint nickname, “Law and Order.” Speaking at the Boston College commencement in 1986, Cardinal Law warned the university against losing its Catholic identity: “My prayer is for a Boston College ever more clearly Catholic.” During a 1998 visit to the United States, Irish President Mary McAleese met Cardinal Law. He criticized her for supporting the ordination of women as Catholic priests. McAleese replied that she was “the president of Ireland and not just of Catholic Ireland.” In 1990, he restored the Latin Mass, allowing it to be said at Holy Trinity Church in the South End. As an undergraduate, Cardinal Law had campaigned for Democratic presidential nominee Adlai Stevenson. As cardinal, he was friendly with President George H.W. Bush and his wife, Barbara. An occasional overnight guest at the summer White House at Kennebunkport, Maine, he spoke to the president monthly. In 1999, Cardinal Law publicly, and unsuccessfully, opposed two nominations to the Supreme Judicial Court, of Margaret Marshall as chief justice and Judith Cowin as associate justice, saying their records left them “open to serious charges of anti-Catholicism.” He was more successful a year later, when he urged that the Interstate 93 crossing over the Charles River honor the late head of the Anti-Defamation League of New England, and it was subsequently named the Leonard P. Zakim Bunker Hill Memorial Bridge. Cardinal Law encouraged interfaith relations. “For Cardinal Law, in the Jewish community, there is a reverence,” Harold Schwartz, a former chairman of the Anti-Defamation League, said in 2002. Zakim once said that an extemporaneous talk about the significance of the Auschwitz death camp that the cardinal gave to a group of Catholics in 1986 “was the best presentation about the Holocaust that I’ve ever heard from a non-Jew.” An example of Cardinal Law’s sensitivity to the Jewish community was his urging a group of Polish Carmelite nuns (an aunt of the cardinal’s had been a Carmelite) to move their convent from its location on the Auschwitz grounds. Poland was one of several countries Cardinal Law visited during his tenure. Others included Mexico, Nicaragua, and Cuba. Cardinal Law, who spoke fluent Spanish, visited the island nation five times and met with Fidel Castro on several occasions, once for more than four hours. Cardinal Law, Boston College religious historian Thomas Wangler said in 1990, was “the first archbishop of Boston to have a foreign policy.” Clergy sex abuse in the archdiocese preceded Cardinal Law’s arrival in Boston, in 1984, and its first significant US public disclosure was elsewhere (in Louisiana, in 1985). But in Boston, revelations about the Rev. John J. Geoghan’s long history of sexual molestation of children triggered the scandal locally. His actions first came to the attention of archdiocesan officials during the tenure of Cushing (1944-1970), and Geoghan was ordered to receive counseling by Medeiros as early as 1980. Less than a year after Cardinal Law assumed leadership of the archdiocese, he agreed to the removal of Geoghan from a Dorchester parish. Less than two months later, Cardinal Law assigned him to St. Julia Parish, in Weston. Auxiliary Bishop John M. D’Arcy objected, noting in a memo, “If something happens, the parishioners . . . will be convinced the Archdiocese has no concerns for their welfare and simply sends them priest with problems.” Geoghan stayed at St. Julia’s. Clergy sex abuse became front-page news in Massachusetts in 1992, with accusations against James R. Porter, a former priest in the Fall River diocese. A year later, he would be sentenced to 18 to 20 years in prison. Cardinal Law, in his regular column for the archdiocesan newspaper, The Pilot, wrote: “From such evil acts, like a pebble dropped into a placid pool of water, there are ever-widening concentric circles of betrayal and anguish.” Cardinal Law decried press attention to Porter. “The papers like to focus on the faults of a few,” he said. “We deplore that. . . . By all means, we call down God’s power on the media, particularly the Globe.” In July 2001, Cardinal Law wrote in The Pilot that “Never was there an effort on my part to shift a problem from one place to the next.” The column was a response to press reports which had run in The Boston Phoenix, The Boston Herald, and the Globe about Geoghan and how the archdiocese had handled his case. The Globe successfully sued to have court documents relating to Geoghan unsealed. With those documents and a database compiled from publicly available archdiocesan reports, the Globe Spotlight team began amassing information on clergy sex abuse in the archdiocese and the church hierarchy’s covering up the scandal and protecting priests even at the risk of possible future victims. Those events form the basis of the feature film “Spotlight.” Len Cariou plays Cardinal Law. The first Spotlight story, which ran on Jan. 6, 2002, focused on Geoghan. Intense public outcry ensued. Within days, a beleaguered Cardinal Law was offering apologies and attempting to justify his actions. Several hundred articles followed over the course of the year. Signs began to appear, “Honk if you want the cardinal to resign.” On “The Tonight Show,” Jay Leno referred to “Cardinal Above the Law” and described an episode of the television series “E.R.” on which “doctors in Boston try desperately to remove Cardinal Law’s foot from his mouth.” A public opinion poll showed that 75 percent of US Catholics thought Cardinal Law was lying about his knowledge of the scandal and 64 percent felt he should resign. Only 18 percent of local Catholics professed to have a favorable opinion of the cardinal. Late in the year, 58 priests publicly called for his resignation. On May 18, Cardinal Law released a letter, which was read to congregations throughout the archdiocese: “Bewilderment has given rise to anger and distrust. In the process, my credibility has been publicly questioned and I have become for some an object of contempt. I understand how this is so, and I am profoundly sorry that the inadequacy of past policies and flaws in past decisions have contributed to this situation.” In June, Cardinal Law said in a Globe interview, “The primary focus has got to be on children, and if it is, then the way you handle these other problems is going to be different, and it’s that focus that has come to me with a new clarity.” In August, he became the first sitting prelate to be sworn in as a trial witness. Some Catholics steadily supported Cardinal Law. In November, Harvard Law School professor and future US ambassador to the Vatican Mary Ann Glendon spoke at a conference in Rome. She concluded her remarks by saying, “I often hear it said that the Globe will receive a Pulitzer Prize for its reporting” on the scandal. “All I can say is that if fairness and accuracy have anything to do with it, awarding the Pulitzer Prize to The Boston Globe would be like giving the Nobel Peace Prize to Osama bin Laden.” Five months later, the Globe received the Pulitzer Prize for public service. Cardinal Law resigned on Dec. 13. “It is my fervent prayer that this action may help the Archdiocese of Boston to experience the healing, reconciliation, and unity which are so desperately needed,” he said in a prepared statement. “To all those who have suffered from my shortcomings and mistakes, I both apologize to them and beg forgiveness.” O’Malley, bishop of Palm Beach, Fla., was appointed to succeed Cardinal Law, in July 2003. But the impact of the scandal continued for years. The archdiocese agreed to pay $85 million to 552 victims of clergy sex abuse in 2003. It had already paid $10 million to settle 50 previous suits against Geoghan. For a time, the archdiocese explored the possibility of bankruptcy. The grand quarters for the cardinal’s residence and archdiocesan chancery in Brighton, built by the archdiocese’s first cardinal, William H. O’Connell, would be sold to Boston College after Cardinal Law’s resignation to help pay settlements from the many suits arising from the sex-abuse scandal. An only child, Bernard Francis Aloysius Law was born on Nov. 4, 1931, in the city of Torreón, in north-central Mexico. Cardinal Law’s father, Bernard A. Law, a former Army Air Force pilot, worked in commercial aviation. He was Catholic. Cardinal Law’s mother, Helen (Stubblefield) Law, a Presbyterian, later converted to Catholicism. The family moved six times during his youth, and Cardinal Law attended schools in New York, Florida, Georgia, Colombia, and the Virgin Islands. At Charlotte Amalie High School, in St. Thomas, all but one of his teachers were black. Cardinal Law, one of only five white students in his graduating class, was both class president and valedictorian. A history major at Harvard, Cardinal Law was vice president of the university’s Catholic Club. Among his roommates were a Southern Baptist and two Jewish students. Cardinal Law entered St. Joseph Seminary College, in St. Benedict, La., in 1953. “The two years that I spent at St. Joseph’s were perhaps the two most significant years of my life thus far,” he wrote in his Harvard 25th reunion report. In 1955, he entered the Pontifical College Josephinum, in Worthington, Ohio. Cardinal Law was ordained a priest in 1961 for the Diocese of Natchez-Jackson. His first appointment was as an assistant pastor in Vicksburg, Miss. He would never have his own parish. It would later be suggested that Cardinal Law’s limited pastoral experience contributed to his response to the sex-abuse scandal, leading him to see it from the viewpoint of priest and institution rather than victim and family. He was soon made editor of The Mississippi Register, the diocese’s statewide weekly newspaper. Its strong support for the civil rights movement brought Cardinal Law death threats. “Mississippi in the ’60s was all that one might imagine and more,” Cardinal Law wrote in his 25th reunion report. “To have been a part of that significant moment of our history is in itself a grace, a gift.” In 1965, Cardinal Law attended the last session of the Second Vatican Council. He moved to Washington, D.C., in 1968 to become executive director of the Bishops’ Committee for Ecumenical and Interreligious Affairs. His three years in the post introduced Cardinal Law to leading figures in the US church hierarchy. He became a protégé of William Baum, Cardinal Law’s predecessor as executive director, and later archbishop of Washington, D.C. Baum also preceded Cardinal Law as bishop of Springfield-Cape Girardeau. Cardinal Law served in Missouri from 1973-1983, having returned to Mississippi to be vicar general of Natchez-Jackson from 1971-1973. “Delighted at being planted in the beautiful Ozarks,” he wrote in his 25th reunion report, he added that “The more active involvement in social concerns of the ’60s has now been placed in a broader context of pastoral ministry.” Arriving at Logan Airport after being named archbishop, Cardinal Law drew laughter when he said that the Vatican’s apostolic delegate had told him that “after Boston, there is only heaven.” Following his resignation, Cardinal Law lived at a convent in Clinton, Md., until his appointment as archpriest of St. Mary Major. The post, while largely ceremonial, is considered prestigious. The church, built in the fifth century and one of Rome’s most famous, is a popular destination for pilgrims and tourists. The pope visits it semiannually. Cardinal Law, who held the title of archbishop emeritus of Boston, stepped down as archpriest in 2011. Cardinal Law voted in the 2005 conclave that elected Pope Benedict XVI. Some victims-rights groups objected to his participation. The Rev. Keith Pecklers, a Jesuit and professor at the Pontifical Gregorian University in Rome, said at the time in a Globe interview, “The 117 cardinals who are voting are all human beings and they have flaws as we all do. Holiness can come through suffering, from being broken or humbled. And that is Cardinal Law’s experience, I would say.” Because cardinals over 80 do not vote for pope, Cardinal Law did not participate in the conclave eight years later that elected Pope Francis. The day after the new pope’s election, Francis went to pray at St. Mary Major Basilica, where he greeted Cardinal Law “discreetly,” as a Vatican spokesman put it. Writing a month before his resignation, in his Harvard 50th reunion report, Cardinal Law gave this answer to the question of what he would have done differently in life: “Obviously, I wish I would have had the insight I have now about many problems, especially the terrible scourge of the sexual abuse of children. Hindsight would have avoided some horrible mistakes.” Mark Feeney can be reached at [email protected] ||||| VATICAN CITY (Reuters) - Cardinal Bernard Law, the former Archbishop of Boston who resigned in disgrace after covering up years of sexual abuse of children by priests and whose name became a byword for scandal in the Catholic Church, died on Wednesday. The Vatican announced his death just before dawn. It did not give a cause of death but sources close to Law, who died in a hospital in Rome, said he had been suffering from the complications of diabetes, liver failure and a build-up of fluids around the heart, known as pericardial effusion. The telegram of condolences Pope Francis sent to the dean of the College of Cardinals was unusually short and bland compared to those for other cardinals before. Francis said he was praying that the merciful God would “welcome him in eternal peace.” The pope did not mention that Law had been Archbishop of Boston and a brief Vatican biography made no mention of the circumstances of his resignation 15 years ago. Law was Archbishop of Boston, one of the most prestigious and wealthy American archdioceses, for 18 years when Pope John Paul reluctantly accepted his resignation on Dec. 13, 2002, after a tumultuous year in Church history. A succession of devastating news stories by Boston Globe reporters showed how priests who sexually abused children had been moved from parish to parish for years under Law’s tenure without parishioners or law authorities being informed. “No words can convey the pain these survivors and their loved ones suffered,” SNAP, a victims’ group, said. “Survivors of child sexual assault in Boston, who were first betrayed by Law’s cover-up of sex crimes and then doubly betrayed by his subsequent promotion to Rome, were those most hurt,” SNAP said in a statement. Law’s resignation sent shockwaves through the American Church and had a trickle down effect around the world as the cover-up techniques used in Boston were discovered to have been used in country after country. The story of how the Globe team brought the scandal to light in a city where few wanted to cross the politically powerful Church was told in the 2015 film “Spotlight”, which won the Oscar for Best Picture. The situation in Boston turned out to be the tip of an iceberg of abuse and its cover-up, where churchmen preferred protecting the reputation of the institution rather than the innocence of children. Thousands of cases came to light around the world as investigations encouraged long-silent victims to go public, shattering the Church’s reputation in places such as Ireland, and forcing it to pay some $2 billion in compensation. “As Archbishop of Boston, Cardinal Law served at a time when the Church failed seriously in its responsibilities to provide pastoral care for her people, and with tragic outcomes failed to care for the children of our parish communities. I deeply regret that reality and its consequences,” Law’s successor in Boston, Cardinal Sean O‘Malley, said in a statement. Six months after his resignation, the Massachusetts attorney general’s office announced that Law and others would not face criminal charges. GOLDEN PARACHUTE FILE PHOTO - Cardinal Bernard Law of the Boston Archdioceses addresses the U.S. Conference of Catholic Bishops about their stand on the [Iraq] situation, during their annual meeting in Washington, November 12, 2002. REUTERS/Brendan McDermid/File Photo After a period in a monastery in the United States, Law moved to Rome. In 2004 Pope John Paul appointed him to be archpriest of the Rome Basilica of Santa Maria Maggiore, one of the four major basilica’s of Christendom, whose gold leaf ceiling is said to be made from the first batch of the precious metal Columbus brought back from the Americas. He is likely to be buried there. In relative terms it was an immense fall from grace. Such posts are symbolic and ceremonial. But victims of sexual abuse were outraged because it gave Law a second career and a golden parachute that allowed him to stay close to the center of power in Rome and serve as a member or adviser in several influential Vatican departments. He also maintained the rank of cardinal and participated in the conclave that elected Pope Benedict in 2005. Before he became ill, Law was a regular on the diplomatic circuit, attending receptions, including many in the gardens of the U.S. Embassy to the Vatican. Slideshow (4 Images) While Law was an awkward presence at U.S. receptions for a few years after his resignation, at Italian events he was treated with the same effusive obsequiousness bestowed on all cardinals - something Law appeared to enjoy. He always declined to talk about events in Boston. “I‘m retired from that,” he told a reporter at one reception. FOOT DRAGGING O‘Malley, Law’s successor, heads a Vatican commission advising Pope Francis on how to root out sexual abuse in the Church. But the credibility of the commission, which was formed in 2014, has been hurt by the resignation of two high-level lay members who have accused the Vatican of dragging its feet. The terms of most members expired recently and it is not clear what Pope Francis will do with it. Last September, Francis, addressing the commission, said the Catholic Church had moved too slowly to confront abuse. “When consciousness arrives late, the means to resolve the problems also arrive late. I am aware of this difficulty but it is reality and I say it plainly: We arrived late. The old practice of moving people around and not confronting the problem made consciences fall asleep,” the pope said. Bernard Francis Law was born on Nov. 4, 1931, in Torreon, Mexico, the son of a U.S. Army official and a musician. He graduated from Harvard University and was ordained a priest in 1961. His first assignment was in Mississippi, where he received death threats for championing civil rights. As bishop of Springfield–Cape Girardeau in Missouri, he opened a home for battered women and a center to help Vietnamese boat people. The Vatican said Law’s funeral would be held on Thursday afternoon in St. Peter’s Basilica. The Mass will be said by a senior cardinal and the pope will participate in the final blessing, a normal procedure for cardinals. ||||| (CNN) Cardinal Bernard Law, the former Boston archbishop who resigned in disgrace during the Catholic Church's sex abuse scandal, has died, the Vatican confirmed. He was 86. Law died early Wednesday in Rome following a long illness , the Vatican said. Law moved to Italy to serve as archpriest of the Papal Liberian Basilica of St. Mary Major after he was forced to resign in 2002 as archbishop of Boston. Law's name became emblematic of the scandal that continues to trouble the church and its followers after a Boston Globe investigation revealed that he and other bishops covered up child abuse by priests in the Boston Archdiocese. Law at the time apologized to victims of John Geoghan, a priest who had been moved from parish to parish, despite Law's knowledge of his abuse of young boys. Geoghan was convicted in 2002 of indecent assault and battery on a 10-year-old boy. Law never faced criminal sanctions for his role in allowing abusive priests to remain in parishes. The scandal reverberated through the church, exposing similar allegations worldwide that compromised its moral authority and led to years of multimillion-dollar settlements. Pope Francis will give a "final commendation," or blessing, as he has for cardinals' funerals previously. Law will get a full cardinal's funeral at the Vatican's St. Peter's Basilica on Thursday afternoon, with Cardinal Angelo Sodano, dean of the College of Cardinals, presiding.Pope Francis will give a "final commendation," or blessing, as he has for cardinals' funerals previously. Survivors recount betrayal To his detractors, Law's second career at the Vatican was a slap in the face to victims of clergy sex abuse, one that further undermined the church's legitimacy. "Survivors of child sexual assault in Boston, who were first betrayed by Law's cover-up of sex crimes and then doubly betrayed by his subsequent promotion to Rome, were those most hurt," according to a statement after his death from Survivors Network of those Abused by Priests . "No words can convey the pain these survivors and their loved ones suffered." JUST WATCHED Pope open to married men becoming priests Replay More Videos ... MUST WATCH Pope open to married men becoming priests 04:17 The group advised the Vatican to keep the abuse survivors in mind when planning Law's funeral. "Every single Catholic should ask Pope Francis and the Vatican why," the survivors' group said. "Why Law's life was so celebrated when Boston's clergy sex abuse survivors suffered so greatly? Why was Law promoted when Boston's Catholic children were sexually abused, ignored, and pushed aside time and time again?" Widespread child abuse by the Catholic clergy in the Boston Archdiocese was uncovered by The Boston Globe's Spotlight investigative reporting team , which won a Pulitzer Prize for its efforts. A big-screen dramatization of the team's investigation in the 2015 movie, "Spotlight," won the 2016 Best Picture Academy Award, bringing the story to a much wider audience. Law's successor as Boston's archbishop, Cardinal Sean O'Malley, reacted to Law's death in part by apologizing to victims of sex abuse by clergy. "I recognize that Cardinal Law's passing brings forth a wide range of emotions on the part of many people. I am particularly cognizant of all who experienced the trauma of sexual abuse by clergy, whose lives were so seriously impacted by those crimes, and their families and loved ones," O'Malley said. "Cardinal Law served at a time when the church failed seriously in its responsibilities to provide pastoral care for her people, and with tragic outcomes failed to care for the children of our parish communities. I deeply regret that reality and its consequences," O'Malley said. However, he called it a "sad reality" that the scandal has come to define Law's legacy, overshadowing his work in the civil rights era and leadership in the interfaith movement following the Second Vatican Council. "I think all of us are more than one dimensional and I think, to be realistic, we have to recognize that there was more to this man than his mistakes," he said in a news conference on Wednesday. Rise of Boston's spiritual leader Law was born in Torreon, Mexico, on November 4, 1931, to Helen and Bernard Law, an Air Force colonel. He completed his postgraduate studies at St. Joseph's Seminary in Louisiana and at the Pontifical College Josephinum in Columbus, Ohio. He was ordained as a priest on May 21, 1961, in the diocese of Natchez-Jackson, Mississippi, and became vicar general of that diocese in 1971. In 1973, he was appointed bishop of the Springfield-Cape Girardeau diocese in southern Missouri. He served as chairman of the Bishops' Committee on Ecumenical and Interracial Affairs, and in 1976, he was named to the Vatican Commission on Religious Relations with Jews. The posts were stepping stones to his becoming the spiritual leader of Boston's large and influential Catholic community. In 1984, Pope John Paul II appointed Law to be the archbishop of the Boston Archdiocese, with its 362 parishes serving 2.1 million members. That same year, Law received a letter from a bishop expressing concerns about then-Rev. Geoghan. Law assigned Geoghan to another parish despite the allegations. In 1985, Pope John Paul II elevated Law to cardinal, one of just 13 Americans holding that office at the time. JUST WATCHED A Catholic Church cover-up? Replay More Videos ... MUST WATCH A Catholic Church cover-up? 03:16 Calls for resignation Law attempted to resign as archbishop of Boston in April 2002, but Pope John Paul II rejected his request. In 2002, a judge presiding over the child rape case of the Rev. Paul Shanley ordered Cardinal Law to be deposed by lawyers of one of Shanley's victims. Law testified about his supervision of Geoghan in 2002, saying he relied on his assistants to investigate charges of abuse. In May 2002, he apologized for his role in the clergy abuse scandal in a letter distributed throughout the archdiocese. But he denied knowledge of sexual abuse allegations against Shanley until 1993. In August 2002, Law appeared in court to testify about a settlement reached between the archdiocese of Boston and victims of clergy abuse. The archdiocese rescinded the monetary offer shortly afterward. That December, as calls grew for him to resign, Law was subpoenaed to appear before a grand jury investigating "possible criminal violations by church officials who supervised priests accused of sexually abusing children." Days later, he resigned as chairman of the board of trustees of the Catholic University of America, followed by his resignation as archbishop of Boston. Catholic Church abuses under scrutiny The breakdown of trust in the Catholic Church continues to reverberate around the world. JUST WATCHED Archbishop: 'This is a shameful past' Replay More Videos ... MUST WATCH Archbishop: 'This is a shameful past' 01:03 This month, the Australian Royal Commission into Institutional Responses to Child Sexual Abuse delivered, after five years of work, 189 recommendations to address what it described as a "serious failure" by Australia's institutions to protect its most vulnerable citizens. The country's senior Catholic leaders, however, rejected recommendations by the wide-reaching investigation, declining to end mandatory celibacy for priests and break the secrecy of confession. Of survivors who reported abuse in a religious institution, more than 60% said it occurred in a Catholic organization, the report found. When asked if he forgave Law, O'Malley said that forgiveness is what Christianity is all about. But he acknowledged that in Law's case, forgiveness did not come easy. "Hopefully, out of this, it will help to remind all of our Catholics that this is not something that has been solved," he said Wednesday. "The healing is still necessary and we must all be vigilant, particularly for prevention of child abuse." He surmised, though, that the church would handle such transgressions differently today. "I think there's a much greater understanding and sensitivity to the situation," he said. "There's been enough growth and consciousness of this problem in the Holy See that that would not happen.

– He was considered a voice for immigrants, youth, and the poor, but that was before a widespread child sex abuse scandal tarnished his reputation. Cardinal Bernard Law, who resigned as archbishop of the Boston Archdiocese in 2002, died early Wednesday at age 86 from complications of diabetes, liver failure, and fluid around the heart, per CNN and Reuters. Law died in Rome, where he served in the largely ceremonial role of archpriest of the Papal Liberian Basilica of St. Mary Major. The post followed a tumultuous exit in Boston, after church documents showed Law had protected priests accused of child sex abuse, moving them from church to church, per the Boston Herald. The scandal uncovered by the Boston Globe would reverberate throughout the Catholic Church, exposing similar cases around the world. Born in Mexico in 1931, Law was educated at Harvard and ordained as a priest in Mississippi in 1961. He would go on to be made bishop in Missouri before Pope John Paul II appointed him archbishop of the Boston Archdiocese in 1984. He was elevated to cardinal in 1985. Decades later, when it was revealed he had for years shielded accused priests before clergy were required to report abuse, he was recalled to the Vatican and given a new position, to the dismay of abuse victims. "He was a typical supervisor who allowed the victims and their families to be destroyed, by turning his back on children in need of protection," a lawyer who helped win multi-million-dollar settlements for victims tells the Herald. "To all those who have suffered from my shortcomings and mistakes, I both apologize to them and beg forgiveness," Law said in 2002, per the Globe.

<s>[INST]Cardinal Bernard Law, the disgraced former archbishop of Boston whose years of shielding sexually abusive priests caused generations of pain, has died at the age of 86, a source close to Law told the Herald. Law served as archbishop of Boston from 1984 until his resignation in December 13, 2002, after church documents revealed he was deeply involved in the process of shielding and moving priests who had been accused of sexually abusing children — stunning Catholics and community leaders who had known him as a relatively progressive archbishop, deeply concerned about racial issues, youth issues, and outreach to Cuba. Attorney Mitchell Garabedian, who represented the victims of priest sex abuse and won multi-million-dollar suits against archdioceses that sheltered priests, said last night that with news in recent days of Law’s impending death, “Many of my clients have expressed that Cardinal Law represents all that was wrong with the Catholic church in allowing children to be abused at the hands of priests. “He was a typical supervisor who allowed the victims and their families to be destroyed, by turning his back on children in need of protection,” Garabedian said. He said his clients voiced “disdain” for Law and “pain.” “This has reminded many of my clients of how painful child abuse is,” Garabedian said. Named archbishop of Boston Jan. 11, 1984, documents show he immediately became embroiled in the priest sex abuse scandal, when he received a letter from a bishop expressing concerns about Rev. John Geoghan — a priest later convicted of abusing children who was eventually murdered in prison. Barbara Dorris, executive director for SNAP — Survivors Network of those Abused by Priests — said of survivors’ reaction to Law’s death, “I don’t think there’s going to be any great sadness.” In the scandal that unfolded over the course of the decade and remain still unresolved, she said, “He was the first big name that got out there, where there were documents to prove what was done. We all hoped that church officials would do the right thing and he would be removed and live out the rest of his days in some out of the way place.” She noted instead he was recalled to the Vatican and given a new title and position in the church. Law would eventually say in apology: “With all my heart, I wish to apologize once again for the harm done to the victims of sexual abuse by priests. I do so in my own name, but also in the name of my brother priests. These days are particularly painful for the victims of John Geoghan. My apology to them and their families, and particularly to those who were abused in assignments which I made, comes from a grieving heart. I am indeed profoundly sorry. “The trust that was broken in the lives of those suffering the effects of abuse is a trust which was built upon the selfless lives of thousands of priests who have served faithfully and well in this archdiocese throughout its history,” Law said. “One of the sad consequences of these instances of abuse, a consequence which pales in comparison to the harm done to these most innocent of victims, is that they have placed under a cloud of suspicion the faithful priests who serve the mission of the Church with integrity.” ||||| Cardinal Bernard F. Law, whose 19-year tenure as head of the Archdiocese of Boston ended in his resignation after it was revealed he had failed to remove sexually abusive priests from the ministry, setting off a scandal that reached around the world, died Tuesday. He was 86. The Vatican’s newspaper confirmed his death early Wednesday. � morto a 86 anni il cardinale statunitense Bernard Francis Law. Dal 1984 al 2002 era stato arcivescovo di Boston — L'Osservatore Romano (@oss_romano) December 20, 2017 Cardinal Law will be buried in Rome, according to a statement from his successor, Cardinal Sean P. O’Malley. Advertisement O’Malley wrote that Cardinal Law’s passing “brings forth a wide range of emotions on the part of many people.” Get Today's Headlines in your inbox: The day's top stories delivered every morning. Sign Up Thank you for signing up! Sign up for more newsletters here “As Archbishop of Boston, Cardinal Law served at a time when the Church failed seriously in its responsibilities to provide pastoral care for her people, and with tragic outcomes failed to care for the children of our parish communities,” he said. Boston’s eighth bishop and fourth archbishop, Cardinal Law was the highest-ranking official in the history of the US church to leave office in public disgrace. Although he had not broken any laws in the Commonwealth — clergy were not required to report child sex abuse until 2002 — his actions led to a sense of betrayal among many Boston Catholics that the church is still dealing with today. The abuse scandal was “the greatest tragedy to befall children — ever” in the Commonwealth, the attorney general’s office said in 2003, and “as archbishop, and therefore chief executive of the archdiocese, Cardinal Bernard Law bears ultimate responsibility for the tragic treatment of children that occurred during his tenure. But by no means does he bear sole responsibility.” The attorney general’s office said the abuse extended over six decades and involved at least 237 priests and 789 children; of those, 48 priests and other archdiocesan employees were alleged to have abused children while Law was leader of the Boston archdiocese. Advertisement In 2004, after Cardinal Law’s resignation, Pope John Paul II appointed him archpriest of the Patriarchal Basilica of St. Mary Major, and he moved to Rome. The controversial appointment was a reminder of the regard in which the Vatican held Cardinal Law. Widely seen as a Vatican loyalist and champion of church orthodoxy, he had been a favorite of John Paul II and Cardinal Joseph Ratzinger, prefect of the Sacred Congregation for the Doctrine of the Faith, who later became Pope Benedict XVI. At a bishops synod in Rome in 1985, Cardinal Law proposed the publication of a new Catholic catechism. The result was the first universal catechism since the Council of Trent, in the 16th century. Cardinal Law was given responsibility for drafting the catechism’s English translation. Cardinal Law was just 41 when he was named bishop of Missouri’s Springfield-Cape Girardeau diocese. Few US priests become bishops before 45. Another sign of Vatican favor was Cardinal Law’s having served as archbishop for only a little more than a year before receiving his red hat. The archdiocese’s first cardinal, William H. O’Connell, had served four years, Cardinal Richard J. Cushing 14, and Cardinal Humberto J. Medeiros three. Harvard educated and the onetime editor of a diocesan newspaper, in Mississippi, Cardinal Law appeared to be a departure from a more insular, less media-attuned church, when he was named archbishop of Boston in 1984. Yet in a key respect, he was a throwback: Cardinal Law believed in being in charge and staying in touch. Whenever a priest in the archdiocese died, Cardinal Law would attend the funeral. He also would go to great lengths to visit hospitalized priests and their relatives. Cardinal Law’s former secretary once joked that the worst torture for his boss would be being bound up with a phone ringing just beyond his reach. For a time, he used a helicopter to get around the 2,500-square-mile archdiocese. He introduced a cabinet system to administer the archdiocese, as well as a fifth episcopal region, Merrimack. The other regions are South, West, Central, and North. Advertisement Cardinal Law had the solemn manner and stately bearing of one accustomed to deference. According to a parishioner of one of the most notorious sexually abusive priests, the Rev. Paul Shanley, Cardinal Law was dismissive when she warned him about Shanley’s behavior. “See my bishops,” he said. “That’s why I have them.” As a young man, he had thought of the Foreign Service as a career; and with his thatch of white hair, thick build, square jaw, and deliberate speech, he had the distinguished appearance and demeanor of a banker or diplomat. More than that, Cardinal Law conveyed the sense of being someone conscious of having such an appearance and manner. He may have lacked the colorfulness and common touch of Cardinal Cushing; but he shared Cushing’s comfort with being in the spotlight. This contrasted sharply with Cardinal Law’s immediate predecessor, Cardinal Medeiros, who had been ill at ease with the public aspects of being a prelate. Cardinal Law embraced those duties. Where Medeiros had suffered from comparisons with the much-beloved figure of Cushing, Cardinal Law benefited from comparisons with Medeiros. Medeiros, an immigrant from the Azores who grew up in Fall River, had never been fully accepted by his largely Irish flock. Cardinal Law did not face that problem. “I have a sense of being loved and accepted,” he said at the time of his elevation to cardinal. As the historian Thomas O’Connor put it in “Boston Catholics: A History of the Church and Its People,” “Law’s appointment was roundly greeted with enthusiasm by local residents as a welcome return to a more familiar Boston ecclesiastical tradition.” The clearest sign of that enthusiasm was financial. Donations to the archdiocese rose 50 percent after Cardinal Law’s arrival and within five years had doubled. The archdiocese had accumulated an enormous debt load as a result of Cushing’s extensive building program. One reason for Medeiros’s relative lack of popularity was his having to make budget cuts and focus on administrative matters at the expense of pastoral duties he would have preferred to focus on. By the time of his death, Medeiros had largely retired the debt. So Cardinal Law could take over the archdiocese under relatively happy financial circumstances. One consequence was his being able to institute the archdiocese’s first capital fund drive. Unlike Medeiros, Cardinal Law did not have to deal with the divisiveness of court-ordered school desegregation, which cast such a shadow over the city in the 1970s. Involvement in the controversy was thrust upon Medeiros. In contrast, Cardinal Law’s involvement in political issues could be of his own choosing. That involvement was considerable. “Boston Catholics” relates the response of an anonymous diocesan priest to the news of Cardinal Law’s appointment: “Oh God, we’re getting a Midwestern liberal!” That characterization wasn’t entirely wrong. Cardinal Law supported lifting the embargo on Cuba and favored forgiving Third World debt obligations. He opposed the death penalty, advocated for public housing, and vigorously reached out to the growing Hispanic, Haitian, and Southeast Asian immigrant communities in the archdiocese. He urged defeat of a referendum to make English the official language of Lowell. More often, Cardinal Law took conservative positions, both doctrinally and politically. In his first speech as archbishop, he called abortion a “national disgrace” and the “primordial evil of our time, the cloud that shrouds the conscience of our world.” A year later, he referred to abortion as “the critical issue of the moment” and criticized US Representative Geraldine Ferraro, the Democratic vice presidential nominee in 1984, for her support of abortion rights. Ferraro was also criticized by Cardinal John J. O’Connor of New York. Cardinal Law and O’Connor had been named archbishops within two weeks of each other. Their conservative political views and consistent support of church orthodoxy inspired a joint nickname, “Law and Order.” Speaking at the Boston College commencement in 1986, Cardinal Law warned the university against losing its Catholic identity: “My prayer is for a Boston College ever more clearly Catholic.” During a 1998 visit to the United States, Irish President Mary McAleese met Cardinal Law. He criticized her for supporting the ordination of women as Catholic priests. McAleese replied that she was “the president of Ireland and not just of Catholic Ireland.” In 1990, he restored the Latin Mass, allowing it to be said at Holy Trinity Church in the South End. As an undergraduate, Cardinal Law had campaigned for Democratic presidential nominee Adlai Stevenson. As cardinal, he was friendly with President George H.W. Bush and his wife, Barbara. An occasional overnight guest at the summer White House at Kennebunkport, Maine, he spoke to the president monthly. In 1999, Cardinal Law publicly, and unsuccessfully, opposed two nominations to the Supreme Judicial Court, of Margaret Marshall as chief justice and Judith Cowin as associate justice, saying their records left them “open to serious charges of anti-Catholicism.” He was more successful a year later, when he urged that the Interstate 93 crossing over the Charles River honor the late head of the Anti-Defamation League of New England, and it was subsequently named the Leonard P. Zakim Bunker Hill Memorial Bridge. Cardinal Law encouraged interfaith relations. “For Cardinal Law, in the Jewish community, there is a reverence,” Harold Schwartz, a former chairman of the Anti-Defamation League, said in 2002. Zakim once said that an extemporaneous talk about the significance of the Auschwitz death camp that the cardinal gave to a group of Catholics in 1986 “was the best presentation about the Holocaust that I’ve ever heard from a non-Jew.” An example of Cardinal Law’s sensitivity to the Jewish community was his urging a group of Polish Carmelite nuns (an aunt of the cardinal’s had been a Carmelite) to move their convent from its location on the Auschwitz grounds. Poland was one of several countries Cardinal Law visited during his tenure. Others included Mexico, Nicaragua, and Cuba. Cardinal Law, who spoke fluent Spanish, visited the island nation five times and met with Fidel Castro on several occasions, once for more than four hours. Cardinal Law, Boston College religious historian Thomas Wangler said in 1990, was “the first archbishop of Boston to have a foreign policy.” Clergy sex abuse in the archdiocese preceded Cardinal Law’s arrival in Boston, in 1984, and its first significant US public disclosure was elsewhere (in Louisiana, in 1985). But in Boston, revelations about the Rev. John J. Geoghan’s long history of sexual molestation of children triggered the scandal locally. His actions first came to the attention of archdiocesan officials during the tenure of Cushing (1944-1970), and Geoghan was ordered to receive counseling by Medeiros as early as 1980. Less than a year after Cardinal Law assumed leadership of the archdiocese, he agreed to the removal of Geoghan from a Dorchester parish. Less than two months later, Cardinal Law assigned him to St. Julia Parish, in Weston. Auxiliary Bishop John M. D’Arcy objected, noting in a memo, “If something happens, the parishioners . . . will be convinced the Archdiocese has no concerns for their welfare and simply sends them priest with problems.” Geoghan stayed at St. Julia’s. Clergy sex abuse became front-page news in Massachusetts in 1992, with accusations against James R. Porter, a former priest in the Fall River diocese. A year later, he would be sentenced to 18 to 20 years in prison. Cardinal Law, in his regular column for the archdiocesan newspaper, The Pilot, wrote: “From such evil acts, like a pebble dropped into a placid pool of water, there are ever-widening concentric circles of betrayal and anguish.” Cardinal Law decried press attention to Porter. “The papers like to focus on the faults of a few,” he said. “We deplore that. . . . By all means, we call down God’s power on the media, particularly the Globe.” In July 2001, Cardinal Law wrote in The Pilot that “Never was there an effort on my part to shift a problem from one place to the next.” The column was a response to press reports which had run in The Boston Phoenix, The Boston Herald, and the Globe about Geoghan and how the archdiocese had handled his case. The Globe successfully sued to have court documents relating to Geoghan unsealed. With those documents and a database compiled from publicly available archdiocesan reports, the Globe Spotlight team began amassing information on clergy sex abuse in the archdiocese and the church hierarchy’s covering up the scandal and protecting priests even at the risk of possible future victims. Those events form the basis of the feature film “Spotlight.” Len Cariou plays Cardinal Law. The first Spotlight story, which ran on Jan. 6, 2002, focused on Geoghan. Intense public outcry ensued. Within days, a beleaguered Cardinal Law was offering apologies and attempting to justify his actions. Several hundred articles followed over the course of the year. Signs began to appear, “Honk if you want the cardinal to resign.” On “The Tonight Show,” Jay Leno referred to “Cardinal Above the Law” and described an episode of the television series “E.R.” on which “doctors in Boston try desperately to remove Cardinal Law’s foot from his mouth.” A public opinion poll showed that 75 percent of US Catholics thought Cardinal Law was lying about his knowledge of the scandal and 64 percent felt he should resign. Only 18 percent of local Catholics professed to have a favorable opinion of the cardinal. Late in the year, 58 priests publicly called for his resignation. On May 18, Cardinal Law released a letter, which was read to congregations throughout the archdiocese: “Bewilderment has given rise to anger and distrust. In the process, my credibility has been publicly questioned and I have become for some an object of contempt. I understand how this is so, and I am profoundly sorry that the inadequacy of past policies and flaws in past decisions have contributed to this situation.” In June, Cardinal Law said in a Globe interview, “The primary focus has got to be on children, and if it is, then the way you handle these other problems is going to be different, and it’s that focus that has come to me with a new clarity.” In August, he became the first sitting prelate to be sworn in as a trial witness. Some Catholics steadily supported Cardinal Law. In November, Harvard Law School professor and future US ambassador to the Vatican Mary Ann Glendon spoke at a conference in Rome. She concluded her remarks by saying, “I often hear it said that the Globe will receive a Pulitzer Prize for its reporting” on the scandal. “All I can say is that if fairness and accuracy have anything to do with it, awarding the Pulitzer Prize to The Boston Globe would be like giving the Nobel Peace Prize to Osama bin Laden.” Five months later, the Globe received the Pulitzer Prize for public service. Cardinal Law resigned on Dec. 13. “It is my fervent prayer that this action may help the Archdiocese of Boston to experience the healing, reconciliation, and unity which are so desperately needed,” he said in a prepared statement. “To all those who have suffered from my shortcomings and mistakes, I both apologize to them and beg forgiveness.” O’Malley, bishop of Palm Beach, Fla., was appointed to succeed Cardinal Law, in July 2003. But the impact of the scandal continued for years. The archdiocese agreed to pay $85 million to 552 victims of clergy sex abuse in 2003. It had already paid $10 million to settle 50 previous suits against Geoghan. For a time, the archdiocese explored the possibility of bankruptcy. The grand quarters for the cardinal’s residence and archdiocesan chancery in Brighton, built by the archdiocese’s first cardinal, William H. O’Connell, would be sold to Boston College after Cardinal Law’s resignation to help pay settlements from the many suits arising from the sex-abuse scandal. An only child, Bernard Francis Aloysius Law was born on Nov. 4, 1931, in the city of Torreón, in north-central Mexico. Cardinal Law’s father, Bernard A. Law, a former Army Air Force pilot, worked in commercial aviation. He was Catholic. Cardinal Law’s mother, Helen (Stubblefield) Law, a Presbyterian, later converted to Catholicism. The family moved six times during his youth, and Cardinal Law attended schools in New York, Florida, Georgia, Colombia, and the Virgin Islands. At Charlotte Amalie High School, in St. Thomas, all but one of his teachers were black. Cardinal Law, one of only five white students in his graduating class, was both class president and valedictorian. A history major at Harvard, Cardinal Law was vice president of the university’s Catholic Club. Among his roommates were a Southern Baptist and two Jewish students. Cardinal Law entered St. Joseph Seminary College, in St. Benedict, La., in 1953. “The two years that I spent at St. Joseph’s were perhaps the two most significant years of my life thus far,” he wrote in his Harvard 25th reunion report. In 1955, he entered the Pontifical College Josephinum, in Worthington, Ohio. Cardinal Law was ordained a priest in 1961 for the Diocese of Natchez-Jackson. His first appointment was as an assistant pastor in Vicksburg, Miss. He would never have his own parish. It would later be suggested that Cardinal Law’s limited pastoral experience contributed to his response to the sex-abuse scandal, leading him to see it from the viewpoint of priest and institution rather than victim and family. He was soon made editor of The Mississippi Register, the diocese’s statewide weekly newspaper. Its strong support for the civil rights movement brought Cardinal Law death threats. “Mississippi in the ’60s was all that one might imagine and more,” Cardinal Law wrote in his 25th reunion report. “To have been a part of that significant moment of our history is in itself a grace, a gift.” In 1965, Cardinal Law attended the last session of the Second Vatican Council. He moved to Washington, D.C., in 1968 to become executive director of the Bishops’ Committee for Ecumenical and Interreligious Affairs. His three years in the post introduced Cardinal Law to leading figures in the US church hierarchy. He became a protégé of William Baum, Cardinal Law’s predecessor as executive director, and later archbishop of Washington, D.C. Baum also preceded Cardinal Law as bishop of Springfield-Cape Girardeau. Cardinal Law served in Missouri from 1973-1983, having returned to Mississippi to be vicar general of Natchez-Jackson from 1971-1973. “Delighted at being planted in the beautiful Ozarks,” he wrote in his 25th reunion report, he added that “The more active involvement in social concerns of the ’60s has now been placed in a broader context of pastoral ministry.” Arriving at Logan Airport after being named archbishop, Cardinal Law drew laughter when he said that the Vatican’s apostolic delegate had told him that “after Boston, there is only heaven.” Following his resignation, Cardinal Law lived at a convent in Clinton, Md., until his appointment as archpriest of St. Mary Major. The post, while largely ceremonial, is considered prestigious. The church, built in the fifth century and one of Rome’s most famous, is a popular destination for pilgrims and tourists. The pope visits it semiannually. Cardinal Law, who held the title of archbishop emeritus of Boston, stepped down as archpriest in 2011. Cardinal Law voted in the 2005 conclave that elected Pope Benedict XVI. Some victims-rights groups objected to his participation. The Rev. Keith Pecklers, a Jesuit and professor at the Pontifical Gregorian University in Rome, said at the time in a Globe interview, “The 117 cardinals who are voting are all human beings and they have flaws as we all do. Holiness can come through suffering, from being broken or humbled. And that is Cardinal Law’s experience, I would say.” Because cardinals over 80 do not vote for pope, Cardinal Law did not participate in the conclave eight years later that elected Pope Francis. The day after the new pope’s election, Francis went to pray at St. Mary Major Basilica, where he greeted Cardinal Law “discreetly,” as a Vatican spokesman put it. Writing a month before his resignation, in his Harvard 50th reunion report, Cardinal Law gave this answer to the question of what he would have done differently in life: “Obviously, I wish I would have had the insight I have now about many problems, especially the terrible scourge of the sexual abuse of children. Hindsight would have avoided some horrible mistakes.” Mark Feeney can be reached at [email protected] ||||| VATICAN CITY (Reuters) - Cardinal Bernard Law, the former Archbishop of Boston who resigned in disgrace after covering up years of sexual abuse of children by priests and whose name became a byword for scandal in the Catholic Church, died on Wednesday. The Vatican announced his death just before dawn. It did not give a cause of death but sources close to Law, who died in a hospital in Rome, said he had been suffering from the complications of diabetes, liver failure and a build-up of fluids around the heart, known as pericardial effusion. The telegram of condolences Pope Francis sent to the dean of the College of Cardinals was unusually short and bland compared to those for other cardinals before. Francis said he was praying that the merciful God would “welcome him in eternal peace.” The pope did not mention that Law had been Archbishop of Boston and a brief Vatican biography made no mention of the circumstances of his resignation 15 years ago. Law was Archbishop of Boston, one of the most prestigious and wealthy American archdioceses, for 18 years when Pope John Paul reluctantly accepted his resignation on Dec. 13, 2002, after a tumultuous year in Church history. A succession of devastating news stories by Boston Globe reporters showed how priests who sexually abused children had been moved from parish to parish for years under Law’s tenure without parishioners or law authorities being informed. “No words can convey the pain these survivors and their loved ones suffered,” SNAP, a victims’ group, said. “Survivors of child sexual assault in Boston, who were first betrayed by Law’s cover-up of sex crimes and then doubly betrayed by his subsequent promotion to Rome, were those most hurt,” SNAP said in a statement. Law’s resignation sent shockwaves through the American Church and had a trickle down effect around the world as the cover-up techniques used in Boston were discovered to have been used in country after country. The story of how the Globe team brought the scandal to light in a city where few wanted to cross the politically powerful Church was told in the 2015 film “Spotlight”, which won the Oscar for Best Picture. The situation in Boston turned out to be the tip of an iceberg of abuse and its cover-up, where churchmen preferred protecting the reputation of the institution rather than the innocence of children. Thousands of cases came to light around the world as investigations encouraged long-silent victims to go public, shattering the Church’s reputation in places such as Ireland, and forcing it to pay some $2 billion in compensation. “As Archbishop of Boston, Cardinal Law served at a time when the Church failed seriously in its responsibilities to provide pastoral care for her people, and with tragic outcomes failed to care for the children of our parish communities. I deeply regret that reality and its consequences,” Law’s successor in Boston, Cardinal Sean O‘Malley, said in a statement. Six months after his resignation, the Massachusetts attorney general’s office announced that Law and others would not face criminal charges. GOLDEN PARACHUTE FILE PHOTO - Cardinal Bernard Law of the Boston Archdioceses addresses the U.S. Conference of Catholic Bishops about their stand on the [Iraq] situation, during their annual meeting in Washington, November 12, 2002. REUTERS/Brendan McDermid/File Photo After a period in a monastery in the United States, Law moved to Rome. In 2004 Pope John Paul appointed him to be archpriest of the Rome Basilica of Santa Maria Maggiore, one of the four major basilica’s of Christendom, whose gold leaf ceiling is said to be made from the first batch of the precious metal Columbus brought back from the Americas. He is likely to be buried there. In relative terms it was an immense fall from grace. Such posts are symbolic and ceremonial. But victims of sexual abuse were outraged because it gave Law a second career and a golden parachute that allowed him to stay close to the center of power in Rome and serve as a member or adviser in several influential Vatican departments. He also maintained the rank of cardinal and participated in the conclave that elected Pope Benedict in 2005. Before he became ill, Law was a regular on the diplomatic circuit, attending receptions, including many in the gardens of the U.S. Embassy to the Vatican. Slideshow (4 Images) While Law was an awkward presence at U.S. receptions for a few years after his resignation, at Italian events he was treated with the same effusive obsequiousness bestowed on all cardinals - something Law appeared to enjoy. He always declined to talk about events in Boston. “I‘m retired from that,” he told a reporter at one reception. FOOT DRAGGING O‘Malley, Law’s successor, heads a Vatican commission advising Pope Francis on how to root out sexual abuse in the Church. But the credibility of the commission, which was formed in 2014, has been hurt by the resignation of two high-level lay members who have accused the Vatican of dragging its feet. The terms of most members expired recently and it is not clear what Pope Francis will do with it. Last September, Francis, addressing the commission, said the Catholic Church had moved too slowly to confront abuse. “When consciousness arrives late, the means to resolve the problems also arrive late. I am aware of this difficulty but it is reality and I say it plainly: We arrived late. The old practice of moving people around and not confronting the problem made consciences fall asleep,” the pope said. Bernard Francis Law was born on Nov. 4, 1931, in Torreon, Mexico, the son of a U.S. Army official and a musician. He graduated from Harvard University and was ordained a priest in 1961. His first assignment was in Mississippi, where he received death threats for championing civil rights. As bishop of Springfield–Cape Girardeau in Missouri, he opened a home for battered women and a center to help Vietnamese boat people. The Vatican said Law’s funeral would be held on Thursday afternoon in St. Peter’s Basilica. The Mass will be said by a senior cardinal and the pope will participate in the final blessing, a normal procedure for cardinals. ||||| (CNN) Cardinal Bernard Law, the former Boston archbishop who resigned in disgrace during the Catholic Church's sex abuse scandal, has died, the Vatican confirmed. He was 86. Law died early Wednesday in Rome following a long illness , the Vatican said. Law moved to Italy to serve as archpriest of the Papal Liberian Basilica of St. Mary Major after he was forced to resign in 2002 as archbishop of Boston. Law's name became emblematic of the scandal that continues to trouble the church and its followers after a Boston Globe investigation revealed that he and other bishops covered up child abuse by priests in the Boston Archdiocese. Law at the time apologized to victims of John Geoghan, a priest who had been moved from parish to parish, despite Law's knowledge of his abuse of young boys. Geoghan was convicted in 2002 of indecent assault and battery on a 10-year-old boy. Law never faced criminal sanctions for his role in allowing abusive priests to remain in parishes. The scandal reverberated through the church, exposing similar allegations worldwide that compromised its moral authority and led to years of multimillion-dollar settlements. Pope Francis will give a "final commendation," or blessing, as he has for cardinals' funerals previously. Law will get a full cardinal's funeral at the Vatican's St. Peter's Basilica on Thursday afternoon, with Cardinal Angelo Sodano, dean of the College of Cardinals, presiding.Pope Francis will give a "final commendation," or blessing, as he has for cardinals' funerals previously. Survivors recount betrayal To his detractors, Law's second career at the Vatican was a slap in the face to victims of clergy sex abuse, one that further undermined the church's legitimacy. "Survivors of child sexual assault in Boston, who were first betrayed by Law's cover-up of sex crimes and then doubly betrayed by his subsequent promotion to Rome, were those most hurt," according to a statement after his death from Survivors Network of those Abused by Priests . "No words can convey the pain these survivors and their loved ones suffered." JUST WATCHED Pope open to married men becoming priests Replay More Videos ... MUST WATCH Pope open to married men becoming priests 04:17 The group advised the Vatican to keep the abuse survivors in mind when planning Law's funeral. "Every single Catholic should ask Pope Francis and the Vatican why," the survivors' group said. "Why Law's life was so celebrated when Boston's clergy sex abuse survivors suffered so greatly? Why was Law promoted when Boston's Catholic children were sexually abused, ignored, and pushed aside time and time again?" Widespread child abuse by the Catholic clergy in the Boston Archdiocese was uncovered by The Boston Globe's Spotlight investigative reporting team , which won a Pulitzer Prize for its efforts. A big-screen dramatization of the team's investigation in the 2015 movie, "Spotlight," won the 2016 Best Picture Academy Award, bringing the story to a much wider audience. Law's successor as Boston's archbishop, Cardinal Sean O'Malley, reacted to Law's death in part by apologizing to victims of sex abuse by clergy. "I recognize that Cardinal Law's passing brings forth a wide range of emotions on the part of many people. I am particularly cognizant of all who experienced the trauma of sexual abuse by clergy, whose lives were so seriously impacted by those crimes, and their families and loved ones," O'Malley said. "Cardinal Law served at a time when the church failed seriously in its responsibilities to provide pastoral care for her people, and with tragic outcomes failed to care for the children of our parish communities. I deeply regret that reality and its consequences," O'Malley said. However, he called it a "sad reality" that the scandal has come to define Law's legacy, overshadowing his work in the civil rights era and leadership in the interfaith movement following the Second Vatican Council. "I think all of us are more than one dimensional and I think, to be realistic, we have to recognize that there was more to this man than his mistakes," he said in a news conference on Wednesday. Rise of Boston's spiritual leader Law was born in Torreon, Mexico, on November 4, 1931, to Helen and Bernard Law, an Air Force colonel. He completed his postgraduate studies at St. Joseph's Seminary in Louisiana and at the Pontifical College Josephinum in Columbus, Ohio. He was ordained as a priest on May 21, 1961, in the diocese of Natchez-Jackson, Mississippi, and became vicar general of that diocese in 1971. In 1973, he was appointed bishop of the Springfield-Cape Girardeau diocese in southern Missouri. He served as chairman of the Bishops' Committee on Ecumenical and Interracial Affairs, and in 1976, he was named to the Vatican Commission on Religious Relations with Jews. The posts were stepping stones to his becoming the spiritual leader of Boston's large and influential Catholic community. In 1984, Pope John Paul II appointed Law to be the archbishop of the Boston Archdiocese, with its 362 parishes serving 2.1 million members. That same year, Law received a letter from a bishop expressing concerns about then-Rev. Geoghan. Law assigned Geoghan to another parish despite the allegations. In 1985, Pope John Paul II elevated Law to cardinal, one of just 13 Americans holding that office at the time. JUST WATCHED A Catholic Church cover-up? Replay More Videos ... MUST WATCH A Catholic Church cover-up? 03:16 Calls for resignation Law attempted to resign as archbishop of Boston in April 2002, but Pope John Paul II rejected his request. In 2002, a judge presiding over the child rape case of the Rev. Paul Shanley ordered Cardinal Law to be deposed by lawyers of one of Shanley's victims. Law testified about his supervision of Geoghan in 2002, saying he relied on his assistants to investigate charges of abuse. In May 2002, he apologized for his role in the clergy abuse scandal in a letter distributed throughout the archdiocese. But he denied knowledge of sexual abuse allegations against Shanley until 1993. In August 2002, Law appeared in court to testify about a settlement reached between the archdiocese of Boston and victims of clergy abuse. The archdiocese rescinded the monetary offer shortly afterward. That December, as calls grew for him to resign, Law was subpoenaed to appear before a grand jury investigating "possible criminal violations by church officials who supervised priests accused of sexually abusing children." Days later, he resigned as chairman of the board of trustees of the Catholic University of America, followed by his resignation as archbishop of Boston. Catholic Church abuses under scrutiny The breakdown of trust in the Catholic Church continues to reverberate around the world. JUST WATCHED Archbishop: 'This is a shameful past' Replay More Videos ... MUST WATCH Archbishop: 'This is a shameful past' 01:03 This month, the Australian Royal Commission into Institutional Responses to Child Sexual Abuse delivered, after five years of work, 189 recommendations to address what it described as a "serious failure" by Australia's institutions to protect its most vulnerable citizens. The country's senior Catholic leaders, however, rejected recommendations by the wide-reaching investigation, declining to end mandatory celibacy for priests and break the secrecy of confession. Of survivors who reported abuse in a religious institution, more than 60% said it occurred in a Catholic organization, the report found. When asked if he forgave Law, O'Malley said that forgiveness is what Christianity is all about. But he acknowledged that in Law's case, forgiveness did not come easy. "Hopefully, out of this, it will help to remind all of our Catholics that this is not something that has been solved," he said Wednesday. "The healing is still necessary and we must all be vigilant, particularly for prevention of child abuse." He surmised, though, that the church would handle such transgressions differently today. "I think there's a much greater understanding and sensitivity to the situation," he said. "There's been enough growth and consciousness of this problem in the Holy See that that would not happen.[/INST]– He was considered a voice for immigrants, youth, and the poor, but that was before a widespread child sex abuse scandal tarnished his reputation. Cardinal Bernard Law, who resigned as archbishop of the Boston Archdiocese in 2002, died early Wednesday at age 86 from complications of diabetes, liver failure, and fluid around the heart, per CNN and Reuters. Law died in Rome, where he served in the largely ceremonial role of archpriest of the Papal Liberian Basilica of St. Mary Major. The post followed a tumultuous exit in Boston, after church documents showed Law had protected priests accused of child sex abuse, moving them from church to church, per the Boston Herald. The scandal uncovered by the Boston Globe would reverberate throughout the Catholic Church, exposing similar cases around the world. Born in Mexico in 1931, Law was educated at Harvard and ordained as a priest in Mississippi in 1961. He would go on to be made bishop in Missouri before Pope John Paul II appointed him archbishop of the Boston Archdiocese in 1984. He was elevated to cardinal in 1985. Decades later, when it was revealed he had for years shielded accused priests before clergy were required to report abuse, he was recalled to the Vatican and given a new position, to the dismay of abuse victims. "He was a typical supervisor who allowed the victims and their families to be destroyed, by turning his back on children in need of protection," a lawyer who helped win multi-million-dollar settlements for victims tells the Herald. "To all those who have suffered from my shortcomings and mistakes, I both apologize to them and beg forgiveness," Law said in 2002, per the Globe.</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Disaster Savings and Resilient Construction Act of 2013''. SEC. 2. DISASTER RESILIENT PROPERTY TAX CREDIT. (a) In General.--Subpart D of part IV of subchapter A of chapter 1 of the Internal Revenue Code of 1986 is amended by inserting after section 30D the following new section: ``SEC. 30E. DISASTER RESILIENT PROPERTY. ``(a) General Rule.--There shall be allowed as a credit against the tax imposed by this chapter for the taxable year an amount equal to the applicable amount for each qualified building placed in service during the taxable year. ``(b) Applicable Amount.--For purposes of subsection (a)-- ``(1) Commercial property.--In the case of a qualified commercial property, the applicable amount is the lesser of-- ``(A) 1 percent of the cost of the building, or ``(B) $25,000 per building. ``(2) Residential property.--In the case of a qualified residential property, the applicable amount is the lesser of-- ``(A) 1 percent of the cost of the property (or construction cost for rehabilitation of the property), or ``(B) $3,000 per property. ``(c) Qualified Building.--For purposes of subsection (a)-- ``(1) In general.--The term `qualified building' means a building-- ``(A) owned by the taxpayer in a disaster area determined as a result of a federally declared major disaster, ``(B) the construction of which began after the date of such disaster in that area, ``(C) which-- ``(i) is qualified commercial property placed in service for commercial purposes, or ``(ii) is qualified residential property is placed in service for residential purposes, and ``(D) for which a certificate of occupancy is issued before the end of the 3-year period beginning on the date of such disaster declaration in that area. ``(2) Qualified commercial property.--The term `qualified commercial property' means a building that is-- ``(A) located in the United States, ``(B) defined in the scope of the 2009 or later International Building Code published by the International Code Council, and ``(C) designed and constructed to meet resilient construction requirements. ``(3) Qualified residential property.--The term `qualified residential property' means a building that is-- ``(A) located in the United States, ``(B) defined in the scope of the 2009 or later International Residential Code published by the International Code Council, and ``(C) designed and constructed to meet resilient construction requirements. ``(d) Resilient Construction Requirements.--For purposes of this section-- ``(1) In general.--The resilient construction requirements with respect to a property are that the property is designed and constructed to-- ``(A) resist hazards brought on by a major disaster and continues to provide its primary functions after a major disaster, ``(B) reduce the magnitude or duration of a disruptive event, and ``(C) have the absorptive capacity, adaptive capacity, recoverability to withstand a potentially disruptive event. ``(2) Treated as meeting resiliency requirements.--For purposes of paragraph (1)-- ``(A) in the case of a qualified commercial property, the property shall be treated as meeting the requirements specified in paragraph (1) if the property is a building which-- ``(i) was designed to meet the requirements of the 2009 or later International Building Code published by the International Code Council and received the Insurance Institute for Business and Home Safety FORTIFIED for Safer Business designation, or ``(ii) was designed and built in a jurisdiction that requires commercial buildings to meet the requirements of the 2009 or later International Building Code published by the International Code Council with amendments that are equivalent or more restrictive than the requirements described in FORTIFIED for Safer Business Standards published by the Insurance Institute for Business and Home Safety and received a certificate of occupancy (or other documentation stating that it has met the requirements of the building code) from the jurisdiction, and ``(B) in the case of a qualified residential property, the property shall be treated as meeting the requirements specified in paragraph (1) if the property is a building which was designed to meet the requirements of the 2009 or later International Residential Code published by the International Code Council, and meets one of the following requirements: ``(i) The building received the Insurance Institute for Business and Home Safety as FORTIFIED for Safer Living designation. ``(ii) The building received the Insurance Institute for Business and Home Safety as FORTIFIED for Existing Homes designation, silver level. ``(iii) It was designed and built in a jurisdiction that requires residential buildings to meet the requirements of the 2009 or later International Building Code published by the International Code Council with amendments that are equivalent or more restrictive than the requirements described in FORTIFIED for Safer Living Builders Guide published by the Insurance Institute for Business and Home Safety and received a certificate of occupancy (or other documentation stating that it has met the requirements of the building code) from the jurisdiction. ``(3) Absorptive capacity.--The term `absorptive capacity' means the ability of the construction to endure a disruption without significant deviation from normal operating performance. ``(4) Adaptive capacity.--The term `adaptive capacity' means the ability of the construction to adapt to a drastic change in normal operating conditions. ``(5) Recoverability.--The term `recoverability' means the ability of the construction to recover quickly, and at low cost, from potentially disruptive events. ``(e) Other Definitions.--For purposes of this section-- ``(1) Construction.--The term `construction' includes new construction and reconstruction and rehabilitation that meets resilient construction requirements. ``(2) Federally declared major disaster.--The term `federally declared major disaster' means a disaster subsequently determined by the President of the United States to be a `major disaster' that warrants assistance by the Federal Government under the Robert T. Stafford Disaster Relief and Emergency Assistance Act. ``(3) Disaster area.--The term `disaster area' means the area so determined to warrant such assistance. ``(f) Application With Other Credits.-- ``(1) Business credit treated as part of general business credit.--So much of the credit which would be allowed under subsection (a) for any taxable year (determined without regard to this subsection) that is attributable to property of a character subject to an allowance for depreciation shall be treated as a credit listed in section 38(b) for such taxable year (and not allowed under subsection (a)). ``(2) Personal credit.--For purposes of this title, the credit allowed under subsection (a) for any taxable year (determined after application of paragraph (1)) shall be treated as a credit allowable under subpart A for such taxable year. ``(g) Basis Reduction.--For purposes of this subtitle, the basis of any property for which a credit is allowable under subsection (a) shall be reduced by the amount of such credit so allowed. ``(h) Termination.--This section shall not apply to any property for which a certificate for occupancy is issued after December 31, 2017.''. (b) Credit Made Part of General Business Credit.--Section 38(b) of such Code, as amended by this Act, is amended by striking ``plus'' at the end of paragraph (35), by striking the period at the end of paragraph (36) and inserting ``, plus'', and by adding at the end the following new paragraph: ``(37) the portion of the disaster resilient property credit to which section 30E(f)(1) applies.''. (c) Basis Adjustment.--Subsection (a) of section 1016 is amended by striking ``and'' at the end of paragraph (30), by striking the period at the end of paragraph (31) and inserting a comma, by striking ``and'' at the end of paragraph (36), by striking the period at the end of paragraph (37) and inserting ``, and'', and by adding at the end the following new paragraph: ``(38) to the extent provided in section 30E(g), in the case of amounts with respect to which a credit has been allowed under section 30E.''. (d) Clerical Amendment.--The table of sections for subpart B of part IV of subchapter A of chapter 1 of such Code is amended by inserting after the item relating to section 30D the following new item: ``Sec. 30E. Disaster resilient property.''. (e) Effective Date.--The amendments made by this section shall apply to property for which a certificate for occupancy is issued after the date of the enactment of this Act.

Disaster Savings and Resilient Construction Act of 2013 - Amends the Internal Revenue Code to allow a business-related tax credit for a specified portion of the cost of commercial and residential buildings&nbsp;that comply with resilient construction requirements in a federally-declared major disaster area. Defines "resilient construction requirements" as&nbsp;requirements that such&nbsp;buildings are designed and constructed to: (1) resist hazards brought&nbsp;on by a major disaster; (2) continue to provide their primary functions after a major disaster; (3) reduce the magnitude or duration of a disruptive event; and (4)&nbsp;have the absorptive capacity, adaptive capacity, and recoverability to withstand a potentially disruptive event. Terminates such credit for any any property for which a certificate of occupancy is issued after December 31, 2017.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Disaster Savings and Resilient Construction Act of 2013''. SEC. 2. DISASTER RESILIENT PROPERTY TAX CREDIT. (a) In General.--Subpart D of part IV of subchapter A of chapter 1 of the Internal Revenue Code of 1986 is amended by inserting after section 30D the following new section: ``SEC. 30E. DISASTER RESILIENT PROPERTY. ``(a) General Rule.--There shall be allowed as a credit against the tax imposed by this chapter for the taxable year an amount equal to the applicable amount for each qualified building placed in service during the taxable year. ``(b) Applicable Amount.--For purposes of subsection (a)-- ``(1) Commercial property.--In the case of a qualified commercial property, the applicable amount is the lesser of-- ``(A) 1 percent of the cost of the building, or ``(B) $25,000 per building. ``(2) Residential property.--In the case of a qualified residential property, the applicable amount is the lesser of-- ``(A) 1 percent of the cost of the property (or construction cost for rehabilitation of the property), or ``(B) $3,000 per property. ``(c) Qualified Building.--For purposes of subsection (a)-- ``(1) In general.--The term `qualified building' means a building-- ``(A) owned by the taxpayer in a disaster area determined as a result of a federally declared major disaster, ``(B) the construction of which began after the date of such disaster in that area, ``(C) which-- ``(i) is qualified commercial property placed in service for commercial purposes, or ``(ii) is qualified residential property is placed in service for residential purposes, and ``(D) for which a certificate of occupancy is issued before the end of the 3-year period beginning on the date of such disaster declaration in that area. ``(2) Qualified commercial property.--The term `qualified commercial property' means a building that is-- ``(A) located in the United States, ``(B) defined in the scope of the 2009 or later International Building Code published by the International Code Council, and ``(C) designed and constructed to meet resilient construction requirements. ``(3) Qualified residential property.--The term `qualified residential property' means a building that is-- ``(A) located in the United States, ``(B) defined in the scope of the 2009 or later International Residential Code published by the International Code Council, and ``(C) designed and constructed to meet resilient construction requirements. ``(d) Resilient Construction Requirements.--For purposes of this section-- ``(1) In general.--The resilient construction requirements with respect to a property are that the property is designed and constructed to-- ``(A) resist hazards brought on by a major disaster and continues to provide its primary functions after a major disaster, ``(B) reduce the magnitude or duration of a disruptive event, and ``(C) have the absorptive capacity, adaptive capacity, recoverability to withstand a potentially disruptive event. ``(2) Treated as meeting resiliency requirements.--For purposes of paragraph (1)-- ``(A) in the case of a qualified commercial property, the property shall be treated as meeting the requirements specified in paragraph (1) if the property is a building which-- ``(i) was designed to meet the requirements of the 2009 or later International Building Code published by the International Code Council and received the Insurance Institute for Business and Home Safety FORTIFIED for Safer Business designation, or ``(ii) was designed and built in a jurisdiction that requires commercial buildings to meet the requirements of the 2009 or later International Building Code published by the International Code Council with amendments that are equivalent or more restrictive than the requirements described in FORTIFIED for Safer Business Standards published by the Insurance Institute for Business and Home Safety and received a certificate of occupancy (or other documentation stating that it has met the requirements of the building code) from the jurisdiction, and ``(B) in the case of a qualified residential property, the property shall be treated as meeting the requirements specified in paragraph (1) if the property is a building which was designed to meet the requirements of the 2009 or later International Residential Code published by the International Code Council, and meets one of the following requirements: ``(i) The building received the Insurance Institute for Business and Home Safety as FORTIFIED for Safer Living designation. ``(ii) The building received the Insurance Institute for Business and Home Safety as FORTIFIED for Existing Homes designation, silver level. ``(iii) It was designed and built in a jurisdiction that requires residential buildings to meet the requirements of the 2009 or later International Building Code published by the International Code Council with amendments that are equivalent or more restrictive than the requirements described in FORTIFIED for Safer Living Builders Guide published by the Insurance Institute for Business and Home Safety and received a certificate of occupancy (or other documentation stating that it has met the requirements of the building code) from the jurisdiction. ``(3) Absorptive capacity.--The term `absorptive capacity' means the ability of the construction to endure a disruption without significant deviation from normal operating performance. ``(4) Adaptive capacity.--The term `adaptive capacity' means the ability of the construction to adapt to a drastic change in normal operating conditions. ``(5) Recoverability.--The term `recoverability' means the ability of the construction to recover quickly, and at low cost, from potentially disruptive events. ``(e) Other Definitions.--For purposes of this section-- ``(1) Construction.--The term `construction' includes new construction and reconstruction and rehabilitation that meets resilient construction requirements. ``(2) Federally declared major disaster.--The term `federally declared major disaster' means a disaster subsequently determined by the President of the United States to be a `major disaster' that warrants assistance by the Federal Government under the Robert T. Stafford Disaster Relief and Emergency Assistance Act. ``(3) Disaster area.--The term `disaster area' means the area so determined to warrant such assistance. ``(f) Application With Other Credits.-- ``(1) Business credit treated as part of general business credit.--So much of the credit which would be allowed under subsection (a) for any taxable year (determined without regard to this subsection) that is attributable to property of a character subject to an allowance for depreciation shall be treated as a credit listed in section 38(b) for such taxable year (and not allowed under subsection (a)). ``(2) Personal credit.--For purposes of this title, the credit allowed under subsection (a) for any taxable year (determined after application of paragraph (1)) shall be treated as a credit allowable under subpart A for such taxable year. ``(g) Basis Reduction.--For purposes of this subtitle, the basis of any property for which a credit is allowable under subsection (a) shall be reduced by the amount of such credit so allowed. ``(h) Termination.--This section shall not apply to any property for which a certificate for occupancy is issued after December 31, 2017.''. (b) Credit Made Part of General Business Credit.--Section 38(b) of such Code, as amended by this Act, is amended by striking ``plus'' at the end of paragraph (35), by striking the period at the end of paragraph (36) and inserting ``, plus'', and by adding at the end the following new paragraph: ``(37) the portion of the disaster resilient property credit to which section 30E(f)(1) applies.''. (c) Basis Adjustment.--Subsection (a) of section 1016 is amended by striking ``and'' at the end of paragraph (30), by striking the period at the end of paragraph (31) and inserting a comma, by striking ``and'' at the end of paragraph (36), by striking the period at the end of paragraph (37) and inserting ``, and'', and by adding at the end the following new paragraph: ``(38) to the extent provided in section 30E(g), in the case of amounts with respect to which a credit has been allowed under section 30E.''. (d) Clerical Amendment.--The table of sections for subpart B of part IV of subchapter A of chapter 1 of such Code is amended by inserting after the item relating to section 30D the following new item: ``Sec. 30E. Disaster resilient property.''. (e) Effective Date.--The amendments made by this section shall apply to property for which a certificate for occupancy is issued after the date of the enactment of this Act.[/INST]Disaster Savings and Resilient Construction Act of 2013 - Amends the Internal Revenue Code to allow a business-related tax credit for a specified portion of the cost of commercial and residential buildings&nbsp;that comply with resilient construction requirements in a federally-declared major disaster area. Defines "resilient construction requirements" as&nbsp;requirements that such&nbsp;buildings are designed and constructed to: (1) resist hazards brought&nbsp;on by a major disaster; (2) continue to provide their primary functions after a major disaster; (3) reduce the magnitude or duration of a disruptive event; and (4)&nbsp;have the absorptive capacity, adaptive capacity, and recoverability to withstand a potentially disruptive event. Terminates such credit for any any property for which a certificate of occupancy is issued after December 31, 2017.</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Private Fund Investment Advisers Registration Act of 2009''. SEC. 2. DEFINITIONS. Section 202(a) of the Investment Advisers Act of 1940 (15 U.S.C. 80b-2(a)) is amended by adding at the end the following new paragraphs: ``(29) Private fund.--The term `private fund' means an issuer that would be an investment company under section 3(a) of the Investment Company Act of 1940 (15 U.S.C. 80a-3(a)) but for the exception provided from that definition by either section 3(c)(1) or section 3(c)(7) of such Act ``(30) Foreign private fund adviser.--The term `foreign private fund adviser' means an investment adviser who-- ``(A) has no place of business in the United States; ``(B) during the preceding 12 months has had-- ``(i) fewer than 15 clients in the United States; and ``(ii) assets under management attributable to clients in the United States of less than $25,000,000, or such higher amount as the Commission may, by rule, deem appropriate in the public interest or for the protection of investors; and ``(C) neither holds itself out generally to the public in the United States as an investment adviser, nor acts as an investment adviser to any investment company registered under the Investment Company Act of 1940, or a company which has elected to be a business development company pursuant to section 54 of the Investment Company Act of 1940 (15 U.S.C. 80a-53) and has not withdrawn such election.''. SEC. 3. ELIMINATION OF PRIVATE ADVISER EXEMPTION; LIMITED EXEMPTION FOR FOREIGN PRIVATE FUND ADVISERS; LIMITED INTRASTATE EXEMPTION. Section 203(b) of the Investment Advisers Act of 1940 (15 U.S.C. 80b-3(b)) is amended-- (1) in paragraph (1), by inserting ``, except an investment adviser who acts as an investment adviser to any private fund,'' after ``any investment adviser''; (2) by amending paragraph (3) to read as follows: ``(3) any investment adviser that is a foreign private fund adviser;''; (3) in paragraph (5), by striking ``or'' at the end; (4) in paragraph (6)-- (A) in subparagraph (A), by striking ``or''; (B) in subparagraph (B), by striking the period at the end and adding ``; or''; and (C) by adding at the end the following new subparagraph: ``(C) a private fund; or''; and (5) by adding at the end the following: ``(7) any investment adviser who solely advises-- ``(A) small business investment companies licensed under the Small Business Investment Act of 1958; ``(B) entities that have received from the Small Business Administration notice to proceed to qualify for a license, which notice or license has not been revoked; or ``(C) applicants, related to one or more licensed small business investment companies covered in subparagraph (A), that have applied for another license, which application remains pending.''. SEC. 4. COLLECTION OF SYSTEMIC RISK DATA. Section 204 of the Investment Advisers Act of 1940 (15 U.S.C. 80b- 4) is amended-- (1) by redesignating subsections (b) and (c) as subsections (c) and (d), respectively; and (2) by inserting after subsection (a) the following new subsection: ``(b) Records and Reports of Private Funds.-- ``(1) In general.--The Commission is authorized to require any investment adviser registered under this Act to maintain such records of and file with the Commission such reports regarding private funds advised by the investment adviser as are necessary or appropriate in the public interest and for the protection of investors or for the assessment of systemic risk as the Commission determines in consultation with the Board of Governors of the Federal Reserve System. The Commission is authorized to provide or make available to the Board of Governors of the Federal Reserve System, and to any other entity that the Commission identifies as having systemic risk responsibility, those reports or records or the information contained therein. The records and reports of any private fund, to which any such investment adviser provides investment advice, maintained or filed by an investment adviser registered under this Act, shall be deemed to be the records and reports of the investment adviser. ``(2) Required information.--The records and reports required to be maintained or filed with the Commission under this subsection shall include, for each private fund advised by the investment adviser-- ``(A) the amount of assets under management; ``(B) the use of leverage (including off-balance sheet leverage); ``(C) counterparty credit risk exposures; ``(D) trading and investment positions; ``(E) trading practices; and ``(F) such other information as the Commission, in consultation with the Board of Governors of the Federal Reserve System, determines necessary or appropriate in the public interest and for the protection of investors or for the assessment of systemic risk. ``(3) Optional information.--The Commission may require the reporting of such additional information from private fund advisers as the Commission determines necessary. In making such determination, the Commission, taking into account the public interest and potential to contribute to systemic risk, may set different reporting requirements for different classes of private fund advisers, based on the particular types or sizes of private funds advised by such advisers. ``(4) Maintenance of records.--An investment adviser registered under this Act is required to maintain and keep such records of private funds advised by the investment adviser for such period or periods as the Commission, by rule or regulation, may prescribe as necessary or appropriate in the public interest and for the protection of investors or for the assessment of systemic risk. ``(5) Examination of records.-- ``(A) Periodic and special examinations.--All records of a private fund maintained by an investment adviser registered under this Act shall be subject at any time and from time to time to such periodic, special, and other examinations by the Commission, or any member or representative thereof, as the Commission may prescribe. ``(B) Availability of records.--An investment adviser registered under this Act shall make available to the Commission or its representatives any copies or extracts from such records as may be prepared without undue effort, expense, or delay as the Commission or its representatives may reasonably request. ``(6) Information sharing.--The Commission shall make available to the Board of Governors of the Federal Reserve System, and to any other entity that the Commission identifies as having systemic risk responsibility, copies of all reports, documents, records, and information filed with or provided to the Commission by an investment adviser under this subsection as the Board, or such other entity, may consider necessary for the purpose of assessing the systemic risk of a private fund. All such reports, documents, records, and information obtained by the Board, or such other entity, from the Commission under this subsection shall be kept confidential in a manner consistent with confidentiality established by the Commission pursuant to paragraph (8). ``(7) Disclosures of certain private fund information.--An investment adviser registered under this Act shall provide such reports, records, and other documents to investors, prospective investors, counterparties, and creditors, of any private fund advised by the investment adviser as the Commission, by rule or regulation, may prescribe as necessary or appropriate in the public interest and for the protection of investors or for the assessment of systemic risk. ``(8) Confidentiality of reports.--Notwithstanding any other provision of law, the Commission shall not be compelled to disclose any report or information contained therein required to be filed with the Commission under this subsection. Nothing in this paragraph shall authorize the Commission to withhold information from the Congress or prevent the Commission from complying with a request for information from any other Federal department or agency or any self-regulatory organization requesting the report or information for purposes within the scope of its jurisdiction, or complying with an order of a court of the United States in an action brought by the United States or the Commission. For purposes of section 552 of title 5, United States Code, this paragraph shall be considered a statute described in subsection (b)(3)(B) of such section.''. SEC. 5. ELIMINATION OF DISCLOSURE PROVISION. Section 210 of the Investment Advisers Act of 1940 (15 U.S.C. 80b- 10) is amended by striking subsection (c). SEC. 6. EXEMPTION OF AND REPORTING BY VENTURE CAPITAL FUND ADVISERS. Section 203 of the Investment Advisers Act of 1940 (15 U.S.C. 80b- 3) is amended by adding at the end the following new subsection: ``(l) Exemption of and Reporting by Venture Capital Fund Advisers.--The Commission shall identify and define the term `venture capital fund' and shall provide an adviser to such a fund an exemption from the registration requirements under this section (excluding any such fund whose adviser is exempt from registration pursuant to paragraph (7) of subsection (b)). The Commission shall require such advisers to maintain such records and provide to the Commission such annual or other reports as the Commission determines necessary or appropriate in the public interest or for the protection of investors.''. SEC. 7. EXEMPTION OF AND REPORTING BY CERTAIN PRIVATE FUND ADVISERS. Section 203 of the Investment Advisers Act of 1940 (15 U.S.C. 80b- 3), as amended by section 6, is further amended by adding at the end the following new subsections: ``(m) Exemption of and Reporting by Certain Private Fund Advisers.-- ``(1) In general.--The Commission shall provide an exemption from the registration requirements under this section to any investment adviser of private funds, if each of such private funds has assets under management in the United States of less than $150,000,000. ``(2) Reporting.--The Commission shall require investment advisers exempted by reason of this subsection to maintain such records and provide to the Commission such annual or other reports as the Commission determines necessary or appropriate in the public interest or for the protection of investors. ``(n) Registration and Examination of Mid-sized Private Fund Advisers.--In prescribing regulations to carry out the requirements of this section with respect to investment advisers acting as investment advisers to mid-sized private funds, the Commission shall take into account the size, governance, and investment strategy of such funds to determine whether they pose systemic risk, and shall provide for registration and examination procedures with respect to the investment advisers of such funds which reflect the level of systemic risk posed by such funds.''. SEC. 8. CLARIFICATION OF RULEMAKING AUTHORITY. Section 211 of the Investment Advisers Act of 1940 (15 U.S.C. 80b- 11) is amended-- (1) by amending subsection (a) to read as follows: ``(a) The Commission shall have authority from time to time to make, issue, amend, and rescind such rules and regulations and such orders as are necessary or appropriate to the exercise of the functions and powers conferred upon the Commission elsewhere in this title, including rules and regulations defining technical, trade, and other terms used in this title. For the purposes of its rules and regulations, the Commission may-- ``(1) classify persons and matters within its jurisdiction based upon, but not limited to-- ``(A) size; ``(B) scope; ``(C) business model; ``(D) compensation scheme; or ``(E) potential to create or increase systemic risk; ``(2) prescribe different requirements for different classes of persons or matters; and ``(3) ascribe different meanings to terms (including the term `client', except the Commission shall not ascribe a meaning to the term `client' that would include an investor in a private fund managed by an investment adviser, where such private fund has entered into an advisory contract with such adviser) used in different sections of this title as the Commission determines necessary to effect the purposes of this title.''; and (2) by adding at the end the following new subsection: ``(e) The Commission and the Commodity Futures Trading Commission shall, after consultation with the Board of Governors of the Federal Reserve System, within 12 months after the date of enactment of the Private Fund Investment Advisers Registration Act of 2009, jointly promulgate rules to establish the form and content of the reports required to be filed with the Commission under sections 203(l) and 204(b) and with the Commodity Futures Trading Commission by investment advisers that are registered both under the Investment Advisers Act of 1940 (15 U.S.C. 80b-1 et seq.) and the Commodity Exchange Act (7 U.S.C. 1 et seq.).''. SEC. 9. GAO STUDY. (a) Study Required.--The Comptroller General of the United States shall carry out a study to assess the annual costs on industry members and their investors due to the registration requirements and ongoing reporting requirements under this Act and the amendments made by this Act. (b) Report to the Congress.--Not later than the end of the 2-year period beginning on the date of the enactment of this Act, the Comptroller General of the United States shall submit a report to the Congress containing the findings and determinations made by the Comptroller General in carrying out the study required under subsection (a). SEC. 10. EFFECTIVE DATE; TRANSITION PERIOD. (a) Effective Date.--This Act, and the amendments made by this Act, shall take effect with respect to investment advisers after the end of the 1-year period beginning on the date of the enactment of this Act. (b) Transition Period.--The Securities and Exchange Commission shall prescribe rules and regulations to permit an investment adviser who will be required to register with the Securities and Exchange Commission by reason of this Act with the option of registering with the Securities and Exchange Commission before the date described under subsection (a). SEC. 11. QUALIFIED CLIENT STANDARD. Section 205(e) of the Investment Advisers Act of 1940 (15 U.S.C. 80b-5(e)) is amended by adding at the end the following: ``With respect to any factor used by the Commission in making a determination under this subsection, if the Commission uses a dollar amount test in connection with such factor, such as a net asset threshold, the Commission shall, not later than one year after the date of the enactment of the Private Fund Investment Advisers Registration Act of 2009, and every 5 years thereafter, adjust for the effects of inflation on such test. Any such adjustment that is not a multiple of $1,000 shall be rounded to the nearest multiple of $1,000.''.

Private Fund Investment Advisers Registration Act of 2009 - (Sec. 3) Amends the Investment Advisers Act of 1940 to repeal the exemption for, and apply registration requirements to, a private fund investment adviser. Exempts from such registration requirements, however, any investment adviser who solely advises: (1) small business investment companies licensed under the Small Business Investment Act of 1958; (2) entities that the Small Business Administration (SBA) has notified to proceed to qualify for a license, if the notice or license has not been revoked; or (3) applicants, related to one or more licensed small business investment companies, that have a pending application for another license. (Sec. 4) Subjects to Securities Exchange Commission (SEC) recordkeeping requirements any registered investment adviser who advises private funds. Authorizes the SEC to make such records, especially those relating to systemic risk, available to the Board of Governors of the Federal Reserve System and any other entity that has systemic risk responsibility. (Sec. 5) Repeals the declaration that no provision of such Act shall be construed to require, or to authorize the SEC to require, any investment adviser engaged in rendering investment supervisory services to disclose the identity, investments, or affairs of any client, except insofar as such disclosure may be necessary or appropriate in a particular proceeding or investigation having as its object the enforcement of a provision or provisions of the Act. (Thus, allows interpretation of the Act to require, or authorize the SEC to require, an investment adviser to disclose the identity, investments, or affairs of any client.) (Sec. 6) Directs the SEC to exempt from the registration requirements of this Act: (1) venture capital fund advisers; and (2) investment advisers of private funds, each of which has assets under management in the United States of less than $150 million. Directs the SEC to require such advisers, however, to maintain records and make annual reports to the SEC. (Sec. 7) Requires the SEC, in prescribing regulations for registration of advisers to mid-sized private funds, to: (1) take into account the size, governance, and investment strategy of such funds to determine whether they pose systemic risk; and (2) provide for registration and examination procedures for such advisers which reflect the level of systemic risk posed by the funds. (Sec. 8) Modifies SEC rulemaking authority. Authorizes the SEC to ascribe different meanings to terms, but prohibits including in the term "client" an investor in a private fund managed by an investment adviser with whom the private fund has entered into an advisory contract. Directs the SEC and the Commodity Futures Trading Commission (CFTC) to promulgate rules jointly for the mandatory reports filed by certain registered investment advisers. (Sec. 9) Directs the Comptroller General to assess the annual costs on industry members and their investors because of the registration requirements and ongoing reporting requirements of this Act. (Sec. 11) Amends the Investment Advisers Act of 1940 with respect to SEC authority to exempt any person or transaction (or any class or classes of them) from certain investment advisory contract requirements to the extent that the exemption relates to an investment advisory contract with any person that the Commission determines does not need the protections of such requirements. Requires the SEC, with respect to any factor involving a dollar amount test (e.g. a net asset threshold) it uses to make such a determination, to adjust that test for inflation every five years.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Private Fund Investment Advisers Registration Act of 2009''. SEC. 2. DEFINITIONS. Section 202(a) of the Investment Advisers Act of 1940 (15 U.S.C. 80b-2(a)) is amended by adding at the end the following new paragraphs: ``(29) Private fund.--The term `private fund' means an issuer that would be an investment company under section 3(a) of the Investment Company Act of 1940 (15 U.S.C. 80a-3(a)) but for the exception provided from that definition by either section 3(c)(1) or section 3(c)(7) of such Act ``(30) Foreign private fund adviser.--The term `foreign private fund adviser' means an investment adviser who-- ``(A) has no place of business in the United States; ``(B) during the preceding 12 months has had-- ``(i) fewer than 15 clients in the United States; and ``(ii) assets under management attributable to clients in the United States of less than $25,000,000, or such higher amount as the Commission may, by rule, deem appropriate in the public interest or for the protection of investors; and ``(C) neither holds itself out generally to the public in the United States as an investment adviser, nor acts as an investment adviser to any investment company registered under the Investment Company Act of 1940, or a company which has elected to be a business development company pursuant to section 54 of the Investment Company Act of 1940 (15 U.S.C. 80a-53) and has not withdrawn such election.''. SEC. 3. ELIMINATION OF PRIVATE ADVISER EXEMPTION; LIMITED EXEMPTION FOR FOREIGN PRIVATE FUND ADVISERS; LIMITED INTRASTATE EXEMPTION. Section 203(b) of the Investment Advisers Act of 1940 (15 U.S.C. 80b-3(b)) is amended-- (1) in paragraph (1), by inserting ``, except an investment adviser who acts as an investment adviser to any private fund,'' after ``any investment adviser''; (2) by amending paragraph (3) to read as follows: ``(3) any investment adviser that is a foreign private fund adviser;''; (3) in paragraph (5), by striking ``or'' at the end; (4) in paragraph (6)-- (A) in subparagraph (A), by striking ``or''; (B) in subparagraph (B), by striking the period at the end and adding ``; or''; and (C) by adding at the end the following new subparagraph: ``(C) a private fund; or''; and (5) by adding at the end the following: ``(7) any investment adviser who solely advises-- ``(A) small business investment companies licensed under the Small Business Investment Act of 1958; ``(B) entities that have received from the Small Business Administration notice to proceed to qualify for a license, which notice or license has not been revoked; or ``(C) applicants, related to one or more licensed small business investment companies covered in subparagraph (A), that have applied for another license, which application remains pending.''. SEC. 4. COLLECTION OF SYSTEMIC RISK DATA. Section 204 of the Investment Advisers Act of 1940 (15 U.S.C. 80b- 4) is amended-- (1) by redesignating subsections (b) and (c) as subsections (c) and (d), respectively; and (2) by inserting after subsection (a) the following new subsection: ``(b) Records and Reports of Private Funds.-- ``(1) In general.--The Commission is authorized to require any investment adviser registered under this Act to maintain such records of and file with the Commission such reports regarding private funds advised by the investment adviser as are necessary or appropriate in the public interest and for the protection of investors or for the assessment of systemic risk as the Commission determines in consultation with the Board of Governors of the Federal Reserve System. The Commission is authorized to provide or make available to the Board of Governors of the Federal Reserve System, and to any other entity that the Commission identifies as having systemic risk responsibility, those reports or records or the information contained therein. The records and reports of any private fund, to which any such investment adviser provides investment advice, maintained or filed by an investment adviser registered under this Act, shall be deemed to be the records and reports of the investment adviser. ``(2) Required information.--The records and reports required to be maintained or filed with the Commission under this subsection shall include, for each private fund advised by the investment adviser-- ``(A) the amount of assets under management; ``(B) the use of leverage (including off-balance sheet leverage); ``(C) counterparty credit risk exposures; ``(D) trading and investment positions; ``(E) trading practices; and ``(F) such other information as the Commission, in consultation with the Board of Governors of the Federal Reserve System, determines necessary or appropriate in the public interest and for the protection of investors or for the assessment of systemic risk. ``(3) Optional information.--The Commission may require the reporting of such additional information from private fund advisers as the Commission determines necessary. In making such determination, the Commission, taking into account the public interest and potential to contribute to systemic risk, may set different reporting requirements for different classes of private fund advisers, based on the particular types or sizes of private funds advised by such advisers. ``(4) Maintenance of records.--An investment adviser registered under this Act is required to maintain and keep such records of private funds advised by the investment adviser for such period or periods as the Commission, by rule or regulation, may prescribe as necessary or appropriate in the public interest and for the protection of investors or for the assessment of systemic risk. ``(5) Examination of records.-- ``(A) Periodic and special examinations.--All records of a private fund maintained by an investment adviser registered under this Act shall be subject at any time and from time to time to such periodic, special, and other examinations by the Commission, or any member or representative thereof, as the Commission may prescribe. ``(B) Availability of records.--An investment adviser registered under this Act shall make available to the Commission or its representatives any copies or extracts from such records as may be prepared without undue effort, expense, or delay as the Commission or its representatives may reasonably request. ``(6) Information sharing.--The Commission shall make available to the Board of Governors of the Federal Reserve System, and to any other entity that the Commission identifies as having systemic risk responsibility, copies of all reports, documents, records, and information filed with or provided to the Commission by an investment adviser under this subsection as the Board, or such other entity, may consider necessary for the purpose of assessing the systemic risk of a private fund. All such reports, documents, records, and information obtained by the Board, or such other entity, from the Commission under this subsection shall be kept confidential in a manner consistent with confidentiality established by the Commission pursuant to paragraph (8). ``(7) Disclosures of certain private fund information.--An investment adviser registered under this Act shall provide such reports, records, and other documents to investors, prospective investors, counterparties, and creditors, of any private fund advised by the investment adviser as the Commission, by rule or regulation, may prescribe as necessary or appropriate in the public interest and for the protection of investors or for the assessment of systemic risk. ``(8) Confidentiality of reports.--Notwithstanding any other provision of law, the Commission shall not be compelled to disclose any report or information contained therein required to be filed with the Commission under this subsection. Nothing in this paragraph shall authorize the Commission to withhold information from the Congress or prevent the Commission from complying with a request for information from any other Federal department or agency or any self-regulatory organization requesting the report or information for purposes within the scope of its jurisdiction, or complying with an order of a court of the United States in an action brought by the United States or the Commission. For purposes of section 552 of title 5, United States Code, this paragraph shall be considered a statute described in subsection (b)(3)(B) of such section.''. SEC. 5. ELIMINATION OF DISCLOSURE PROVISION. Section 210 of the Investment Advisers Act of 1940 (15 U.S.C. 80b- 10) is amended by striking subsection (c). SEC. 6. EXEMPTION OF AND REPORTING BY VENTURE CAPITAL FUND ADVISERS. Section 203 of the Investment Advisers Act of 1940 (15 U.S.C. 80b- 3) is amended by adding at the end the following new subsection: ``(l) Exemption of and Reporting by Venture Capital Fund Advisers.--The Commission shall identify and define the term `venture capital fund' and shall provide an adviser to such a fund an exemption from the registration requirements under this section (excluding any such fund whose adviser is exempt from registration pursuant to paragraph (7) of subsection (b)). The Commission shall require such advisers to maintain such records and provide to the Commission such annual or other reports as the Commission determines necessary or appropriate in the public interest or for the protection of investors.''. SEC. 7. EXEMPTION OF AND REPORTING BY CERTAIN PRIVATE FUND ADVISERS. Section 203 of the Investment Advisers Act of 1940 (15 U.S.C. 80b- 3), as amended by section 6, is further amended by adding at the end the following new subsections: ``(m) Exemption of and Reporting by Certain Private Fund Advisers.-- ``(1) In general.--The Commission shall provide an exemption from the registration requirements under this section to any investment adviser of private funds, if each of such private funds has assets under management in the United States of less than $150,000,000. ``(2) Reporting.--The Commission shall require investment advisers exempted by reason of this subsection to maintain such records and provide to the Commission such annual or other reports as the Commission determines necessary or appropriate in the public interest or for the protection of investors. ``(n) Registration and Examination of Mid-sized Private Fund Advisers.--In prescribing regulations to carry out the requirements of this section with respect to investment advisers acting as investment advisers to mid-sized private funds, the Commission shall take into account the size, governance, and investment strategy of such funds to determine whether they pose systemic risk, and shall provide for registration and examination procedures with respect to the investment advisers of such funds which reflect the level of systemic risk posed by such funds.''. SEC. 8. CLARIFICATION OF RULEMAKING AUTHORITY. Section 211 of the Investment Advisers Act of 1940 (15 U.S.C. 80b- 11) is amended-- (1) by amending subsection (a) to read as follows: ``(a) The Commission shall have authority from time to time to make, issue, amend, and rescind such rules and regulations and such orders as are necessary or appropriate to the exercise of the functions and powers conferred upon the Commission elsewhere in this title, including rules and regulations defining technical, trade, and other terms used in this title. For the purposes of its rules and regulations, the Commission may-- ``(1) classify persons and matters within its jurisdiction based upon, but not limited to-- ``(A) size; ``(B) scope; ``(C) business model; ``(D) compensation scheme; or ``(E) potential to create or increase systemic risk; ``(2) prescribe different requirements for different classes of persons or matters; and ``(3) ascribe different meanings to terms (including the term `client', except the Commission shall not ascribe a meaning to the term `client' that would include an investor in a private fund managed by an investment adviser, where such private fund has entered into an advisory contract with such adviser) used in different sections of this title as the Commission determines necessary to effect the purposes of this title.''; and (2) by adding at the end the following new subsection: ``(e) The Commission and the Commodity Futures Trading Commission shall, after consultation with the Board of Governors of the Federal Reserve System, within 12 months after the date of enactment of the Private Fund Investment Advisers Registration Act of 2009, jointly promulgate rules to establish the form and content of the reports required to be filed with the Commission under sections 203(l) and 204(b) and with the Commodity Futures Trading Commission by investment advisers that are registered both under the Investment Advisers Act of 1940 (15 U.S.C. 80b-1 et seq.) and the Commodity Exchange Act (7 U.S.C. 1 et seq.).''. SEC. 9. GAO STUDY. (a) Study Required.--The Comptroller General of the United States shall carry out a study to assess the annual costs on industry members and their investors due to the registration requirements and ongoing reporting requirements under this Act and the amendments made by this Act. (b) Report to the Congress.--Not later than the end of the 2-year period beginning on the date of the enactment of this Act, the Comptroller General of the United States shall submit a report to the Congress containing the findings and determinations made by the Comptroller General in carrying out the study required under subsection (a). SEC. 10. EFFECTIVE DATE; TRANSITION PERIOD. (a) Effective Date.--This Act, and the amendments made by this Act, shall take effect with respect to investment advisers after the end of the 1-year period beginning on the date of the enactment of this Act. (b) Transition Period.--The Securities and Exchange Commission shall prescribe rules and regulations to permit an investment adviser who will be required to register with the Securities and Exchange Commission by reason of this Act with the option of registering with the Securities and Exchange Commission before the date described under subsection (a). SEC. 11. QUALIFIED CLIENT STANDARD. Section 205(e) of the Investment Advisers Act of 1940 (15 U.S.C. 80b-5(e)) is amended by adding at the end the following: ``With respect to any factor used by the Commission in making a determination under this subsection, if the Commission uses a dollar amount test in connection with such factor, such as a net asset threshold, the Commission shall, not later than one year after the date of the enactment of the Private Fund Investment Advisers Registration Act of 2009, and every 5 years thereafter, adjust for the effects of inflation on such test. Any such adjustment that is not a multiple of $1,000 shall be rounded to the nearest multiple of $1,000.''.[/INST]Private Fund Investment Advisers Registration Act of 2009 - (Sec. 3) Amends the Investment Advisers Act of 1940 to repeal the exemption for, and apply registration requirements to, a private fund investment adviser. Exempts from such registration requirements, however, any investment adviser who solely advises: (1) small business investment companies licensed under the Small Business Investment Act of 1958; (2) entities that the Small Business Administration (SBA) has notified to proceed to qualify for a license, if the notice or license has not been revoked; or (3) applicants, related to one or more licensed small business investment companies, that have a pending application for another license. (Sec. 4) Subjects to Securities Exchange Commission (SEC) recordkeeping requirements any registered investment adviser who advises private funds. Authorizes the SEC to make such records, especially those relating to systemic risk, available to the Board of Governors of the Federal Reserve System and any other entity that has systemic risk responsibility. (Sec. 5) Repeals the declaration that no provision of such Act shall be construed to require, or to authorize the SEC to require, any investment adviser engaged in rendering investment supervisory services to disclose the identity, investments, or affairs of any client, except insofar as such disclosure may be necessary or appropriate in a particular proceeding or investigation having as its object the enforcement of a provision or provisions of the Act. (Thus, allows interpretation of the Act to require, or authorize the SEC to require, an investment adviser to disclose the identity, investments, or affairs of any client.) (Sec. 6) Directs the SEC to exempt from the registration requirements of this Act: (1) venture capital fund advisers; and (2) investment advisers of private funds, each of which has assets under management in the United States of less than $150 million. Directs the SEC to require such advisers, however, to maintain records and make annual reports to the SEC. (Sec. 7) Requires the SEC, in prescribing regulations for registration of advisers to mid-sized private funds, to: (1) take into account the size, governance, and investment strategy of such funds to determine whether they pose systemic risk; and (2) provide for registration and examination procedures for such advisers which reflect the level of systemic risk posed by the funds. (Sec. 8) Modifies SEC rulemaking authority. Authorizes the SEC to ascribe different meanings to terms, but prohibits including in the term "client" an investor in a private fund managed by an investment adviser with whom the private fund has entered into an advisory contract. Directs the SEC and the Commodity Futures Trading Commission (CFTC) to promulgate rules jointly for the mandatory reports filed by certain registered investment advisers. (Sec. 9) Directs the Comptroller General to assess the annual costs on industry members and their investors because of the registration requirements and ongoing reporting requirements of this Act. (Sec. 11) Amends the Investment Advisers Act of 1940 with respect to SEC authority to exempt any person or transaction (or any class or classes of them) from certain investment advisory contract requirements to the extent that the exemption relates to an investment advisory contract with any person that the Commission determines does not need the protections of such requirements. Requires the SEC, with respect to any factor involving a dollar amount test (e.g. a net asset threshold) it uses to make such a determination, to adjust that test for inflation every five years.</s>

urinary tract infections ( utis ) are the second most common infections in community practice . worldwide , about 150 million people are diagnosed with uti each year costing the global economy in excess of 6 billion us dollars . all over the world , escherichia coli accounts for 75% to 90% of uti isolates and staphylococcus saprophyticus accounts for 5% to 15% of cases of uncomplicated cystitis . antibiotics used in the therapy of uti are usually able to reach high urinary concentrations , which are likely to be clinically effective . fluoroquinolones are preferred as initial agents for empiric therapy of uti in areas where resistance is likely to be of concern [ 3 , 4 ] . this is because they have a high bacteriologic and clinical cure rates , as well as low rates of resistance , among most common uropathogens . ciprofloxacin is the most frequently prescribed fluoroquinolone for utis because of its availability in oral and intravenous formulations . ciprofloxacin has shown an excellent activity against pathogens commonly encountered in complicated utis . it is well absorbed from oral doses and is rapidly excreted from the body under normal conditions [ 3 , 5 , 6 ] . for instance , in china , from 1998 to 2002 the incidence of ciprofloxacin resistance increased steadily from 46.6% to 59.4% . in spain , it was 14.7% , and in bangladesh , it was 26.0% . however , in previous studies in gaza strip , the resistance to ciprofloxacin among all isolates in 2000 was 4.1% and among e coli was only 2.9% whereas , it increased to 11.3% in 2002 . evolving changes in drug resistance in various communities have forced the importance to a reassessment of local empiric choices for managing uti [ 8 , 12 ] . the present study describes the most common organisms causing uti in gaza strip and evaluates the antibacterial activity of ciprofloxacin against recently isolated uti pathogens . a total of 1278 clean voided midstream urine samples were collected from the main three gaza strip governmental hospitals ( al shefaa , khan younis , and the gaza european hospital ) from uti adult outpatients ( the physician suspected infection ) aged 1860 years during january to june 2004 . one sample per patient was collected consecutively from each of the 1278 uti suspected cases ( 831 female and 447 male ) to avoid strain duplication . positive culture was defined as the culture of a single microorganism at a concentration of 10 cfu / ml . the nature of the work followed in the present study was fully explained to all subjects , and the study was conducted with their informed consent . each specimen was inoculated on both blood agar ( with 5% defibrinated sheep blood ) and macconkey agar plates using a 0.01 ml standard loop ( for semiquantitative counts ) and incubated aerobically at 37c for 2448 hours and the number of colonies was counted . significant growth was identified biochemically and serologically in a systematic way according to standard methods . staphylococci were identified by catalase , coagulase , novobiocin , dnase , and staphylococcus latex tests . the initial characterization of enterococci was based on catalase reaction , hemolysis , and colony morphology . further identification of enterococci was accomplished by the use of bile esculin test . enterococci were also confirmed by a serologic procedure strep - check test antimicrobial susceptibility testing of the bacterial isolates was performed by the disk diffusion method in accordance with the national committee for clinical laboratory standards ( nccls ) . quality controls employed standard strains of e coli atcc 25922 , pseudomonas aeruginosa atcc 27853 , and enterococcus faecalis 29212 . interpretive criteria for susceptibility or resistance followed nccls guidelines . for this report , we present susceptibility data for amoxycillin , 25 g ; cephalexin , 30 g ; cefuroxime , 30 g ; ceftazidime , 30 g ; cotrimoxazole , 1.2523.75 g ; nalidixic acid , 30 g ; ciprofloxacin , 5 g ; doxycycline , 30 iu ; nitrofurantoin , 300 g ; gentamycin , 10 g ; and amikacin , 30 g . the ciprofloxacin minimum inhibitory concentration ( mic ) was confirmed by e - test strips ( ab biodisk , solna , sweden ) . the ciprofloxacin mic ( g / ml ) used to define resistant isolates was 4 , as outlined by the national committee for clinical laboratory standards . statistical analysis was performed by the chi - square test and p values of 0.05 were considered significant . a total of 1278 clean voided midstream urine samples were collected from the main three gaza strip governmental hospitals ( al shefaa , khan younis , and the gaza european hospital ) from uti adult outpatients ( the physician suspected infection ) aged 1860 years during january to june 2004 . one sample per patient was collected consecutively from each of the 1278 uti suspected cases ( 831 female and 447 male ) to avoid strain duplication . positive culture was defined as the culture of a single microorganism at a concentration of 10 cfu / ml . the nature of the work followed in the present study was fully explained to all subjects , and the study was conducted with their informed consent . each specimen was inoculated on both blood agar ( with 5% defibrinated sheep blood ) and macconkey agar plates using a 0.01 ml standard loop ( for semiquantitative counts ) and incubated aerobically at 37c for 2448 hours and the number of colonies was counted . significant growth was identified biochemically and serologically in a systematic way according to standard methods . staphylococci were identified by catalase , coagulase , novobiocin , dnase , and staphylococcus latex tests . the initial characterization of enterococci was based on catalase reaction , hemolysis , and colony morphology . further identification of enterococci was accomplished by the use of bile esculin test . enterococci were also confirmed by a serologic procedure strep - check test antimicrobial susceptibility testing of the bacterial isolates was performed by the disk diffusion method in accordance with the national committee for clinical laboratory standards ( nccls ) . quality controls employed standard strains of e coli atcc 25922 , pseudomonas aeruginosa atcc 27853 , and enterococcus faecalis 29212 . , we present susceptibility data for amoxycillin , 25 g ; cephalexin , 30 g ; cefuroxime , 30 g ; ceftazidime , 30 g ; cotrimoxazole , 1.2523.75 g ; nalidixic acid , 30 g ; ciprofloxacin , 5 g ; doxycycline , 30 iu ; nitrofurantoin , 300 g ; gentamycin , 10 g ; and amikacin , 30 g . the ciprofloxacin minimum inhibitory concentration ( mic ) was confirmed by e - test strips ( ab biodisk , solna , sweden ) . the ciprofloxacin mic ( g / ml ) used to define resistant isolates was 4 , as outlined by the national committee for clinical laboratory standards . statistical analysis was performed by the chi - square test and p values of 0.05 were considered significant . of the 1278 urine samples processed , 492 ( 38.5% ) showed positive monomicrobial cultures . gram - negative bacteria represented 437 ( 91.0% ) of the positive bacterial cultures ( 480 ) , whereas gram - positive were 43 ( 9.0% ) . twelve isolates ( 2.5% of 492 ) of yeast were encountered during the screening of uti specimens . the yeast isolates were not included in this analysis because our study is concerned only with bacterial uropathogens and their antimicrobial susceptibility . the overall sex distribution of the subjects was 831 ( 65.0% ) females and 447 ( 35.0% ) males and the sex distribution for the 480 positive cultures was 360 ( 75.0% ) females and 120 ( 25.0% ) males with a statistical significance ( p = .03 ) predominance of females with uti . a summary of the different microorganisms isolated during the study period is shown in table 1 . it is clear that e coli was the predominant uropathogen ( 52.5% ) causing uti followed by proteus mirabilis ( 9.8% ) and klebsiella pneumonia ( 9.2% ) whereas e faecalis was the most common uropathogen ( 5.2% ) isolated among the gram - positive bacteria . high rates of resistance were found to amoxycillin ( 82.5% ) , followed by cotrimoxazole ( 64.4% ) and doxycycline ( 63.1% ) while the lowest resistance was to amikacin and ceftazidime ( 10.0% ) . the mics for ciprofloxacin resistant isolates evenly ranged from 4 to 32 g / ml with a mean of 25.0 g / ml . the isolated bacteria showed wide differences in their susceptibility to the tested antimicrobial drugs . a high resistance rate to ciprofloxacin was observed among the acinetobacter haemolyticus ( 28.6% ) , s saprophyticus ( 25.0% ) , and p aeruginosa ( 20.0% ) whereas e faecalis was the lowest resistant one ( 9.1% ) . the resistance to nitrofurantoin was only 2.7% among e coli and 28.6% among a haemolyticus . on the other hand , the resistance to nalidixic acid was 16.0% among e coli and 57.1% among a haemolyticus . the importance of this study lies in describing the most common bacteria causing uti among outpatients in gaza strip and their resistance to 11 selected antimicrobial agents . the sex distribution of patients in the present study is consistent with that of other studies [ 17 , 18 ] . the significant differences in uti rates between females and males are thought to be due to anatomical differences between the sexes . among other factors , the length of the urethra , a drier environment surrounding the meatus , and antibacterial properties of prostatic fluid contribute to a lower rate of infection in males . in this study , the predominance of e coli among gram - negative bacteria followed by p mirabilis , k pneumonia , and , among gram - positive bacteria , e faecalis ( table 1 ) , was similar to many authors results all over the world [ 20 , 21 , 22 , 23 ] . the prevalence of e coli may be due to its existence as a normal flora in the large intestine and female vagina . the possible source of e faecalis infection could be due to a previous catheterization and those patients may be considered complicated uti cases . notably , comparison among different studies concerning resistance of uropathogens to different antimicrobial agents should take into account the different periods in which such studies were carried out as well as various socioeconomical , socioepidemiological , and clinical parameters of the target population . moreover , the comparison must consider the limitation of resistance to antimicrobials , which can vary from country to another . the resistance of antimicrobial agents tested showed high resistance rates to amoxycillin , cotrimoxazole , and doxycycline while the lowest resistance was to amikacin and ceftazidime . the resistance rate of ciprofloxacin was 15.0% whereas , in a previous study ( 2000 ) carried out in gaza strip , lower resistance to ciprofloxacin ( 4.1% ) was reported . the widespread and more often the misuse of antimicrobial drugs in gaza strip have led to a general rise in the emergence of resistant bacteria , particularly to ciprofloxacin . higher resistance was reported in the usa to ampicillin and cotrimoxazole whereas , for ciprofloxacin resistance , lower rates were found in other countries [ 25 , 26 ] . among gram - negative bacteria , e coli , k pneumonia , and enterobacter cloacae were more susceptible to nitrofurantoin ( table 2 ) . these data suggest that nitrofurantoin may still be useful for the treatment of utis , especially for the mentioned organisms . when comparing the high resistance rates in this study to ciprofloxacin against acinetobacter haemolyticus , s saprophyticus , p aeruginosa , e coli , and e faecalis with other authors , higher resistance rates there are many reasons for this alarming phenomenon , including inappropriate prescribing of antibiotics and poor infection control strategies . the situation in gaza strip , in terms of antimicrobial drug use , is not so different from that of many developing countries , where people usually take antimicrobial drugs without prescription or without performing the necessary culture testing . the considerably high mic values for ciprofloxacin reflects the extent of treatment problem for resistant isolates . overall susceptibility testing of this study demonstrates increased resistance to many commonly used agents especially to ciprofloxacin and illustrates the need for a continuous evaluation for the common antibiotics used in the therapy of uropathogens . amx , amoxycillin ; cf , cephalexin ; ctx , cefuroxime ; ctz , ceftazidime ; gm , gentamycin ; an , amikacin ; sxt , cotrimoxazole ; dox , doxycycline ; na , nalidixic acid ; cip , ciprofloxacin ; and nf , nitrofurantoin .

this article presents the incidence of ciprofloxacin resistance among 480 clinical isolates obtained from patients with urinary tract infection ( uti ) during january to june 2004 in gaza strip , palestine . the resistance rates observed were 15.0% to ciprofloxacin , 82.5% to amoxycillin , 64.4% to cotrimoxazole , 63.1% to doxycycline , 32.5% to cephalexin , 31.9% to nalidixic acid , and 10.0% to amikacin . high resistance to ciprofloxacin was detected among acinetobacter haemolyticus ( 28.6% ) , staphylococcus saprophyticus ( 25.0% ) , pseudomonas aeruginosa ( 20.0% ) , klebsiella pneumonia ( 17.6% ) , and escherichia coli ( 12.0% ) . minimal inhibitory concentration ( mic ) of ciprofloxacin evenly ranged from 4 to 32 g / ml with a mean of 25.0 g / ml . this study indicates emerging ciprofloxacin resistance among urinary tract infection isolates . increasing resistance against ciprofloxacin demands coordinated monitoring of its activity and rational use of the antibiotics .

<s>[INST]urinary tract infections ( utis ) are the second most common infections in community practice . worldwide , about 150 million people are diagnosed with uti each year costing the global economy in excess of 6 billion us dollars . all over the world , escherichia coli accounts for 75% to 90% of uti isolates and staphylococcus saprophyticus accounts for 5% to 15% of cases of uncomplicated cystitis . antibiotics used in the therapy of uti are usually able to reach high urinary concentrations , which are likely to be clinically effective . fluoroquinolones are preferred as initial agents for empiric therapy of uti in areas where resistance is likely to be of concern [ 3 , 4 ] . this is because they have a high bacteriologic and clinical cure rates , as well as low rates of resistance , among most common uropathogens . ciprofloxacin is the most frequently prescribed fluoroquinolone for utis because of its availability in oral and intravenous formulations . ciprofloxacin has shown an excellent activity against pathogens commonly encountered in complicated utis . it is well absorbed from oral doses and is rapidly excreted from the body under normal conditions [ 3 , 5 , 6 ] . for instance , in china , from 1998 to 2002 the incidence of ciprofloxacin resistance increased steadily from 46.6% to 59.4% . in spain , it was 14.7% , and in bangladesh , it was 26.0% . however , in previous studies in gaza strip , the resistance to ciprofloxacin among all isolates in 2000 was 4.1% and among e coli was only 2.9% whereas , it increased to 11.3% in 2002 . evolving changes in drug resistance in various communities have forced the importance to a reassessment of local empiric choices for managing uti [ 8 , 12 ] . the present study describes the most common organisms causing uti in gaza strip and evaluates the antibacterial activity of ciprofloxacin against recently isolated uti pathogens . a total of 1278 clean voided midstream urine samples were collected from the main three gaza strip governmental hospitals ( al shefaa , khan younis , and the gaza european hospital ) from uti adult outpatients ( the physician suspected infection ) aged 1860 years during january to june 2004 . one sample per patient was collected consecutively from each of the 1278 uti suspected cases ( 831 female and 447 male ) to avoid strain duplication . positive culture was defined as the culture of a single microorganism at a concentration of 10 cfu / ml . the nature of the work followed in the present study was fully explained to all subjects , and the study was conducted with their informed consent . each specimen was inoculated on both blood agar ( with 5% defibrinated sheep blood ) and macconkey agar plates using a 0.01 ml standard loop ( for semiquantitative counts ) and incubated aerobically at 37c for 2448 hours and the number of colonies was counted . significant growth was identified biochemically and serologically in a systematic way according to standard methods . staphylococci were identified by catalase , coagulase , novobiocin , dnase , and staphylococcus latex tests . the initial characterization of enterococci was based on catalase reaction , hemolysis , and colony morphology . further identification of enterococci was accomplished by the use of bile esculin test . enterococci were also confirmed by a serologic procedure strep - check test antimicrobial susceptibility testing of the bacterial isolates was performed by the disk diffusion method in accordance with the national committee for clinical laboratory standards ( nccls ) . quality controls employed standard strains of e coli atcc 25922 , pseudomonas aeruginosa atcc 27853 , and enterococcus faecalis 29212 . interpretive criteria for susceptibility or resistance followed nccls guidelines . for this report , we present susceptibility data for amoxycillin , 25 g ; cephalexin , 30 g ; cefuroxime , 30 g ; ceftazidime , 30 g ; cotrimoxazole , 1.2523.75 g ; nalidixic acid , 30 g ; ciprofloxacin , 5 g ; doxycycline , 30 iu ; nitrofurantoin , 300 g ; gentamycin , 10 g ; and amikacin , 30 g . the ciprofloxacin minimum inhibitory concentration ( mic ) was confirmed by e - test strips ( ab biodisk , solna , sweden ) . the ciprofloxacin mic ( g / ml ) used to define resistant isolates was 4 , as outlined by the national committee for clinical laboratory standards . statistical analysis was performed by the chi - square test and p values of 0.05 were considered significant . a total of 1278 clean voided midstream urine samples were collected from the main three gaza strip governmental hospitals ( al shefaa , khan younis , and the gaza european hospital ) from uti adult outpatients ( the physician suspected infection ) aged 1860 years during january to june 2004 . one sample per patient was collected consecutively from each of the 1278 uti suspected cases ( 831 female and 447 male ) to avoid strain duplication . positive culture was defined as the culture of a single microorganism at a concentration of 10 cfu / ml . the nature of the work followed in the present study was fully explained to all subjects , and the study was conducted with their informed consent . each specimen was inoculated on both blood agar ( with 5% defibrinated sheep blood ) and macconkey agar plates using a 0.01 ml standard loop ( for semiquantitative counts ) and incubated aerobically at 37c for 2448 hours and the number of colonies was counted . significant growth was identified biochemically and serologically in a systematic way according to standard methods . staphylococci were identified by catalase , coagulase , novobiocin , dnase , and staphylococcus latex tests . the initial characterization of enterococci was based on catalase reaction , hemolysis , and colony morphology . further identification of enterococci was accomplished by the use of bile esculin test . enterococci were also confirmed by a serologic procedure strep - check test antimicrobial susceptibility testing of the bacterial isolates was performed by the disk diffusion method in accordance with the national committee for clinical laboratory standards ( nccls ) . quality controls employed standard strains of e coli atcc 25922 , pseudomonas aeruginosa atcc 27853 , and enterococcus faecalis 29212 . , we present susceptibility data for amoxycillin , 25 g ; cephalexin , 30 g ; cefuroxime , 30 g ; ceftazidime , 30 g ; cotrimoxazole , 1.2523.75 g ; nalidixic acid , 30 g ; ciprofloxacin , 5 g ; doxycycline , 30 iu ; nitrofurantoin , 300 g ; gentamycin , 10 g ; and amikacin , 30 g . the ciprofloxacin minimum inhibitory concentration ( mic ) was confirmed by e - test strips ( ab biodisk , solna , sweden ) . the ciprofloxacin mic ( g / ml ) used to define resistant isolates was 4 , as outlined by the national committee for clinical laboratory standards . statistical analysis was performed by the chi - square test and p values of 0.05 were considered significant . of the 1278 urine samples processed , 492 ( 38.5% ) showed positive monomicrobial cultures . gram - negative bacteria represented 437 ( 91.0% ) of the positive bacterial cultures ( 480 ) , whereas gram - positive were 43 ( 9.0% ) . twelve isolates ( 2.5% of 492 ) of yeast were encountered during the screening of uti specimens . the yeast isolates were not included in this analysis because our study is concerned only with bacterial uropathogens and their antimicrobial susceptibility . the overall sex distribution of the subjects was 831 ( 65.0% ) females and 447 ( 35.0% ) males and the sex distribution for the 480 positive cultures was 360 ( 75.0% ) females and 120 ( 25.0% ) males with a statistical significance ( p = .03 ) predominance of females with uti . a summary of the different microorganisms isolated during the study period is shown in table 1 . it is clear that e coli was the predominant uropathogen ( 52.5% ) causing uti followed by proteus mirabilis ( 9.8% ) and klebsiella pneumonia ( 9.2% ) whereas e faecalis was the most common uropathogen ( 5.2% ) isolated among the gram - positive bacteria . high rates of resistance were found to amoxycillin ( 82.5% ) , followed by cotrimoxazole ( 64.4% ) and doxycycline ( 63.1% ) while the lowest resistance was to amikacin and ceftazidime ( 10.0% ) . the mics for ciprofloxacin resistant isolates evenly ranged from 4 to 32 g / ml with a mean of 25.0 g / ml . the isolated bacteria showed wide differences in their susceptibility to the tested antimicrobial drugs . a high resistance rate to ciprofloxacin was observed among the acinetobacter haemolyticus ( 28.6% ) , s saprophyticus ( 25.0% ) , and p aeruginosa ( 20.0% ) whereas e faecalis was the lowest resistant one ( 9.1% ) . the resistance to nitrofurantoin was only 2.7% among e coli and 28.6% among a haemolyticus . on the other hand , the resistance to nalidixic acid was 16.0% among e coli and 57.1% among a haemolyticus . the importance of this study lies in describing the most common bacteria causing uti among outpatients in gaza strip and their resistance to 11 selected antimicrobial agents . the sex distribution of patients in the present study is consistent with that of other studies [ 17 , 18 ] . the significant differences in uti rates between females and males are thought to be due to anatomical differences between the sexes . among other factors , the length of the urethra , a drier environment surrounding the meatus , and antibacterial properties of prostatic fluid contribute to a lower rate of infection in males . in this study , the predominance of e coli among gram - negative bacteria followed by p mirabilis , k pneumonia , and , among gram - positive bacteria , e faecalis ( table 1 ) , was similar to many authors results all over the world [ 20 , 21 , 22 , 23 ] . the prevalence of e coli may be due to its existence as a normal flora in the large intestine and female vagina . the possible source of e faecalis infection could be due to a previous catheterization and those patients may be considered complicated uti cases . notably , comparison among different studies concerning resistance of uropathogens to different antimicrobial agents should take into account the different periods in which such studies were carried out as well as various socioeconomical , socioepidemiological , and clinical parameters of the target population . moreover , the comparison must consider the limitation of resistance to antimicrobials , which can vary from country to another . the resistance of antimicrobial agents tested showed high resistance rates to amoxycillin , cotrimoxazole , and doxycycline while the lowest resistance was to amikacin and ceftazidime . the resistance rate of ciprofloxacin was 15.0% whereas , in a previous study ( 2000 ) carried out in gaza strip , lower resistance to ciprofloxacin ( 4.1% ) was reported . the widespread and more often the misuse of antimicrobial drugs in gaza strip have led to a general rise in the emergence of resistant bacteria , particularly to ciprofloxacin . higher resistance was reported in the usa to ampicillin and cotrimoxazole whereas , for ciprofloxacin resistance , lower rates were found in other countries [ 25 , 26 ] . among gram - negative bacteria , e coli , k pneumonia , and enterobacter cloacae were more susceptible to nitrofurantoin ( table 2 ) . these data suggest that nitrofurantoin may still be useful for the treatment of utis , especially for the mentioned organisms . when comparing the high resistance rates in this study to ciprofloxacin against acinetobacter haemolyticus , s saprophyticus , p aeruginosa , e coli , and e faecalis with other authors , higher resistance rates there are many reasons for this alarming phenomenon , including inappropriate prescribing of antibiotics and poor infection control strategies . the situation in gaza strip , in terms of antimicrobial drug use , is not so different from that of many developing countries , where people usually take antimicrobial drugs without prescription or without performing the necessary culture testing . the considerably high mic values for ciprofloxacin reflects the extent of treatment problem for resistant isolates . overall susceptibility testing of this study demonstrates increased resistance to many commonly used agents especially to ciprofloxacin and illustrates the need for a continuous evaluation for the common antibiotics used in the therapy of uropathogens . amx , amoxycillin ; cf , cephalexin ; ctx , cefuroxime ; ctz , ceftazidime ; gm , gentamycin ; an , amikacin ; sxt , cotrimoxazole ; dox , doxycycline ; na , nalidixic acid ; cip , ciprofloxacin ; and nf , nitrofurantoin .[/INST]this article presents the incidence of ciprofloxacin resistance among 480 clinical isolates obtained from patients with urinary tract infection ( uti ) during january to june 2004 in gaza strip , palestine . the resistance rates observed were 15.0% to ciprofloxacin , 82.5% to amoxycillin , 64.4% to cotrimoxazole , 63.1% to doxycycline , 32.5% to cephalexin , 31.9% to nalidixic acid , and 10.0% to amikacin . high resistance to ciprofloxacin was detected among acinetobacter haemolyticus ( 28.6% ) , staphylococcus saprophyticus ( 25.0% ) , pseudomonas aeruginosa ( 20.0% ) , klebsiella pneumonia ( 17.6% ) , and escherichia coli ( 12.0% ) . minimal inhibitory concentration ( mic ) of ciprofloxacin evenly ranged from 4 to 32 g / ml with a mean of 25.0 g / ml . this study indicates emerging ciprofloxacin resistance among urinary tract infection isolates . increasing resistance against ciprofloxacin demands coordinated monitoring of its activity and rational use of the antibiotics .</s>

despite a long history of research on the glass transition @xcite , this phenomenon is still commonly regarded as an unresolved problem . in recent years a variety of new theoretical and phenomenological approaches of the glass transition ( e.g. , @xcite ) stimulated new experimental investigations of the dynamic response of glass - forming liquids ( see , e.g. @xcite ) . here dielectric spectroscopy has played an important role , mainly due to the broad dynamic range accessible with this method ( e.g. , @xcite ) . spectra of the dielectric loss @xmath1 show a variety of features , the microscopic origin of most of them being still controversially discussed . most prominent is the @xmath0-peak associated with the well known @xmath0- or structural - relaxation process . the comparison of the non - trivial temperature dependence of the @xmath0-relaxation time with theoretical predictions states an important test for any model of the glass - transition . some decades above the @xmath0-peak frequency @xmath2 , an excess wing ( also called high - frequency wing or tail ) shows up as high - frequency excess contribution to the power law @xmath3 , commonly found at @xmath4 . this excess wing seems to be a universal feature of glass - forming liquids as can be deduced from the scaling behavior found by nagel and coworkers @xcite . based on this universal scaling of @xmath0-relaxation and excess wing , nagel and coworkers @xcite proposed a divergence of the static susceptibility which essentially implies a constant loss behavior at high frequencies and low temperatures as has early been predicted by wong and angell @xcite . the interest in even higher frequencies , in the ghz - thz region , was mainly stimulated by the mode coupling theory ( mct ) @xcite , which explains the glass transition in terms of a dynamic phase transition at a critical temperature @xmath5significantly above the glass temperature @xmath6 . from neutron- and light - scattering experiments it is well known that in the thz region the so - called boson peak shows up in the imaginary part of the susceptibility of glass - forming liquids . for the transition region between @xmath7-process and boson peak , mct predicts an additional contribution , now commonly termed fast @xmath8-relaxation . but also other models predict fast processes , the most prominent being the coupling model by ngai and coworkers @xcite . this transition region was mainly investigated by neutron and light scattering and indeed indications for additional fast processes were found @xcite . the scattering results were described within the framework of mct and partly good agreement with the theoretical results was obtained . however , the applicability of the mct for glass - forming liquids , especially at low temperatures near @xmath6 , is still a matter of controversy . dielectric data were scarce in the relevant high - frequency region as for classical dielectric methods the region above ghz is not accessible . only recently , our group was able to obtain continuous dielectric spectra on glass - forming liquids extending well into the submillimeter wavelength region @xcite . the existence of a broad minimum in @xmath9 was found which can not be explained by a simple crossover from the structural ( @xmath0- ) relaxation to the far - infrared ( fir ) vibrational response . similar to the scattering results , clear indications for additional fast processes prevailing in this transition region were found . for glass - forming glycerol , by combining classical dielectric spectroscopy , coaxial transmission , quasi - optic submillimeter and far - infrared techniques , spectra covering 18 decades of frequency and extending well into the thz range were obtained @xcite . this allowed for the observation of the complete dynamic response including the boson peak . in addition , dielectric spectra up to 380 ghz were obtained in [ ca(no@xmath10)@xmath11@xmath12[kno@xmath10]@xmath14 ( ckn ) and [ ca(no@xmath10)@xmath11@xmath12[rbno@xmath10]@xmath14 ( crn ) @xcite . both are ionically conducting , molten - salt glass formers with relatively high fragility @xcite , @xmath15 @xcite . in contrast , glycerol is a rather strong hydrogen - bonded glass - former with a fragility parameter of @xmath16 @xcite . in many respects , especially concerning the high - frequency response near the boson peak and the agreement of the dielectric data with mct predictions and with the scattering results , glycerol and the molten salts behave qualitatively different . in order to clarify the origin of these differences and in the light of the dependence of the boson peak contribution on fragility @xcite , it seemed of interest to investigate a fragile , but molecular glass - former . for this purpose we have chosen propylene carbonate ( pc ) which like glycerol is a molecular glass former , but can be characterized as a fragile ( @xmath17,@xcite ) van der waals liquid . preliminary results on pc in a somewhat restricted frequency range have been published earlier @xcite . in the present paper we present extended results covering the complete dynamic range including the boson peak . we address all features seen in the dielectric spectra , i.e. the @xmath7-response , the excess wing , the fast @xmath8-relaxation region and the boson peak . the results are compared with a variety of theoretical predictions and with the findings from other experimental methods . the measurements presented in this article have been performed using a variety of different techniques to cover nearly 20 decades in frequency . the lowest frequencies ( @xmath18 @xmath19hz ) were investigated in the time - domain using a spectrometer that is based on a design described by mopsik @xcite . the complex dielectric constant was calculated from the measured response function via a fourier transformation . the autobalance bridges hp4284 and hp4285 were used in the range @xmath20 hz @xmath21 mhz . for the radio - frequency and microwave range ( @xmath22 mhz @xmath23 ghz ) a reflectometric technique was employed @xcite using the hp4191 and hp4291 impedance analyzers and the hp8510 network analyzer . in addition , at frequencies @xmath24 mhz @xmath25 ghz data were taken in transmission with the hp8510 network analyzer using 7 mm coaxial lines of various lengths ( between 10 and 300 mm ) filled with the sample material . closed - cycle refrigerators , n@xmath26- , and he - cryostats have been used to cover the relevant temperature ranges . at frequencies @xmath27 ghz @xmath28 thz a quasi - optical submillimeter spectrometer was used with an experimental arrangement similar to a mach - zehnder interferometer @xcite . this setup allows for measuring the frequency dependence of both the transmission and the phase shift of a monochromatic electromagnetic beam through the sample . the frequency range up to 1.2thz is covered continuously by 10 tunable narrow - band backward - wave oscillators ( bwos ) . the signal was detected by a golay cell or a pumped he bolometer and amplified using lock - in techniques . the liquid was put in specially designed cells made of polished stainless steel with thin plane - parallel quartz windows ; depending on the range of frequency and temperature the thickness of the sample cell was between 1 mm and 30 mm . the sample cell was placed in a home - made cryostat and cooled by a continuous flow of nitrogen gas . the data were analyzed using optical formulae for multilayer interference @xcite with the known thickness and optical parameters of the windows in order to get the real and imaginary part of the dielectric constant of the sample as a function of frequency at various temperatures . at higher frequencies ( 600ghz @xmath29 3thz ) the samples were investigated with a fourier - transform infrared spectrometer covering a regime from 450ghz to 10thz . this set - up allows the measurement of the transmission or reflection only , whereas the phase shift caused by the sample can not be determined . to cover the complete frequency range , a single @xmath30 curve at a given temperature is superimposed using results from the various setups . the time - domain results are obtained in arbitrary units and scaled by one factor to match the autobalance bridge results . for the measurements at @xmath22 ghz @xmath31 ghz there are some uncertainties of the absolute values originating from an ill - defined geometry of the samples or parasitic elements . these results have been partly shifted by one scaling factor per measurement series which led to a good match at both the low and the high frequency side . typically , shifting factors of less than @xmath32 had to be applied to obtain smooth curves . the submillimeter - frequency results and , at losses @xmath33 , also the coaxial transmission measurements provide excellent absolute values of @xmath34 and @xmath35 . the values for @xmath1 from the infrared measurements were calculated consistently with the kramers - kronig relation assuming a reasonable behavior of the dielectric constant @xmath36 which is almost constant in this frequency regime . in this latter case , the error bars for @xmath1 were estimated by variation of the assumed @xmath34 behavior . as sample material , propylene carbonate ( @xmath37 k @xcite , @xmath38 k ) with a purity of @xmath39 , was used . to avoid crystallization polished sample holders had to be used in the various experiments . however , occasional crystallization , mainly at temperatures around @xmath40 k could not be avoided completely . therefore some measurements were performed after heating up to @xmath41 and direct cooling to each measurement temperature with relatively fast cooling rates ( @xmath22 k / min ) . figures [ eps1 ] and [ eps2 ] show @xmath43 and @xmath44 for various temperatures in the whole accessible frequency range . @xmath9 ( fig . [ eps2 ] ) exhibits the typical asymmetrically shaped @xmath0-relaxation peaks shifting through the frequency window with temperature . they are accompanied by relaxation steps in @xmath43 as seen in fig . [ eps1 ] . in most respects the data agree well with the results of earlier dielectric investigations of pc @xcite which were restricted to smaller frequency and temperature ranges . however , some differences show up in the absolute values ( see below ) . the solid lines in figs . [ eps1 ] and [ eps2 ] are fits of the @xmath0-relaxation region with the empirical cole - davidson function @xcite , @xmath45 , performed simultaneously for real and imaginary part . @xmath46 and @xmath47 denote the low- and high - frequency limit of the dielectric constant , respectively . a good fit of the peak region was achieved . very close to the maximum the loss curves can also be described by the fourier transform of the kohlrausch - williams - watts ( kww ) function @xcite , @xmath48 $ ] , ( dotted lines , shown for 173 k , only ) . for all temperatures investigated the kww fit is of lower quality than the cd fit . this can be ascribed to the fact that there is a significant difference of cd and kww response concerning the loss - peak region . for the kww response the curvature near the peak is retained somewhat further above the peak frequency and a power law @xmath49 is approached at significantly higher frequencies only . therefore , in most cases the exponent @xmath50 obtained from the kww fits differs significantly from the power law exponent @xmath8 actually observed for @xmath4 . in contrast , for the cd fits @xmath51 is found . despite the kww function is more widely used nowadays , in the authors experience dielectric loss data in glass - forming materials are often described much better by the cd function @xcite . the inset of fig . [ eps2 ] shows the temperature dependence of the frequency @xmath52 which is virtually identical to the peak frequency @xmath2 . here @xmath53 denotes the mean relaxation time @xcite calculated from @xmath54 for the cd function and @xmath55 ( @xmath56 denoting the gamma function ) for the kww function . the results from the cd ( circles ) and the kww fits ( pluses ) agree perfectly well and are in accord with previously published data @xcite . @xmath57 shows the well known deviations from thermally activated behavior , typical for fragile glass - formers . it can be parameterized using the vogel - fulcher - tammann ( vft ) equation @xcite ( line in the inset of fig . [ eps2 ] ; see section [ discalp ] ) . in figure [ betchi](a ) the relaxation strengths @xmath58 @xmath59 obtained from the cd and kww fits are shown . one has to be aware that @xmath60 resulting from the fits is somewhat smaller that @xmath60 read off from the @xmath61 data of fig . [ eps1 ] . as seen in fig . [ eps1 ] , the fits overestimate @xmath47 because there is an additional decrease of @xmath43 corresponding to the excess wing contribution ( see below ) which is not taken into account by the cd fits . consequently @xmath60 shown in fig . [ betchi](a ) presents the relaxation strength of the @xmath0-process alone , without the excess wing contribution . @xmath60 decreases monotonically with temperature which is in accord with previous reports @xcite . however , the decrease found in the present work is somewhat less steep than reported earlier . unfortunately , in @xcite where a rather broad temperature and frequency range was investigated no absolute values of @xmath60 were reported . the results from the high frequency measurements of payne and theodorou @xcite are compatible with our data at @xmath62 k except for their lowest temperature ( @xmath63 k ) where a much higher value ( @xmath64 ) was found . however , the relaxation time at @xmath65 k reported by these authors deviates by more than one decade from that found in the present and other works @xcite which sheds some doubt upon the significance of the results at this temperature . also from the results of huck _ _ @xcite and angell _ et al . _ _ _ near @xmath66 k a much higher magnitude of @xmath60 ( @xmath67 ) than determined here can be read off . the determination of the absolute values of @xmath68 is a difficult task as it depends on the shifting factors necessary to match results from different experimental set - ups and on the subtraction of possible stray capacitances inherent to some methods . we believe , that due to the broad overlap of the frequency ranges of the various devices used in the present work , the reproducibility of results with different sample holders , and the simultaneous fitting of @xmath43 and @xmath44 , fig . [ betchi](a ) gives a good estimate of the absolute value of @xmath60 . figure [ betchi](b ) shows the width parameter obtained from both fitting procedures . both , @xmath69 and @xmath50 increase nearly linearly with temperature up to about @xmath70 k. above this temperature a tendency to saturate at a value below unity is observed . this is in contrast to @xcite where @xmath71 was reported to saturate at unity for high temperatures . this discrepancy may be due to the smaller frequency range available in @xcite which for high temperatures leads to a restriction of the data at the high - frequency side of the loss peaks , that is essential for the determination of @xmath69 . unfortunately , no @xmath44 data of pc are shown in @xcite . at frequencies about 2 - 3 decades above @xmath2 deviations of @xmath72 from the cd - fits show up . for low temperatures these deviations can be described as second power law , @xmath73 with @xmath74 , in addition to the power law @xmath75 constituting the high frequency flank of the @xmath0-peak . the exponent @xmath76 decreases with decreasing temperature as found previously for pc and other glass - forming materials @xcite . the excess wing is accompanied by a decrease in @xmath61 as mentioned above . it shows up as a somewhat smoother rounding of the @xmath43 curves ( compared , e.g. , to the cd behavior ) when approaching @xmath47 ( fig . [ eps1 ] ) . for @xmath77 k the exponent @xmath76 has reached a value almost identical with @xmath69 ( fig . [ eps2 ] ) and for @xmath78 k the excess wing seems to have merged with the @xmath0-peak . for @xmath79 @xmath78 k the deviations of the experimental data from the cd - fits are due to the fast dynamic processes described in the following section . at high frequencies , succeeding the excess wing for low and the @xmath0-peak for high temperatures , @xmath80 exhibits a smooth transition into a shallow minimum . such a minimum was earlier observed in glycerol @xcite , salol @xcite , the molten salts ckn @xcite and crn @xcite , and the plastic crystals cyclo - octanol @xcite and ortho - carborane @xcite . with increasing temperature , the amplitude @xmath81 and frequency position @xmath82 of the minimum increases . for room temperature the measurements have been extended into the fir region . here no minimum is observed , but a shoulder shows up near 1 thz . this shoulder is indicative of the so - called boson peak known mainly from neutron- and light - scattering measurements @xcite . indeed , for pc the boson peak , determined from light - scattering measurements @xcite , is located just above 1 thz . as the peak frequency and amplitude is only weakly temperature dependent , it becomes obvious that the high - frequency flank of the @xmath9-minimum is identical to the low - frequency flank of the boson peak . the frequency dependence in this region can be approximately described by a power law @xmath83 . the exponent @xmath84 increases with decreasing temperature and seems to approach a linear behavior as indicated by the dash - dotted line in fig . [ eps2 ] . in @xmath43 for these frequencies the onset of a relaxation step corresponding to the boson peak can be seen ( fig . [ eps1 ] ) . in fig . [ vgl ] we compare @xmath9 with @xmath85 calculated from the light scattering results on pc @xcite . as the light scattering results give no information on the absolute values of @xmath1 , the datasets have been scaled to yield a comparable height of the boson peak . while the dielectric results in pc are qualitatively similar to the light scattering results ( succession of @xmath0-peak , minimum , and boson peak ) , quantitative differences show up : the @xmath0-peak is located at a significantly lower frequency and the ratio of the amplitudes of @xmath0- and boson peak is higher for the dielectric measurements . the latter behavior was also found in our experiments on glycerol @xcite and salol @xcite , and in molecular dynamics simulations of ortho - terphenyl @xcite and of a system of rigid diatomic molecules @xcite . the results from a very recent neutron scattering study of pc @xcite indicate an even smaller ratio of @xmath0- and boson peak amplitude than for light scattering . clearly the position of the minimum differs between the different methods , also in accordance with results on other systems @xcite . in contrast , the increase towards the boson peak exhibits almost identical power laws for the dielectric and light scattering measurements . the most significant result of an analysis of the @xmath0-relaxation process is the temperature dependence of the @xmath0-relaxation time which is compared to various predictions in fig . figure [ tau](a ) shows the same fit with the vft equation @xcite , as in the inset of fig . [ eps2 ] . a vft temperature @xmath87 k and a strength parameter @xmath88were determined , the latter characterizing pc as fragile glass former @xcite . while the vft equation is primarily an empirical description , a theoretical foundation was given in various models , e.g. the adam - gibbs theory @xcite or the free volume theory @xcite . in fig . [ tau](a ) it becomes obvious that , above a crossover temperature @xmath89 k , deviations from vft behavior show up , similar to those seen in earlier work @xcite . in @xcite and @xcite a transition to thermally activated behavior was suggested as demonstrated by the dashed line in fig . [ tau](a ) . @xmath90 was interpreted @xcite as temperature below which the potential energy landscape becomes important . however , one has to state that also alternative descriptions are possible , e.g. using vft behavior at high and a thermally activated behavior at low temperatures or a combination of vft functions @xcite . in addition , stickel et al . @xcite performed an analysis of relaxation - time data on pc extending to temperatures above room temperature using a temperature - derivative method @xcite . they reported a transition between two vft laws at about @xmath70 k and a second transition to thermally activated behavior above about @xmath91 k. overall , as demonstrated in fig . [ tau](a ) , the three - parameter vft function is not able to describe the data in the whole temperature range and a crossover to a different behavior has to be assumed to overcome this difficulty . a four - parameter function for the description of @xmath92 is the outcome of the extended free volume ( efv ) theory @xcite . in the efv theory the supercooled liquid is assumed to be divided into liquid - like and solid - like regions . at a temperature @xmath93 a transition from percolating ( fluid ) to isolated liquid - like regions ( solid glass state ) occurs . by addressing the entropy of the glass - forming system and making use of percolation theory the following result for @xmath92 was obtained : good fits with eq . ( [ eqefv ] ) for a variety of glass - formers were reported @xcite . figure [ tau](b ) shows a fit of @xmath92 of pc with eq . ( [ eqefv ] ) and @xmath95 k. indeed , the efv theory gives a very good description of the present data and @xmath93 is almost identical to the calorimetric @xmath96 k @xcite . while the vft and efv predictions lead to critical temperatures near or below @xmath6 , the @xmath97 of mct is predicted to be located well above @xmath98 . the simplest version of mct , the idealized mct @xcite , predicts a critical behavior of the @xmath0-relaxation timescale , @xmath99 with a critical exponent @xmath100 that is determined by @xmath101 . here @xmath84 and @xmath76 are the low- and high - frequency power law exponents of the @xmath9-minimum as will be explained in detail in section [ secdiscfastmin ] . the solid line in fig . [ tau](c ) is a fit with the three - parameter function , eq . [ eqmctfp ] with @xmath102 and @xmath103 k fixed to the values obtained from the analysis of the @xmath9-minimum ( sect . [ secdiscfastmin ] ) . even with all parameters free , very similar values result , namely @xmath104 k and @xmath105 . for the fits , only data above 200 k were used where a good agreement of data and fit was achieved . in order to describe the data at lower temperatures a vft fit can be employed ( dashed line ) . the observed absence of critical behavior at @xmath97 in the experimental data is expected within the extended mct @xcite . here the structural arrest found in idealized mct for @xmath106is avoided by the assumption of thermally activated hopping processes . mct also predicts that , at least for @xmath107 , the relaxation times determined with different experimental methods should follow a common temperature behavior . indeed , while there is a difference in the absolute values of @xmath108 from light scattering @xcite and dielectric measurements ( leading to the different @xmath0-peak positions in fig . [ vgl ] ) , which can be understood considering the different correlation functions of both methods @xcite , they can be transferred into each other by a temperature independent factor of about 3 ( not shown ) . finally , we compare the results to the predictions of the frustration - limited domain ( fld ) model by kivelson , tarjus , and coworkers @xcite . this theory postulates a narrowly avoided critical point at a temperature @xmath109 above the melting point . the theory is based on the assumption that there is a locally preferred structure ( lps ) which , however , is not able to tile space periodically . without this geometrical constraint the system would condense into the lps at @xmath109 . in real systems somewhat below @xmath109 , frustration - limited domains with the lps are formed . such a scenario is intuitive for the simple system of spherical molecules . here the lps is an icosahedral short - range order but one can not tile space with this structure . by using a phenomenological scaling approach , a prediction for the temperature dependent relaxation rate was obtained : @xmath110 \text { for } % t < t^{\ast } \label{kiveq}\end{aligned}\ ] ] clearly , among the analyses presented in fig . [ tau ] , the one employing the combination of vft and thermally activated behavior [ fig . [ tau](a ) ] seems least reasonable as there is no theoretical base for such a behavior . as could be expected , the two four - parameter functions ( efv and fld model ) provide the best descriptions of the data as was also found for a similar comparison performed for dielectric results on salol @xcite . as mentioned above , the huge deviations seen for the ( idealized ) mct approach could be expected . this setback may be overcome when employing the extended mct , which is out of the scope of the present work . an argument in favor of the mct - fit is the fact that only one parameter was varied , @xmath97 and @xmath111 being fixed as mentioned above . the mct also makes distinct predictions for the temperature dependence of the relaxation strength @xmath60 and the spectral form of the @xmath7-process @xcite . according to idealized mct , for @xmath112 , the relaxation strength and the spectral form of the @xmath0-process should be temperature independent ( time - temperature superposition principle ) . in addition , for @xmath113 , @xmath114^{% % tcimacro{\unicode[m]{0xbd}}% % beginexpansion { \frac12}% % endexpansion } $ ] follows from extended mct . in fig . [ betchi](a ) the solid line was calculated using the mct prediction with @xmath103 k as deduced in section [ secdiscfastmin ] . due to the scattering of the data no definite conclusion can be drawn , but at least the data do not contradict mct . in contrast schoenhals _ et al . _ @xcite reported clear deviations of their @xmath115 ( given in arbitrary units ) from mct predictions @xcite . concerning the predicted temperature independent spectral form of the @xmath0-peak for @xmath107 , a tendency to saturate is indeed seen for @xmath71 and @xmath116 in fig . [ betchi ] , however at temperatures clearly above @xmath97 , only . but a reasonable description of the @xmath0-peaks for @xmath107 is also possible with a constant @xmath117 . again this is in contrast to the statements made in @xcite . overall it is difficult to make a decisive statement about the validity of mct in pc from the analysis of the @xmath0-process alone . the excess wing ( also called high - frequency wing or tail ) seems to be a universal feature of glass - forming liquids @xcite , but up to now its microscopic origin remains unclear . a phenomenological function taking account of the @xmath0-peak and the wing has been proposed recently @xcite . in many cases it is possible to describe the @xmath7-peak including the wing using a model of dynamically correlated domains @xcite but for low temperatures and extremely broadband data deviations show up @xcite . nagel and coworkers @xcite found that the @xmath118-curves for different temperatures and even for different materials , including the @xmath0-peak and the wing , can be scaled onto one master curve by an appropriate choice of the x- and y - axis . this intriguing scaling behavior strongly suggests a correlation between @xmath0-process and the high - frequency wing . during the last years some criticism of the nagel - scaling arose concerning its universality @xcite and accuracy @xcite and minor modifications of the original scaling procedure have been proposed @xcite . however , it is still commonly believed that the nagel - scaling is of significance for our understanding of the glass - forming liquids and many efforts have been made to check its validity in a variety of materials @xcite . in fig . [ scal ] we have applied the modified scaling approach proposed by dendzik _ this procedure was shown to lead to somewhat better scaling in the @xmath0-peak region and allows for an unequivocal determination of the scaling parameters . in addition , the modified procedure is able to collapse different cd - curves onto one master curve @xcite which is not the case for the original nagel - scaling @xcite . as demonstrated in fig . [ eps2 ] , the cd function gives an excellent description of the @xmath0-peak region in @xmath30 . the application of the modified scaling requires the determination of parameters @xmath119 , @xmath120 , and @xmath8 . here @xmath119 and @xmath120 are defined as frequency and amplitude of the intersection point of the two power laws @xmath121 for @xmath122 and @xmath75 for @xmath4 . in fig . [ scal ] we show the pc results in addition to glycerol data taken from @xcite , scaled according to @xcite , i.e. with @xmath123 and @xmath124 $ ] . indeed , the @xmath0-peak and the excess wing region can nicely be scaled onto one master curve for each material . the deviations from this master curve seen in fig . [ scal ] occur in the wing and boson peak region which can not be scaled in this way . the scaling transfers the cd behavior of the @xmath0-peak to a constant , @xmath125 , at its low frequency side ( @xmath126 and to a linear decrease , @xmath127 ( solid lines in fig . [ scal ] ) at its high - frequency side ( @xmath128 ) . the excess wing shows up as a more shallow linear decrease deviating from the @xmath129 line above @xmath130 . due to the large frequency region available for the present work this linear decrease can be observed up to @xmath131 for pc while the maximum value observed up to now was @xmath132 @xcite . due to this larger range it becomes obvious that the curves for glycerol and pc show significant deviations from each other at @xmath133 as demonstrated in the upper inset of fig . in contrast , the original nagel - scaling @xcite scales the curves for both materials perfectly well in this high - frequency region @xcite . as mentioned above , the wing seems to merge with the @xmath0-peak above about @xmath70 k. in fig . [ scal ] this corresponds to a direct transition from @xmath129 behavior to the non - scaling linear decrease corresponding to the minimum region ( see lower inset of fig . [ scal ] ) . here only two linear regions for @xmath128 can be distinguished while at lower temperatures three such regions are seen ( associated with @xmath7-peak , excess wing , and minimum ) . for glycerol a similar merging of wing and @xmath0-peak is observed at temperatures above about @xmath134 k. finally we want to mention that it is also possible to describe the excess wing by an additional relaxation process superimposed to the @xmath0-process @xcite . such secondary processes , usually termed ( slow ) @xmath135-processes , can often be ascribed to an internal change of the molecular conformation . however , in the light of the universal properties of the wing for different glass - forming liquids revealed by the nagel - scaling , it is unreasonable to ascribe it to this type of @xmath8-relaxations which depend on the specific molecular structure . the finding that secondary relaxation processes can show up also in simple glass formers led to the assumption of a more fundamental reason for these so - called johari - goldstein @xmath8-processes @xcite . also recent theoretical developments @xcite within the coupling model @xcite may point in the direction of a universal slow @xmath8-relaxation , closely connected to the @xmath0-process . it can not be excluded that the wing and these possible intrinsic @xmath136-relaxations are manifestations of the same microscopic mechanism . in fig . [ mctfits ] , a magnified view of the high - frequency region of @xmath9 is shown . in the inset we tried to analyze the minimum region in terms of a simple crossover from @xmath0-relaxation or excess wing to the boson peak . for the low frequency wing of the boson peak a linear or steeper increase of @xmath44 can be assumed as is commonly found for a variety of glass - formers @xcite . indeed , for the lowest temperatures investigated , where vibrational contributions can be assumed to become dominant , a linear increase of @xmath9 ( dashed line in fig . [ mctfits ] ) is approached . also , in order for the boson peak to appear in the light- or neutron - scattering spectra ( where it was first observed ) , @xmath138 must increase steeper than linearly towards the boson peak . the dashed lines in the inset of fig . [ mctfits ] have been calculated by a sum of two power laws , @xmath139 with @xmath140 @xcite . @xmath76 was chosen to match the power law seen in @xmath44 between @xmath22 ghz and the @xmath141minimum . clearly there is no way to obtain a reasonable fit of the experimental data in this way . this analysis clearly implies the presence of additional fast processes in this region , usually termed fast @xmath8-processes . similar findings were obtained for a variety of glass - formers @xcite . fast processes are not considered in the efv model @xcite , which provides the best fits to the dynamics of the @xmath0-process ( section [ discalp ] ) . within this model , molecules are assumed to move within cages formed by their next neighbors and diffusional motion occurs by hopping into free volume available to the molecule . it is interesting that this picture is qualitatively similar to that of mct where fast processes are a natural consequence of the theory . but a theoretical investigation of these possible fast processes in the efv is missing . in the fld model @xcite the @xmath0-relaxation is identified with the restructuring of the flds and occurs on a length scale given by their characteristic size . within the fld framework there is a second length scale , the correlation length @xmath142 of the lps . it was argued @xcite that the experimentally observed fast @xmath136-processes may be ascribed to fast relaxations taking place on this smaller length scale of the fld model . however , up to now a theoretical elaboration of the fast processes within fld theory is missing . another model predicting fast processes is the coupling model ( cm ) of ngai and coworkers @xcite . here the fast process is part of the @xmath0-relaxation , defined in the time domain . the @xmath0-relaxation is assumed to be composed of a fast exponential decay with relaxation time @xmath143 at short times @xmath144 , and a slower kww behavior with relaxation time @xmath145 and stretching parameter @xmath146 at @xmath147 . the crossover time @xmath148 was stated to be of the order of ps for most systems @xcite . demanding continuity at @xmath148 leads to the relation : @xmath149 this allows for the determination of the relaxation time @xmath143 of the fast process , if the kww - parameters of the slow process are known . the parameters determined from the kww - fits of the @xmath0-relaxation in pc ( section [ discalp ] ) result in a factor @xmath150 for the highest temperature and @xmath151 for @xmath152 k. obviously , the fast process inherent in the cm is located at much lower frequencies than the @xmath9-minimum and therefore can not be brought into play for the explanation of the excess intensity in this region . instead additional contributions need to be assumed but , as shown in the beginning of this section , a combination of @xmath7-process ( even including the cm 's fast process ) and boson peak alone can not take account of the experimental data . further contributions may arise @xcite , e.g. , from a constant loss term as early proposed by wong and angell @xcite and/or a possible @xmath153 behavior , both seemingly universal features in the dielectric response of glassy ionic conductors @xcite . possible microscopic explanations for these contributions were proposed in @xcite . indeed , the data in pc near the @xmath9-minimum can well be described by adding a term @xmath154 to the ansatz of eq . [ pheno ] @xcite . in this way , by adjusting the parameters to achieve a smooth transition to the cd - curves describing the @xmath0-peak , quite impressive fits over 17 decades of frequency are possible . of course this could be expected considering the large amount of parameters involved in the fitting , but nevertheless it can not be excluded that such a simple superposition ansatz of different independent contributions is correct . very recently a model was proposed considering a low - frequency relaxation - like part of the vibration susceptibility function responsible for the boson peak @xcite . this relaxation - like response was shown to arise from anharmonicity of vibrations and invoked to explain the quasielastic line seen in light and neutron scattering . this quasielastic contribution corresponds to the fast @xmath8-process seen in the region below the boson peak in the susceptibility spectra . within this framework , the fast process should show up as peak with @xmath155 and @xmath156 at its low and high - frequency side , respectively . for the absolute value of the exponent @xmath0 , reasonable values ranging between 0.375 and 1 were given in @xcite , depending on the system . of course no peak is seen between @xmath0- and boson peak in the spectra of pc ( figs . [ eps2 ] and [ mctfits ] ) but the @xmath157-wing of the fast @xmath8-process may be obscured by the domination of the boson peak at higher frequencies . a severe argument against this picture is the smooth transition of @xmath9 from the minimum to the boson peak with only one power law , which seems unlikely to result from the superposition of the @xmath158-wing of the fast @xmath8-process and the low frequency wing of the boson peak ( steeper than @xmath159 , see above ) . however , this possibility can not fully be excluded and at least this model provides an explanation for the sublinear increase seen for @xmath160 . it is interesting , that within this theoretical framework a crossover temperature of the fast relaxation was obtained which was found to be of similar magnitude as the critical temperature @xmath97 of mct @xcite . as mentioned in the introduction , a fast process in the minimum region of @xmath44 is one of the main outcomes of mct , a prediction which led to the huge interest in this high - frequency region . within idealized mct , above @xmath97 , the high and low - frequency wings close to the minimum of @xmath9 are described by power laws with exponents @xmath84 and @xmath76 , respectively . the minimum region can be approximated by the interpolation formula @xcite : @xmath162 and @xmath163 denote position and amplitude of the minimum , respectively . the exponents @xmath84 and @xmath76 are temperature independent and constrained by the exponent parameter @xmath164 where @xmath165 denotes the gamma function . this restricts the exponent @xmath84 to values below @xmath166 , i.e. a significantly sublinear increase of @xmath72 at frequencies above the minimum is predicted . we found a consistent description of the @xmath1-minima at @xmath167 k using @xmath168 which implies @xmath169 and @xmath170 ( solid lines in fig . [ mctfits ] ) . the obtained @xmath171 agrees with that determined from the preliminary data published previously @xcite . it is identical to @xmath171 deduced from light scattering results @xcite and also consistent with a recent analysis of solvation dynamics experiments on pc @xcite . in addition , a preliminary analysis of the susceptibility minimum from recent neutron scattering measurements @xcite yields @xmath172 , consistent with the present value . at high frequencies the fits with eq . [ eqmctmin ] are limited by the onset of the decrease at the high - frequency wing of the boson peak . quite a different behavior was seen in glycerol @xcite where the mct fits are limited at high frequencies by an additional increase , that can not be described by eq . [ eqmctmin ] . in @xcite it was argued that this deviation in glycerol is due to the vibrational boson peak contribution which is not taken into account by eq . [ eqmctmin ] . in pc this contribution seems to be of less importance . this is in accord with the finding of sokolov _ et al_. @xcite that the amplitude ratio of boson peak and fast process is largest for strong glass formers , glycerol being much stronger than pc ( see also section [ secdiscfastbos ] ) . the deviations of data and fits , seen at low frequencies in fig . [ mctfits ] , can be ascribed to the growing importance of the @xmath7-relaxation which is not taken into account by the simple interpolation formula , eq . [ eqmctmin ] . the critical temperature @xmath97 should manifest itself in the temperature dependence of the @xmath72-minimum . for @xmath107 mct predicts the following relations : @xmath173 and @xmath174{0xbd}}% % beginexpansion { \frac12}% % endexpansion } $ ] . figure [ mopa ] shows the results for @xmath175 , @xmath176 , and also for @xmath92 ( same data as in fig . [ tau ] ) . here representations have been chosen that lead to straight lines that extrapolate to @xmath97 if the predicted critical temperature dependences are obeyed . indeed , as indicated by the solid lines , all three data sets can be described consistently with a critical temperature @xmath177 k , in agreement with the results determined from the preliminary data published previously @xcite . this lies in the same range as the @xmath97 obtained from light scattering @xcite ( @xmath178 k ) , neutron scattering @xcite ( @xmath40 - @xmath70 k ) , and solvation dynamics experiments @xcite ( @xmath179 k ) . also the @xmath180 k , deduced from a preliminary analysis of the susceptibility minimum from recent neutron scattering experiments @xcite , agrees well with the present value . for temperatures near @xmath97 the @xmath181-data deviate from the predicted behavior as also seen in fig . [ tau](c ) . within mct this can be ascribed to a smearing out of the critical behavior near @xmath97 due to hopping processes which are considered in extended versions of mct only @xcite . in addition , the above critical temperature dependences of @xmath182 , @xmath162 and @xmath2 should be valid only for temperatures not too far above @xmath97 and the deviations seen for @xmath162 and @xmath183 at high temperatures ( fig . [ mopa ] ) may be due to this fact . therefore there is a problem concerning the proper choice of the temperature range to be used for the determination of @xmath97 . while the critical behavior proposed in fig . [ mopa ] seems reasonable , some uncertainties concerning the value of @xmath97 remain which can only be clarified by an analysis within the extended mct . mct predicts a significant change in the behavior of @xmath118 at @xmath97 : for @xmath113 , within idealized mct @xmath72 should exhibit a so - called knee at a frequency @xmath184 , i.e. a change of power law from @xmath185 at @xmath186 @xmath187 to @xmath188 at @xmath189 . within idealized mct , at @xmath113 the minimum and the @xmath0-peak should vanish but both phenomena are restored by the hopping processes invoked in extended mct @xcite . at first , from fig . [ mctfits ] it becomes obvious that the fits with eq . [ eqmctmin ] with @xmath168 will no longer work at @xmath113 because the high frequency wing of the minimum becomes successively steeper below this temperature , i.e. the frequency dependence of @xmath118 changes significantly below @xmath97 . in fig . [ mctfits ] , a @xmath190 behavior with @xmath169 as determined for @xmath107 is shown as dashed line matching the region just below the boson peak for the @xmath191 k and @xmath192 k curves . for lower frequencies the experimental data exhibit a downward deviation from the @xmath193-extrapolations , i.e. really a knee appears . whatsoever , in light of the rather large experimental uncertainties in this region it seems quite audacious to assign the observed feature to the knee of mct . according to mct , @xmath187 and the amplitude at the knee , @xmath194 , should also exhibit critical behavior , @xmath195 and @xmath196{0xbd}}% % beginexpansion { \frac12}% % endexpansion } $ ] with the proportionality factors in close connection of the proportionality factors in the critical behavior of the minimum @xcite . in fig . [ mopa](a ) and ( b ) the two values read off from fig . [ mctfits ] are denoted as pluses . having in mind the extreme uncertainties in the knee position , the data seem to be consistent with a @xmath197 of @xmath178 k. however , the position of the knee is not in accord with the position of the miniumum above @xmath97 @xcite . overall , a lack of significance of the observed knee - feature has to be stated but at least the data show where the knee may be located and where more experimental work has to be done to check for its presence and temperature evolution in pc . the comparison of dielectric and the scattering results is shown in fig . as mentioned above ( section [ resfast ] ) the significantly larger ratio of @xmath0- and boson peak amplitude for dielectric compared with light scattering results seems to be a rather universal property of glass - forming materials @xcite . recently , an explanation for this finding was given by considering the different dependencies of the probes on orientational fluctuations @xcite . in addition , in a recent theoretical work @xcite mct was generalized to molecular liquids of molecules with orientational degrees of freedom . the resulting mct equations were solved for a system of dipolar hard spheres and a larger ratio of @xmath0- and boson peak amplitude for @xmath198 was obtained in accordance with the experimental findings . further , it is one of the main predictions of mct @xcite that the same parameters @xmath199and @xmath171should arise from all observables coupling to the density fluctuations . this is indeed the case for propylene - carbonate ( see above ) . but also the position of the @xmath1- ( respectively @xmath200- ) minima should be the same , independent of the experimental method which is also valid when including orientational degrees of freedom @xcite . however , as seen in fig . [ vgl ] , this seems not to be the case . an explanation for a similar behavior found from molecular dynamics simulations of a system of rigid diatomic molecules was given in terms of @xmath201{0xb0}}% % beginexpansion { { } ^\circ}% % endexpansion $ ] flips of the non - spherical molecules which can not be taken into account by a hard sphere model @xcite . in this context , it may be mentioned that for the mobile - ion glass - former ckn a rather good agreement of the minimum position from different experimental methods was found @xcite . here orientational degrees of freedom are not important which corroborates the above explanation in terms of @xmath201{0xb0}}% % beginexpansion { { } ^\circ}% % endexpansion $ ] flips . the boson peak is a universal feature of glass - forming materials showing up in light and neutron scattering but also as excess contribution in specific heat measurements . a variety of explanations of the boson peak has been proposed , e.g. , in terms of the soft potential model @xcite , phonon localization models @xcite , or a model of coupled harmonic oscillators with a distribution of force constants @xcite . also mct includes contributions leading to a peak at thz as was shown using a schematic two - correlator model @xcite . however , up to now there is no consensus concerning the microscopic origin of this phenomenon . it can not be the aim of the present paper to compare the results with the proposed models , especially in the light of the rather restricted data base for @xmath202 thz . however , some experimental facts deserve to be emphasized which may be of importance for the understanding of the boson peak . figure [ pcgly ] shows the high frequency region of @xmath30 for pc and glycerol . clearly , both materials exhibit quite different behavior in the boson peak region : for pc only one power law is seen at frequencies @xmath203 forming simultaneously the high frequency wing of the @xmath1-minimum and the low frequency wing of the boson peak . in marked contrast , for glycerol two regimes can be distinguished : directly above @xmath82 , there is a rather shallow increase of @xmath9 which together with the left wing of the minimum can be well fitted with the mct prediction , eq . [ eqmctmin ] @xcite . at higher frequencies a very steep increase appears , approaching @xmath204 for @xmath205 . this different behavior of pc and glycerol also becomes obvious in the scaling plot of fig . [ scal ] . for both materials the @xmath9 -minimum corresponds to the deviation from the master curve , that shows up as a third linear region in the scaling plot . but for glycerol in addition a minimum is seen in fig . [ scal ] . in the scaling plot this minimum marks the transition point between the two regimes at @xmath203 , described above . it seems that in glycerol the fast @xmath8-process giving rise to the shallow minimum in @xmath9 or the third linear region in the scaling plot , is obscured at higher frequencies by the boson peak contribution . this arguing seems to be in accord with the finding of sokolov _ et al_. @xcite of a higher amplitude - ratio of boson peak and fast process for strong glass formers . however , at least near @xmath6 this ratio , e.g. measured by comparing boson - peak and minimum amplitude in fig . [ pcgly ] , is quite similar for both materials . for high temperatures , @xmath167 k for pc and @xmath206 k for glycerol , the fast @xmath136-process in pc has indeed a higher amplitude if curves with similar values of @xmath2 are compared . this fact also explains the good fits with mct up to the boson peak frequency ( section [ secdiscfastmin ] ) in pc . however , for lower temperatures the different characteristics of pc and glycerol has to be ascribed either to a more shallow left wing of the boson peak for pc ( @xmath207 instead of @xmath208 ) or to a steeper increase of the high frequency wing of the minimum , thereby obscuring the steeper boson peak wing . interestingly , while there might be some problems for the new model by novikov @xcite in explaining the pc results ( see section [ secdiscfastmin ] ) , glycerol seems to fit into this picture : below the boson peak , two distinct regions are seen which can be ascribed to the relaxation - like and the main part of the vibrational excitations . concerning mct , it has to be mentioned that the light scattering results on glycerol @xcite exhibit quite similar characteristics as the dielectric results @xcite . the light scattering results were successfully described using the schematic two - correlator mct model mentioned above @xcite . but it is not clear if mct is able to provide an explanation for the qualitative difference of the glycerol and pc dielectric data . dielectric data on glass - forming pc in an exceptionally broad frequency range have been presented and compared with the results from light scattering and to broadband dielectric results on glycerol . a comparison of the findings concerning @xmath0-relaxation , excess wing , @xmath72-minimum , and boson peak on various theoretical and phenomenological predictions has been performed . the temperature dependence of the @xmath0-relaxation time is in accord with the efv and the fld models and at high temperatures also with that of idealized mct . the temperature dependences of the relaxation strength and the width parameter of the @xmath0-relaxation were determined and some differences to the findings from previous works were found . the excess wing in pc was shown to follow the modified nagel scaling proposed by dendzik et al . @xcite but at high frequencies the curves of pc and glycerol do not scale onto each other . overall , it is not possible to arrive at a decision in favor or against one of the models on the dynamics of glass - forming materials from the results obtained at the first 15 decades of frequency alone . at higher frequencies above about 1 ghz a minimum in @xmath118 is detected . in this region , clearly fast processes contribute to the dielectric loss , a finding for which most models provide no explanation . while the minimum can be well described by the sum of power laws and a constant loss contribution @xcite , the theoretical foundation for these contributions is unclear at present but currently is being developed . in contrast , mct provides a microscopic explanation for the high - frequency data , at least at high temperatures . in addition , the analysis within mct yields values for @xmath97 and @xmath171 , that are in agreement with those determined from other experimental methods . also the differences in the susceptibilities obtained from dielectric and light scattering experiments seem to be in accord with recent extensions of mct . at low temperatures , @xmath209 @xmath97 , at least a qualitative agreement of the results ( presence of a fast process and possible occurrence of a knee ) with mct can be stated , but more work is needed for a quantitative comparison . overall , certain aspects of the results found in the present work can be explained by different models , but in our judgement mct provides the most consistent picture providing explanations for the largest variety of experimental facts , including the high - frequency processes . this may be partly due to the large amount of predictions made by mct , covering almost all aspects of the dynamic response of glass - forming materials , while other models are somewhat restricted in this respect . however , just this agreement of the data with the many different predictions of mct speaks in favor of the theory . admittedly , it is not possible to arrive at a final decisive conclusion concerning the applicability of mct for pc and alternative explanations may be possible . also many questions need to be solved , e.g. the behavior below @xmath97 should be compared with the extended mct , the differences to the scattering results should be compared quantitatively to mct ( considering orientational degrees of freedom of dipolar , non - spherical molecules ) , and the qualitatively different behavior of pc and glycerol in the boson peak region should be addressed . finally , in the boson peak region we find significant differences between glycerol and pc which wait for a theoretical explanation . but also more experimental work is needed , e.g. concerning the temperature evolution of the boson peak and a higher precision of the data at low temperatures in order to investigate in detail the possible occurrence of a knee in @xmath9 of pc . we gratefully acknowledge stimulating discussion with c.a . angell , r. bhmer , h.z . cummins , w. gtze , k.l . ngai , m. ohl , r. schilling , w. schirmacher , and j. wuttke . we thank m. ohl and j. wuttke for providing the neutron scattering results of ref . @xcite prior to publication . this work was supported by the deutsche forschungsgemeinschaft , grant - 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cryst . solids * 203 * , 300 ( 1996 ) ; k.l . ngai , h. jain , and o. kanert , j. non - cryst . solids * 222 * , 383 ( 1997 ) . p. lunkenheimer , u. schneider , r. brand , and a. loidl , submitted to _ proceedings of the 8th tohwa university international symposium on slow dynamics in complex systems _ ( aip conference proceedings , new york , 1999 ) .

dielectric spectroscopy covering more than 18 decades of frequency has been performed on propylene carbonate in its liquid and supercooled - liquid state . using quasi - optic submillimeter and far - infrared spectroscopy the dielectric response was investigated up to frequencies well into the microscopic regime . we discuss the @xmath0-process whose characteristic timescale is observed over 14 decades of frequency and the excess wing showing up at frequencies some three decades above the peak frequency . special attention is given to the high - frequency response of the dielectric loss in the crossover regime between @xmath0-peak and boson - peak . similar to our previous results in other glass forming materials we find evidence for additional processes in the crossover regime . however , significant differences concerning the spectral form at high frequencies are found . we compare our results to the susceptibilities obtained from light scattering and to the predictions of various models of the glass transition .

<s>[INST]despite a long history of research on the glass transition @xcite , this phenomenon is still commonly regarded as an unresolved problem . in recent years a variety of new theoretical and phenomenological approaches of the glass transition ( e.g. , @xcite ) stimulated new experimental investigations of the dynamic response of glass - forming liquids ( see , e.g. @xcite ) . here dielectric spectroscopy has played an important role , mainly due to the broad dynamic range accessible with this method ( e.g. , @xcite ) . spectra of the dielectric loss @xmath1 show a variety of features , the microscopic origin of most of them being still controversially discussed . most prominent is the @xmath0-peak associated with the well known @xmath0- or structural - relaxation process . the comparison of the non - trivial temperature dependence of the @xmath0-relaxation time with theoretical predictions states an important test for any model of the glass - transition . some decades above the @xmath0-peak frequency @xmath2 , an excess wing ( also called high - frequency wing or tail ) shows up as high - frequency excess contribution to the power law @xmath3 , commonly found at @xmath4 . this excess wing seems to be a universal feature of glass - forming liquids as can be deduced from the scaling behavior found by nagel and coworkers @xcite . based on this universal scaling of @xmath0-relaxation and excess wing , nagel and coworkers @xcite proposed a divergence of the static susceptibility which essentially implies a constant loss behavior at high frequencies and low temperatures as has early been predicted by wong and angell @xcite . the interest in even higher frequencies , in the ghz - thz region , was mainly stimulated by the mode coupling theory ( mct ) @xcite , which explains the glass transition in terms of a dynamic phase transition at a critical temperature @xmath5significantly above the glass temperature @xmath6 . from neutron- and light - scattering experiments it is well known that in the thz region the so - called boson peak shows up in the imaginary part of the susceptibility of glass - forming liquids . for the transition region between @xmath7-process and boson peak , mct predicts an additional contribution , now commonly termed fast @xmath8-relaxation . but also other models predict fast processes , the most prominent being the coupling model by ngai and coworkers @xcite . this transition region was mainly investigated by neutron and light scattering and indeed indications for additional fast processes were found @xcite . the scattering results were described within the framework of mct and partly good agreement with the theoretical results was obtained . however , the applicability of the mct for glass - forming liquids , especially at low temperatures near @xmath6 , is still a matter of controversy . dielectric data were scarce in the relevant high - frequency region as for classical dielectric methods the region above ghz is not accessible . only recently , our group was able to obtain continuous dielectric spectra on glass - forming liquids extending well into the submillimeter wavelength region @xcite . the existence of a broad minimum in @xmath9 was found which can not be explained by a simple crossover from the structural ( @xmath0- ) relaxation to the far - infrared ( fir ) vibrational response . similar to the scattering results , clear indications for additional fast processes prevailing in this transition region were found . for glass - forming glycerol , by combining classical dielectric spectroscopy , coaxial transmission , quasi - optic submillimeter and far - infrared techniques , spectra covering 18 decades of frequency and extending well into the thz range were obtained @xcite . this allowed for the observation of the complete dynamic response including the boson peak . in addition , dielectric spectra up to 380 ghz were obtained in [ ca(no@xmath10)@xmath11@xmath12[kno@xmath10]@xmath14 ( ckn ) and [ ca(no@xmath10)@xmath11@xmath12[rbno@xmath10]@xmath14 ( crn ) @xcite . both are ionically conducting , molten - salt glass formers with relatively high fragility @xcite , @xmath15 @xcite . in contrast , glycerol is a rather strong hydrogen - bonded glass - former with a fragility parameter of @xmath16 @xcite . in many respects , especially concerning the high - frequency response near the boson peak and the agreement of the dielectric data with mct predictions and with the scattering results , glycerol and the molten salts behave qualitatively different . in order to clarify the origin of these differences and in the light of the dependence of the boson peak contribution on fragility @xcite , it seemed of interest to investigate a fragile , but molecular glass - former . for this purpose we have chosen propylene carbonate ( pc ) which like glycerol is a molecular glass former , but can be characterized as a fragile ( @xmath17,@xcite ) van der waals liquid . preliminary results on pc in a somewhat restricted frequency range have been published earlier @xcite . in the present paper we present extended results covering the complete dynamic range including the boson peak . we address all features seen in the dielectric spectra , i.e. the @xmath7-response , the excess wing , the fast @xmath8-relaxation region and the boson peak . the results are compared with a variety of theoretical predictions and with the findings from other experimental methods . the measurements presented in this article have been performed using a variety of different techniques to cover nearly 20 decades in frequency . the lowest frequencies ( @xmath18 @xmath19hz ) were investigated in the time - domain using a spectrometer that is based on a design described by mopsik @xcite . the complex dielectric constant was calculated from the measured response function via a fourier transformation . the autobalance bridges hp4284 and hp4285 were used in the range @xmath20 hz @xmath21 mhz . for the radio - frequency and microwave range ( @xmath22 mhz @xmath23 ghz ) a reflectometric technique was employed @xcite using the hp4191 and hp4291 impedance analyzers and the hp8510 network analyzer . in addition , at frequencies @xmath24 mhz @xmath25 ghz data were taken in transmission with the hp8510 network analyzer using 7 mm coaxial lines of various lengths ( between 10 and 300 mm ) filled with the sample material . closed - cycle refrigerators , n@xmath26- , and he - cryostats have been used to cover the relevant temperature ranges . at frequencies @xmath27 ghz @xmath28 thz a quasi - optical submillimeter spectrometer was used with an experimental arrangement similar to a mach - zehnder interferometer @xcite . this setup allows for measuring the frequency dependence of both the transmission and the phase shift of a monochromatic electromagnetic beam through the sample . the frequency range up to 1.2thz is covered continuously by 10 tunable narrow - band backward - wave oscillators ( bwos ) . the signal was detected by a golay cell or a pumped he bolometer and amplified using lock - in techniques . the liquid was put in specially designed cells made of polished stainless steel with thin plane - parallel quartz windows ; depending on the range of frequency and temperature the thickness of the sample cell was between 1 mm and 30 mm . the sample cell was placed in a home - made cryostat and cooled by a continuous flow of nitrogen gas . the data were analyzed using optical formulae for multilayer interference @xcite with the known thickness and optical parameters of the windows in order to get the real and imaginary part of the dielectric constant of the sample as a function of frequency at various temperatures . at higher frequencies ( 600ghz @xmath29 3thz ) the samples were investigated with a fourier - transform infrared spectrometer covering a regime from 450ghz to 10thz . this set - up allows the measurement of the transmission or reflection only , whereas the phase shift caused by the sample can not be determined . to cover the complete frequency range , a single @xmath30 curve at a given temperature is superimposed using results from the various setups . the time - domain results are obtained in arbitrary units and scaled by one factor to match the autobalance bridge results . for the measurements at @xmath22 ghz @xmath31 ghz there are some uncertainties of the absolute values originating from an ill - defined geometry of the samples or parasitic elements . these results have been partly shifted by one scaling factor per measurement series which led to a good match at both the low and the high frequency side . typically , shifting factors of less than @xmath32 had to be applied to obtain smooth curves . the submillimeter - frequency results and , at losses @xmath33 , also the coaxial transmission measurements provide excellent absolute values of @xmath34 and @xmath35 . the values for @xmath1 from the infrared measurements were calculated consistently with the kramers - kronig relation assuming a reasonable behavior of the dielectric constant @xmath36 which is almost constant in this frequency regime . in this latter case , the error bars for @xmath1 were estimated by variation of the assumed @xmath34 behavior . as sample material , propylene carbonate ( @xmath37 k @xcite , @xmath38 k ) with a purity of @xmath39 , was used . to avoid crystallization polished sample holders had to be used in the various experiments . however , occasional crystallization , mainly at temperatures around @xmath40 k could not be avoided completely . therefore some measurements were performed after heating up to @xmath41 and direct cooling to each measurement temperature with relatively fast cooling rates ( @xmath22 k / min ) . figures [ eps1 ] and [ eps2 ] show @xmath43 and @xmath44 for various temperatures in the whole accessible frequency range . @xmath9 ( fig . [ eps2 ] ) exhibits the typical asymmetrically shaped @xmath0-relaxation peaks shifting through the frequency window with temperature . they are accompanied by relaxation steps in @xmath43 as seen in fig . [ eps1 ] . in most respects the data agree well with the results of earlier dielectric investigations of pc @xcite which were restricted to smaller frequency and temperature ranges . however , some differences show up in the absolute values ( see below ) . the solid lines in figs . [ eps1 ] and [ eps2 ] are fits of the @xmath0-relaxation region with the empirical cole - davidson function @xcite , @xmath45 , performed simultaneously for real and imaginary part . @xmath46 and @xmath47 denote the low- and high - frequency limit of the dielectric constant , respectively . a good fit of the peak region was achieved . very close to the maximum the loss curves can also be described by the fourier transform of the kohlrausch - williams - watts ( kww ) function @xcite , @xmath48 $ ] , ( dotted lines , shown for 173 k , only ) . for all temperatures investigated the kww fit is of lower quality than the cd fit . this can be ascribed to the fact that there is a significant difference of cd and kww response concerning the loss - peak region . for the kww response the curvature near the peak is retained somewhat further above the peak frequency and a power law @xmath49 is approached at significantly higher frequencies only . therefore , in most cases the exponent @xmath50 obtained from the kww fits differs significantly from the power law exponent @xmath8 actually observed for @xmath4 . in contrast , for the cd fits @xmath51 is found . despite the kww function is more widely used nowadays , in the authors experience dielectric loss data in glass - forming materials are often described much better by the cd function @xcite . the inset of fig . [ eps2 ] shows the temperature dependence of the frequency @xmath52 which is virtually identical to the peak frequency @xmath2 . here @xmath53 denotes the mean relaxation time @xcite calculated from @xmath54 for the cd function and @xmath55 ( @xmath56 denoting the gamma function ) for the kww function . the results from the cd ( circles ) and the kww fits ( pluses ) agree perfectly well and are in accord with previously published data @xcite . @xmath57 shows the well known deviations from thermally activated behavior , typical for fragile glass - formers . it can be parameterized using the vogel - fulcher - tammann ( vft ) equation @xcite ( line in the inset of fig . [ eps2 ] ; see section [ discalp ] ) . in figure [ betchi](a ) the relaxation strengths @xmath58 @xmath59 obtained from the cd and kww fits are shown . one has to be aware that @xmath60 resulting from the fits is somewhat smaller that @xmath60 read off from the @xmath61 data of fig . [ eps1 ] . as seen in fig . [ eps1 ] , the fits overestimate @xmath47 because there is an additional decrease of @xmath43 corresponding to the excess wing contribution ( see below ) which is not taken into account by the cd fits . consequently @xmath60 shown in fig . [ betchi](a ) presents the relaxation strength of the @xmath0-process alone , without the excess wing contribution . @xmath60 decreases monotonically with temperature which is in accord with previous reports @xcite . however , the decrease found in the present work is somewhat less steep than reported earlier . unfortunately , in @xcite where a rather broad temperature and frequency range was investigated no absolute values of @xmath60 were reported . the results from the high frequency measurements of payne and theodorou @xcite are compatible with our data at @xmath62 k except for their lowest temperature ( @xmath63 k ) where a much higher value ( @xmath64 ) was found . however , the relaxation time at @xmath65 k reported by these authors deviates by more than one decade from that found in the present and other works @xcite which sheds some doubt upon the significance of the results at this temperature . also from the results of huck _ _ @xcite and angell _ et al . _ _ _ near @xmath66 k a much higher magnitude of @xmath60 ( @xmath67 ) than determined here can be read off . the determination of the absolute values of @xmath68 is a difficult task as it depends on the shifting factors necessary to match results from different experimental set - ups and on the subtraction of possible stray capacitances inherent to some methods . we believe , that due to the broad overlap of the frequency ranges of the various devices used in the present work , the reproducibility of results with different sample holders , and the simultaneous fitting of @xmath43 and @xmath44 , fig . [ betchi](a ) gives a good estimate of the absolute value of @xmath60 . figure [ betchi](b ) shows the width parameter obtained from both fitting procedures . both , @xmath69 and @xmath50 increase nearly linearly with temperature up to about @xmath70 k. above this temperature a tendency to saturate at a value below unity is observed . this is in contrast to @xcite where @xmath71 was reported to saturate at unity for high temperatures . this discrepancy may be due to the smaller frequency range available in @xcite which for high temperatures leads to a restriction of the data at the high - frequency side of the loss peaks , that is essential for the determination of @xmath69 . unfortunately , no @xmath44 data of pc are shown in @xcite . at frequencies about 2 - 3 decades above @xmath2 deviations of @xmath72 from the cd - fits show up . for low temperatures these deviations can be described as second power law , @xmath73 with @xmath74 , in addition to the power law @xmath75 constituting the high frequency flank of the @xmath0-peak . the exponent @xmath76 decreases with decreasing temperature as found previously for pc and other glass - forming materials @xcite . the excess wing is accompanied by a decrease in @xmath61 as mentioned above . it shows up as a somewhat smoother rounding of the @xmath43 curves ( compared , e.g. , to the cd behavior ) when approaching @xmath47 ( fig . [ eps1 ] ) . for @xmath77 k the exponent @xmath76 has reached a value almost identical with @xmath69 ( fig . [ eps2 ] ) and for @xmath78 k the excess wing seems to have merged with the @xmath0-peak . for @xmath79 @xmath78 k the deviations of the experimental data from the cd - fits are due to the fast dynamic processes described in the following section . at high frequencies , succeeding the excess wing for low and the @xmath0-peak for high temperatures , @xmath80 exhibits a smooth transition into a shallow minimum . such a minimum was earlier observed in glycerol @xcite , salol @xcite , the molten salts ckn @xcite and crn @xcite , and the plastic crystals cyclo - octanol @xcite and ortho - carborane @xcite . with increasing temperature , the amplitude @xmath81 and frequency position @xmath82 of the minimum increases . for room temperature the measurements have been extended into the fir region . here no minimum is observed , but a shoulder shows up near 1 thz . this shoulder is indicative of the so - called boson peak known mainly from neutron- and light - scattering measurements @xcite . indeed , for pc the boson peak , determined from light - scattering measurements @xcite , is located just above 1 thz . as the peak frequency and amplitude is only weakly temperature dependent , it becomes obvious that the high - frequency flank of the @xmath9-minimum is identical to the low - frequency flank of the boson peak . the frequency dependence in this region can be approximately described by a power law @xmath83 . the exponent @xmath84 increases with decreasing temperature and seems to approach a linear behavior as indicated by the dash - dotted line in fig . [ eps2 ] . in @xmath43 for these frequencies the onset of a relaxation step corresponding to the boson peak can be seen ( fig . [ eps1 ] ) . in fig . [ vgl ] we compare @xmath9 with @xmath85 calculated from the light scattering results on pc @xcite . as the light scattering results give no information on the absolute values of @xmath1 , the datasets have been scaled to yield a comparable height of the boson peak . while the dielectric results in pc are qualitatively similar to the light scattering results ( succession of @xmath0-peak , minimum , and boson peak ) , quantitative differences show up : the @xmath0-peak is located at a significantly lower frequency and the ratio of the amplitudes of @xmath0- and boson peak is higher for the dielectric measurements . the latter behavior was also found in our experiments on glycerol @xcite and salol @xcite , and in molecular dynamics simulations of ortho - terphenyl @xcite and of a system of rigid diatomic molecules @xcite . the results from a very recent neutron scattering study of pc @xcite indicate an even smaller ratio of @xmath0- and boson peak amplitude than for light scattering . clearly the position of the minimum differs between the different methods , also in accordance with results on other systems @xcite . in contrast , the increase towards the boson peak exhibits almost identical power laws for the dielectric and light scattering measurements . the most significant result of an analysis of the @xmath0-relaxation process is the temperature dependence of the @xmath0-relaxation time which is compared to various predictions in fig . figure [ tau](a ) shows the same fit with the vft equation @xcite , as in the inset of fig . [ eps2 ] . a vft temperature @xmath87 k and a strength parameter @xmath88were determined , the latter characterizing pc as fragile glass former @xcite . while the vft equation is primarily an empirical description , a theoretical foundation was given in various models , e.g. the adam - gibbs theory @xcite or the free volume theory @xcite . in fig . [ tau](a ) it becomes obvious that , above a crossover temperature @xmath89 k , deviations from vft behavior show up , similar to those seen in earlier work @xcite . in @xcite and @xcite a transition to thermally activated behavior was suggested as demonstrated by the dashed line in fig . [ tau](a ) . @xmath90 was interpreted @xcite as temperature below which the potential energy landscape becomes important . however , one has to state that also alternative descriptions are possible , e.g. using vft behavior at high and a thermally activated behavior at low temperatures or a combination of vft functions @xcite . in addition , stickel et al . @xcite performed an analysis of relaxation - time data on pc extending to temperatures above room temperature using a temperature - derivative method @xcite . they reported a transition between two vft laws at about @xmath70 k and a second transition to thermally activated behavior above about @xmath91 k. overall , as demonstrated in fig . [ tau](a ) , the three - parameter vft function is not able to describe the data in the whole temperature range and a crossover to a different behavior has to be assumed to overcome this difficulty . a four - parameter function for the description of @xmath92 is the outcome of the extended free volume ( efv ) theory @xcite . in the efv theory the supercooled liquid is assumed to be divided into liquid - like and solid - like regions . at a temperature @xmath93 a transition from percolating ( fluid ) to isolated liquid - like regions ( solid glass state ) occurs . by addressing the entropy of the glass - forming system and making use of percolation theory the following result for @xmath92 was obtained : good fits with eq . ( [ eqefv ] ) for a variety of glass - formers were reported @xcite . figure [ tau](b ) shows a fit of @xmath92 of pc with eq . ( [ eqefv ] ) and @xmath95 k. indeed , the efv theory gives a very good description of the present data and @xmath93 is almost identical to the calorimetric @xmath96 k @xcite . while the vft and efv predictions lead to critical temperatures near or below @xmath6 , the @xmath97 of mct is predicted to be located well above @xmath98 . the simplest version of mct , the idealized mct @xcite , predicts a critical behavior of the @xmath0-relaxation timescale , @xmath99 with a critical exponent @xmath100 that is determined by @xmath101 . here @xmath84 and @xmath76 are the low- and high - frequency power law exponents of the @xmath9-minimum as will be explained in detail in section [ secdiscfastmin ] . the solid line in fig . [ tau](c ) is a fit with the three - parameter function , eq . [ eqmctfp ] with @xmath102 and @xmath103 k fixed to the values obtained from the analysis of the @xmath9-minimum ( sect . [ secdiscfastmin ] ) . even with all parameters free , very similar values result , namely @xmath104 k and @xmath105 . for the fits , only data above 200 k were used where a good agreement of data and fit was achieved . in order to describe the data at lower temperatures a vft fit can be employed ( dashed line ) . the observed absence of critical behavior at @xmath97 in the experimental data is expected within the extended mct @xcite . here the structural arrest found in idealized mct for @xmath106is avoided by the assumption of thermally activated hopping processes . mct also predicts that , at least for @xmath107 , the relaxation times determined with different experimental methods should follow a common temperature behavior . indeed , while there is a difference in the absolute values of @xmath108 from light scattering @xcite and dielectric measurements ( leading to the different @xmath0-peak positions in fig . [ vgl ] ) , which can be understood considering the different correlation functions of both methods @xcite , they can be transferred into each other by a temperature independent factor of about 3 ( not shown ) . finally , we compare the results to the predictions of the frustration - limited domain ( fld ) model by kivelson , tarjus , and coworkers @xcite . this theory postulates a narrowly avoided critical point at a temperature @xmath109 above the melting point . the theory is based on the assumption that there is a locally preferred structure ( lps ) which , however , is not able to tile space periodically . without this geometrical constraint the system would condense into the lps at @xmath109 . in real systems somewhat below @xmath109 , frustration - limited domains with the lps are formed . such a scenario is intuitive for the simple system of spherical molecules . here the lps is an icosahedral short - range order but one can not tile space with this structure . by using a phenomenological scaling approach , a prediction for the temperature dependent relaxation rate was obtained : @xmath110 \text { for } % t < t^{\ast } \label{kiveq}\end{aligned}\ ] ] clearly , among the analyses presented in fig . [ tau ] , the one employing the combination of vft and thermally activated behavior [ fig . [ tau](a ) ] seems least reasonable as there is no theoretical base for such a behavior . as could be expected , the two four - parameter functions ( efv and fld model ) provide the best descriptions of the data as was also found for a similar comparison performed for dielectric results on salol @xcite . as mentioned above , the huge deviations seen for the ( idealized ) mct approach could be expected . this setback may be overcome when employing the extended mct , which is out of the scope of the present work . an argument in favor of the mct - fit is the fact that only one parameter was varied , @xmath97 and @xmath111 being fixed as mentioned above . the mct also makes distinct predictions for the temperature dependence of the relaxation strength @xmath60 and the spectral form of the @xmath7-process @xcite . according to idealized mct , for @xmath112 , the relaxation strength and the spectral form of the @xmath0-process should be temperature independent ( time - temperature superposition principle ) . in addition , for @xmath113 , @xmath114^{% % tcimacro{\unicode[m]{0xbd}}% % beginexpansion { \frac12}% % endexpansion } $ ] follows from extended mct . in fig . [ betchi](a ) the solid line was calculated using the mct prediction with @xmath103 k as deduced in section [ secdiscfastmin ] . due to the scattering of the data no definite conclusion can be drawn , but at least the data do not contradict mct . in contrast schoenhals _ et al . _ @xcite reported clear deviations of their @xmath115 ( given in arbitrary units ) from mct predictions @xcite . concerning the predicted temperature independent spectral form of the @xmath0-peak for @xmath107 , a tendency to saturate is indeed seen for @xmath71 and @xmath116 in fig . [ betchi ] , however at temperatures clearly above @xmath97 , only . but a reasonable description of the @xmath0-peaks for @xmath107 is also possible with a constant @xmath117 . again this is in contrast to the statements made in @xcite . overall it is difficult to make a decisive statement about the validity of mct in pc from the analysis of the @xmath0-process alone . the excess wing ( also called high - frequency wing or tail ) seems to be a universal feature of glass - forming liquids @xcite , but up to now its microscopic origin remains unclear . a phenomenological function taking account of the @xmath0-peak and the wing has been proposed recently @xcite . in many cases it is possible to describe the @xmath7-peak including the wing using a model of dynamically correlated domains @xcite but for low temperatures and extremely broadband data deviations show up @xcite . nagel and coworkers @xcite found that the @xmath118-curves for different temperatures and even for different materials , including the @xmath0-peak and the wing , can be scaled onto one master curve by an appropriate choice of the x- and y - axis . this intriguing scaling behavior strongly suggests a correlation between @xmath0-process and the high - frequency wing . during the last years some criticism of the nagel - scaling arose concerning its universality @xcite and accuracy @xcite and minor modifications of the original scaling procedure have been proposed @xcite . however , it is still commonly believed that the nagel - scaling is of significance for our understanding of the glass - forming liquids and many efforts have been made to check its validity in a variety of materials @xcite . in fig . [ scal ] we have applied the modified scaling approach proposed by dendzik _ this procedure was shown to lead to somewhat better scaling in the @xmath0-peak region and allows for an unequivocal determination of the scaling parameters . in addition , the modified procedure is able to collapse different cd - curves onto one master curve @xcite which is not the case for the original nagel - scaling @xcite . as demonstrated in fig . [ eps2 ] , the cd function gives an excellent description of the @xmath0-peak region in @xmath30 . the application of the modified scaling requires the determination of parameters @xmath119 , @xmath120 , and @xmath8 . here @xmath119 and @xmath120 are defined as frequency and amplitude of the intersection point of the two power laws @xmath121 for @xmath122 and @xmath75 for @xmath4 . in fig . [ scal ] we show the pc results in addition to glycerol data taken from @xcite , scaled according to @xcite , i.e. with @xmath123 and @xmath124 $ ] . indeed , the @xmath0-peak and the excess wing region can nicely be scaled onto one master curve for each material . the deviations from this master curve seen in fig . [ scal ] occur in the wing and boson peak region which can not be scaled in this way . the scaling transfers the cd behavior of the @xmath0-peak to a constant , @xmath125 , at its low frequency side ( @xmath126 and to a linear decrease , @xmath127 ( solid lines in fig . [ scal ] ) at its high - frequency side ( @xmath128 ) . the excess wing shows up as a more shallow linear decrease deviating from the @xmath129 line above @xmath130 . due to the large frequency region available for the present work this linear decrease can be observed up to @xmath131 for pc while the maximum value observed up to now was @xmath132 @xcite . due to this larger range it becomes obvious that the curves for glycerol and pc show significant deviations from each other at @xmath133 as demonstrated in the upper inset of fig . in contrast , the original nagel - scaling @xcite scales the curves for both materials perfectly well in this high - frequency region @xcite . as mentioned above , the wing seems to merge with the @xmath0-peak above about @xmath70 k. in fig . [ scal ] this corresponds to a direct transition from @xmath129 behavior to the non - scaling linear decrease corresponding to the minimum region ( see lower inset of fig . [ scal ] ) . here only two linear regions for @xmath128 can be distinguished while at lower temperatures three such regions are seen ( associated with @xmath7-peak , excess wing , and minimum ) . for glycerol a similar merging of wing and @xmath0-peak is observed at temperatures above about @xmath134 k. finally we want to mention that it is also possible to describe the excess wing by an additional relaxation process superimposed to the @xmath0-process @xcite . such secondary processes , usually termed ( slow ) @xmath135-processes , can often be ascribed to an internal change of the molecular conformation . however , in the light of the universal properties of the wing for different glass - forming liquids revealed by the nagel - scaling , it is unreasonable to ascribe it to this type of @xmath8-relaxations which depend on the specific molecular structure . the finding that secondary relaxation processes can show up also in simple glass formers led to the assumption of a more fundamental reason for these so - called johari - goldstein @xmath8-processes @xcite . also recent theoretical developments @xcite within the coupling model @xcite may point in the direction of a universal slow @xmath8-relaxation , closely connected to the @xmath0-process . it can not be excluded that the wing and these possible intrinsic @xmath136-relaxations are manifestations of the same microscopic mechanism . in fig . [ mctfits ] , a magnified view of the high - frequency region of @xmath9 is shown . in the inset we tried to analyze the minimum region in terms of a simple crossover from @xmath0-relaxation or excess wing to the boson peak . for the low frequency wing of the boson peak a linear or steeper increase of @xmath44 can be assumed as is commonly found for a variety of glass - formers @xcite . indeed , for the lowest temperatures investigated , where vibrational contributions can be assumed to become dominant , a linear increase of @xmath9 ( dashed line in fig . [ mctfits ] ) is approached . also , in order for the boson peak to appear in the light- or neutron - scattering spectra ( where it was first observed ) , @xmath138 must increase steeper than linearly towards the boson peak . the dashed lines in the inset of fig . [ mctfits ] have been calculated by a sum of two power laws , @xmath139 with @xmath140 @xcite . @xmath76 was chosen to match the power law seen in @xmath44 between @xmath22 ghz and the @xmath141minimum . clearly there is no way to obtain a reasonable fit of the experimental data in this way . this analysis clearly implies the presence of additional fast processes in this region , usually termed fast @xmath8-processes . similar findings were obtained for a variety of glass - formers @xcite . fast processes are not considered in the efv model @xcite , which provides the best fits to the dynamics of the @xmath0-process ( section [ discalp ] ) . within this model , molecules are assumed to move within cages formed by their next neighbors and diffusional motion occurs by hopping into free volume available to the molecule . it is interesting that this picture is qualitatively similar to that of mct where fast processes are a natural consequence of the theory . but a theoretical investigation of these possible fast processes in the efv is missing . in the fld model @xcite the @xmath0-relaxation is identified with the restructuring of the flds and occurs on a length scale given by their characteristic size . within the fld framework there is a second length scale , the correlation length @xmath142 of the lps . it was argued @xcite that the experimentally observed fast @xmath136-processes may be ascribed to fast relaxations taking place on this smaller length scale of the fld model . however , up to now a theoretical elaboration of the fast processes within fld theory is missing . another model predicting fast processes is the coupling model ( cm ) of ngai and coworkers @xcite . here the fast process is part of the @xmath0-relaxation , defined in the time domain . the @xmath0-relaxation is assumed to be composed of a fast exponential decay with relaxation time @xmath143 at short times @xmath144 , and a slower kww behavior with relaxation time @xmath145 and stretching parameter @xmath146 at @xmath147 . the crossover time @xmath148 was stated to be of the order of ps for most systems @xcite . demanding continuity at @xmath148 leads to the relation : @xmath149 this allows for the determination of the relaxation time @xmath143 of the fast process , if the kww - parameters of the slow process are known . the parameters determined from the kww - fits of the @xmath0-relaxation in pc ( section [ discalp ] ) result in a factor @xmath150 for the highest temperature and @xmath151 for @xmath152 k. obviously , the fast process inherent in the cm is located at much lower frequencies than the @xmath9-minimum and therefore can not be brought into play for the explanation of the excess intensity in this region . instead additional contributions need to be assumed but , as shown in the beginning of this section , a combination of @xmath7-process ( even including the cm 's fast process ) and boson peak alone can not take account of the experimental data . further contributions may arise @xcite , e.g. , from a constant loss term as early proposed by wong and angell @xcite and/or a possible @xmath153 behavior , both seemingly universal features in the dielectric response of glassy ionic conductors @xcite . possible microscopic explanations for these contributions were proposed in @xcite . indeed , the data in pc near the @xmath9-minimum can well be described by adding a term @xmath154 to the ansatz of eq . [ pheno ] @xcite . in this way , by adjusting the parameters to achieve a smooth transition to the cd - curves describing the @xmath0-peak , quite impressive fits over 17 decades of frequency are possible . of course this could be expected considering the large amount of parameters involved in the fitting , but nevertheless it can not be excluded that such a simple superposition ansatz of different independent contributions is correct . very recently a model was proposed considering a low - frequency relaxation - like part of the vibration susceptibility function responsible for the boson peak @xcite . this relaxation - like response was shown to arise from anharmonicity of vibrations and invoked to explain the quasielastic line seen in light and neutron scattering . this quasielastic contribution corresponds to the fast @xmath8-process seen in the region below the boson peak in the susceptibility spectra . within this framework , the fast process should show up as peak with @xmath155 and @xmath156 at its low and high - frequency side , respectively . for the absolute value of the exponent @xmath0 , reasonable values ranging between 0.375 and 1 were given in @xcite , depending on the system . of course no peak is seen between @xmath0- and boson peak in the spectra of pc ( figs . [ eps2 ] and [ mctfits ] ) but the @xmath157-wing of the fast @xmath8-process may be obscured by the domination of the boson peak at higher frequencies . a severe argument against this picture is the smooth transition of @xmath9 from the minimum to the boson peak with only one power law , which seems unlikely to result from the superposition of the @xmath158-wing of the fast @xmath8-process and the low frequency wing of the boson peak ( steeper than @xmath159 , see above ) . however , this possibility can not fully be excluded and at least this model provides an explanation for the sublinear increase seen for @xmath160 . it is interesting , that within this theoretical framework a crossover temperature of the fast relaxation was obtained which was found to be of similar magnitude as the critical temperature @xmath97 of mct @xcite . as mentioned in the introduction , a fast process in the minimum region of @xmath44 is one of the main outcomes of mct , a prediction which led to the huge interest in this high - frequency region . within idealized mct , above @xmath97 , the high and low - frequency wings close to the minimum of @xmath9 are described by power laws with exponents @xmath84 and @xmath76 , respectively . the minimum region can be approximated by the interpolation formula @xcite : @xmath162 and @xmath163 denote position and amplitude of the minimum , respectively . the exponents @xmath84 and @xmath76 are temperature independent and constrained by the exponent parameter @xmath164 where @xmath165 denotes the gamma function . this restricts the exponent @xmath84 to values below @xmath166 , i.e. a significantly sublinear increase of @xmath72 at frequencies above the minimum is predicted . we found a consistent description of the @xmath1-minima at @xmath167 k using @xmath168 which implies @xmath169 and @xmath170 ( solid lines in fig . [ mctfits ] ) . the obtained @xmath171 agrees with that determined from the preliminary data published previously @xcite . it is identical to @xmath171 deduced from light scattering results @xcite and also consistent with a recent analysis of solvation dynamics experiments on pc @xcite . in addition , a preliminary analysis of the susceptibility minimum from recent neutron scattering measurements @xcite yields @xmath172 , consistent with the present value . at high frequencies the fits with eq . [ eqmctmin ] are limited by the onset of the decrease at the high - frequency wing of the boson peak . quite a different behavior was seen in glycerol @xcite where the mct fits are limited at high frequencies by an additional increase , that can not be described by eq . [ eqmctmin ] . in @xcite it was argued that this deviation in glycerol is due to the vibrational boson peak contribution which is not taken into account by eq . [ eqmctmin ] . in pc this contribution seems to be of less importance . this is in accord with the finding of sokolov _ et al_. @xcite that the amplitude ratio of boson peak and fast process is largest for strong glass formers , glycerol being much stronger than pc ( see also section [ secdiscfastbos ] ) . the deviations of data and fits , seen at low frequencies in fig . [ mctfits ] , can be ascribed to the growing importance of the @xmath7-relaxation which is not taken into account by the simple interpolation formula , eq . [ eqmctmin ] . the critical temperature @xmath97 should manifest itself in the temperature dependence of the @xmath72-minimum . for @xmath107 mct predicts the following relations : @xmath173 and @xmath174{0xbd}}% % beginexpansion { \frac12}% % endexpansion } $ ] . figure [ mopa ] shows the results for @xmath175 , @xmath176 , and also for @xmath92 ( same data as in fig . [ tau ] ) . here representations have been chosen that lead to straight lines that extrapolate to @xmath97 if the predicted critical temperature dependences are obeyed . indeed , as indicated by the solid lines , all three data sets can be described consistently with a critical temperature @xmath177 k , in agreement with the results determined from the preliminary data published previously @xcite . this lies in the same range as the @xmath97 obtained from light scattering @xcite ( @xmath178 k ) , neutron scattering @xcite ( @xmath40 - @xmath70 k ) , and solvation dynamics experiments @xcite ( @xmath179 k ) . also the @xmath180 k , deduced from a preliminary analysis of the susceptibility minimum from recent neutron scattering experiments @xcite , agrees well with the present value . for temperatures near @xmath97 the @xmath181-data deviate from the predicted behavior as also seen in fig . [ tau](c ) . within mct this can be ascribed to a smearing out of the critical behavior near @xmath97 due to hopping processes which are considered in extended versions of mct only @xcite . in addition , the above critical temperature dependences of @xmath182 , @xmath162 and @xmath2 should be valid only for temperatures not too far above @xmath97 and the deviations seen for @xmath162 and @xmath183 at high temperatures ( fig . [ mopa ] ) may be due to this fact . therefore there is a problem concerning the proper choice of the temperature range to be used for the determination of @xmath97 . while the critical behavior proposed in fig . [ mopa ] seems reasonable , some uncertainties concerning the value of @xmath97 remain which can only be clarified by an analysis within the extended mct . mct predicts a significant change in the behavior of @xmath118 at @xmath97 : for @xmath113 , within idealized mct @xmath72 should exhibit a so - called knee at a frequency @xmath184 , i.e. a change of power law from @xmath185 at @xmath186 @xmath187 to @xmath188 at @xmath189 . within idealized mct , at @xmath113 the minimum and the @xmath0-peak should vanish but both phenomena are restored by the hopping processes invoked in extended mct @xcite . at first , from fig . [ mctfits ] it becomes obvious that the fits with eq . [ eqmctmin ] with @xmath168 will no longer work at @xmath113 because the high frequency wing of the minimum becomes successively steeper below this temperature , i.e. the frequency dependence of @xmath118 changes significantly below @xmath97 . in fig . [ mctfits ] , a @xmath190 behavior with @xmath169 as determined for @xmath107 is shown as dashed line matching the region just below the boson peak for the @xmath191 k and @xmath192 k curves . for lower frequencies the experimental data exhibit a downward deviation from the @xmath193-extrapolations , i.e. really a knee appears . whatsoever , in light of the rather large experimental uncertainties in this region it seems quite audacious to assign the observed feature to the knee of mct . according to mct , @xmath187 and the amplitude at the knee , @xmath194 , should also exhibit critical behavior , @xmath195 and @xmath196{0xbd}}% % beginexpansion { \frac12}% % endexpansion } $ ] with the proportionality factors in close connection of the proportionality factors in the critical behavior of the minimum @xcite . in fig . [ mopa](a ) and ( b ) the two values read off from fig . [ mctfits ] are denoted as pluses . having in mind the extreme uncertainties in the knee position , the data seem to be consistent with a @xmath197 of @xmath178 k. however , the position of the knee is not in accord with the position of the miniumum above @xmath97 @xcite . overall , a lack of significance of the observed knee - feature has to be stated but at least the data show where the knee may be located and where more experimental work has to be done to check for its presence and temperature evolution in pc . the comparison of dielectric and the scattering results is shown in fig . as mentioned above ( section [ resfast ] ) the significantly larger ratio of @xmath0- and boson peak amplitude for dielectric compared with light scattering results seems to be a rather universal property of glass - forming materials @xcite . recently , an explanation for this finding was given by considering the different dependencies of the probes on orientational fluctuations @xcite . in addition , in a recent theoretical work @xcite mct was generalized to molecular liquids of molecules with orientational degrees of freedom . the resulting mct equations were solved for a system of dipolar hard spheres and a larger ratio of @xmath0- and boson peak amplitude for @xmath198 was obtained in accordance with the experimental findings . further , it is one of the main predictions of mct @xcite that the same parameters @xmath199and @xmath171should arise from all observables coupling to the density fluctuations . this is indeed the case for propylene - carbonate ( see above ) . but also the position of the @xmath1- ( respectively @xmath200- ) minima should be the same , independent of the experimental method which is also valid when including orientational degrees of freedom @xcite . however , as seen in fig . [ vgl ] , this seems not to be the case . an explanation for a similar behavior found from molecular dynamics simulations of a system of rigid diatomic molecules was given in terms of @xmath201{0xb0}}% % beginexpansion { { } ^\circ}% % endexpansion $ ] flips of the non - spherical molecules which can not be taken into account by a hard sphere model @xcite . in this context , it may be mentioned that for the mobile - ion glass - former ckn a rather good agreement of the minimum position from different experimental methods was found @xcite . here orientational degrees of freedom are not important which corroborates the above explanation in terms of @xmath201{0xb0}}% % beginexpansion { { } ^\circ}% % endexpansion $ ] flips . the boson peak is a universal feature of glass - forming materials showing up in light and neutron scattering but also as excess contribution in specific heat measurements . a variety of explanations of the boson peak has been proposed , e.g. , in terms of the soft potential model @xcite , phonon localization models @xcite , or a model of coupled harmonic oscillators with a distribution of force constants @xcite . also mct includes contributions leading to a peak at thz as was shown using a schematic two - correlator model @xcite . however , up to now there is no consensus concerning the microscopic origin of this phenomenon . it can not be the aim of the present paper to compare the results with the proposed models , especially in the light of the rather restricted data base for @xmath202 thz . however , some experimental facts deserve to be emphasized which may be of importance for the understanding of the boson peak . figure [ pcgly ] shows the high frequency region of @xmath30 for pc and glycerol . clearly , both materials exhibit quite different behavior in the boson peak region : for pc only one power law is seen at frequencies @xmath203 forming simultaneously the high frequency wing of the @xmath1-minimum and the low frequency wing of the boson peak . in marked contrast , for glycerol two regimes can be distinguished : directly above @xmath82 , there is a rather shallow increase of @xmath9 which together with the left wing of the minimum can be well fitted with the mct prediction , eq . [ eqmctmin ] @xcite . at higher frequencies a very steep increase appears , approaching @xmath204 for @xmath205 . this different behavior of pc and glycerol also becomes obvious in the scaling plot of fig . [ scal ] . for both materials the @xmath9 -minimum corresponds to the deviation from the master curve , that shows up as a third linear region in the scaling plot . but for glycerol in addition a minimum is seen in fig . [ scal ] . in the scaling plot this minimum marks the transition point between the two regimes at @xmath203 , described above . it seems that in glycerol the fast @xmath8-process giving rise to the shallow minimum in @xmath9 or the third linear region in the scaling plot , is obscured at higher frequencies by the boson peak contribution . this arguing seems to be in accord with the finding of sokolov _ et al_. @xcite of a higher amplitude - ratio of boson peak and fast process for strong glass formers . however , at least near @xmath6 this ratio , e.g. measured by comparing boson - peak and minimum amplitude in fig . [ pcgly ] , is quite similar for both materials . for high temperatures , @xmath167 k for pc and @xmath206 k for glycerol , the fast @xmath136-process in pc has indeed a higher amplitude if curves with similar values of @xmath2 are compared . this fact also explains the good fits with mct up to the boson peak frequency ( section [ secdiscfastmin ] ) in pc . however , for lower temperatures the different characteristics of pc and glycerol has to be ascribed either to a more shallow left wing of the boson peak for pc ( @xmath207 instead of @xmath208 ) or to a steeper increase of the high frequency wing of the minimum , thereby obscuring the steeper boson peak wing . interestingly , while there might be some problems for the new model by novikov @xcite in explaining the pc results ( see section [ secdiscfastmin ] ) , glycerol seems to fit into this picture : below the boson peak , two distinct regions are seen which can be ascribed to the relaxation - like and the main part of the vibrational excitations . concerning mct , it has to be mentioned that the light scattering results on glycerol @xcite exhibit quite similar characteristics as the dielectric results @xcite . the light scattering results were successfully described using the schematic two - correlator mct model mentioned above @xcite . but it is not clear if mct is able to provide an explanation for the qualitative difference of the glycerol and pc dielectric data . dielectric data on glass - forming pc in an exceptionally broad frequency range have been presented and compared with the results from light scattering and to broadband dielectric results on glycerol . a comparison of the findings concerning @xmath0-relaxation , excess wing , @xmath72-minimum , and boson peak on various theoretical and phenomenological predictions has been performed . the temperature dependence of the @xmath0-relaxation time is in accord with the efv and the fld models and at high temperatures also with that of idealized mct . the temperature dependences of the relaxation strength and the width parameter of the @xmath0-relaxation were determined and some differences to the findings from previous works were found . the excess wing in pc was shown to follow the modified nagel scaling proposed by dendzik et al . @xcite but at high frequencies the curves of pc and glycerol do not scale onto each other . overall , it is not possible to arrive at a decision in favor or against one of the models on the dynamics of glass - forming materials from the results obtained at the first 15 decades of frequency alone . at higher frequencies above about 1 ghz a minimum in @xmath118 is detected . in this region , clearly fast processes contribute to the dielectric loss , a finding for which most models provide no explanation . while the minimum can be well described by the sum of power laws and a constant loss contribution @xcite , the theoretical foundation for these contributions is unclear at present but currently is being developed . in contrast , mct provides a microscopic explanation for the high - frequency data , at least at high temperatures . in addition , the analysis within mct yields values for @xmath97 and @xmath171 , that are in agreement with those determined from other experimental methods . also the differences in the susceptibilities obtained from dielectric and light scattering experiments seem to be in accord with recent extensions of mct . at low temperatures , @xmath209 @xmath97 , at least a qualitative agreement of the results ( presence of a fast process and possible occurrence of a knee ) with mct can be stated , but more work is needed for a quantitative comparison . overall , certain aspects of the results found in the present work can be explained by different models , but in our judgement mct provides the most consistent picture providing explanations for the largest variety of experimental facts , including the high - frequency processes . this may be partly due to the large amount of predictions made by mct , covering almost all aspects of the dynamic response of glass - forming materials , while other models are somewhat restricted in this respect . however , just this agreement of the data with the many different predictions of mct speaks in favor of the theory . admittedly , it is not possible to arrive at a final decisive conclusion concerning the applicability of mct for pc and alternative explanations may be possible . also many questions need to be solved , e.g. the behavior below @xmath97 should be compared with the extended mct , the differences to the scattering results should be compared quantitatively to mct ( considering orientational degrees of freedom of dipolar , non - spherical molecules ) , and the qualitatively different behavior of pc and glycerol in the boson peak region should be addressed . finally , in the boson peak region we find significant differences between glycerol and pc which wait for a theoretical explanation . but also more experimental work is needed , e.g. concerning the temperature evolution of the boson peak and a higher precision of the data at low temperatures in order to investigate in detail the possible occurrence of a knee in @xmath9 of pc . we gratefully acknowledge stimulating discussion with c.a . angell , r. bhmer , h.z . cummins , w. gtze , k.l . ngai , m. ohl , r. schilling , w. schirmacher , and j. wuttke . we thank m. ohl and j. wuttke for providing the neutron scattering results of ref . @xcite prior to publication . this work was supported by the deutsche forschungsgemeinschaft , grant - no . lo264/8 - 1 and partly by the bmbf , contract - no . 13n6917 . d. kivelson , s.a . kivelson , x - l . zhao , z. nussinov , and g. tarjus , physica a * 219 * , 27 ( 1995 ) ; g. tarjus , d. kivelson , and s. kivelson , in : _ supercooled liquids : advances and novel applications _ , ed . fourkas , d. kivelson , u. mohanty , and k.a . nelson ( acs publications , washington , dc , 1997 ) p. 67 . see collection of papers in : _ dynamics of glass transition and related topics _ t. odagaki , y hiwatari , and j. matsui [ progr . * 126 * ( 1997 ) ] ; _ structure and dynamics of glasses and glass formers _ , angell , k.l . ngai , j. kieffer , t. egami , and g.u . nienhaus ( materials research society symposium proceedings , vol . 455 , pittsburgh , 1997 ) . j. wuttke , j. hernandez , g. li , g. coddens , h.z . cummins , f. fujara , w. petry , and h. sillescu , phys . lett . * 72 * , 3052 ( 1994 ) ; j. wuttke , w. petry , g. coddens , and f. fujara , phys . rev . e * 52 * , 4026 ( 1995 ) . ngai , c. cramer , t. saatkamp , and k. funke , in : _ proceedings of the workshop on non - equilibrium phenomena in supercooled fluids , glasses , and amorphous materials _ , eds . m. giordano , d. leporini , and m. tosi ( world scientific , singapore , 1996 ) p. 3 . p. lunkenheimer , a. pimenov , m. dressel , b. gorshunov , u. schneider , b. schiener , and a. loidl , in : _ supercooled liquids : advances and novel applications _ , fourkas , d. kivelson , u. mohanty , and k.a . nelson ( acs publications , washington , dc , 1997 ) p. 168 . p. lunkenheimer , a. pimenov , m. dressel , b. gorshunov , u. schneider , b. schiener , r. bhmer , and a. loidl , in : _ structure and dynamics of glasses and glass formers _ , angell , k.l . ngai , j. kieffer , t. egami , and g.u . nienhaus ( materials research society symposium proceedings , vol . 455 , pittsburgh , 1997 ) p. 47 . volkov , yu.g . goncharov , g.v . kozlov , s.p . lebedev , and a.m. prokhorov , infrared phys . * 25 * , 369 ( 1985 ) ; a.a . volkov _ , _ kozlov , s.p . lebedev , and a.m. prokhorov , infrared phys . * 29 * , 747 ( 1989 ) . p. lunkenheimer , r. brand , u. schneider , and a. loidl , submitted to _ proceedings of the 8th tohwa university international symposium on slow dynamics in complex systems _ ( aip conference proceedings , new york , 1999 ) . in a recent investigation @xcite we have shown that the excess wing is not universally present in _ orientationally _ disordered materials , i.e. it seems to be a property inherent to _ structural _ glass - formers . u. strom , j.r . hendrickson , r.j . wagner , and p.c . taylor , solid state commun . * 15 * , 1871 ( 1974 ) ; u. strom and p.c . taylor , phys . b * 16 * , 5512 ( 1977 ) ; c. liu and c.a . angell , j. chem . phys . * 93 * , 7378 ( 1990 ) . one has to be aware that the assumption of an additive superposition of different contributions to the susceptibility may be oversimplified , [ for an alternative see , e.g. , j. colmenero , a. arbe , and a. alegria , phys . lett . * 71 * , 2603 ( 1993 ) ] but at least it seems sufficient for a preliminary analysis . lee , h.f . liu , and a.s . nowick , phys . lett . * 67 * , 1559 ( 1991 ) ; d.l . sidebottom , p.f . green , and r.k . brow , phys . rev . lett . * 74 * , 5068 ( 1995 ) ; c. cramer , k. funke , and t. saatkamp , philos . mag . b * 71 * , 701 ( 1995 ) . r.h . cole and e. tombari , j. non - cryst . solids * 131 - 133 * , 969 ( 1991 ) ; k.l . ngai , u. strom , and o. kanert , phys . chem . glasses * 33 * , 109 ( 1992 ) ; b.s . lim , a.v . vaysleyb , and a.s . nowick , appl . a * 56 * , 8 ( 1993 ) ; s.r . elliott , solid state ionics * 70/71 * , 27 ( 1994 ) ; d.l . sidebottom , p.f . green , and r.k . brow , j. non - cryst . solids * 203 * , 300 ( 1996 ) ; k.l . ngai , h. jain , and o. kanert , j. non - cryst . solids * 222 * , 383 ( 1997 ) . p. lunkenheimer , u. schneider , r. brand , and a. loidl , submitted to _ proceedings of the 8th tohwa university international symposium on slow dynamics in complex systems _ ( aip conference proceedings , new york , 1999 ) .[/INST] dielectric spectroscopy covering more than 18 decades of frequency has been performed on propylene carbonate in its liquid and supercooled - liquid state . using quasi - optic submillimeter and far - infrared spectroscopy the dielectric response was investigated up to frequencies well into the microscopic regime . we discuss the @xmath0-process whose characteristic timescale is observed over 14 decades of frequency and the excess wing showing up at frequencies some three decades above the peak frequency . special attention is given to the high - frequency response of the dielectric loss in the crossover regime between @xmath0-peak and boson - peak . similar to our previous results in other glass forming materials we find evidence for additional processes in the crossover regime . however , significant differences concerning the spectral form at high frequencies are found . we compare our results to the susceptibilities obtained from light scattering and to the predictions of various models of the glass transition . </s>

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President Trump protests 20 show all President Trump protests 1/20 Patrons hold a sign as people march by while protesting the election of Republican Donald Trump as the president of the United States in downtown Los Angeles, California Reuters 2/20 Demonstrators rally following the election of Republican Donald Trump as President of the United States, in Oakland, California Reuters 3/20 Demonstrators march following the election of Donald Trump as President of the United States Reuters 4/20 Thousands of protesters rallied across the United States expressing shock and anger over Donald Trump's election, vowing to oppose divisive views they say helped the Republican billionaire win the presidency AFP/Getty Images 5/20 Demonstrators protest outside the Chicago Theatre in Chicago, Illinois Getty 6/20 A police officer aims a launcher after demonstrators threw projectiles toward a line of officers during a demonstration in Oakland, California Reuters 7/20 An officer examines a vandalized police vehicle as demonstrators riot in Oakland, California Reuters 8/20 Demonstrators take over the Hollywood 101 Freeway just north of Los Angeles City Hall in protest against the election of Republican Donald Trump as President of the United States Reuters 9/20 A woman holds up a sign reading 'Trump you are an Idiot' as demonstrators gather during a protest against President-elect Donald Trump outside the City Hall building in Los Angeles, California EPA 10/20 A masked demonstrator gestures toward a police line during a demonstration in Oakland, California Reuters 11/20 Demonstrators protest against the election of Republican Donald Trump as President of the United States, near the Trump International Hotel & Tower in Las Vegas, Nevada Reuters 12/20 Musician Lagy Gaga stages a protest against Republican presidential nominee Donald Trump on a sanitation truck outside Trump Tower in New York City Getty 13/20 A woman yells as she takes part in a protest against President-elect Donald Trump in Seattle's Capitol Hill neighborhood AP 14/20 A man dressed in red-white-and-blue sits on the curb during a protest against President-elect Donald Trump in Seattle's Capitol Hill neighborhood AP 15/20 A protester sets off fireworks during a protest against President-elect Donald Trumpin Seattle's Capitol Hill neighborhood AP 16/20 University of California, Davis students protest on campus in Davis, California, U.S. following the election of Donald Trump as President of the United States Reuters 17/20 An Oakland police officer checks out damage after a window was broken by protesters at a car dealership in downtown Oakland, Calif AP 18/20 A protester faces a police line in downtown Oakland, Calif AP 19/20 President-elect Donald Trumpís victory set off multiple protests AP 20/20 A fire burns during protests in Oakland, Calif AP Mr Trump launched his campaign on the promise of building the wall to keep out undocumented immigrants – whom he called rapists, drug traffickers, and criminals. It remains unclear if Mr Trump’s wall would supplement the existing barriers in urban areas along the 1,900 mile border, constructed by the Army Corps of Engineers in the mid-1990s, or simply replace it. Bloomberg’s Thomas Penny pointed out that Magal saw an increase of six per cent on Wednesday. Sharp rise in shares of Israeli border wall building companyhttps://t.co/e1JsEkt3an pic.twitter.com/HX4bweBa1l — Thomas Penny (@ThomasWPenny) November 9, 2016 “We would join forces with a major US defence company that has experience with such projects worldwide,” Magal CEO Saar Koursh told Bloomberg in August. “We’ve done it in the past and we would definitely want to do it.” The company had previously seen a surge in business with the rise in global anxieties over Isis amid the Syrian refugee crisis. USA: Donald Trump will build the BIGGEST anti-Mexico wall... apparently “The border business was down, but then came Isis and the Syrian conflict,” he said. “The world is changing and borders are coming back big-time.” Another sector apparently benefitting from Mr Trump’s election win is the private prison industry. Two companies, Corrections Corp and GEO Group, saw significant gains, recouping losses they suffered after the Department of Justice announced it would discontinue the use of federal private prisons. It is likely that a President Trump would reverse that decision. “Private prisons would likely be a clear winner under Trump,” analysts for Height Securities LLC wrote, “as his administration will likely rescind the DOJ’s contract phase-out and [Immigration and Customs Enforcement] capacity to house detainees will come under stress.” ||||| Guns stocks are tumbling and prison stocks are soaring after Donald Trump won the presidential election. Corrections Corp. of America CXW, -1.40% was the biggest percentage gainer listed on the New York Stock Exchange Wednesday, with shares closing up 43%. Shares of Geo Group GEO, -0.08% which has corrections and other facilities in North America and abroad, closed up 21%. The gain Wednesday marked the biggest one-day percentage gain for the company since June 2000. The Obama administration in August announced plans to phase out some private prison use, which potentially could be reversed in a Trump administration. By comparison, the S&P 500 SPX, +0.46% was 1% Wednesday, and it has gained 3.5% so far this week. Meanwhile, shares of gun maker Sturm, Ruger & Co. Inc. RGR, -1.78% closed down 14.5% . Smith & Wesson Holding Corporation US:SWHC shares closed down 15%. Gun sales ticked up after of President Obama’s elections on concerns that laws around gun control would become more restrictive, said Chris Krueger, senior research analyst at Lake Street Capital. Now he believes gun buyers are more confident that Trump will protect gun-carry laws, so they’re not rushing out to buy them, leading to a drop in the stock, he said. In California, voters passed a ballot measure that tightened gun-control laws in the state. Washington state residents voted to restrict access to firearms for people that have been deemed by a court to be a threat. Nevada residents voted to expand background checks for gun purchases. Krueger said these initiatives were somewhat expected, which is why the stocks don’t seem to be reacting much to them. Additionally, he said gun enthusiasts are bullied by the prospect of a pro-gun nominee appointed to the Supreme Court by Trump. “I think today it’s more about the presidential election than the gun-control initiatives,” Krueger said.

– This is a good time to be in the wall-building business: Shares in Israeli firm Magal Security System, which helped build the wall around Gaza and many other barriers around the world, jumped around 6% Wednesday in the wake of Donald Trump's surprise election victory, the Independent reports. Trump has promised to build a wall along the border with Mexico and make Mexico pay for it, though Mexico says the latter part of that promise isn't going to happen. In August, Magal chief Saar Koursh made it clear he was hoping to get the Trump contract. "The border business was down, but then came ISIS and the Syrian conflict," he told Bloomberg. "The world is changing and borders are coming back big-time." MarketWatch reports that prison stocks were another big winner Wednesday, with Corrections Corp. of America up 43%, possibly because investors believe Trump will scrap Obama's plan to phase out private federal prisons. Gun shares, however, were down, which analysts say was because Trump isn't expected to tighten gun control laws, meaning nobody is in a big hurry to stock up on firearms.

<s>[INST]The Israeli company that built the wall around Gaza saw a spike in shares when it became clear Donald Trump would become the next President of the United States – making the possibility of a wall at the Mexico border more tangible. Magal Security Systems Ltd had already been salivating at the prospect of a Trump win and what that would mean for the barrier-building business. The company experienced gains over the years, as they expanded their work from the Gaza Strip to Egypt, Somalia, and other countries in Africa. President Trump protests 20 show all President Trump protests 1/20 Patrons hold a sign as people march by while protesting the election of Republican Donald Trump as the president of the United States in downtown Los Angeles, California Reuters 2/20 Demonstrators rally following the election of Republican Donald Trump as President of the United States, in Oakland, California Reuters 3/20 Demonstrators march following the election of Donald Trump as President of the United States Reuters 4/20 Thousands of protesters rallied across the United States expressing shock and anger over Donald Trump's election, vowing to oppose divisive views they say helped the Republican billionaire win the presidency AFP/Getty Images 5/20 Demonstrators protest outside the Chicago Theatre in Chicago, Illinois Getty 6/20 A police officer aims a launcher after demonstrators threw projectiles toward a line of officers during a demonstration in Oakland, California Reuters 7/20 An officer examines a vandalized police vehicle as demonstrators riot in Oakland, California Reuters 8/20 Demonstrators take over the Hollywood 101 Freeway just north of Los Angeles City Hall in protest against the election of Republican Donald Trump as President of the United States Reuters 9/20 A woman holds up a sign reading 'Trump you are an Idiot' as demonstrators gather during a protest against President-elect Donald Trump outside the City Hall building in Los Angeles, California EPA 10/20 A masked demonstrator gestures toward a police line during a demonstration in Oakland, California Reuters 11/20 Demonstrators protest against the election of Republican Donald Trump as President of the United States, near the Trump International Hotel & Tower in Las Vegas, Nevada Reuters 12/20 Musician Lagy Gaga stages a protest against Republican presidential nominee Donald Trump on a sanitation truck outside Trump Tower in New York City Getty 13/20 A woman yells as she takes part in a protest against President-elect Donald Trump in Seattle's Capitol Hill neighborhood AP 14/20 A man dressed in red-white-and-blue sits on the curb during a protest against President-elect Donald Trump in Seattle's Capitol Hill neighborhood AP 15/20 A protester sets off fireworks during a protest against President-elect Donald Trumpin Seattle's Capitol Hill neighborhood AP 16/20 University of California, Davis students protest on campus in Davis, California, U.S. following the election of Donald Trump as President of the United States Reuters 17/20 An Oakland police officer checks out damage after a window was broken by protesters at a car dealership in downtown Oakland, Calif AP 18/20 A protester faces a police line in downtown Oakland, Calif AP 19/20 President-elect Donald Trumpís victory set off multiple protests AP 20/20 A fire burns during protests in Oakland, Calif AP Mr Trump launched his campaign on the promise of building the wall to keep out undocumented immigrants – whom he called rapists, drug traffickers, and criminals. It remains unclear if Mr Trump’s wall would supplement the existing barriers in urban areas along the 1,900 mile border, constructed by the Army Corps of Engineers in the mid-1990s, or simply replace it. Bloomberg’s Thomas Penny pointed out that Magal saw an increase of six per cent on Wednesday. Sharp rise in shares of Israeli border wall building companyhttps://t.co/e1JsEkt3an pic.twitter.com/HX4bweBa1l — Thomas Penny (@ThomasWPenny) November 9, 2016 “We would join forces with a major US defence company that has experience with such projects worldwide,” Magal CEO Saar Koursh told Bloomberg in August. “We’ve done it in the past and we would definitely want to do it.” The company had previously seen a surge in business with the rise in global anxieties over Isis amid the Syrian refugee crisis. USA: Donald Trump will build the BIGGEST anti-Mexico wall... apparently “The border business was down, but then came Isis and the Syrian conflict,” he said. “The world is changing and borders are coming back big-time.” Another sector apparently benefitting from Mr Trump’s election win is the private prison industry. Two companies, Corrections Corp and GEO Group, saw significant gains, recouping losses they suffered after the Department of Justice announced it would discontinue the use of federal private prisons. It is likely that a President Trump would reverse that decision. “Private prisons would likely be a clear winner under Trump,” analysts for Height Securities LLC wrote, “as his administration will likely rescind the DOJ’s contract phase-out and [Immigration and Customs Enforcement] capacity to house detainees will come under stress.” ||||| Guns stocks are tumbling and prison stocks are soaring after Donald Trump won the presidential election. Corrections Corp. of America CXW, -1.40% was the biggest percentage gainer listed on the New York Stock Exchange Wednesday, with shares closing up 43%. Shares of Geo Group GEO, -0.08% which has corrections and other facilities in North America and abroad, closed up 21%. The gain Wednesday marked the biggest one-day percentage gain for the company since June 2000. The Obama administration in August announced plans to phase out some private prison use, which potentially could be reversed in a Trump administration. By comparison, the S&P 500 SPX, +0.46% was 1% Wednesday, and it has gained 3.5% so far this week. Meanwhile, shares of gun maker Sturm, Ruger & Co. Inc. RGR, -1.78% closed down 14.5% . Smith & Wesson Holding Corporation US:SWHC shares closed down 15%. Gun sales ticked up after of President Obama’s elections on concerns that laws around gun control would become more restrictive, said Chris Krueger, senior research analyst at Lake Street Capital. Now he believes gun buyers are more confident that Trump will protect gun-carry laws, so they’re not rushing out to buy them, leading to a drop in the stock, he said. In California, voters passed a ballot measure that tightened gun-control laws in the state. Washington state residents voted to restrict access to firearms for people that have been deemed by a court to be a threat. Nevada residents voted to expand background checks for gun purchases. Krueger said these initiatives were somewhat expected, which is why the stocks don’t seem to be reacting much to them. Additionally, he said gun enthusiasts are bullied by the prospect of a pro-gun nominee appointed to the Supreme Court by Trump. “I think today it’s more about the presidential election than the gun-control initiatives,” Krueger said.[/INST]– This is a good time to be in the wall-building business: Shares in Israeli firm Magal Security System, which helped build the wall around Gaza and many other barriers around the world, jumped around 6% Wednesday in the wake of Donald Trump's surprise election victory, the Independent reports. Trump has promised to build a wall along the border with Mexico and make Mexico pay for it, though Mexico says the latter part of that promise isn't going to happen. In August, Magal chief Saar Koursh made it clear he was hoping to get the Trump contract. "The border business was down, but then came ISIS and the Syrian conflict," he told Bloomberg. "The world is changing and borders are coming back big-time." MarketWatch reports that prison stocks were another big winner Wednesday, with Corrections Corp. of America up 43%, possibly because investors believe Trump will scrap Obama's plan to phase out private federal prisons. Gun shares, however, were down, which analysts say was because Trump isn't expected to tighten gun control laws, meaning nobody is in a big hurry to stock up on firearms.</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Indian Tribal Justice Technical and Legal Assistance Act of 2000''. SEC. 2. FINDINGS. The Congress finds and declares that-- (1) there is a government-to-government relationship between the United States and Indian tribes; (2) Indian tribes are sovereign entities and are responsible for exercising governmental authority over Indian lands; (3) the rate of violent crime committed in Indian country is approximately twice the rate of violent crime committed in the United States as a whole; (4) in any community, a high rate of violent crime is a major obstacle to investment, job creation and economic growth; (5) tribal justice systems are an essential part of tribal governments and serve as important forums for ensuring the health and safety and the political integrity of tribal governments; (6) Congress and the Federal courts have repeatedly recognized tribal justice systems as the most appropriate forums for the adjudication of disputes affecting personal and property rights on Native lands; (7) enhancing tribal court systems and improving access to those systems serves the dual Federal goals of tribal political self-determination and economic self-sufficiency; (8) there is both inadequate funding and an inadequate coordinating mechanism to meet the technical and legal assistance needs of tribal justice systems and this lack of adequate technical and legal assistance funding impairs their operation; (9) tribal court membership organizations have served a critical role in providing training and technical assistance for development and enhancement of tribal justice systems; (10) Indian legal services programs, as funded partially through the Legal Services Corporation, have an established record of providing cost effective legal assistance to Indian people in tribal court forums, and also contribute significantly to the development of tribal courts and tribal jurisprudence; and (11) the provision of adequate technical assistance to tribal courts and legal assistance to both individuals and tribal courts is an essential element in the development of strong tribal court systems. SEC. 3. PURPOSES. The purposes of this Act are as follows: (1) to carry out the responsibility of the United States to Indian tribes and members of Indian tribes by ensuring access to quality technical and legal assistance. (2) To strengthen and improve the capacity of tribal court systems that address civil and criminal causes of action under the jurisdiction of Indian tribes. (3) To strengthen tribal governments and the economies of Indian tribes through the enhancement and, where appropriate, development of tribal court systems for the administration of justice in Indian country by providing technical and legal assistance services. (4) To encourage collaborative efforts between national or regional membership organizations and associations whose membership consists of judicial system personnel within tribal justice systems; non-profit entities which provide legal assistance services for Indian tribes, members of Indian tribes, and/or tribal justice systems. (5) To assist in the development of tribal judicial systems by supplementing prior congressional efforts such as the Indian Tribal Justice Act (Public Law 103-176). SEC. 4. DEFINITIONS. For purposes of this Act: (1) Attorney general.--The term ``Attorney General'' means the Attorney General of the United States. (2) Indian lands.--The term ``Indian lands'' shall include lands within the definition of ``Indian country'', as defined in section 1151 of title 18, United States Code; or ``Indian reservations'', as defined in section 3(d) of the Indian Financing Act of 1974 (25 U.S.C. 1452(d)), or section 4(10) of the Indian Child Welfare Act (25 U.S.C 1903(10)). For purposes of the preceding sentence, such section 3(d) of the Indian Financing Act shall be applied by treating the term ``former Indian reservations in Oklahoma'' as including only lands which are within the jurisdictional area of an Oklahoma Indian Tribe (as determined by the Secretary of the Interior) and are recognized by such Secretary as eligible for trust land status under part 151 of title 25, Code of Federal Regulations (as in effect on the date of enactment of this sentence). (3) Indian tribe.--The term ``Indian tribe'' means any Indian tribe, band, nation, pueblo, or other organized group or community which administers justice or plans to administer justice under its inherent authority or the authority of the United States and which is recognized as eligible for the special programs and services provided by the United States to Indian tribes because of their status as Indians. (4) Judicial personnel.--The term ``judicial personnel'' means any judge, magistrate, court counselor, court clerk, court administrator, bailiff, probation officer, officer of the court, dispute resolution facilitator, or other official, employee, or volunteer within the tribal judicial system. (5) Non-profit entities.--The term ``non-profit entity'' or ``non-profit entities'' has the meaning given that term in section 501(c)(3) of the Internal Revenue Code of 1986. (6) Office of tribal justice.--The term ``Office of Tribal Justice'' means the Office of Tribal Justice in the United States Department of Justice. (7) Tribal justice system.--The term ``tribal court'', ``tribal court system'', or ``tribal justice system'' means the entire judicial branch, and employees thereof, of an Indian tribe, including, but not limited to, traditional methods and fora for dispute resolution, trial courts, appellate courts, including inter-tribal appellate courts, alternative dispute resolution systems, and circuit rider systems, established by inherent tribunal authority whether or not they constitute a court of record. TITLE I--TRAINING AND TECHNICAL ASSISTANCE, CIVIL AND CRIMINAL LEGAL ASSISTANCE GRANTS SEC. 101. TRIBAL JUSTICE TRAINING AND TECHNICAL ASSISTANCE GRANTS. Subject to the availability of appropriations, the Attorney General, in consultation with the Office of Tribal Justice, shall award grants to national or regional membership organizations and associations whose membership consists of judicial system personnel within tribal justice systems which submit an application to the Attorney General in such form and manner as the Attorney General may prescribe to provide training and technical assistance for the development, enrichment, enhancement of tribal justice systems, or other purposes consistent with this Act. SEC. 102. TRIBAL CIVIL LEGAL ASSISTANCE GRANTS. Subject to the availability of appropriations, the Attorney General, in consultation with the Office of Tribal Justice, shall award grants to non-profit entities, as defined under section 501(c)(3) of the Internal Revenue Code of 1986, which provide legal assistance services for Indian tribes, members of Indian tribes, or tribal justice systems pursuant to Federal poverty guidelines that submit an application to the Attorney General in such form and manner as the Attorney General may prescribe for the provision of civil legal assistance to members of Indian tribes and tribal justice systems, and/ or other purposes consistent with this Act. SEC. 103. TRIBAL CRIMINAL ASSISTANCE GRANTS. Subject to the availability of appropriations, the Attorney General, in consultation with the Office of Tribal Justice, shall award grants to non-profit entities, as defined by section 501(c)(3) of the Internal Revenue Code of 1986, which provide legal assistance services for Indian tribes, members of Indian tribes, or tribal justice systems pursuant to Federal poverty guidelines that submit an application to the Attorney General in such form and manner as the Attorney General may prescribe for the provision of criminal legal assistance to members of Indian tribes and tribal justice systems, and/or other purposes consistent with this Act. Funding under this title may apply to programs, procedures, or proceedings involving adult criminal actions, juvenile delinquency actions, and/or guardian-ad-litem appointments arising out of criminal or delinquency acts. SEC. 104. NO OFFSET. No Federal agency shall offset funds made available pursuant to this Act for Indian tribal court membership organizations or Indian legal services organizations against other funds otherwise available for use in connection with technical or legal assistance to tribal justice systems or members of Indian tribes. SEC. 105. TRIBAL AUTHORITY. Nothing in this Act shall be construed to-- (1) encroach upon or diminish in any way the inherent sovereign authority of each tribal government to determine the role of the tribal justice system within the tribal government or to enact and enforce tribal laws; (2) diminish in any way the authority of tribal governments to appoint personnel; (3) impair the rights of each tribal government to determine the nature of its own legal system or the appointment of authority within the tribal government; (4) alter in any way any tribal traditional dispute resolution fora; (5) imply that any tribal justice system is an instrumentality of the United States; or (6) diminish the trust responsibility of the United States to Indian tribal governments and tribal justice systems of such governments. SEC. 106. AUTHORIZATION OF APPROPRIATIONS. For purposes of carrying out the activities under this title, there are authorized to be appropriated such sums as are necessary for fiscal years 2000 through 2004. TITLE II--INDIAN TRIBAL COURTS SEC. 201. GRANTS. (a) In General.--The Attorney General may award grants and provide technical assistance to Indian tribes to enable such tribes to carry out programs to support-- (1) the development, enhancement, and continuing operation of tribal justice systems; and (2) the development and implementation of-- (A) tribal codes and sentencing guidelines; (B) inter-tribal courts and appellate systems; (C) tribal probation services, diversion programs, and alternative sentencing provisions; (D) tribal juvenile services and multi-disciplinary protocols for child physical and sexual abuse; and (E) traditional tribal judicial practices, traditional tribal justice systems, and traditional methods of dispute resolution. (b) Consultation.--In carrying out this section, the Attorney General may consult with the Office of Tribal Justice and any other appropriate tribal or Federal officials. (c) Regulations.--The Attorney General may promulgate such regulations and guidelines as may be necessary to carry out this title. (d) Authorization of Appropriations.--For purposes of carrying out the activities under this section, there are authorized to be appropriated such sums as are necessary for fiscal years 2000 through 2004. SEC. 202. TRIBAL JUSTICE SYSTEMS. Section 201 of the Indian Tribal Justice Act (25 U.S.C. 3621) is amended-- (1) in subsection (a), by striking ``1994, 1995, 1996, 1997, 1998, 1999, and 2000'' and inserting ``2000 through 2007''; (2) in subsection (b), by striking ``1994, 1995, 1996, 1997, 1998, 1999, and 2000'' and inserting ``2000 through 2007''; (3) in subsection (c), by striking ``1994, 1995, 1996, 1997, 1998, 1999, and 2000'' and inserting ``2000 through 2007''; and (4) in subsection (d), by striking ``1994, 1995, 1996, 1997, 1998, 1999, and 2000'' and inserting ``2000 through 2007''. TITLE III--TECHNICAL AMENDMENTS TO ALASKA NATIVE CLAIMS SETTLEMENT ACT SEC. 301. ALASKA NATIVE VETERANS. Section 41 of the Alaska Native Claims Settlement Act (43 U.S.C. 1629g) is amended as follows: (1) Subsection (a)(3)(I)(4) is amended by striking ``and Reindeer'' and inserting ``or''. (2) Subsection (a)(4)(B) is amended by striking ``; and'' and inserting ``; or''. (3) Subsection (b)(1)(B)(i) is amended by striking ``June 2, 1971'' and inserting ``December 31, 1971''. (4) Subsection (b)(2) is amended by striking the matter preceding subparagraph (A) and inserting the following: ``(2) The personal representative or special administrator, appointed in an Alaska State court proceeding of the estate of a decedent who was eligible under subsection (b)(1)(A) may, for the benefit of the heirs, select an allotment if the decedent was a veteran who served in South East Asia at any time during the period beginning August 5, 1964, and ending December 31, 1971, and during that period the decedent--''. SEC. 302. LEVIES ON SETTLEMENT TRUST INTERESTS. Section 39(c) of the Alaska Native Claims Settlement Act (43 U.S.C. 1629e(c)) is amended by adding at the end the following new paragraph: ``(8) A beneficiary's interest in a settlement trust and the distributions thereon shall be subject to creditor action (including without limitation, levy attachment, pledge, lien, judgment execution, assignment, and the insolvency and bankruptcy laws) only to the extent that Settlement Common Stock and the distributions thereon are subject to such creditor action under section 7(h) of this Act.''. TITLE IV--NATIONAL LEADERSHIP SYMPOSIUM FOR AMERICAN INDIAN, ALASKAN NATIVE, AND NATIVE HAWAIIAN YOUTH SEC. 401. ADMINISTRATION OF NATIONAL LEADERSHIP SYMPOSIUM FOR AMERICAN INDIAN, ALASKAN NATIVE, AND NATIVE HAWAIIAN YOUTH. (a) In General.--There are authorized to be appropriated to the Secretary of Education for the Washington Workshops Foundation $2,200,000 for administration of a national leadership symposium for American Indian, Alaskan Native, and Native Hawaiian youth on the traditions and values of American democracy. (b) Content of Symposium.--The symposium administered under subsection (a) shall-- (1) be comprised of youth seminar programs which study the workings and practices of American national government in Washington, DC, to be held in conjunction with the opening of the Smithsonian National Museum of the American Indian; and (2) envision the participation and enhancement of American Indian, Alaskan Native, and Native Hawaiian youth in the American political process by interfacing in the first-hand operations of the United States Government. Speaker of the House of Representatives. Vice President of the United States and President of the Senate.

Prohibits Federal agencies from offsetting funds made available for Indian tribal court membership organizations or Indian legal services organizations against other funds otherwise available for use in connection with technical or legal assistance to tribal justice systems or members. Authorizes appropriations. Title II: Indian Tribal Courts - Authorizes the Attorney General to award grants and provide technical assistance to enable Indian tribes to carry out programs to support: (1) the development, enhancement, and continuing operation of tribal justice systems; and (2) the development and implementation of tribal codes and sentencing guidelines; inter-tribal courts and appellate systems; tribal probation services, diversion programs, and alternative sentencing provisions; tribal juvenile services and multi-disciplinary protocols for child physical and sexual abuse; and traditional tribal judicial practices, tribal justice systems, and methods of dispute resolution. Authorizes appropriations. Amends the Indian Tribal Justice Act to extend the authorization of appropriations relating to tribal justice systems through FY 2007. Title III: Technical Amendments to Alaska Native Claims Settlement Act - Amends the Alaska Native Claims Settlement Act to make technical amendments to provisions regarding open season for allotments for certain Alaska Native veterans. Revises eligibility requirements to make a veteran eligible for an allotment if the veteran served at least six months between January 1, 1969, and December 31, 1971 (currently, June 2, 1971), and meets other existing requirements. Changes provisions regarding the authority of a personal representative of a decedent to select an allotment to authorize such representative or a special administrator appointed in an Alaska State court to select an allotment if the decedent was a veteran who served in Southeast Asia at any time during August 5, 1964, and December 31, 1971, and during such period: (1) was killed in action; (2) was wounded in action and died as a consequence of the wound; or (3) died while a prisoner of war. (Current law allows personal representatives to select such allotments if, between January 1, 1969, and December 31, 1971, one of such events occurred with respect to the decedent.) Subjects a beneficiary's interest in a settlement trust and the distributions thereon to creditor action only to the extent that Settlement Common Stock and related distributions are subject to such action under the Act. Title IV: National Leadership Symposium For American Indian, Alaskan Native, and Native Hawaiian Youth - Authorizes appropriations to the Secretary of Education for the Washington Workshops Foundation for administration of a national leadership symposium for American Indian, Alaskan Native, and Native Hawaiian youth on the traditions and values of American democracy.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Indian Tribal Justice Technical and Legal Assistance Act of 2000''. SEC. 2. FINDINGS. The Congress finds and declares that-- (1) there is a government-to-government relationship between the United States and Indian tribes; (2) Indian tribes are sovereign entities and are responsible for exercising governmental authority over Indian lands; (3) the rate of violent crime committed in Indian country is approximately twice the rate of violent crime committed in the United States as a whole; (4) in any community, a high rate of violent crime is a major obstacle to investment, job creation and economic growth; (5) tribal justice systems are an essential part of tribal governments and serve as important forums for ensuring the health and safety and the political integrity of tribal governments; (6) Congress and the Federal courts have repeatedly recognized tribal justice systems as the most appropriate forums for the adjudication of disputes affecting personal and property rights on Native lands; (7) enhancing tribal court systems and improving access to those systems serves the dual Federal goals of tribal political self-determination and economic self-sufficiency; (8) there is both inadequate funding and an inadequate coordinating mechanism to meet the technical and legal assistance needs of tribal justice systems and this lack of adequate technical and legal assistance funding impairs their operation; (9) tribal court membership organizations have served a critical role in providing training and technical assistance for development and enhancement of tribal justice systems; (10) Indian legal services programs, as funded partially through the Legal Services Corporation, have an established record of providing cost effective legal assistance to Indian people in tribal court forums, and also contribute significantly to the development of tribal courts and tribal jurisprudence; and (11) the provision of adequate technical assistance to tribal courts and legal assistance to both individuals and tribal courts is an essential element in the development of strong tribal court systems. SEC. 3. PURPOSES. The purposes of this Act are as follows: (1) to carry out the responsibility of the United States to Indian tribes and members of Indian tribes by ensuring access to quality technical and legal assistance. (2) To strengthen and improve the capacity of tribal court systems that address civil and criminal causes of action under the jurisdiction of Indian tribes. (3) To strengthen tribal governments and the economies of Indian tribes through the enhancement and, where appropriate, development of tribal court systems for the administration of justice in Indian country by providing technical and legal assistance services. (4) To encourage collaborative efforts between national or regional membership organizations and associations whose membership consists of judicial system personnel within tribal justice systems; non-profit entities which provide legal assistance services for Indian tribes, members of Indian tribes, and/or tribal justice systems. (5) To assist in the development of tribal judicial systems by supplementing prior congressional efforts such as the Indian Tribal Justice Act (Public Law 103-176). SEC. 4. DEFINITIONS. For purposes of this Act: (1) Attorney general.--The term ``Attorney General'' means the Attorney General of the United States. (2) Indian lands.--The term ``Indian lands'' shall include lands within the definition of ``Indian country'', as defined in section 1151 of title 18, United States Code; or ``Indian reservations'', as defined in section 3(d) of the Indian Financing Act of 1974 (25 U.S.C. 1452(d)), or section 4(10) of the Indian Child Welfare Act (25 U.S.C 1903(10)). For purposes of the preceding sentence, such section 3(d) of the Indian Financing Act shall be applied by treating the term ``former Indian reservations in Oklahoma'' as including only lands which are within the jurisdictional area of an Oklahoma Indian Tribe (as determined by the Secretary of the Interior) and are recognized by such Secretary as eligible for trust land status under part 151 of title 25, Code of Federal Regulations (as in effect on the date of enactment of this sentence). (3) Indian tribe.--The term ``Indian tribe'' means any Indian tribe, band, nation, pueblo, or other organized group or community which administers justice or plans to administer justice under its inherent authority or the authority of the United States and which is recognized as eligible for the special programs and services provided by the United States to Indian tribes because of their status as Indians. (4) Judicial personnel.--The term ``judicial personnel'' means any judge, magistrate, court counselor, court clerk, court administrator, bailiff, probation officer, officer of the court, dispute resolution facilitator, or other official, employee, or volunteer within the tribal judicial system. (5) Non-profit entities.--The term ``non-profit entity'' or ``non-profit entities'' has the meaning given that term in section 501(c)(3) of the Internal Revenue Code of 1986. (6) Office of tribal justice.--The term ``Office of Tribal Justice'' means the Office of Tribal Justice in the United States Department of Justice. (7) Tribal justice system.--The term ``tribal court'', ``tribal court system'', or ``tribal justice system'' means the entire judicial branch, and employees thereof, of an Indian tribe, including, but not limited to, traditional methods and fora for dispute resolution, trial courts, appellate courts, including inter-tribal appellate courts, alternative dispute resolution systems, and circuit rider systems, established by inherent tribunal authority whether or not they constitute a court of record. TITLE I--TRAINING AND TECHNICAL ASSISTANCE, CIVIL AND CRIMINAL LEGAL ASSISTANCE GRANTS SEC. 101. TRIBAL JUSTICE TRAINING AND TECHNICAL ASSISTANCE GRANTS. Subject to the availability of appropriations, the Attorney General, in consultation with the Office of Tribal Justice, shall award grants to national or regional membership organizations and associations whose membership consists of judicial system personnel within tribal justice systems which submit an application to the Attorney General in such form and manner as the Attorney General may prescribe to provide training and technical assistance for the development, enrichment, enhancement of tribal justice systems, or other purposes consistent with this Act. SEC. 102. TRIBAL CIVIL LEGAL ASSISTANCE GRANTS. Subject to the availability of appropriations, the Attorney General, in consultation with the Office of Tribal Justice, shall award grants to non-profit entities, as defined under section 501(c)(3) of the Internal Revenue Code of 1986, which provide legal assistance services for Indian tribes, members of Indian tribes, or tribal justice systems pursuant to Federal poverty guidelines that submit an application to the Attorney General in such form and manner as the Attorney General may prescribe for the provision of civil legal assistance to members of Indian tribes and tribal justice systems, and/ or other purposes consistent with this Act. SEC. 103. TRIBAL CRIMINAL ASSISTANCE GRANTS. Subject to the availability of appropriations, the Attorney General, in consultation with the Office of Tribal Justice, shall award grants to non-profit entities, as defined by section 501(c)(3) of the Internal Revenue Code of 1986, which provide legal assistance services for Indian tribes, members of Indian tribes, or tribal justice systems pursuant to Federal poverty guidelines that submit an application to the Attorney General in such form and manner as the Attorney General may prescribe for the provision of criminal legal assistance to members of Indian tribes and tribal justice systems, and/or other purposes consistent with this Act. Funding under this title may apply to programs, procedures, or proceedings involving adult criminal actions, juvenile delinquency actions, and/or guardian-ad-litem appointments arising out of criminal or delinquency acts. SEC. 104. NO OFFSET. No Federal agency shall offset funds made available pursuant to this Act for Indian tribal court membership organizations or Indian legal services organizations against other funds otherwise available for use in connection with technical or legal assistance to tribal justice systems or members of Indian tribes. SEC. 105. TRIBAL AUTHORITY. Nothing in this Act shall be construed to-- (1) encroach upon or diminish in any way the inherent sovereign authority of each tribal government to determine the role of the tribal justice system within the tribal government or to enact and enforce tribal laws; (2) diminish in any way the authority of tribal governments to appoint personnel; (3) impair the rights of each tribal government to determine the nature of its own legal system or the appointment of authority within the tribal government; (4) alter in any way any tribal traditional dispute resolution fora; (5) imply that any tribal justice system is an instrumentality of the United States; or (6) diminish the trust responsibility of the United States to Indian tribal governments and tribal justice systems of such governments. SEC. 106. AUTHORIZATION OF APPROPRIATIONS. For purposes of carrying out the activities under this title, there are authorized to be appropriated such sums as are necessary for fiscal years 2000 through 2004. TITLE II--INDIAN TRIBAL COURTS SEC. 201. GRANTS. (a) In General.--The Attorney General may award grants and provide technical assistance to Indian tribes to enable such tribes to carry out programs to support-- (1) the development, enhancement, and continuing operation of tribal justice systems; and (2) the development and implementation of-- (A) tribal codes and sentencing guidelines; (B) inter-tribal courts and appellate systems; (C) tribal probation services, diversion programs, and alternative sentencing provisions; (D) tribal juvenile services and multi-disciplinary protocols for child physical and sexual abuse; and (E) traditional tribal judicial practices, traditional tribal justice systems, and traditional methods of dispute resolution. (b) Consultation.--In carrying out this section, the Attorney General may consult with the Office of Tribal Justice and any other appropriate tribal or Federal officials. (c) Regulations.--The Attorney General may promulgate such regulations and guidelines as may be necessary to carry out this title. (d) Authorization of Appropriations.--For purposes of carrying out the activities under this section, there are authorized to be appropriated such sums as are necessary for fiscal years 2000 through 2004. SEC. 202. TRIBAL JUSTICE SYSTEMS. Section 201 of the Indian Tribal Justice Act (25 U.S.C. 3621) is amended-- (1) in subsection (a), by striking ``1994, 1995, 1996, 1997, 1998, 1999, and 2000'' and inserting ``2000 through 2007''; (2) in subsection (b), by striking ``1994, 1995, 1996, 1997, 1998, 1999, and 2000'' and inserting ``2000 through 2007''; (3) in subsection (c), by striking ``1994, 1995, 1996, 1997, 1998, 1999, and 2000'' and inserting ``2000 through 2007''; and (4) in subsection (d), by striking ``1994, 1995, 1996, 1997, 1998, 1999, and 2000'' and inserting ``2000 through 2007''. TITLE III--TECHNICAL AMENDMENTS TO ALASKA NATIVE CLAIMS SETTLEMENT ACT SEC. 301. ALASKA NATIVE VETERANS. Section 41 of the Alaska Native Claims Settlement Act (43 U.S.C. 1629g) is amended as follows: (1) Subsection (a)(3)(I)(4) is amended by striking ``and Reindeer'' and inserting ``or''. (2) Subsection (a)(4)(B) is amended by striking ``; and'' and inserting ``; or''. (3) Subsection (b)(1)(B)(i) is amended by striking ``June 2, 1971'' and inserting ``December 31, 1971''. (4) Subsection (b)(2) is amended by striking the matter preceding subparagraph (A) and inserting the following: ``(2) The personal representative or special administrator, appointed in an Alaska State court proceeding of the estate of a decedent who was eligible under subsection (b)(1)(A) may, for the benefit of the heirs, select an allotment if the decedent was a veteran who served in South East Asia at any time during the period beginning August 5, 1964, and ending December 31, 1971, and during that period the decedent--''. SEC. 302. LEVIES ON SETTLEMENT TRUST INTERESTS. Section 39(c) of the Alaska Native Claims Settlement Act (43 U.S.C. 1629e(c)) is amended by adding at the end the following new paragraph: ``(8) A beneficiary's interest in a settlement trust and the distributions thereon shall be subject to creditor action (including without limitation, levy attachment, pledge, lien, judgment execution, assignment, and the insolvency and bankruptcy laws) only to the extent that Settlement Common Stock and the distributions thereon are subject to such creditor action under section 7(h) of this Act.''. TITLE IV--NATIONAL LEADERSHIP SYMPOSIUM FOR AMERICAN INDIAN, ALASKAN NATIVE, AND NATIVE HAWAIIAN YOUTH SEC. 401. ADMINISTRATION OF NATIONAL LEADERSHIP SYMPOSIUM FOR AMERICAN INDIAN, ALASKAN NATIVE, AND NATIVE HAWAIIAN YOUTH. (a) In General.--There are authorized to be appropriated to the Secretary of Education for the Washington Workshops Foundation $2,200,000 for administration of a national leadership symposium for American Indian, Alaskan Native, and Native Hawaiian youth on the traditions and values of American democracy. (b) Content of Symposium.--The symposium administered under subsection (a) shall-- (1) be comprised of youth seminar programs which study the workings and practices of American national government in Washington, DC, to be held in conjunction with the opening of the Smithsonian National Museum of the American Indian; and (2) envision the participation and enhancement of American Indian, Alaskan Native, and Native Hawaiian youth in the American political process by interfacing in the first-hand operations of the United States Government. Speaker of the House of Representatives. Vice President of the United States and President of the Senate.[/INST]Prohibits Federal agencies from offsetting funds made available for Indian tribal court membership organizations or Indian legal services organizations against other funds otherwise available for use in connection with technical or legal assistance to tribal justice systems or members. Authorizes appropriations. Title II: Indian Tribal Courts - Authorizes the Attorney General to award grants and provide technical assistance to enable Indian tribes to carry out programs to support: (1) the development, enhancement, and continuing operation of tribal justice systems; and (2) the development and implementation of tribal codes and sentencing guidelines; inter-tribal courts and appellate systems; tribal probation services, diversion programs, and alternative sentencing provisions; tribal juvenile services and multi-disciplinary protocols for child physical and sexual abuse; and traditional tribal judicial practices, tribal justice systems, and methods of dispute resolution. Authorizes appropriations. Amends the Indian Tribal Justice Act to extend the authorization of appropriations relating to tribal justice systems through FY 2007. Title III: Technical Amendments to Alaska Native Claims Settlement Act - Amends the Alaska Native Claims Settlement Act to make technical amendments to provisions regarding open season for allotments for certain Alaska Native veterans. Revises eligibility requirements to make a veteran eligible for an allotment if the veteran served at least six months between January 1, 1969, and December 31, 1971 (currently, June 2, 1971), and meets other existing requirements. Changes provisions regarding the authority of a personal representative of a decedent to select an allotment to authorize such representative or a special administrator appointed in an Alaska State court to select an allotment if the decedent was a veteran who served in Southeast Asia at any time during August 5, 1964, and December 31, 1971, and during such period: (1) was killed in action; (2) was wounded in action and died as a consequence of the wound; or (3) died while a prisoner of war. (Current law allows personal representatives to select such allotments if, between January 1, 1969, and December 31, 1971, one of such events occurred with respect to the decedent.) Subjects a beneficiary's interest in a settlement trust and the distributions thereon to creditor action only to the extent that Settlement Common Stock and related distributions are subject to such action under the Act. Title IV: National Leadership Symposium For American Indian, Alaskan Native, and Native Hawaiian Youth - Authorizes appropriations to the Secretary of Education for the Washington Workshops Foundation for administration of a national leadership symposium for American Indian, Alaskan Native, and Native Hawaiian youth on the traditions and values of American democracy.</s>

although numerous progresses were made , the principal limitation of allogeneic hematopoietic stem cell transplantation ( hsct ) except relapse remains the transplant - related mortality ( trm ) . in addition to graft - versus - host disease ( gvhd ) , infections contribute to trm in many patients . infections occur rapidly after transplantation during the immunosuppressed period , which is a consequence of conditioning regimen , serotherapy , progressive reconstitution of immune system , and administration of immunosuppressive agents . besides fungal and bacterial infections , there is also a risk of reactivation and viral infection . barr virus ( ebv ) , cytomegalovirus ( cmv ) , and adenovirus ( adv ) are the most important in this setting . in severely immunocompromised patient , adv causes severe respiratory disease , hepatitis , colitis , encephalitis , pancreatitis , hemorrhagic cystitis , and keratoconjunctivitis 13 . disseminated adv disease is the most common presentation of the disease in allogeneic hsct patients 15 . adv infection is more frequent in the pediatric population and risks factors for development of this infection include gvhd and the use of immunosuppressive agents 16 . we describe herein a case of an adult patient presenting , 5 months after haplo - identical allogeneic hsct , with an isolated fulminant hepatitis due to adv . a 27-year - old woman presented with acute myeloblastic leukemia ( fab 6 ) secondary to myelodysplastic syndrome in august 2012 . on diagnosis , the karyotype was normal ; in molecular biology , there were wt1 + , a single mutation of cebpa ( mutation tad1 from cebpa ) , and no mutation of nmp1 . , she received two cycles of high - dose ara - c associated with pegfilgrastim . she relapsed on april 2014 and she received ara - c and idarubicine as salvage therapy . the patient was a single child and a search for unrelated hla - identical donor was started at the time of relapse . no hla - identical unrelated donor was identified after 12 weeks of research and a haplo - identical allogeneic hsct from her mother was scheduled . the conditioning regimen was an association of fludarabine , cyclophosphamide , busulfan , antithymocyte globulin , and cyclophosphamide post graft infusion 7 . the gvhd prophylaxis consisted on the association of tacrolimus ( tac ) and mycophenolate mofetil ( mmf ) 7 . the stem cell source was peripheral blood stem cells ( pbsc ) with 4.32 10e6 cd34+/kg . the recipient was cmv+ , hsv+ , hhv6 + , toxo+ , ebv+ , and vzv+ . the transplantation was not complicated except for the beginning of sinusoidal occlusive syndrome ( sos ) treated with diuretics and ursodeoxycholic acid ( the dosage reached was 750 mg three times a day ) . at day 21 , tac was stopped as she developed schizocytes , and mmf was continued alone with a progressive tapering with an aim to stop at 6 months after transplantation . hematological recuperation occurred on day 18 with a chimerism of 100% donor on both peripheral blood ( pb ) and bone marrow ( bm ) . she was discharged on day 27 after transplantation . during the first three months of follow - up at outpatient clinic , ebv , hhv6 , toxoplasmosis , her posttransplantation course was characterized by cmv reactivation at day 56 and she was treated with valgancyclovir ( one box obtained from compassionate use of the belgian hematopoietic society ( bhs ) program ) during for 6 weeks . at routine follow - up of 3 months after transplantation , there was no evidence of relapse ; the chimerism was 100% donor on both pb and bm . cd3 count:16 10e3/mm , cd4 count : 4 10e3/mm , cd8 count : 12 10e3/mm with a cd4:cd8 ratio of 0.33 ; igg : 9.07 g / l , iga 0.59 g / l and igm 0.08 g / l ; hg 8.1 g / dl , white cells ( wc ) count : 2.0 10e3/mm with neutro 1.61 10e3/mm , and platelets count : 89 10e3/mm . we decided on account of these results , to collect donor lymphocytes in case of new cmv reactivation 11 . after 3 months of follow - up , we continued to watch the pcr for cmv in blood every week . a second cmv reactivation occurred on day 121 and the patient was treated with valgancyclovir ( two boxes were obtained in the compassionate use of bhs program ) , but the dose had to be reduced after 1 week as she developed severe toxic pancytopenia ( hg : 7.0 g / dl , neutro : 0.5 granulocyte - colony stimulating factor ( g - csf ) was started three times a week and she received serum immunoglobulin weekly as supportive care . a donor lymphocyte injection ( dli ) of 1 10e5 cd3+/kg was administrated on day 134 to improve the immune antiviral response . three weeks after the dli , she was admitted in the hematological department with fever ( 38.5 ) , nausea , vomiting , loss of weight , loss of appetite , and severe oral candidiasis . her blood tests showed hg : 9.1 g / dl , wc : 2.7 10e3/mm , plat : 56 10e3/mm , crp : 86 mg / l , na : 135 mmol / l , k : 3.0 mmol / l , protein : 67 g / l , creatinine : 1.06 mg / dl , t bili : 0.2 mg / dl , d bili < 0.1 mg / dl , ast : 228 u / l , alt : 136 u / l , alp : 105 u / l , and gamma gt 75 u / l . posaconazole was stopped because a toxic cause was suspected and ursodeoxycholic acid for a first time was reintroduced with an improvement in hepatic test in for a first time . a gastric fibroscopy with biopsies was performed to search gvhd . within 48 h of admission , she developed diarrhea . bacteriological , viral , and fungal stool analyses were performed and ceftazidim was replaced empirically by tazocillin and metronidazole . mmf was discontinued and a short course of steroids was started . at this time , foscavir was started to replace valgancyclovir because the absorption of the medication was not optimal due to diarrhea . during hospitalization , cmv pcr there is no evidence of gvhd on gastric biopsies and oral candidiasis secondary to candida albicans was confirmed . chest , abdominal , and pelvic ct showed several large hypodense lesions in the right liver with confluence ( fig.1 ) . a liver biopsy was scheduled but postponed because she developed a sepsis with staphylococcus hominis in blood cultures on port at day 148 . the diarrhea stopped without evidence of gvhd and the dose of steroids was rapidly decreased . at day 154 , she presented a rash on 2025% of corporeal surface and profuse diarrhea ( > 1 l/24 h ) , biopsies of gut and skin were realized and the steroids were reached to 2 mg / kg / day for 4 days . within 3 days , she developed hepatomegaly with pain , ascitis , edema , and fever reaching 40c . at day 158 , the blood test showed pancytopenia ( with severe neutropenia despite g - csf ) , severe hepatic cytolysis , and cholestasis ( table1 ) . cmv , ebv , hhv6 , toxoplasmosis , adenovirus , hbv , and hcv pcr were realized in blood samples . a bm aspiration was been realized to search for haemophagocytosis ( because she developed a rash associated with pancytopenia , she had a cmv reactivation , elevation of ferritine level , and severe perturbation of hepatic tests ) 12 . there was no evidence of haemophagocytosis or viral infection on bm but there were signs of myelotoxicity due to drug toxicity . at day 159 , a liver biopsy was obtained by transjugular approach , after that , she developed disseminated intravascular coagulation with continued bleeding in jugular vein . the patient died from hepatic failure , 2 days later in the intensive care department despite a maximum supportive care . seven days after her death , we obtained the results from viral pcr on blood and biopsies . there was no evidence of viral infection or gvhd on gut and skin biopsies but the pcr for adv was positive . values of liver tests ast ( u / l ) ; alt ( u / l ) ; ldh ( u / l ) ; alp ( u / l ) ; gamma gt ( u / l ) ; total bilirubin ( mg / dl ) ; direct bilirubin ( mg / dl ) ; albumin ( g / dl ) . ct of abdomen shows several hypodense lesions in the right liver with confluence into a single lesion ( 10 6 cm ) . the liver biopsy showed a patchy necrosis in the perivenular , parenchyma , and periportal areas . around the necrotic areas , many hepatocytes showed nuclear inclusion bodies . . therefore , we conclude the pathological diagnosis as a confluent hepatic necrosis due to adenovirus infection ( fig.2 ) . concerning the macrophage activation syndrome , there were some macrophages showing hemophagocytosis , but in very limited number , insufficient to diagnose hemophagocytosis . many hepatocytes show nuclear inclusion bodies , which are positive for adenovirus immunohistochemistry ( hematoxylin and eosin staining , insert : adenovirus immunohistochemistry ) . hepatitis has been previously reported as part of systemic adenovirus infections where other organs are more seriously affected . death from isolated hepatitis with hepatic failure is rare in adult after allogeneic hsct and < 10 cases are described in medical literature . this case shows that 5 months after haploidentical allogeneic hsct , our patient remains deeply immunosuppressed despite one injection of donor lymphocytes . the differential diagnosis was very difficult because gvhd and drug toxicity were also suspected ; moreover , the result from the adenovirus pcr in blood was not rapidly available ( 7 days in this case ) to start an appropriate treatment . the lack of rapid diagnosis lead to recommend to check very regularly adenovirus pcr in haplo - identical allogeneic hsct patients until complete immune reconstitution in the aim to start rapidly a pre - emptive treatment in case of reactivation or infection . written informed consent was obtained from the next of kin of the patient for publication of this case report and any accompanying images .

key clinical messagethe principal limitation of allogeneic hematopoietic stem cell transplantation except relapse remains the transplant - related mortality ( trm ) . in addition to graft - versus - host disease ( gvhd ) , infections contribute to trm in many patients . we describe herein a case of an adult patient presenting 5 months after haplo - identical transplantation an isolated fulminant hepatitis due to adenovirus .

<s>[INST]although numerous progresses were made , the principal limitation of allogeneic hematopoietic stem cell transplantation ( hsct ) except relapse remains the transplant - related mortality ( trm ) . in addition to graft - versus - host disease ( gvhd ) , infections contribute to trm in many patients . infections occur rapidly after transplantation during the immunosuppressed period , which is a consequence of conditioning regimen , serotherapy , progressive reconstitution of immune system , and administration of immunosuppressive agents . besides fungal and bacterial infections , there is also a risk of reactivation and viral infection . barr virus ( ebv ) , cytomegalovirus ( cmv ) , and adenovirus ( adv ) are the most important in this setting . in severely immunocompromised patient , adv causes severe respiratory disease , hepatitis , colitis , encephalitis , pancreatitis , hemorrhagic cystitis , and keratoconjunctivitis 13 . disseminated adv disease is the most common presentation of the disease in allogeneic hsct patients 15 . adv infection is more frequent in the pediatric population and risks factors for development of this infection include gvhd and the use of immunosuppressive agents 16 . we describe herein a case of an adult patient presenting , 5 months after haplo - identical allogeneic hsct , with an isolated fulminant hepatitis due to adv . a 27-year - old woman presented with acute myeloblastic leukemia ( fab 6 ) secondary to myelodysplastic syndrome in august 2012 . on diagnosis , the karyotype was normal ; in molecular biology , there were wt1 + , a single mutation of cebpa ( mutation tad1 from cebpa ) , and no mutation of nmp1 . , she received two cycles of high - dose ara - c associated with pegfilgrastim . she relapsed on april 2014 and she received ara - c and idarubicine as salvage therapy . the patient was a single child and a search for unrelated hla - identical donor was started at the time of relapse . no hla - identical unrelated donor was identified after 12 weeks of research and a haplo - identical allogeneic hsct from her mother was scheduled . the conditioning regimen was an association of fludarabine , cyclophosphamide , busulfan , antithymocyte globulin , and cyclophosphamide post graft infusion 7 . the gvhd prophylaxis consisted on the association of tacrolimus ( tac ) and mycophenolate mofetil ( mmf ) 7 . the stem cell source was peripheral blood stem cells ( pbsc ) with 4.32 10e6 cd34+/kg . the recipient was cmv+ , hsv+ , hhv6 + , toxo+ , ebv+ , and vzv+ . the transplantation was not complicated except for the beginning of sinusoidal occlusive syndrome ( sos ) treated with diuretics and ursodeoxycholic acid ( the dosage reached was 750 mg three times a day ) . at day 21 , tac was stopped as she developed schizocytes , and mmf was continued alone with a progressive tapering with an aim to stop at 6 months after transplantation . hematological recuperation occurred on day 18 with a chimerism of 100% donor on both peripheral blood ( pb ) and bone marrow ( bm ) . she was discharged on day 27 after transplantation . during the first three months of follow - up at outpatient clinic , ebv , hhv6 , toxoplasmosis , her posttransplantation course was characterized by cmv reactivation at day 56 and she was treated with valgancyclovir ( one box obtained from compassionate use of the belgian hematopoietic society ( bhs ) program ) during for 6 weeks . at routine follow - up of 3 months after transplantation , there was no evidence of relapse ; the chimerism was 100% donor on both pb and bm . cd3 count:16 10e3/mm , cd4 count : 4 10e3/mm , cd8 count : 12 10e3/mm with a cd4:cd8 ratio of 0.33 ; igg : 9.07 g / l , iga 0.59 g / l and igm 0.08 g / l ; hg 8.1 g / dl , white cells ( wc ) count : 2.0 10e3/mm with neutro 1.61 10e3/mm , and platelets count : 89 10e3/mm . we decided on account of these results , to collect donor lymphocytes in case of new cmv reactivation 11 . after 3 months of follow - up , we continued to watch the pcr for cmv in blood every week . a second cmv reactivation occurred on day 121 and the patient was treated with valgancyclovir ( two boxes were obtained in the compassionate use of bhs program ) , but the dose had to be reduced after 1 week as she developed severe toxic pancytopenia ( hg : 7.0 g / dl , neutro : 0.5 granulocyte - colony stimulating factor ( g - csf ) was started three times a week and she received serum immunoglobulin weekly as supportive care . a donor lymphocyte injection ( dli ) of 1 10e5 cd3+/kg was administrated on day 134 to improve the immune antiviral response . three weeks after the dli , she was admitted in the hematological department with fever ( 38.5 ) , nausea , vomiting , loss of weight , loss of appetite , and severe oral candidiasis . her blood tests showed hg : 9.1 g / dl , wc : 2.7 10e3/mm , plat : 56 10e3/mm , crp : 86 mg / l , na : 135 mmol / l , k : 3.0 mmol / l , protein : 67 g / l , creatinine : 1.06 mg / dl , t bili : 0.2 mg / dl , d bili < 0.1 mg / dl , ast : 228 u / l , alt : 136 u / l , alp : 105 u / l , and gamma gt 75 u / l . posaconazole was stopped because a toxic cause was suspected and ursodeoxycholic acid for a first time was reintroduced with an improvement in hepatic test in for a first time . a gastric fibroscopy with biopsies was performed to search gvhd . within 48 h of admission , she developed diarrhea . bacteriological , viral , and fungal stool analyses were performed and ceftazidim was replaced empirically by tazocillin and metronidazole . mmf was discontinued and a short course of steroids was started . at this time , foscavir was started to replace valgancyclovir because the absorption of the medication was not optimal due to diarrhea . during hospitalization , cmv pcr there is no evidence of gvhd on gastric biopsies and oral candidiasis secondary to candida albicans was confirmed . chest , abdominal , and pelvic ct showed several large hypodense lesions in the right liver with confluence ( fig.1 ) . a liver biopsy was scheduled but postponed because she developed a sepsis with staphylococcus hominis in blood cultures on port at day 148 . the diarrhea stopped without evidence of gvhd and the dose of steroids was rapidly decreased . at day 154 , she presented a rash on 2025% of corporeal surface and profuse diarrhea ( > 1 l/24 h ) , biopsies of gut and skin were realized and the steroids were reached to 2 mg / kg / day for 4 days . within 3 days , she developed hepatomegaly with pain , ascitis , edema , and fever reaching 40c . at day 158 , the blood test showed pancytopenia ( with severe neutropenia despite g - csf ) , severe hepatic cytolysis , and cholestasis ( table1 ) . cmv , ebv , hhv6 , toxoplasmosis , adenovirus , hbv , and hcv pcr were realized in blood samples . a bm aspiration was been realized to search for haemophagocytosis ( because she developed a rash associated with pancytopenia , she had a cmv reactivation , elevation of ferritine level , and severe perturbation of hepatic tests ) 12 . there was no evidence of haemophagocytosis or viral infection on bm but there were signs of myelotoxicity due to drug toxicity . at day 159 , a liver biopsy was obtained by transjugular approach , after that , she developed disseminated intravascular coagulation with continued bleeding in jugular vein . the patient died from hepatic failure , 2 days later in the intensive care department despite a maximum supportive care . seven days after her death , we obtained the results from viral pcr on blood and biopsies . there was no evidence of viral infection or gvhd on gut and skin biopsies but the pcr for adv was positive . values of liver tests ast ( u / l ) ; alt ( u / l ) ; ldh ( u / l ) ; alp ( u / l ) ; gamma gt ( u / l ) ; total bilirubin ( mg / dl ) ; direct bilirubin ( mg / dl ) ; albumin ( g / dl ) . ct of abdomen shows several hypodense lesions in the right liver with confluence into a single lesion ( 10 6 cm ) . the liver biopsy showed a patchy necrosis in the perivenular , parenchyma , and periportal areas . around the necrotic areas , many hepatocytes showed nuclear inclusion bodies . . therefore , we conclude the pathological diagnosis as a confluent hepatic necrosis due to adenovirus infection ( fig.2 ) . concerning the macrophage activation syndrome , there were some macrophages showing hemophagocytosis , but in very limited number , insufficient to diagnose hemophagocytosis . many hepatocytes show nuclear inclusion bodies , which are positive for adenovirus immunohistochemistry ( hematoxylin and eosin staining , insert : adenovirus immunohistochemistry ) . hepatitis has been previously reported as part of systemic adenovirus infections where other organs are more seriously affected . death from isolated hepatitis with hepatic failure is rare in adult after allogeneic hsct and < 10 cases are described in medical literature . this case shows that 5 months after haploidentical allogeneic hsct , our patient remains deeply immunosuppressed despite one injection of donor lymphocytes . the differential diagnosis was very difficult because gvhd and drug toxicity were also suspected ; moreover , the result from the adenovirus pcr in blood was not rapidly available ( 7 days in this case ) to start an appropriate treatment . the lack of rapid diagnosis lead to recommend to check very regularly adenovirus pcr in haplo - identical allogeneic hsct patients until complete immune reconstitution in the aim to start rapidly a pre - emptive treatment in case of reactivation or infection . written informed consent was obtained from the next of kin of the patient for publication of this case report and any accompanying images . [/INST]key clinical messagethe principal limitation of allogeneic hematopoietic stem cell transplantation except relapse remains the transplant - related mortality ( trm ) . in addition to graft - versus - host disease ( gvhd ) , infections contribute to trm in many patients . we describe herein a case of an adult patient presenting 5 months after haplo - identical transplantation an isolated fulminant hepatitis due to adenovirus .</s>

robotic manipulation of deformable objects is a challenging problem especially because of the complexity of the many different ways an object can deform . searching within such a high dimensional state space makes it difficult to recognize , track , and manipulate deformable objects . in this paper we present a feed - forward , model - driven approach to address this challenge , using a pre - computed , simulated database of deformable thin - shell object models , where the bending of the mesh models is predominant @xcite . the models are detailed , robust , and easy to construct , and using a physics engine one can accurately predict the behavior of the objects in simulation , which can then be applied to a real physical setting . this work bridges the gap between the simulation world and the real world . the predictive , feed - forward , model - driven approach takes advantages of the simulation and generates a large number of instances for learning approaches , which not only alleviates the burden of data collection , which can be efficiently done in simulation , but also makes adaptation of the methods to other application areas easier and faster . mesh models of common deformable garments are simulated with the garments picked up in multiple different poses under gravity , and stored in a database for fast and efficient retrieval . to validate this approach , we developed a comprehensive pipeline for manipulating clothing as in a typical laundry task . first , the database is used to estimate categories and poses of garments in arbitrary positions . a fully featured 3d volumetric model of the garment is constructed in real - time and volumetric features are then used to obtain the most similar model in the database to predict the object category and pose . second , the database can significantly benefit the manipulation of deformable objects via non - rigid registration , providing accurate correspondences between the reconstructed object model and the database models . third , the accurate model simulation can also be used to optimize the trajectories for manipulation of deformable objects , such as the folding of garments . in addition , the simulation can be easily adapted to new garment models . extensive experimental results are shown for the tasks above using a variety of different clothing . [ cols="^ " , ] in this paper , we introduced a simulation database of common deformable garments to facilitate recognition and manipulation . the database contains five different garments within three categories : sweater , pants , and shorts . each garment is fully simulated with a number of depth images and 3d mesh models for all the semantic labeled grasping points . we demonstrated three applications of using the database to improve the recognition and the manipulation of deformable objects . the first is training from the simulated mesh models to recognizing an unknown object by 3d shape - based features . the second is applying the simulated mesh model to guide the iterative regrasping of the garment using both rigid and non - rigid registrations . the third is importing the mesh model into the simulator and computing optimized trajectories for manipulation of the deformable objects . ee extensively tested the three applications with designed experiments such as garment recognition via pick up , unfolding the garment to a known desired state and laying flat , and using pe - computed folding plans to fold it using a novel trajecotry optimization method that prevents common folding errors . we have addressed all the phases of the pipeline in figure [ fig : entire_pipeline ] individually . however , there are still some system and hardware issues that prevent the system from being a completely seamless pipeline . these are due to 1 ) kinematic constraints on the baxter robot which limits its ability to work with larger garments on a normal size table , and 2 ) our need to manually mount the iron on the robot hand for the ironing task . while the focus of our work has been on clothing , we want to underline the point that model - driven , feed forward prediction can work well in complex environments with many unknown states . while we have not yet attempted this , we believe that the ideas in this paper can be ported to similar domains such as food handling ( soft deformable objects " ) and articulated rigid objects that have multiple kinematic states . we d like to thank j. weisz , j. varley , and r. ying for many discussions , p. m. lopez for the help of folding plan . we d also like to thank nvidia corporation , and intel corporation for the hardware support . this material is based upon work supported by the national science foundation under grant no . 1217904 . e. grinspun , a. n. hirani , m. desbrun , and p. schrder . discrete shells . in _ proceedings of the 2003 acm siggraph / eurographics symposium on computer animation _ , sca 03 , pages 6267 , aire - la - ville , switzerland , switzerland , 2003 . eurographics association . isbn 1 - 58113 - 659 - 5 . y h r.tsai . rapid and accurate computation of the distance function using grids . _ journal of computational physics _ , 1780 ( 1):0 175 195 , 2002 . issn 0021 - 9991 . doi : http://dx.doi.org/10.1006/jcph.2002.7028 . t - h - l le , m. jilich , a. landini , m. zoppi , d. zlatanov , and r. molfino . on the development of a specialized flexible gripper for garment handling . _ journal of automation and control engineering _ , 10 ( 3 ) , 2013 . h. li , r. w. sumner , and m. pauly . global correspondence optimization for non - rigid registration of depth scans . in _ proceedings of the symposium on geometry processing _ , sgp 08 , pages 14211430 , aire - la - ville , switzerland , switzerland , 2008 . eurographics association . r. a. newcombe , a. j. davison , s. izadi , p. kohli , o. hilliges , j. shotton , d. molyneaux , s. hodges , d. kim , and a. fitzgibbon . kinectfusion : real - time dense surface mapping and tracking . in _ ismar _ , pages 127136 , 2011 . g. k. l. tam , z - q cheng , y - k lai , f. c. langbein , y liu , d. marshall , r.r . martin , x - f sun , and p.l . rosin . registration of 3d point clouds and meshes : a survey from rigid to nonrigid . _ visualization and computer graphics , ieee transactions on _ , 190 ( 7):0 11991217 , july 2013 . issn 1077 - 2626 . doi : 10.1109/tvcg.2012.310 .

robotic manipulation of deformable objects is a difficult problem especially because of the complexity of the many different ways an object can deform . searching such a high dimensional state space makes it difficult to recognize , track , and manipulate deformable objects . in this paper , we introduce a _ predictive , model - driven _ approach to address this challenge , using a pre - computed , simulated database of deformable object models . mesh models of common deformable garments are simulated with the garments picked up in multiple different poses under gravity , and stored in a database for fast and efficient retrieval . to validate this approach , we developed a comprehensive pipeline for manipulating clothing as in a typical laundry task . first , the database is used for category and pose estimation for a garment in an arbitrary position . a fully featured 3d model of the garment is constructed in real - time and volumetric features are then used to obtain the most similar model in the database to predict the object category and pose . second , the database can significantly benefit the manipulation of deformable objects via non - rigid registration , providing accurate correspondences between the reconstructed object model and the database models . third , the accurate model simulation can also be used to optimize the trajectories for manipulation of deformable objects , such as the folding of garments . extensive experimental results are shown for the tasks above using a variety of different clothing .

<s>[INST]robotic manipulation of deformable objects is a challenging problem especially because of the complexity of the many different ways an object can deform . searching within such a high dimensional state space makes it difficult to recognize , track , and manipulate deformable objects . in this paper we present a feed - forward , model - driven approach to address this challenge , using a pre - computed , simulated database of deformable thin - shell object models , where the bending of the mesh models is predominant @xcite . the models are detailed , robust , and easy to construct , and using a physics engine one can accurately predict the behavior of the objects in simulation , which can then be applied to a real physical setting . this work bridges the gap between the simulation world and the real world . the predictive , feed - forward , model - driven approach takes advantages of the simulation and generates a large number of instances for learning approaches , which not only alleviates the burden of data collection , which can be efficiently done in simulation , but also makes adaptation of the methods to other application areas easier and faster . mesh models of common deformable garments are simulated with the garments picked up in multiple different poses under gravity , and stored in a database for fast and efficient retrieval . to validate this approach , we developed a comprehensive pipeline for manipulating clothing as in a typical laundry task . first , the database is used to estimate categories and poses of garments in arbitrary positions . a fully featured 3d volumetric model of the garment is constructed in real - time and volumetric features are then used to obtain the most similar model in the database to predict the object category and pose . second , the database can significantly benefit the manipulation of deformable objects via non - rigid registration , providing accurate correspondences between the reconstructed object model and the database models . third , the accurate model simulation can also be used to optimize the trajectories for manipulation of deformable objects , such as the folding of garments . in addition , the simulation can be easily adapted to new garment models . extensive experimental results are shown for the tasks above using a variety of different clothing . [ cols="^ " , ] in this paper , we introduced a simulation database of common deformable garments to facilitate recognition and manipulation . the database contains five different garments within three categories : sweater , pants , and shorts . each garment is fully simulated with a number of depth images and 3d mesh models for all the semantic labeled grasping points . we demonstrated three applications of using the database to improve the recognition and the manipulation of deformable objects . the first is training from the simulated mesh models to recognizing an unknown object by 3d shape - based features . the second is applying the simulated mesh model to guide the iterative regrasping of the garment using both rigid and non - rigid registrations . the third is importing the mesh model into the simulator and computing optimized trajectories for manipulation of the deformable objects . ee extensively tested the three applications with designed experiments such as garment recognition via pick up , unfolding the garment to a known desired state and laying flat , and using pe - computed folding plans to fold it using a novel trajecotry optimization method that prevents common folding errors . we have addressed all the phases of the pipeline in figure [ fig : entire_pipeline ] individually . however , there are still some system and hardware issues that prevent the system from being a completely seamless pipeline . these are due to 1 ) kinematic constraints on the baxter robot which limits its ability to work with larger garments on a normal size table , and 2 ) our need to manually mount the iron on the robot hand for the ironing task . while the focus of our work has been on clothing , we want to underline the point that model - driven , feed forward prediction can work well in complex environments with many unknown states . while we have not yet attempted this , we believe that the ideas in this paper can be ported to similar domains such as food handling ( soft deformable objects " ) and articulated rigid objects that have multiple kinematic states . we d like to thank j. weisz , j. varley , and r. ying for many discussions , p. m. lopez for the help of folding plan . we d also like to thank nvidia corporation , and intel corporation for the hardware support . this material is based upon work supported by the national science foundation under grant no . 1217904 . e. grinspun , a. n. hirani , m. desbrun , and p. schrder . discrete shells . in _ proceedings of the 2003 acm siggraph / eurographics symposium on computer animation _ , sca 03 , pages 6267 , aire - la - ville , switzerland , switzerland , 2003 . eurographics association . isbn 1 - 58113 - 659 - 5 . y h r.tsai . rapid and accurate computation of the distance function using grids . _ journal of computational physics _ , 1780 ( 1):0 175 195 , 2002 . issn 0021 - 9991 . doi : http://dx.doi.org/10.1006/jcph.2002.7028 . t - h - l le , m. jilich , a. landini , m. zoppi , d. zlatanov , and r. molfino . on the development of a specialized flexible gripper for garment handling . _ journal of automation and control engineering _ , 10 ( 3 ) , 2013 . h. li , r. w. sumner , and m. pauly . global correspondence optimization for non - rigid registration of depth scans . in _ proceedings of the symposium on geometry processing _ , sgp 08 , pages 14211430 , aire - la - ville , switzerland , switzerland , 2008 . eurographics association . r. a. newcombe , a. j. davison , s. izadi , p. kohli , o. hilliges , j. shotton , d. molyneaux , s. hodges , d. kim , and a. fitzgibbon . kinectfusion : real - time dense surface mapping and tracking . in _ ismar _ , pages 127136 , 2011 . g. k. l. tam , z - q cheng , y - k lai , f. c. langbein , y liu , d. marshall , r.r . martin , x - f sun , and p.l . rosin . registration of 3d point clouds and meshes : a survey from rigid to nonrigid . _ visualization and computer graphics , ieee transactions on _ , 190 ( 7):0 11991217 , july 2013 . issn 1077 - 2626 . doi : 10.1109/tvcg.2012.310 .[/INST] robotic manipulation of deformable objects is a difficult problem especially because of the complexity of the many different ways an object can deform . searching such a high dimensional state space makes it difficult to recognize , track , and manipulate deformable objects . in this paper , we introduce a _ predictive , model - driven _ approach to address this challenge , using a pre - computed , simulated database of deformable object models . mesh models of common deformable garments are simulated with the garments picked up in multiple different poses under gravity , and stored in a database for fast and efficient retrieval . to validate this approach , we developed a comprehensive pipeline for manipulating clothing as in a typical laundry task . first , the database is used for category and pose estimation for a garment in an arbitrary position . a fully featured 3d model of the garment is constructed in real - time and volumetric features are then used to obtain the most similar model in the database to predict the object category and pose . second , the database can significantly benefit the manipulation of deformable objects via non - rigid registration , providing accurate correspondences between the reconstructed object model and the database models . third , the accurate model simulation can also be used to optimize the trajectories for manipulation of deformable objects , such as the folding of garments . extensive experimental results are shown for the tasks above using a variety of different clothing . </s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Agency for International Development Efficiency and Effectiveness Act of 1994''. SEC. 2. REDUCTIONS IN SPENDING FOR DEVELOPMENT ASSISTANCE BY THE AGENCY FOR INTERNATIONAL DEVELOPMENT. For fiscal years 1995 through 1999, budget authority and outlays for development assistance shall be less than the CBO baseline by at least the following amounts: (1) Fiscal year 1995.--For fiscal year 1995, budget authority shall be at least $580,000,000 less and outlays shall be at least $40,000,000 less. (2) Fiscal year 1996.--For fiscal year 1996, budget authority shall be at least $600,000,000 less and outlays shall be at least $290,000,000 less. (3) Fiscal year 1997.--For fiscal year 1997, budget authority shall be at least $610,000,000 less and outlays shall be at least $430,000,000 less. (4) Fiscal year 1998.--For fiscal year 1998, budget authority shall be at least $630,000,000 less and outlays shall be at least $500,000,000 less. (5) Fiscal year 1999.--For fiscal year 1999, budget authority shall be at least $640,000,000 less and outlays shall be at least $560,000,000 less. SEC. 3. STEPS TO IMPLEMENT REDUCTIONS. (a) In General.--To achieve the budget savings provided for in section 2, the Agency for International Development shall narrow its focus and fund fewer development assistance projects and activities. This shall be accomplished-- (1) by funding only projects and activities that have objectives that are more attainable than the numerous objectives that are specified in the provisions of law in effect on the date of enactment of this Act; and (2) by funding only projects and activities that are in the countries that are most likely to benefit from such development assistance. (b) Reduction in Number of Recipient Countries.-- (1) In general.--The Agency for International Development shall target development assistance to lower income countries that have economic policies designed to encourage growth through free markets and trade, thereby reducing the number of countries that receive development assistance from that agency to approximately 60. (2) Ineligible countries.--The Agency for International Development may not provide development assistance for-- (A) middle income countries, or (B) lower income countries where development assistance has not shown results. (c) Reduction in Number of Objectives.-- (1) In general.--The Agency for International Development may provide development assistance only for projects and activities that focus on alleviating poverty and promoting economic development. (2) Termination of housing investment guaranty program.-- Guaranties may not be issued under sections 221 and 222 of the Foreign Assistance Act of 1961 after September 30, 1994. (3) Transfer of responsibility for other programs to other agencies.--(A) The President shall transfer responsibility for administering all development assistance programs that have an objective other than alleviating poverty and promoting economic development from the Agency for International Development to an agency of the United States Government whose mission is closer to that objective. (B) In carrying out subparagraph (B), the President-- (i) shall transfer private sector activities from the Agency for International Development to the Overseas Private Investment Corporation; and (ii) shall transfer responsibility for environmental protection activities in developing countries to the Environmental Protection Agency. (4) Transferred programs.--(A) The head of each agency to which responsibility for a program is transferred pursuant to paragraph (3) shall determine, nothwithstanding any other provision of law-- (i) which such programs shall be continued, and (ii) what policies and authorities shall be applicable to any such program that is continued. (B) Programs which are transferred from the Agency for International Development to another agency pursuant to paragraph (3) and continued pursuant to subparagraph (A)(i) of this paragraph shall be carried out by that agency with funds appropriated for that agency rather than with development assistance funds or other funds in budget function 150 (international affairs). (d) Existing Provisions Superseded.--To the extent necessary to achieve the budget savings provided for in section 2, this section supersedes provisions of law enacted prior to the date of enactment of this Act that would otherwise be applicable to development assistance provided by the Agency for International Development. (e) Effective Date.--This section shall be effective as of October 1, 1994. SEC. 4. DEFINITIONS. As used in this Act-- (1) the term ``CBO baseline'' means the baseline budget projections used by the Congressional Budget Office in preparing its February 1993 reported entitled ``Reducing the Deficit: Spending and Revenue Options'', which was submitted to the Committee on the Budget of the House of Representatives and the Committee on the Budget of the Senate pursuant to section 202(f) of the Congressional Budget and Impoundment Control Act of 1974; and (2) the term ``development assistance'' means assistance under chapter 1 of part I of the Foreign Assistance Act of 1961 (relating to the functional development assistance accounts) and assistance under chapter 10 of that part (relating to the Development Fund for Africa). HR 3775 IH

Agency for International Development Efficiency and Effectiveness Act of 1994 - Reduces budget authority and outlays for development assistance by specified amounts below the Congressional Budget Office baseline in FY 1995 through 1999. Requires the Agency for International Development (AID) to narrow its focus and fund fewer development assistance projects to achieve such budget savings. Directs AID to target assistance to lower income countries that have economic policies designed to encourage growth through free markets and trade, thereby reducing the number of countries that receive development assistance to approximately 60. Bars development assistance for middle income countries or lower income countries where such assistance has not shown results. Permits AID to provide assistance only for projects that focus on alleviating poverty and promoting economic development. Terminates the housing investment guaranty program under the Foreign Assistance Act of 1961 after September 30, 1994. Requires the President to transfer responsibility for administering all development assistance programs that have an objective other than alleviating poverty and promoting economic development from AID to a Government agency whose mission is closer to the objective. Transfers: (1) private sector activities to the Overseas Private Investment Corporation; and (2) environmental protection activities in developing countries to the Environmental Protection Agency. Requires transferred programs to be carried out with funds appropriated for that agency rather than with development assistance or international affairs program funds. Provides that this Act supersedes existing law applicable to AID development assistance.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Agency for International Development Efficiency and Effectiveness Act of 1994''. SEC. 2. REDUCTIONS IN SPENDING FOR DEVELOPMENT ASSISTANCE BY THE AGENCY FOR INTERNATIONAL DEVELOPMENT. For fiscal years 1995 through 1999, budget authority and outlays for development assistance shall be less than the CBO baseline by at least the following amounts: (1) Fiscal year 1995.--For fiscal year 1995, budget authority shall be at least $580,000,000 less and outlays shall be at least $40,000,000 less. (2) Fiscal year 1996.--For fiscal year 1996, budget authority shall be at least $600,000,000 less and outlays shall be at least $290,000,000 less. (3) Fiscal year 1997.--For fiscal year 1997, budget authority shall be at least $610,000,000 less and outlays shall be at least $430,000,000 less. (4) Fiscal year 1998.--For fiscal year 1998, budget authority shall be at least $630,000,000 less and outlays shall be at least $500,000,000 less. (5) Fiscal year 1999.--For fiscal year 1999, budget authority shall be at least $640,000,000 less and outlays shall be at least $560,000,000 less. SEC. 3. STEPS TO IMPLEMENT REDUCTIONS. (a) In General.--To achieve the budget savings provided for in section 2, the Agency for International Development shall narrow its focus and fund fewer development assistance projects and activities. This shall be accomplished-- (1) by funding only projects and activities that have objectives that are more attainable than the numerous objectives that are specified in the provisions of law in effect on the date of enactment of this Act; and (2) by funding only projects and activities that are in the countries that are most likely to benefit from such development assistance. (b) Reduction in Number of Recipient Countries.-- (1) In general.--The Agency for International Development shall target development assistance to lower income countries that have economic policies designed to encourage growth through free markets and trade, thereby reducing the number of countries that receive development assistance from that agency to approximately 60. (2) Ineligible countries.--The Agency for International Development may not provide development assistance for-- (A) middle income countries, or (B) lower income countries where development assistance has not shown results. (c) Reduction in Number of Objectives.-- (1) In general.--The Agency for International Development may provide development assistance only for projects and activities that focus on alleviating poverty and promoting economic development. (2) Termination of housing investment guaranty program.-- Guaranties may not be issued under sections 221 and 222 of the Foreign Assistance Act of 1961 after September 30, 1994. (3) Transfer of responsibility for other programs to other agencies.--(A) The President shall transfer responsibility for administering all development assistance programs that have an objective other than alleviating poverty and promoting economic development from the Agency for International Development to an agency of the United States Government whose mission is closer to that objective. (B) In carrying out subparagraph (B), the President-- (i) shall transfer private sector activities from the Agency for International Development to the Overseas Private Investment Corporation; and (ii) shall transfer responsibility for environmental protection activities in developing countries to the Environmental Protection Agency. (4) Transferred programs.--(A) The head of each agency to which responsibility for a program is transferred pursuant to paragraph (3) shall determine, nothwithstanding any other provision of law-- (i) which such programs shall be continued, and (ii) what policies and authorities shall be applicable to any such program that is continued. (B) Programs which are transferred from the Agency for International Development to another agency pursuant to paragraph (3) and continued pursuant to subparagraph (A)(i) of this paragraph shall be carried out by that agency with funds appropriated for that agency rather than with development assistance funds or other funds in budget function 150 (international affairs). (d) Existing Provisions Superseded.--To the extent necessary to achieve the budget savings provided for in section 2, this section supersedes provisions of law enacted prior to the date of enactment of this Act that would otherwise be applicable to development assistance provided by the Agency for International Development. (e) Effective Date.--This section shall be effective as of October 1, 1994. SEC. 4. DEFINITIONS. As used in this Act-- (1) the term ``CBO baseline'' means the baseline budget projections used by the Congressional Budget Office in preparing its February 1993 reported entitled ``Reducing the Deficit: Spending and Revenue Options'', which was submitted to the Committee on the Budget of the House of Representatives and the Committee on the Budget of the Senate pursuant to section 202(f) of the Congressional Budget and Impoundment Control Act of 1974; and (2) the term ``development assistance'' means assistance under chapter 1 of part I of the Foreign Assistance Act of 1961 (relating to the functional development assistance accounts) and assistance under chapter 10 of that part (relating to the Development Fund for Africa). HR 3775 IH[/INST]Agency for International Development Efficiency and Effectiveness Act of 1994 - Reduces budget authority and outlays for development assistance by specified amounts below the Congressional Budget Office baseline in FY 1995 through 1999. Requires the Agency for International Development (AID) to narrow its focus and fund fewer development assistance projects to achieve such budget savings. Directs AID to target assistance to lower income countries that have economic policies designed to encourage growth through free markets and trade, thereby reducing the number of countries that receive development assistance to approximately 60. Bars development assistance for middle income countries or lower income countries where such assistance has not shown results. Permits AID to provide assistance only for projects that focus on alleviating poverty and promoting economic development. Terminates the housing investment guaranty program under the Foreign Assistance Act of 1961 after September 30, 1994. Requires the President to transfer responsibility for administering all development assistance programs that have an objective other than alleviating poverty and promoting economic development from AID to a Government agency whose mission is closer to the objective. Transfers: (1) private sector activities to the Overseas Private Investment Corporation; and (2) environmental protection activities in developing countries to the Environmental Protection Agency. Requires transferred programs to be carried out with funds appropriated for that agency rather than with development assistance or international affairs program funds. Provides that this Act supersedes existing law applicable to AID development assistance.</s>

making detailed measurements of the temperature structure of the solar upper atmosphere is fundamental to constraining the coronal heating problem . recent work has suggested that many structures in the corona have relatively narrow distributions of temperatures ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? this result is difficult to reconcile with the parker nanoflare model of coronal heating @xcite . all theoretical calculations and numerical simulations indicate that magnetic reconnection occurs on spatial scales that are much smaller than can be observed with current instrumentation . this implies that observed temperature distributions should be broad ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . unfortunately , determining the temperature structure of the corona from remote sensing observations is difficult . in principal , measurements of individual emission line intensities should yield this information . the intensity , however , is a convolution of the temperature , density , and geometry along the line of sight and such observations must be inverted to yield the differential emission measure distribution ( dem ) . since the inversion is ill posed it is nt clear what to make of the solution . in their classic paper @xcite write `` consequently , in the derivation of thermal structure from spectral data , observational errors are always magnified and often to such an extent that the solution becomes meaningless . '' the inverse problem can be regularized so that the solution is less sensitive to error but this introduces additional assumptions that may have no physical basis @xcite . in this paper we introduce the application of sparse bayesian inference to the differential emission measure inversion problem . here we are attempting to infer the temperature structure of the atmosphere through observations of optically thin emission lines , @xmath0 where @xmath1 is the observed intensity , @xmath2 is the relevant plasma emissivity , which is assumed to be known , and @xmath3 is the differential emission measure ( dem ) , which is a function of the electron density and path length along the line of sight . as has been done in many previous studies , we assume that the dem can be represented by a sum of simple basis functions . motivated by the `` relevance vector machine , '' a bayesian regression algorithm developed by @xcite , we adopt a prior that encodes a preference for solutions that utilize a minimum number of basis function . the important implication of this assumption is that the complexity of the inferred temperature distribution is determined primarily by the observations and their statistical significance and not by ad hoc assumptions about the solution . to demonstrate the efficacy of this approach we have constructed a test library of 40 dems that cover the range of what we expect to observe in the solar corona . for each distribution we estimate the intensity and statistical uncertainty for a number of emission lines using the effective areas of the extreme ultraviolet imaging spectrometer ( eis , @xcite ) on the _ hinode _ mission . these intensities are used to attempt to recover the input dem . we show that our method outperforms another bayesian dem solver ( mcmc by @xcite ) , which assumes an uninformative prior for the weights . this paper is structured in the following way . we first consider the application of our bayesian framework to a linear `` toy problem '' that closely follows example regression problems that are often found in the literature ( e.g. , * ? ? ? this allows us to make a gentle introduction of the notation and to compare our approach with other established methods . we then consider the application of our approach to the dem inversion problem . in standard linear regression problems we wish to fit a set of @xmath4 observed data points ( @xmath5 ) to some smooth function with free parameters . we assume that the modeled data points ( @xmath6 ) can be written as the linear superposition of a set of specified basis functions @xmath7 and our task is to find the weights ( @xmath8 ) that `` best fit '' the data . in this paper we will assume that the basis functions are simple gaussians @xmath9\ ] ] with a fixed width @xmath10 . anticipating the dem problem we will not assume that the positions of the basis functions ( @xmath11 ) lie on the available data points but are evenly spaced on a fixed domain . for a given set of data the optimal weights can be found by minimizing the familiar expression @xmath12 for which the optimal weights can be found by gradient descent or levenberg - marquardt ( e.g. , * ? ? ? * ) . also recall that we can cast this in matrix form @xmath13 where @xmath14 , which can be solved directly with @xmath15 or iteratively with gradient descent . the challenge is to allow for many degrees of freedom so that we can fit a wide variety of functions while not overfitting the data . to illustrate this , we generate 50 noisy data points from the @xmath16 function . the noise is drawn from a normal distribution with zero mean and a standard deviation of @xmath17 . as is shown in figure [ fig : toyprob ] , a model with with @xmath18 basis functions fits the data points perfectly , but is highly oscillatory . our intuition is that this model will not do a good job of predicting the values of new data points . indeed , if we generate another 50 noisy data points we see that @xmath19 is about an order of magnitude larger for this new set . the traditional approach to constraining such regression problems is penalized least squares , where we minimize a function of the form @xmath20 which can be solved with gradient descent or directly with @xmath21 the parameter @xmath22 balances the goodness of fit against the smoothness of the solution . it can be found by using some of the data ( the training data ) to infer the weights and the remainder of the data ( the test data ) to evaluate the goodness of fit . since the computational complexity of the problem is small , we can determine the value of @xmath22 that best fits the test data through a simple one - dimensional parameter search . figure [ fig : toyprob ] illustrates this approach to the regression problem . this method works well when we have many data points and can easily divide them into training and test sets . unfortunately , for the dem problem we often have a limited number of observed intensities and this `` leave some out '' cross - validation technique is not useful . by reformulating the problem using a bayesian framework we can achieve a similar result without resorting to cross - validation . we write bayes theorem as the product of a likelihood and a hierarchical prior @xmath23 the likelihood is the usual expression assuming normally distributed errors on the observations @xmath24.\ ] ] for the prior on the weights we simply chose a cauchy distribution , @xmath25 we choose an uninformative prior for the hyperparameter @xmath26 , which implicitly assumes that the values for the weights will be only weakly dependent on the value of @xmath26 that we use . we recognize that there are techniques for optimizing the hyperparameters and we will return to this issue in the summary and discussion section . if we are interested in the distributions of the weights implied by the data and our choice of the posterior , we must generate samples from it . the standard approach to this is the metropolis - hastings algorithm @xcite . in the next section we will describe the application of a powerful new parallel sampling technique @xcite that we can apply to this problem . if we are only interested in the set of weights that maximize the posterior , we take the negative log of the posterior , discard all constant terms , and minimize @xmath27 which is similar to equation [ eq : pls ] . this can be minimized using gradient descent . figure [ fig : toyprob ] shows the solution assuming @xmath28 and using all 100 data points simultaneously in the optimization . we see that this approach also avoids overfitting the data , but by limiting the number of non - zero basis functions rather than by limiting the sum of the weights . the cauchy distribution encourages such sparse solutions because it has `` fat tails . '' to see how this comes about consider a simple case where three basis functions could be used to describe the data equally well . in the absence of a prior , the solution is likely to have weights of comparable magnitude , e.g. , @xmath29 , while we would like the solution to be as simple as possible , say @xmath30 . with the assumption of the cauchy prior , however , we have @xmath31 for @xmath32 and we see that we can encode this preference for models with a limited number of non - zero weights into the prior . since the temperature domain of the dem is not unambiguously determined by the data , this preference for sparse solutions is a useful property . we want emission measure to be inferred only when the observations imply that it is statistically significant . we note that this approach does nt eliminate any degeneracy among the solutions . several sets of weights ( e.g , 1,0,0 or 0,1,0 or 0,0,1 in our simple example ) could be nearly equally likely . it could also be that the numerical scheme used to explore the posterior has difficulty with such a multi - modal landscape . we will discuss the problem of degeneracy in more detail in the next section . a more sophisticated bayesian approach to sparsity has been formulated by @xcite , who called his method the relevance vector machine ( rvm ) . here the prior on the weights is assumed to be @xmath33^{1/2 } \exp\left[-\frac{\alpha_m w_m^2}{2}\right],\ ] ] where there is a hyperparameter @xmath34 for each weight and the prior on each hyperparameter is assumed to be a gamma distribution . @xcite iteratively solves for the optimal set of weights and hyperparameters by alternating between maximizing the likelihood with fixed @xmath34 and maximizing the evidence ( the denominator of equation [ eq : bayes ] ) with fixed @xmath8 . as the iteration proceeds , some of the @xmath34 s become large and these basis functions are pruned from the model . upon convergence we are typically left with a model that has only a few remaining basis functions . figure [ fig : toyprob ] illustrates the application of this approach to our @xmath35 problem . the rvm solution is similar to that obtained using the cauchy prior , suggesting that this distribution is consistent with sparsity . the gamma function prior for @xmath34 makes the equivalent regularizing penalty proportional to @xmath36 ( @xcite , equation 33 ) , similar to what we obtain with the cauchy prior , so perhaps this is not surprising . for the scale of problem that we are interested in , the rvm is computationally efficient . unfortunately , the rvm allows for negative weights and can not be used for the emission measure problem since a negative emission measure has no physical meaning . the simple bayesian approach described by equations [ eq : bayes ] and [ eq : log_pos ] , in contrast , is much more computationally expensive to implement , but it can easily accommodate the essential positive definite constraint on the weights . we close this section with a brief comment on mathematical rigor . it is clear that the further we stray from simple least - squares solutions the less certain we are that our mathematical assumptions will have their intended effect . we have certainly not proven that the cauchy prior will always lead to sparse solutions or that our assumptions about the hyper - parameter @xmath26 will not have some perverse consequence in some circumstances . similarly , @xcite has not proven that the iterative approach to the rvm always converges to the optimal solution ( for example , see section of 2.2 of @xcite for cases where the rvm fails to perform optimally ) . our feeling is that considering a wide variety of test problems is the easiest way of dealing with this lack of mathematical certainty . we now turn to the actual problem of interest , inferring the temperature structure of the solar atmosphere from observations of optically thin line emission . specifically , we wish to invert the equation @xmath37 for the line - of - sight differential emission measure distribution @xmath3 given a set of observed intensities ( @xmath1 ) , their associated statistical uncertainties ( @xmath38 ) , and the relevant plasma emissivites ( @xmath39 . this problem differs from the linear problem in that the function we wish to fit is not observed directly , but indirectly through the intensity . as discussed in the previous section , the solution should have several properties : since the density and path length are positive quantities , it must be positive definite ; since in many circumstances we will have only a limited number of observed intensities , it can not rely on cross validation methods for optimizing parameters ; and it should be sparse , inferring emission measure only at temperatures where there is a statistically significant reason to do so . as we will see , the bayesian approach that we applied to the linear problem satisfies all three of these properties . we assume that the product of the temperature and the dem can be represented as the weighted sum of known basis functions , @xmath40 the exponential weight is chosen so that the dem is positive definite . note that since the range of temperatures is large it is more efficient to integrate over intervals of constant log temperature using @xmath41 . putting the extra factor of @xmath42 on the right side of equation [ eq : dem ] allows both the weights and the basis functions to have uniform magnitudes . for the basis functions we chose gaussians in @xmath43 , @xmath44.\ ] ] for a given temperature domain we assume that the basis functions are equally spaced and that the width of each component is @xmath45 so that the width is automatically adjusted depending on the number of components . rcrrrrr mg v 276.579 & 5.45 & 2.06e-10 & 0.00 & 0.41 & 0.00 & 0.29 + mg vi 270.394 & 5.65 & 2.61e-10 & 0.00 & 0.32 & 0.00 & 1.79 + mg vii 280.737 & 5.80 & 1.38e-10 & 0.30 & 0.72 & 0.29 & 1.00 + si vii 275.368 & 5.80 & 2.24e-10 & 0.17 & 0.44 & 0.12 & 1.40 + fe ix 188.497 & 5.90 & 3.65e-10 & 1.72 & 0.74 & 1.37 & 1.26 + fe ix 197.862 & 5.90 & 6.44e-10 & 1.05 & 0.43 & 0.90 & 1.17 + fe x 184.536 & 6.05 & 1.54e-10 & 18.55 & 3.64 & 16.88 & 1.10 + si x 258.375 & 6.15 & 1.52e-10 & 62.36 & 5.65 & 62.28 & 1.00 + fe xi 180.401 & 6.15 & 3.98e-11 & 152.36 & 20.65 & 150.47 & 1.01 + fe xi 188.216 & 6.15 & 3.48e-10 & 76.93 & 4.84 & 75.87 & 1.01 + s x 264.233 & 6.15 & 2.16e-10 & 11.25 & 2.02 & 11.37 & 0.99 + fe xii 195.119 & 6.20 & 7.11e-10 & 209.69 & 5.48 & 217.88 & 0.96 + fe xii 192.394 & 6.20 & 6.01e-10 & 67.57 & 3.41 & 70.20 & 0.96 + fe xiii 202.044 & 6.25 & 1.94e-10 & 115.64 & 7.68 & 120.15 & 0.96 + fe xiii 203.826 & 6.25 & 1.03e-10 & 174.43 & 12.90 & 182.51 & 0.96 + fe xiv 264.787 & 6.30 & 2.22e-10 & 243.24 & 9.07 & 245.37 & 0.99 + fe xiv 270.519 & 6.30 & 2.61e-10 & 124.92 & 5.94 & 125.95 & 0.99 + fe xiv 211.316 & 6.30 & 2.47e-11 & 456.62 & 41.82 & 459.89 & 0.99 + fe xv 284.160 & 6.35 & 9.54e-11 & 6114.98 & 66.95 & 6237.17 & 0.98 + s xiii 256.686 & 6.40 & 1.35e-10 & 517.05 & 17.22 & 526.64 & 0.98 + fe xvi 262.984 & 6.45 & 2.02e-10 & 1028.86 & 19.62 & 1057.81 & 0.97 + ca xiv 193.874 & 6.55 & 6.73e-10 & 246.54 & 6.13 & 259.09 & 0.95 + ar xiv 194.396 & 6.55 & 6.93e-10 & 70.62 & 3.23 & 75.22 & 0.94 + ca xv 200.972 & 6.65 & 2.95e-10 & 210.21 & 8.40 & 213.79 & 0.98 + ca xvi 208.604 & 6.70 & 3.98e-11 & 120.19 & 17.08 & 115.32 & 1.04 + ca xvii 192.858 & 6.75 & 6.25e-10 & 157.95 & 5.10 & 138.12 & 1.14 + aia 94 & 6.85 & & 20.39 & 0.64 & 19.41 & 1.05 [ table : line_list ] with these assumptions it is possible to integrate the emissivity over each basis function , @xmath46 and the calculation of each modeled intensity is reduced to a simple sum . the only differences between this problem and the problem discussed in the previous section are that the intensities are non - linear functions of the weights and , since spectroscopic instruments rarely have uniform sensitivity , each intensity has a uncertainty ( @xmath38 ) . the line - of - sight emission measures observed on the sun are typically large , @xmath47@xmath48 in an active region , for example @xcite . to bias the weights to the domain of interest we introduce a scaling factor into the basis functions so that a weight of zero corresponds to @xmath49 instead of 1 . further we modify the prior on the weights ( equation [ eq : log_prior ] ) by mapping @xmath50 to @xmath51 . given a set of observed intensities and the corresponding atomic data , we can find the optimal values for the weights either by sampling the posterior ( equation [ eq : bayes ] ) or minimizing the negative log - posterior ( equation [ eq : log_pos ] ) . unfortunately , finding global extrema in a high dimensional space is a formidable problem . our approach is to begin by sampling the posterior using the method introduced by @xcite and implemented by @xcite and @xcite , among others . this method differs from the traditional single monte carlo markov chain random walk method for sampling the posterior by utilizing an ensemble of walkers , potentially thousands of them , that can be updated in parallel . further , instead of using a proposal distribution with parameters that must be adjusted to achieve the desired acceptance ratio , updates to the chain are made using the current positions of pairs of walkers @xmath52 where @xmath53 is a random number from the distribution @xmath54 on the domain @xmath55 $ ] . in principle , @xmath56 is an adjustable parameter but the choice @xmath57 appears to work well in all applications @xcite . note that the pairs of walkers are shuffled on each iteration . we implemented this algorithm in a simple c code that was parallelized using openmp . we validated it by sampling from known posteriors , applying it to simple parameter estimation problems , such as fitting spectral profiles with a gaussian , and using it for the linear regression problem in the previous section . to test our approach we need to create some dems and select a line list for our hypothetical observations . in figure [ fig : library_image ] we show the `` library '' of 40 test dems that we have devised . these functions are superpositions of gaussians that are either linear or logarithmic in temperature and range from narrow to very broad , representing the range of curves that have been found in previous studies ( e.g. , * ? ? ? * ; * ? ? ? note that we have deliberately mismatched the widths of the dems in the library and the widths of the basis functions . to complement the dem library we select a series of emission lines that are observed with eis and that are typically used in temperature studies ( e.g. , * ? ? ? these lines are listed in table [ table : line_list ] , where we also list the peak temperature of formation for the ion and the conversion from the radiance observed at the sun to photons detected by the instrument , which is needed to compute the statistical uncertainty for each intensity . this conversion factor is simply the product of the pre - flight effective area @xcite , the solid angle subtended by a pixel , and the exposure time . here we assume the use of the 1 slit and a 100s exposure time . to augment the eis line list we use a calculated intensity for the 94 channel on the the atmospheric imaging assembly ( aia , @xcite ) . this channel can observe 93.932 , which peaks at about @xmath58 . we assume that we are using 94 images that have been processed to remove lower temperature emission ( see the appendix of @xcite ) . errors on the intensity are computed using the standard analysis routine ` aia_bp_estimate_error ` . for all of our emissivity calculations we use the chianti atomic database version 8.0.1 @xcite assuming coronal abundances @xcite , a constant pressure of @xmath59@xmath60 k , and the default ionization fractions . for each emission line the emissivities of all lines with 0.5 are summed to create a composite response . we are now in a position to calculate the dems . to compute the intensities we convolve each distribution in the library with the emissivities for all of the eis lines and the aia 94 channel . we also compute the statistical uncertainty for each of the resulting intensities . for the prior we use @xmath28 . for the sampling we initialize 1,000 walkers with randomly selected weights on the interval @xmath61 $ ] and begin iterating . after a burn - in of @xmath62 accepted samples , the next @xmath63 proposed steps that are accepted are recorded to form the final sampling of the posterior . after each iteration we also recorded the highest value of the posterior and saved the corresponding set of weights . this procedure takes about 45min per dem on a standard 4-core 4ghz intel i7 processor with all four cores utilized . we will discuss how this algorithm could be made more efficient in the next section . in figure [ fig : library_dist ] we show the distributions of the weights obtained for one of the dem calculations ( # 18 ) . the corresponding intensities are shown in table [ table : line_list ] . unfortunately , these posterior distributions are not simple , single peaked functions , but have multiple peaks . as discussed in the previous section , multiple peaks are an inevitable consequence of having many basis functions . recall our simple example of having three degenerate basis functions where each could represent the data equally well . the posterior in this simple case would consist of approximately equal parts ( 1,0,0 ) , ( 0,1,0 ) , and ( 0,0,1 ) and the distribution for each weight would have a strong peak at 0 and a secondary peak at 1 . for the dem problem we have not specified so many basis functions that we expect to see such extreme degeneracy . still , multiple peaks are clearly present in the posterior distributions for many weights . . ] ) and form an envelope on the emission measure distribution . ] so which weights do we use to compute the final dem ? the median and mean of the weight distributions are potentially problematic . the mode of the distribution , however , is generally well behaved . using these weights to compute the dem both reproduces the observed intensities and the input dem very closely . for each run we also used the walker with the highest value of the posterior as initial conditions for a gradient descent calculation . as is illustrated in figure [ fig : library_evo ] , the dems recovered using gradient descent generally matched those recovered using the mode of the posterior weight distribution . in all cases the weights obtained after gradient descent actually produced a higher value for the posterior than the mode , suggesting that using the mode is not optimal . for this reason we use the weights obtained from gradient descent to represent the recovered dem . we have performed this calculation for all of the dems in the library . some example dems are shown in figure [ fig : library_dems ] . the summary of all of the calculations is presented in figure [ fig : library_image ] . in almost all cases the input intensities are reproduced to within a few percent and the general properties of the input dem are also recovered and no emission measure is inferred far away from the peaks in the input distributions . we note that the excellent agreement between the recovered and actual dems is only achieved after a very long burn - in period ( recall that we accepted @xmath62 samples before collecting the samples for the posterior ) . for a burn - in of @xmath64 samples the mode of the posterior distribution resulted in a poor approximation of the input dem with finite weights for most of basis functions . for a burn - in of @xmath65 samples the recovered dems were generally close to the input dems but there were a number of spurious peaks . many of these peaks remained even after performing gradient descent . the sampling of the posterior is computationally expensive and one might wonder if it would be easier to simply select some random initial conditions and then do gradient descent . our experiments with this were not encouraging . in almost all cases the calculation converged to some local maximum far from the solution that we obtained through sampling . we note that we did not study this extensively . our intuition , however , is that the sampling is an invaluable aid in exploring a complex posterior in a high dimensional space and is worth the computational expense . to provide a point of comparison for our calculations we have used another bayesian solver , the `` mcmc '' routine of @xcite , on each set of computed intensities in the dem library . here we use 20 temperature bins in @xmath43 and run 100 simulations on each dem . the resulting dems , which are summarized in figure [ fig : library_image ] , also recovers the main features of each input distribution . we also see , however , that mcmc infers emission measure at temperatures far away from the main peaks in the input distributions . this is not surprising given the assumption of an uninformative prior over the weights . finally , we have also applied this technique to two sets of observed eis intensities . these results are summarized in figure [ fig : observed ] . the sparse technique that we introduced here recovers the observed intensities as well as mcmc . since the dem library was constructed with these types of dems in mind narrow dems for off - limb quiet sun and somewhat broader dems for active regions it is not surprising that the algorithm can recover them . we have explored the application of sparse bayesian inference to the problem of determining the temperature structure of the solar corona . we have found that by adopting a cauchy distribution as a prior for the weights we can encode a preference for a sparse representation of the temperature distribution . thus we can use a rich set of basis functions and recover a wide variety of dems , while limiting the amount of spurious emission measure at other temperatures . we have also shown that a complex , high - dimensional posterior can be explored in detail using the parallel sampling technique of @xcite . the results from this sparse bayesian approach compare favorably to the results obtained from mcmc @xcite . as one would expect , the absence of any constraints on the weights in mcmc leads to considerable emission measure being inferred at temperatures away from the peaks in the input dems . there are two aspects of our algorithm that could be improved . first , we have not considered the optimization of the hyperparameters . the magnitude of the weight penalty ( @xmath26 in equation [ eq : log_prior ] ) , the number of basis functions , and the widths of the basis functions , are left fixed . as mentioned in the discussion of the rvm in the previous section , one method for optimizing the hyperparameters is maximizing the evidence ( see chapter 18 of @xcite for more details ) . unfortunately , our non - linear representation of the dem makes the integration of the evidence analytically intractable . a linear representation of the dem would make many aspects of the problem simpler , but this would require an algorithm for optimizing the weights that incorporates the positive definite constraint . we conjecture that such an approach would be orders of magnitude faster than our current approach . we have limited our comparisons to mcmc . there have been many papers written on dem inversions , but a complete summary of techniques is well beyond the scope of this work . two recent efforts , however , directly address some of the issues that we have discussed in this paper . @xcite implement a penalized least squares algorithm ( equation [ eq : pls ] ) where the hyperparmeter @xmath22 is adjusted using the statistical uncertainty in observations and the non - negativity constraint . as illustrated with our linear problem , this produces solutions that are smooth , but not necessarily sparse , and thus sensitive to the domain specified for the inversion . one typically chooses a temperature range that extends slightly beyond the temperature of formation of the coolest and hottest line that is observed . this is not a particularly controversial assumption and so this is not a major shortcoming . @xcite have implemented an algorithm with a weight penalty based on the l1 norm ( e.g. , * ? ? ? * ; * ? ? ? @xcite do not address the optimization of the hyperparmeter on the weight penalty . they also use a l1 norm for the likelihood and it is not clear if this is consistent with the uncertainties of the observations . both @xcite and @xcite have tested their algorithms on a wide variety of input dems and they perform well . these algorithms are significantly faster than our sparse bayesian method . finally , we stress that our goals for the dem are relatively modest . in general , we simply wish to understand if structures in the solar atmosphere have narrow or broad temperature distributions . we also stress that no amount of mathematical machinery can replace the need for well - calibrated observations that contain emission lines that cover a wide range of temperatures . highly accurate atomic data is also a critical component of any effort to understand the temperature structure of the solar atmosphere ( e.g. , * ? ? ? this work was sponsored by the chief of naval research and nasa s hinode project . hinode is a japanese mission developed and launched by isas / jaxa , with naoj as domestic partner and nasa and stfc ( uk ) as international partners . candela , j. q. 2004 , phd thesis , informatics and mathematical modelling , technical university of denmark , dtu , richard petersens plads , building 321 , dk-2800 kgs . lyngby , supervised by professor lars kai hansen

measuring the temperature structure of the solar atmosphere is critical to understanding how it is heated to high temperatures . unfortunately , the temperature of the upper atmosphere can not be observed directly , but must be inferred from spectrally resolved observations of individual emission lines that span a wide range of temperatures . such observations are `` inverted '' to determine the distribution of plasma temperatures along the line of sight . this inversion is ill - posed and , in the absence of regularization , tends to produce wildly oscillatory solutions . we introduce the application of sparse bayesian inference to the problem of inferring the temperature structure of the solar corona . within a bayesian framework a preference for solutions that utilize a minimum number of basis functions can be encoded into the prior and many ad hoc assumptions can be avoided . we demonstrate the efficacy of the bayesian approach by considering a test library of 40 assumed temperature distributions .

<s>[INST]making detailed measurements of the temperature structure of the solar upper atmosphere is fundamental to constraining the coronal heating problem . recent work has suggested that many structures in the corona have relatively narrow distributions of temperatures ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? this result is difficult to reconcile with the parker nanoflare model of coronal heating @xcite . all theoretical calculations and numerical simulations indicate that magnetic reconnection occurs on spatial scales that are much smaller than can be observed with current instrumentation . this implies that observed temperature distributions should be broad ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . unfortunately , determining the temperature structure of the corona from remote sensing observations is difficult . in principal , measurements of individual emission line intensities should yield this information . the intensity , however , is a convolution of the temperature , density , and geometry along the line of sight and such observations must be inverted to yield the differential emission measure distribution ( dem ) . since the inversion is ill posed it is nt clear what to make of the solution . in their classic paper @xcite write `` consequently , in the derivation of thermal structure from spectral data , observational errors are always magnified and often to such an extent that the solution becomes meaningless . '' the inverse problem can be regularized so that the solution is less sensitive to error but this introduces additional assumptions that may have no physical basis @xcite . in this paper we introduce the application of sparse bayesian inference to the differential emission measure inversion problem . here we are attempting to infer the temperature structure of the atmosphere through observations of optically thin emission lines , @xmath0 where @xmath1 is the observed intensity , @xmath2 is the relevant plasma emissivity , which is assumed to be known , and @xmath3 is the differential emission measure ( dem ) , which is a function of the electron density and path length along the line of sight . as has been done in many previous studies , we assume that the dem can be represented by a sum of simple basis functions . motivated by the `` relevance vector machine , '' a bayesian regression algorithm developed by @xcite , we adopt a prior that encodes a preference for solutions that utilize a minimum number of basis function . the important implication of this assumption is that the complexity of the inferred temperature distribution is determined primarily by the observations and their statistical significance and not by ad hoc assumptions about the solution . to demonstrate the efficacy of this approach we have constructed a test library of 40 dems that cover the range of what we expect to observe in the solar corona . for each distribution we estimate the intensity and statistical uncertainty for a number of emission lines using the effective areas of the extreme ultraviolet imaging spectrometer ( eis , @xcite ) on the _ hinode _ mission . these intensities are used to attempt to recover the input dem . we show that our method outperforms another bayesian dem solver ( mcmc by @xcite ) , which assumes an uninformative prior for the weights . this paper is structured in the following way . we first consider the application of our bayesian framework to a linear `` toy problem '' that closely follows example regression problems that are often found in the literature ( e.g. , * ? ? ? this allows us to make a gentle introduction of the notation and to compare our approach with other established methods . we then consider the application of our approach to the dem inversion problem . in standard linear regression problems we wish to fit a set of @xmath4 observed data points ( @xmath5 ) to some smooth function with free parameters . we assume that the modeled data points ( @xmath6 ) can be written as the linear superposition of a set of specified basis functions @xmath7 and our task is to find the weights ( @xmath8 ) that `` best fit '' the data . in this paper we will assume that the basis functions are simple gaussians @xmath9\ ] ] with a fixed width @xmath10 . anticipating the dem problem we will not assume that the positions of the basis functions ( @xmath11 ) lie on the available data points but are evenly spaced on a fixed domain . for a given set of data the optimal weights can be found by minimizing the familiar expression @xmath12 for which the optimal weights can be found by gradient descent or levenberg - marquardt ( e.g. , * ? ? ? * ) . also recall that we can cast this in matrix form @xmath13 where @xmath14 , which can be solved directly with @xmath15 or iteratively with gradient descent . the challenge is to allow for many degrees of freedom so that we can fit a wide variety of functions while not overfitting the data . to illustrate this , we generate 50 noisy data points from the @xmath16 function . the noise is drawn from a normal distribution with zero mean and a standard deviation of @xmath17 . as is shown in figure [ fig : toyprob ] , a model with with @xmath18 basis functions fits the data points perfectly , but is highly oscillatory . our intuition is that this model will not do a good job of predicting the values of new data points . indeed , if we generate another 50 noisy data points we see that @xmath19 is about an order of magnitude larger for this new set . the traditional approach to constraining such regression problems is penalized least squares , where we minimize a function of the form @xmath20 which can be solved with gradient descent or directly with @xmath21 the parameter @xmath22 balances the goodness of fit against the smoothness of the solution . it can be found by using some of the data ( the training data ) to infer the weights and the remainder of the data ( the test data ) to evaluate the goodness of fit . since the computational complexity of the problem is small , we can determine the value of @xmath22 that best fits the test data through a simple one - dimensional parameter search . figure [ fig : toyprob ] illustrates this approach to the regression problem . this method works well when we have many data points and can easily divide them into training and test sets . unfortunately , for the dem problem we often have a limited number of observed intensities and this `` leave some out '' cross - validation technique is not useful . by reformulating the problem using a bayesian framework we can achieve a similar result without resorting to cross - validation . we write bayes theorem as the product of a likelihood and a hierarchical prior @xmath23 the likelihood is the usual expression assuming normally distributed errors on the observations @xmath24.\ ] ] for the prior on the weights we simply chose a cauchy distribution , @xmath25 we choose an uninformative prior for the hyperparameter @xmath26 , which implicitly assumes that the values for the weights will be only weakly dependent on the value of @xmath26 that we use . we recognize that there are techniques for optimizing the hyperparameters and we will return to this issue in the summary and discussion section . if we are interested in the distributions of the weights implied by the data and our choice of the posterior , we must generate samples from it . the standard approach to this is the metropolis - hastings algorithm @xcite . in the next section we will describe the application of a powerful new parallel sampling technique @xcite that we can apply to this problem . if we are only interested in the set of weights that maximize the posterior , we take the negative log of the posterior , discard all constant terms , and minimize @xmath27 which is similar to equation [ eq : pls ] . this can be minimized using gradient descent . figure [ fig : toyprob ] shows the solution assuming @xmath28 and using all 100 data points simultaneously in the optimization . we see that this approach also avoids overfitting the data , but by limiting the number of non - zero basis functions rather than by limiting the sum of the weights . the cauchy distribution encourages such sparse solutions because it has `` fat tails . '' to see how this comes about consider a simple case where three basis functions could be used to describe the data equally well . in the absence of a prior , the solution is likely to have weights of comparable magnitude , e.g. , @xmath29 , while we would like the solution to be as simple as possible , say @xmath30 . with the assumption of the cauchy prior , however , we have @xmath31 for @xmath32 and we see that we can encode this preference for models with a limited number of non - zero weights into the prior . since the temperature domain of the dem is not unambiguously determined by the data , this preference for sparse solutions is a useful property . we want emission measure to be inferred only when the observations imply that it is statistically significant . we note that this approach does nt eliminate any degeneracy among the solutions . several sets of weights ( e.g , 1,0,0 or 0,1,0 or 0,0,1 in our simple example ) could be nearly equally likely . it could also be that the numerical scheme used to explore the posterior has difficulty with such a multi - modal landscape . we will discuss the problem of degeneracy in more detail in the next section . a more sophisticated bayesian approach to sparsity has been formulated by @xcite , who called his method the relevance vector machine ( rvm ) . here the prior on the weights is assumed to be @xmath33^{1/2 } \exp\left[-\frac{\alpha_m w_m^2}{2}\right],\ ] ] where there is a hyperparameter @xmath34 for each weight and the prior on each hyperparameter is assumed to be a gamma distribution . @xcite iteratively solves for the optimal set of weights and hyperparameters by alternating between maximizing the likelihood with fixed @xmath34 and maximizing the evidence ( the denominator of equation [ eq : bayes ] ) with fixed @xmath8 . as the iteration proceeds , some of the @xmath34 s become large and these basis functions are pruned from the model . upon convergence we are typically left with a model that has only a few remaining basis functions . figure [ fig : toyprob ] illustrates the application of this approach to our @xmath35 problem . the rvm solution is similar to that obtained using the cauchy prior , suggesting that this distribution is consistent with sparsity . the gamma function prior for @xmath34 makes the equivalent regularizing penalty proportional to @xmath36 ( @xcite , equation 33 ) , similar to what we obtain with the cauchy prior , so perhaps this is not surprising . for the scale of problem that we are interested in , the rvm is computationally efficient . unfortunately , the rvm allows for negative weights and can not be used for the emission measure problem since a negative emission measure has no physical meaning . the simple bayesian approach described by equations [ eq : bayes ] and [ eq : log_pos ] , in contrast , is much more computationally expensive to implement , but it can easily accommodate the essential positive definite constraint on the weights . we close this section with a brief comment on mathematical rigor . it is clear that the further we stray from simple least - squares solutions the less certain we are that our mathematical assumptions will have their intended effect . we have certainly not proven that the cauchy prior will always lead to sparse solutions or that our assumptions about the hyper - parameter @xmath26 will not have some perverse consequence in some circumstances . similarly , @xcite has not proven that the iterative approach to the rvm always converges to the optimal solution ( for example , see section of 2.2 of @xcite for cases where the rvm fails to perform optimally ) . our feeling is that considering a wide variety of test problems is the easiest way of dealing with this lack of mathematical certainty . we now turn to the actual problem of interest , inferring the temperature structure of the solar atmosphere from observations of optically thin line emission . specifically , we wish to invert the equation @xmath37 for the line - of - sight differential emission measure distribution @xmath3 given a set of observed intensities ( @xmath1 ) , their associated statistical uncertainties ( @xmath38 ) , and the relevant plasma emissivites ( @xmath39 . this problem differs from the linear problem in that the function we wish to fit is not observed directly , but indirectly through the intensity . as discussed in the previous section , the solution should have several properties : since the density and path length are positive quantities , it must be positive definite ; since in many circumstances we will have only a limited number of observed intensities , it can not rely on cross validation methods for optimizing parameters ; and it should be sparse , inferring emission measure only at temperatures where there is a statistically significant reason to do so . as we will see , the bayesian approach that we applied to the linear problem satisfies all three of these properties . we assume that the product of the temperature and the dem can be represented as the weighted sum of known basis functions , @xmath40 the exponential weight is chosen so that the dem is positive definite . note that since the range of temperatures is large it is more efficient to integrate over intervals of constant log temperature using @xmath41 . putting the extra factor of @xmath42 on the right side of equation [ eq : dem ] allows both the weights and the basis functions to have uniform magnitudes . for the basis functions we chose gaussians in @xmath43 , @xmath44.\ ] ] for a given temperature domain we assume that the basis functions are equally spaced and that the width of each component is @xmath45 so that the width is automatically adjusted depending on the number of components . rcrrrrr mg v 276.579 & 5.45 & 2.06e-10 & 0.00 & 0.41 & 0.00 & 0.29 + mg vi 270.394 & 5.65 & 2.61e-10 & 0.00 & 0.32 & 0.00 & 1.79 + mg vii 280.737 & 5.80 & 1.38e-10 & 0.30 & 0.72 & 0.29 & 1.00 + si vii 275.368 & 5.80 & 2.24e-10 & 0.17 & 0.44 & 0.12 & 1.40 + fe ix 188.497 & 5.90 & 3.65e-10 & 1.72 & 0.74 & 1.37 & 1.26 + fe ix 197.862 & 5.90 & 6.44e-10 & 1.05 & 0.43 & 0.90 & 1.17 + fe x 184.536 & 6.05 & 1.54e-10 & 18.55 & 3.64 & 16.88 & 1.10 + si x 258.375 & 6.15 & 1.52e-10 & 62.36 & 5.65 & 62.28 & 1.00 + fe xi 180.401 & 6.15 & 3.98e-11 & 152.36 & 20.65 & 150.47 & 1.01 + fe xi 188.216 & 6.15 & 3.48e-10 & 76.93 & 4.84 & 75.87 & 1.01 + s x 264.233 & 6.15 & 2.16e-10 & 11.25 & 2.02 & 11.37 & 0.99 + fe xii 195.119 & 6.20 & 7.11e-10 & 209.69 & 5.48 & 217.88 & 0.96 + fe xii 192.394 & 6.20 & 6.01e-10 & 67.57 & 3.41 & 70.20 & 0.96 + fe xiii 202.044 & 6.25 & 1.94e-10 & 115.64 & 7.68 & 120.15 & 0.96 + fe xiii 203.826 & 6.25 & 1.03e-10 & 174.43 & 12.90 & 182.51 & 0.96 + fe xiv 264.787 & 6.30 & 2.22e-10 & 243.24 & 9.07 & 245.37 & 0.99 + fe xiv 270.519 & 6.30 & 2.61e-10 & 124.92 & 5.94 & 125.95 & 0.99 + fe xiv 211.316 & 6.30 & 2.47e-11 & 456.62 & 41.82 & 459.89 & 0.99 + fe xv 284.160 & 6.35 & 9.54e-11 & 6114.98 & 66.95 & 6237.17 & 0.98 + s xiii 256.686 & 6.40 & 1.35e-10 & 517.05 & 17.22 & 526.64 & 0.98 + fe xvi 262.984 & 6.45 & 2.02e-10 & 1028.86 & 19.62 & 1057.81 & 0.97 + ca xiv 193.874 & 6.55 & 6.73e-10 & 246.54 & 6.13 & 259.09 & 0.95 + ar xiv 194.396 & 6.55 & 6.93e-10 & 70.62 & 3.23 & 75.22 & 0.94 + ca xv 200.972 & 6.65 & 2.95e-10 & 210.21 & 8.40 & 213.79 & 0.98 + ca xvi 208.604 & 6.70 & 3.98e-11 & 120.19 & 17.08 & 115.32 & 1.04 + ca xvii 192.858 & 6.75 & 6.25e-10 & 157.95 & 5.10 & 138.12 & 1.14 + aia 94 & 6.85 & & 20.39 & 0.64 & 19.41 & 1.05 [ table : line_list ] with these assumptions it is possible to integrate the emissivity over each basis function , @xmath46 and the calculation of each modeled intensity is reduced to a simple sum . the only differences between this problem and the problem discussed in the previous section are that the intensities are non - linear functions of the weights and , since spectroscopic instruments rarely have uniform sensitivity , each intensity has a uncertainty ( @xmath38 ) . the line - of - sight emission measures observed on the sun are typically large , @xmath47@xmath48 in an active region , for example @xcite . to bias the weights to the domain of interest we introduce a scaling factor into the basis functions so that a weight of zero corresponds to @xmath49 instead of 1 . further we modify the prior on the weights ( equation [ eq : log_prior ] ) by mapping @xmath50 to @xmath51 . given a set of observed intensities and the corresponding atomic data , we can find the optimal values for the weights either by sampling the posterior ( equation [ eq : bayes ] ) or minimizing the negative log - posterior ( equation [ eq : log_pos ] ) . unfortunately , finding global extrema in a high dimensional space is a formidable problem . our approach is to begin by sampling the posterior using the method introduced by @xcite and implemented by @xcite and @xcite , among others . this method differs from the traditional single monte carlo markov chain random walk method for sampling the posterior by utilizing an ensemble of walkers , potentially thousands of them , that can be updated in parallel . further , instead of using a proposal distribution with parameters that must be adjusted to achieve the desired acceptance ratio , updates to the chain are made using the current positions of pairs of walkers @xmath52 where @xmath53 is a random number from the distribution @xmath54 on the domain @xmath55 $ ] . in principle , @xmath56 is an adjustable parameter but the choice @xmath57 appears to work well in all applications @xcite . note that the pairs of walkers are shuffled on each iteration . we implemented this algorithm in a simple c code that was parallelized using openmp . we validated it by sampling from known posteriors , applying it to simple parameter estimation problems , such as fitting spectral profiles with a gaussian , and using it for the linear regression problem in the previous section . to test our approach we need to create some dems and select a line list for our hypothetical observations . in figure [ fig : library_image ] we show the `` library '' of 40 test dems that we have devised . these functions are superpositions of gaussians that are either linear or logarithmic in temperature and range from narrow to very broad , representing the range of curves that have been found in previous studies ( e.g. , * ? ? ? * ; * ? ? ? note that we have deliberately mismatched the widths of the dems in the library and the widths of the basis functions . to complement the dem library we select a series of emission lines that are observed with eis and that are typically used in temperature studies ( e.g. , * ? ? ? these lines are listed in table [ table : line_list ] , where we also list the peak temperature of formation for the ion and the conversion from the radiance observed at the sun to photons detected by the instrument , which is needed to compute the statistical uncertainty for each intensity . this conversion factor is simply the product of the pre - flight effective area @xcite , the solid angle subtended by a pixel , and the exposure time . here we assume the use of the 1 slit and a 100s exposure time . to augment the eis line list we use a calculated intensity for the 94 channel on the the atmospheric imaging assembly ( aia , @xcite ) . this channel can observe 93.932 , which peaks at about @xmath58 . we assume that we are using 94 images that have been processed to remove lower temperature emission ( see the appendix of @xcite ) . errors on the intensity are computed using the standard analysis routine ` aia_bp_estimate_error ` . for all of our emissivity calculations we use the chianti atomic database version 8.0.1 @xcite assuming coronal abundances @xcite , a constant pressure of @xmath59@xmath60 k , and the default ionization fractions . for each emission line the emissivities of all lines with 0.5 are summed to create a composite response . we are now in a position to calculate the dems . to compute the intensities we convolve each distribution in the library with the emissivities for all of the eis lines and the aia 94 channel . we also compute the statistical uncertainty for each of the resulting intensities . for the prior we use @xmath28 . for the sampling we initialize 1,000 walkers with randomly selected weights on the interval @xmath61 $ ] and begin iterating . after a burn - in of @xmath62 accepted samples , the next @xmath63 proposed steps that are accepted are recorded to form the final sampling of the posterior . after each iteration we also recorded the highest value of the posterior and saved the corresponding set of weights . this procedure takes about 45min per dem on a standard 4-core 4ghz intel i7 processor with all four cores utilized . we will discuss how this algorithm could be made more efficient in the next section . in figure [ fig : library_dist ] we show the distributions of the weights obtained for one of the dem calculations ( # 18 ) . the corresponding intensities are shown in table [ table : line_list ] . unfortunately , these posterior distributions are not simple , single peaked functions , but have multiple peaks . as discussed in the previous section , multiple peaks are an inevitable consequence of having many basis functions . recall our simple example of having three degenerate basis functions where each could represent the data equally well . the posterior in this simple case would consist of approximately equal parts ( 1,0,0 ) , ( 0,1,0 ) , and ( 0,0,1 ) and the distribution for each weight would have a strong peak at 0 and a secondary peak at 1 . for the dem problem we have not specified so many basis functions that we expect to see such extreme degeneracy . still , multiple peaks are clearly present in the posterior distributions for many weights . . ] ) and form an envelope on the emission measure distribution . ] so which weights do we use to compute the final dem ? the median and mean of the weight distributions are potentially problematic . the mode of the distribution , however , is generally well behaved . using these weights to compute the dem both reproduces the observed intensities and the input dem very closely . for each run we also used the walker with the highest value of the posterior as initial conditions for a gradient descent calculation . as is illustrated in figure [ fig : library_evo ] , the dems recovered using gradient descent generally matched those recovered using the mode of the posterior weight distribution . in all cases the weights obtained after gradient descent actually produced a higher value for the posterior than the mode , suggesting that using the mode is not optimal . for this reason we use the weights obtained from gradient descent to represent the recovered dem . we have performed this calculation for all of the dems in the library . some example dems are shown in figure [ fig : library_dems ] . the summary of all of the calculations is presented in figure [ fig : library_image ] . in almost all cases the input intensities are reproduced to within a few percent and the general properties of the input dem are also recovered and no emission measure is inferred far away from the peaks in the input distributions . we note that the excellent agreement between the recovered and actual dems is only achieved after a very long burn - in period ( recall that we accepted @xmath62 samples before collecting the samples for the posterior ) . for a burn - in of @xmath64 samples the mode of the posterior distribution resulted in a poor approximation of the input dem with finite weights for most of basis functions . for a burn - in of @xmath65 samples the recovered dems were generally close to the input dems but there were a number of spurious peaks . many of these peaks remained even after performing gradient descent . the sampling of the posterior is computationally expensive and one might wonder if it would be easier to simply select some random initial conditions and then do gradient descent . our experiments with this were not encouraging . in almost all cases the calculation converged to some local maximum far from the solution that we obtained through sampling . we note that we did not study this extensively . our intuition , however , is that the sampling is an invaluable aid in exploring a complex posterior in a high dimensional space and is worth the computational expense . to provide a point of comparison for our calculations we have used another bayesian solver , the `` mcmc '' routine of @xcite , on each set of computed intensities in the dem library . here we use 20 temperature bins in @xmath43 and run 100 simulations on each dem . the resulting dems , which are summarized in figure [ fig : library_image ] , also recovers the main features of each input distribution . we also see , however , that mcmc infers emission measure at temperatures far away from the main peaks in the input distributions . this is not surprising given the assumption of an uninformative prior over the weights . finally , we have also applied this technique to two sets of observed eis intensities . these results are summarized in figure [ fig : observed ] . the sparse technique that we introduced here recovers the observed intensities as well as mcmc . since the dem library was constructed with these types of dems in mind narrow dems for off - limb quiet sun and somewhat broader dems for active regions it is not surprising that the algorithm can recover them . we have explored the application of sparse bayesian inference to the problem of determining the temperature structure of the solar corona . we have found that by adopting a cauchy distribution as a prior for the weights we can encode a preference for a sparse representation of the temperature distribution . thus we can use a rich set of basis functions and recover a wide variety of dems , while limiting the amount of spurious emission measure at other temperatures . we have also shown that a complex , high - dimensional posterior can be explored in detail using the parallel sampling technique of @xcite . the results from this sparse bayesian approach compare favorably to the results obtained from mcmc @xcite . as one would expect , the absence of any constraints on the weights in mcmc leads to considerable emission measure being inferred at temperatures away from the peaks in the input dems . there are two aspects of our algorithm that could be improved . first , we have not considered the optimization of the hyperparameters . the magnitude of the weight penalty ( @xmath26 in equation [ eq : log_prior ] ) , the number of basis functions , and the widths of the basis functions , are left fixed . as mentioned in the discussion of the rvm in the previous section , one method for optimizing the hyperparameters is maximizing the evidence ( see chapter 18 of @xcite for more details ) . unfortunately , our non - linear representation of the dem makes the integration of the evidence analytically intractable . a linear representation of the dem would make many aspects of the problem simpler , but this would require an algorithm for optimizing the weights that incorporates the positive definite constraint . we conjecture that such an approach would be orders of magnitude faster than our current approach . we have limited our comparisons to mcmc . there have been many papers written on dem inversions , but a complete summary of techniques is well beyond the scope of this work . two recent efforts , however , directly address some of the issues that we have discussed in this paper . @xcite implement a penalized least squares algorithm ( equation [ eq : pls ] ) where the hyperparmeter @xmath22 is adjusted using the statistical uncertainty in observations and the non - negativity constraint . as illustrated with our linear problem , this produces solutions that are smooth , but not necessarily sparse , and thus sensitive to the domain specified for the inversion . one typically chooses a temperature range that extends slightly beyond the temperature of formation of the coolest and hottest line that is observed . this is not a particularly controversial assumption and so this is not a major shortcoming . @xcite have implemented an algorithm with a weight penalty based on the l1 norm ( e.g. , * ? ? ? * ; * ? ? ? @xcite do not address the optimization of the hyperparmeter on the weight penalty . they also use a l1 norm for the likelihood and it is not clear if this is consistent with the uncertainties of the observations . both @xcite and @xcite have tested their algorithms on a wide variety of input dems and they perform well . these algorithms are significantly faster than our sparse bayesian method . finally , we stress that our goals for the dem are relatively modest . in general , we simply wish to understand if structures in the solar atmosphere have narrow or broad temperature distributions . we also stress that no amount of mathematical machinery can replace the need for well - calibrated observations that contain emission lines that cover a wide range of temperatures . highly accurate atomic data is also a critical component of any effort to understand the temperature structure of the solar atmosphere ( e.g. , * ? ? ? this work was sponsored by the chief of naval research and nasa s hinode project . hinode is a japanese mission developed and launched by isas / jaxa , with naoj as domestic partner and nasa and stfc ( uk ) as international partners . candela , j. q. 2004 , phd thesis , informatics and mathematical modelling , technical university of denmark , dtu , richard petersens plads , building 321 , dk-2800 kgs . lyngby , supervised by professor lars kai hansen[/INST] measuring the temperature structure of the solar atmosphere is critical to understanding how it is heated to high temperatures . unfortunately , the temperature of the upper atmosphere can not be observed directly , but must be inferred from spectrally resolved observations of individual emission lines that span a wide range of temperatures . such observations are `` inverted '' to determine the distribution of plasma temperatures along the line of sight . this inversion is ill - posed and , in the absence of regularization , tends to produce wildly oscillatory solutions . we introduce the application of sparse bayesian inference to the problem of inferring the temperature structure of the solar corona . within a bayesian framework a preference for solutions that utilize a minimum number of basis functions can be encoded into the prior and many ad hoc assumptions can be avoided . we demonstrate the efficacy of the bayesian approach by considering a test library of 40 assumed temperature distributions . </s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Filipino Veterans' Benefits Improvements Act of 2001''. SEC. 2. RATE OF PAYMENT OF CERTAIN BENEFITS FOR NEW PHILIPPINE SCOUTS RESIDING IN THE UNITED STATES. (a) Redesignation of Provisions.--Section 107 of title 38, United States Code, is amended-- (1) in the second sentence of subsection (a), by striking ``subsection (c)'' and inserting ``subsections (c) and (d)''; and (2) by designating subsection (c), as added by section 332(a)(2) of the Veterans Benefits and Health Care Improvement Act of 2000 (Public Law 106-419; 114 Stat. 1856), as subsection (d). (b) Rate of Payment.--That section is further amended-- (1) in the second sentence of subsection (b), by striking ``Payments'' and inserting ``Except as provided in subsection (c), payments''; and (2) in subsection (c), as added by section 501(a) of H.R. 5482 of the 106th Congress (as enacted by Public Law 106-377 (114 Stat. 1441A-55))-- (A) by inserting ``or (b)'' after ``subsection (a)'' the first place it appears; and (B) by striking ``subsection (a)'' the second place it appears and inserting ``the applicable subsection''. (c) Effective Date.--The amendments made by subsection (b) shall take effect on the date of enactment of this Act, and shall apply to benefits paid for months beginning on or after that date. SEC. 3. RATE OF PAYMENT OF DEPENDENCY AND INDEMNITY COMPENSATION FOR SURVIVING SPOUSES OF CERTAIN FILIPINO VETERANS. (a) Rate of Payment.--Subsection (c) of section 107 of title 38, United States Code, as added by section 501(a) of H.R. 5482 of the 106th Congress (as enacted by Public Law 106-377 (114 Stat. 1441A-55)) and amended by section 2 of this Act, is further amended by inserting ``, and under chapter 13 of this title,'' after ``chapter 11 of this title''. (b) Effective Date.--The amendment made by subsection (a) shall take effect on the date of enactment of this Act, and shall apply to benefits paid for months beginning on or after that date. SEC. 4. ELIGIBILITY OF CERTAIN FILIPINO VETERANS FOR DISABILITY PENSION. (a) Eligibility.--Section 107 of title 38, United States Code, as amended by this Act, is further amended-- (1) in subsection (a)-- (A) in paragraph (3) of the first sentence, by inserting ``15,'' before ``23,''; and (B) in the second sentence, by striking ``subsections (c) and (d)'' and inserting ``subsections (c), (d), and (e)''; and (2) in subsection (b)-- (A) by striking paragraph (2) of the first sentence and inserting the following new paragraph (2): ``(2) chapters 11, 13 (except section 1312(a)), and 15 of this title.''; and (B) in the second sentence, by striking ``subsection (c)'' and inserting ``subsections (c) and (e)''. (b) Rate of Payment.--That section is further amended by adding at the end the following new subsection: ``(e) In the case of benefits under chapter 15 of this title paid by reason of service described in subsection (a) or (b), if-- ``(1) the benefits are paid to an individual residing in the United States who is a citizen of, or an alien lawfully admitted for permanent residence in, the United States, the second sentence of the applicable subsection shall not apply; and ``(2) the benefits are paid to an individual residing in the Republic of the Philippines, the benefits shall be paid (notwithstanding any other provision of law) at the rate of $100 per month.''. (c) Effective Date.--The amendments made by this section shall take effect on the date of enactment of this Act, and shall apply to benefits for months beginning on or after that date. SEC. 5. ELIGIBILITY OF FILIPINO VETERANS FOR HEALTH CARE IN THE UNITED STATES. The text of section 1734 of title 38, United States Code, is amended to read as follows: ``The Secretary, within the limits of Department facilities, shall furnish hospital and nursing home care and medical services to Commonwealth Army veterans and new Philippine Scouts in the same manner as provided for under section 1710 of this title.''. SEC. 6. OUTPATIENT HEALTH CARE FOR VETERANS RESIDING IN THE PHILIPPINES. (a) In General.--Subchapter IV of chapter 17 of title 38, United States Code, is amended-- (1) by redesignating section 1735 as section 1736; and (2) by inserting after section 1734 the following new section 1735: ``Sec. 1735. Outpatient care and services for World War II veterans residing in the Philippines ``(a) Outpatient Health Care.--The Secretary shall furnish care and services to veterans of World War II, Commonwealth Army veterans, and new Philippine Scouts for the treatment of the service-connected disabilities and nonservice-connected disabilities of such veterans and scouts residing in the Republic of the Philippines on an outpatient basis at the Manila VA Outpatient Clinic. ``(b) Limitations.--(1) The amount expended by the Secretary for the purpose of subsection (a) in any fiscal year may not exceed $500,000. ``(2) The authority of the Secretary to furnish care and services under subsection (a) is effective in any fiscal year only to the extent that appropriations are available for that purpose.''. (b) Clerical Amendment.--The table of sections at the beginning of chapter 17 of such title is amended by striking the item relating to section 1735 and inserting after the item relating to section 1734 the following new items: ``1735. Outpatient care and services for World War II veterans residing in the Philippines. ``1736. Definitions.''. (c) Effective Date.--The amendments made by this section shall take effect on the date of the enactment of this Act.

Filipino Veterans' Benefits Improvements Act of 2001 - Redesignates provisions of Federal law which authorize: (1) payment of compensation for the service-connected disability of members of the Philippine Commonwealth Army who served with U.S. armed forces during World War II and who now are U.S. citizens or lawfully reside in the United States; and (2) hospital and nursing home care and medical services for such veterans and new Philippine Scouts in the same manner as U.S. veterans. Limits the disability pension to $100 per month for such veterans who reside in the Philippines.Directs the Secretary of Veterans Affairs to furnish care and services to veterans of World War II, Commonwealth Army veterans, and new Philippine Scouts for the treatment of service-connected disabilities and non-service connected disabilities of such veterans and scouts residing in the Philippines on an outpatient basis at the Manila VA Outpatient Clinic. Limits to $500,000 the amount to be expended during a fiscal year for such services.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Filipino Veterans' Benefits Improvements Act of 2001''. SEC. 2. RATE OF PAYMENT OF CERTAIN BENEFITS FOR NEW PHILIPPINE SCOUTS RESIDING IN THE UNITED STATES. (a) Redesignation of Provisions.--Section 107 of title 38, United States Code, is amended-- (1) in the second sentence of subsection (a), by striking ``subsection (c)'' and inserting ``subsections (c) and (d)''; and (2) by designating subsection (c), as added by section 332(a)(2) of the Veterans Benefits and Health Care Improvement Act of 2000 (Public Law 106-419; 114 Stat. 1856), as subsection (d). (b) Rate of Payment.--That section is further amended-- (1) in the second sentence of subsection (b), by striking ``Payments'' and inserting ``Except as provided in subsection (c), payments''; and (2) in subsection (c), as added by section 501(a) of H.R. 5482 of the 106th Congress (as enacted by Public Law 106-377 (114 Stat. 1441A-55))-- (A) by inserting ``or (b)'' after ``subsection (a)'' the first place it appears; and (B) by striking ``subsection (a)'' the second place it appears and inserting ``the applicable subsection''. (c) Effective Date.--The amendments made by subsection (b) shall take effect on the date of enactment of this Act, and shall apply to benefits paid for months beginning on or after that date. SEC. 3. RATE OF PAYMENT OF DEPENDENCY AND INDEMNITY COMPENSATION FOR SURVIVING SPOUSES OF CERTAIN FILIPINO VETERANS. (a) Rate of Payment.--Subsection (c) of section 107 of title 38, United States Code, as added by section 501(a) of H.R. 5482 of the 106th Congress (as enacted by Public Law 106-377 (114 Stat. 1441A-55)) and amended by section 2 of this Act, is further amended by inserting ``, and under chapter 13 of this title,'' after ``chapter 11 of this title''. (b) Effective Date.--The amendment made by subsection (a) shall take effect on the date of enactment of this Act, and shall apply to benefits paid for months beginning on or after that date. SEC. 4. ELIGIBILITY OF CERTAIN FILIPINO VETERANS FOR DISABILITY PENSION. (a) Eligibility.--Section 107 of title 38, United States Code, as amended by this Act, is further amended-- (1) in subsection (a)-- (A) in paragraph (3) of the first sentence, by inserting ``15,'' before ``23,''; and (B) in the second sentence, by striking ``subsections (c) and (d)'' and inserting ``subsections (c), (d), and (e)''; and (2) in subsection (b)-- (A) by striking paragraph (2) of the first sentence and inserting the following new paragraph (2): ``(2) chapters 11, 13 (except section 1312(a)), and 15 of this title.''; and (B) in the second sentence, by striking ``subsection (c)'' and inserting ``subsections (c) and (e)''. (b) Rate of Payment.--That section is further amended by adding at the end the following new subsection: ``(e) In the case of benefits under chapter 15 of this title paid by reason of service described in subsection (a) or (b), if-- ``(1) the benefits are paid to an individual residing in the United States who is a citizen of, or an alien lawfully admitted for permanent residence in, the United States, the second sentence of the applicable subsection shall not apply; and ``(2) the benefits are paid to an individual residing in the Republic of the Philippines, the benefits shall be paid (notwithstanding any other provision of law) at the rate of $100 per month.''. (c) Effective Date.--The amendments made by this section shall take effect on the date of enactment of this Act, and shall apply to benefits for months beginning on or after that date. SEC. 5. ELIGIBILITY OF FILIPINO VETERANS FOR HEALTH CARE IN THE UNITED STATES. The text of section 1734 of title 38, United States Code, is amended to read as follows: ``The Secretary, within the limits of Department facilities, shall furnish hospital and nursing home care and medical services to Commonwealth Army veterans and new Philippine Scouts in the same manner as provided for under section 1710 of this title.''. SEC. 6. OUTPATIENT HEALTH CARE FOR VETERANS RESIDING IN THE PHILIPPINES. (a) In General.--Subchapter IV of chapter 17 of title 38, United States Code, is amended-- (1) by redesignating section 1735 as section 1736; and (2) by inserting after section 1734 the following new section 1735: ``Sec. 1735. Outpatient care and services for World War II veterans residing in the Philippines ``(a) Outpatient Health Care.--The Secretary shall furnish care and services to veterans of World War II, Commonwealth Army veterans, and new Philippine Scouts for the treatment of the service-connected disabilities and nonservice-connected disabilities of such veterans and scouts residing in the Republic of the Philippines on an outpatient basis at the Manila VA Outpatient Clinic. ``(b) Limitations.--(1) The amount expended by the Secretary for the purpose of subsection (a) in any fiscal year may not exceed $500,000. ``(2) The authority of the Secretary to furnish care and services under subsection (a) is effective in any fiscal year only to the extent that appropriations are available for that purpose.''. (b) Clerical Amendment.--The table of sections at the beginning of chapter 17 of such title is amended by striking the item relating to section 1735 and inserting after the item relating to section 1734 the following new items: ``1735. Outpatient care and services for World War II veterans residing in the Philippines. ``1736. Definitions.''. (c) Effective Date.--The amendments made by this section shall take effect on the date of the enactment of this Act.[/INST]Filipino Veterans' Benefits Improvements Act of 2001 - Redesignates provisions of Federal law which authorize: (1) payment of compensation for the service-connected disability of members of the Philippine Commonwealth Army who served with U.S. armed forces during World War II and who now are U.S. citizens or lawfully reside in the United States; and (2) hospital and nursing home care and medical services for such veterans and new Philippine Scouts in the same manner as U.S. veterans. Limits the disability pension to $100 per month for such veterans who reside in the Philippines.Directs the Secretary of Veterans Affairs to furnish care and services to veterans of World War II, Commonwealth Army veterans, and new Philippine Scouts for the treatment of service-connected disabilities and non-service connected disabilities of such veterans and scouts residing in the Philippines on an outpatient basis at the Manila VA Outpatient Clinic. Limits to $500,000 the amount to be expended during a fiscal year for such services.</s>

A belief that the war in Afghanistan is unwinnable and fear of a future civil war has persuaded Taliban leaders of the merits of a ceasefire, power-sharing and a political deal, according to a group of experts and academics who conducted private talks with senior Taliban figures. Two former Taliban ministers, a former mujahideen commander and an Afghan mediator with experience of negotiating with the Taliban spent between three and five hours in individual discussions with professors Anatol Lieven, Theo Farrell and Rudra Chaudhuri of King's College London and Michael Semple of Harvard. Separately, Matt Waldman, a former key UN official in Kabul involved in promoting dialogue and reconciliation in Afghanistan, has told the Guardian: "It would be a grave mistake to assume the Taliban would settle for nothing less than absolute power." At a press briefing on Monday on their report published by the Royal United Services Institute, Lieven and his colleagues painted a picture of a pragmatic Taliban leadership around Mullah Omar. Three of his group's four interlocutors said they could imagine a "long-term US military role in Afghanistan … so long as the US military presence contributed to Afghan security", Farrell said. But it could be used to attack Afghan's neighbours, including Iran, the Taliban leaders insisted. Semple said the Taliban figures they spoke to were driven by the belief that "war was not winnable" and by "fear of precipitating civil war". Lieven described "real disillusionment and anger with al-Qaida" within the Taliban leadership. However, he said their Taliban interlocutors were "very silent" on the question of the Haqqani network, which has attacked US and Afghan forces from their base in Pakistan. Originally encouraged by the CIA during the war against Soviet forces in Afghanistan, the group has just been proscribed by the US as a terrorist organisation. "Pakistan's influence would be crucial," Lieven described one of their Taliban interlocutors as saying, because Pakistan could undermine a peace agreement. "Taliban leaders know they stand no chance of seizing power now or in the near future," writes Waldman in the Guardian. "They know that even coming close would reinvigorate, potentially augment, the coalition of forces ranged against them. That could trigger a civil war, which they are anxious to avoid." He continues: "Antediluvian theocracy has had its day and thinking Talibs know it," and adds: "Most Taliban leaders deeply resent their dependence on, and manipulation by, Pakistan's intelligence agency, the ISI … They yearn to be taken seriously as a credible, national political force." ||||| LONDON/KABUL (Reuters) - The Afghan Taliban denied a report on Monday that some of their leading members were ready to negotiate a comprehensive peace deal involving a long-term U.S. military presence in Afghanistan. A report to be published by the Royal United Services Institute said some leading Taliban were determined to make a decisive break with al Qaeda as part of a settlement and were open to negotiation about allowing education for girls. “The Taliban would be open to negotiating a ceasefire as part of a general settlement, and also as a bridge between confidence-building measures and the core issue of the distribution of political power in Afghanistan,” the report said. But a spokesman for the Islamist group in Afghanistan denied that any interviews had taken place. “The report is a lie and is baseless,” Zabihullah Mujahid told Reuters from an undisclosed location. “We have never wanted the Americans to stay in Afghanistan and this has always been our position.” The Taliban, who have been fighting against NATO-led troops for 11 years, have always maintained that any negotiations with Afghan authorities and Washington could only be carried out once there were no foreign soldiers on Afghan soil. RUSI said its report, entitled “Taliban Perspectives on Reconciliation”, was based on interviews with four unnamed Taliban figures, two of whom had been ministers in the former Taliban government and were still close to the inner circle of leadership. The report cites a person described as a founding member of the Taliban as saying that the group might accept continuing U.S. counter-terrorist operations targeting al Qaeda in Afghanistan as long as the bases were not used to launch attacks on other countries or for interference in Afghan politics. The report said that from the Taliban’s point of view, any ceasefire would need strong Islamic justification and could not hint at any form of surrender. U.S. officials have said they see signs that insurgent hostility to peace talks may be splintering. With violence in Afghanistan at its worst levels since U.S.-backed forces ousted the Taliban in 2001, the West is eager to pursue such negotiations, given that it plans to withdraw most of a currently 130,000-strong NATO-led foreign force by the end of 2014.

– The Taliban is ready to accept a peace deal that would allow a US military presence in Afghanistan until 2024, according to a group of academics who interviewed senior Taliban figures. The professors say that leading Taliban members have concluded that the "war is not winnable," and they're willing to make concessions in return for a share of political power, reports the Guardian. The Taliban leaders despise the "weak and corrupt" Karzai government, but have also soured on al-Qaeda, according to the academics. The academics say the pragmatic Taliban figures they spoke to could accept a US presence at five bases, as long as the American forces did not attack Afghanistan's neighbors Iran and Pakistan. The Taliban, which has long said that it will not talk peace until foreign troops leave, denies the report. It is "a lie and is baseless," a spokesman tells Reuters. "We have never wanted the Americans to stay in Afghanistan, and this has always been our position." In 2010, a "top Taliban figure" the British brought to Kabul for meetings with Karzai turned out to be a Pakistani shopkeeper.

<s>[INST]A belief that the war in Afghanistan is unwinnable and fear of a future civil war has persuaded Taliban leaders of the merits of a ceasefire, power-sharing and a political deal, according to a group of experts and academics who conducted private talks with senior Taliban figures. Two former Taliban ministers, a former mujahideen commander and an Afghan mediator with experience of negotiating with the Taliban spent between three and five hours in individual discussions with professors Anatol Lieven, Theo Farrell and Rudra Chaudhuri of King's College London and Michael Semple of Harvard. Separately, Matt Waldman, a former key UN official in Kabul involved in promoting dialogue and reconciliation in Afghanistan, has told the Guardian: "It would be a grave mistake to assume the Taliban would settle for nothing less than absolute power." At a press briefing on Monday on their report published by the Royal United Services Institute, Lieven and his colleagues painted a picture of a pragmatic Taliban leadership around Mullah Omar. Three of his group's four interlocutors said they could imagine a "long-term US military role in Afghanistan … so long as the US military presence contributed to Afghan security", Farrell said. But it could be used to attack Afghan's neighbours, including Iran, the Taliban leaders insisted. Semple said the Taliban figures they spoke to were driven by the belief that "war was not winnable" and by "fear of precipitating civil war". Lieven described "real disillusionment and anger with al-Qaida" within the Taliban leadership. However, he said their Taliban interlocutors were "very silent" on the question of the Haqqani network, which has attacked US and Afghan forces from their base in Pakistan. Originally encouraged by the CIA during the war against Soviet forces in Afghanistan, the group has just been proscribed by the US as a terrorist organisation. "Pakistan's influence would be crucial," Lieven described one of their Taliban interlocutors as saying, because Pakistan could undermine a peace agreement. "Taliban leaders know they stand no chance of seizing power now or in the near future," writes Waldman in the Guardian. "They know that even coming close would reinvigorate, potentially augment, the coalition of forces ranged against them. That could trigger a civil war, which they are anxious to avoid." He continues: "Antediluvian theocracy has had its day and thinking Talibs know it," and adds: "Most Taliban leaders deeply resent their dependence on, and manipulation by, Pakistan's intelligence agency, the ISI … They yearn to be taken seriously as a credible, national political force." ||||| LONDON/KABUL (Reuters) - The Afghan Taliban denied a report on Monday that some of their leading members were ready to negotiate a comprehensive peace deal involving a long-term U.S. military presence in Afghanistan. A report to be published by the Royal United Services Institute said some leading Taliban were determined to make a decisive break with al Qaeda as part of a settlement and were open to negotiation about allowing education for girls. “The Taliban would be open to negotiating a ceasefire as part of a general settlement, and also as a bridge between confidence-building measures and the core issue of the distribution of political power in Afghanistan,” the report said. But a spokesman for the Islamist group in Afghanistan denied that any interviews had taken place. “The report is a lie and is baseless,” Zabihullah Mujahid told Reuters from an undisclosed location. “We have never wanted the Americans to stay in Afghanistan and this has always been our position.” The Taliban, who have been fighting against NATO-led troops for 11 years, have always maintained that any negotiations with Afghan authorities and Washington could only be carried out once there were no foreign soldiers on Afghan soil. RUSI said its report, entitled “Taliban Perspectives on Reconciliation”, was based on interviews with four unnamed Taliban figures, two of whom had been ministers in the former Taliban government and were still close to the inner circle of leadership. The report cites a person described as a founding member of the Taliban as saying that the group might accept continuing U.S. counter-terrorist operations targeting al Qaeda in Afghanistan as long as the bases were not used to launch attacks on other countries or for interference in Afghan politics. The report said that from the Taliban’s point of view, any ceasefire would need strong Islamic justification and could not hint at any form of surrender. U.S. officials have said they see signs that insurgent hostility to peace talks may be splintering. With violence in Afghanistan at its worst levels since U.S.-backed forces ousted the Taliban in 2001, the West is eager to pursue such negotiations, given that it plans to withdraw most of a currently 130,000-strong NATO-led foreign force by the end of 2014.[/INST]– The Taliban is ready to accept a peace deal that would allow a US military presence in Afghanistan until 2024, according to a group of academics who interviewed senior Taliban figures. The professors say that leading Taliban members have concluded that the "war is not winnable," and they're willing to make concessions in return for a share of political power, reports the Guardian. The Taliban leaders despise the "weak and corrupt" Karzai government, but have also soured on al-Qaeda, according to the academics. The academics say the pragmatic Taliban figures they spoke to could accept a US presence at five bases, as long as the American forces did not attack Afghanistan's neighbors Iran and Pakistan. The Taliban, which has long said that it will not talk peace until foreign troops leave, denies the report. It is "a lie and is baseless," a spokesman tells Reuters. "We have never wanted the Americans to stay in Afghanistan, and this has always been our position." In 2010, a "top Taliban figure" the British brought to Kabul for meetings with Karzai turned out to be a Pakistani shopkeeper.</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``International Protecting Girls by Preventing Child Marriage Act of 2007''. SEC. 2. FINDINGS. Congress makes the following findings: (1) Child marriage, also known as ``forced marriage'' or ``early marriage'', is a harmful traditional practice that deprives girls of their dignity and human rights. (2) Child marriage as a traditional practice, as well as through coercion or force, is a violation of Article 16 of the Universal Declaration of Human Rights, which states, ``Marriage shall be entered into only with the free and full consent of intending spouses.''. (3) An estimated 51 million girls in developing countries now ages 20-24 were married under the age of 18, and if present trends continue more than 100 million more girls in developing countries will be married as children over the next decade. (4) In developing countries, other than China, approximately one in seven girls marry before the age of 15 and one in three girls are married before the age of 18. (5) Child marriage ``treats young girls as property'' and ``poses grave risks not only to women's basic rights but also their health, economic independence, education, and status in society'', according to the Department of State. (6) In 2005, the Department of State conducted a world-wide survey and found child marriage to be a concern in 64 out of 182 countries surveyed, with child marriage most common in sub- Saharan Africa and parts of South Asia as well as the Middle East (7) In Ethiopia's Amhara region, about half of all girls are married by age 14 with 95 percent not knowing their husbands before marriage, 85 percent unaware they were to be married, and 70 percent reporting their first sexual initiation within marriage taking place before their first menstrual period, according to a 2004 survey. (8) In Afghanistan, where the legal age of marriage for girls is 16 years, 57 percent of marriages involve girls below the age of 16, including girls younger than 10 years, according to the United Nations Children's Fund (UNICEF). (9) In some areas of northern Nigeria, 45 percent of girls are married by age 15 and 73 percent by age 18, with age gaps between girls and the husbands averaging between 12 and 18 years. (10) Between half and three-quarters of all girls are married before the age of 18 in the following countries: Niger, Chad, Bangladesh, Mali, Guinea, the Central African Republic, Nepal, Mozambique, Uganda, Burkina Faso, and India, according to Demographic Health Survey data. (11) Factors perpetuating child marriage include poverty, a lack of educational or employment opportunities for girls, parental concerns to ensure sexual relations within marriage, the dowry system, and the perceived lack of value of girls. (12) Child marriage has negative effects on girls' health, including significantly increased risk of maternal death and morbidity, infant mortality, obstetric fistula, and sexually transmitted diseases, including HIV/AIDS. (13) In developing countries, girls ages 10 to 14 who become pregnant are five times more likely to die during a pregnancy or in childbirth than women ages 20 to 24. (14) Child marriage can result in bonded labor or enslavement, commercial sexual exploitation, and violence against the victims, according to UNICEF. (15) Out-of-school or unschooled girls are at greater risk of child marriage while girls in school face pressure to withdraw from school when secondary school requires monetary costs, travel, or other social costs, including lack of lavatories and supplies for menstruating girls and increased risk of sexual violence. (16) The World Bank reports in 2006 that it is estimated that ``about half of girls in Sub-Saharan Africa who drop out of primary school do so because of poor water and sanitation facilities''. (17) UNICEF reports that investments in improving school sanitation resulted in a 17 percent increase in school enrollment for girls in Guinea and an 11 percent increase for girls in Bangladesh. (18) Investments in girls' schooling, creating safe community spaces for girls, and programs for skills building for out-of-school girls are all effective and demonstrated strategies for preventing child marriage and creating a pathway to empower girls by addressing conditions of poverty, low status, and norms that contribute to child marriage. (19) Most countries with high rates of child marriage have a legally-established minimum age of marriage, yet child marriage persists due to strong traditional norms and the failure to enforce existing laws. SEC. 3. SENSE OF CONGRESS. It is the sense of Congress that-- (1) child marriage is a violation of human rights and the prevention and elimination of child marriage should be a foreign policy goal of the United States; (2) the practice of child marriage undermines United States investments in foreign assistance to promote education and skills building for girls, reduce maternal and child mortality, reduce maternal illness, halt the transmission of HIV/AIDS, prevent gender-based violence, and reduce poverty; and (3) expanding educational opportunities for girls, economic opportunities for women, and reducing maternal and child mortality are critical to achieving the Millennium Development Goals and the global health and development objectives of the United States, including efforts to prevent HIV/AIDS. SEC. 4. ASSISTANCE TO PREVENT THE INCIDENCE OF CHILDHOOD MARRIAGE IN DEVELOPING COUNTRIES. (a) Assistance Authorized.--The President is authorized to provide assistance, including through multilateral, nongovernmental, and faith- based organizations, to prevent the incidence of child marriage in developing countries and to promote the educational, health, economic, social, and legal empowerment of girls and women as part of the strategy to prevent child marriage in developing countries established pursuant to section 5. (b) Priority.--In providing assistance authorized under subsection (a), the President shall give priority to-- (1) areas or regions in developing countries in which 15 percent of girls under the age of 15 are married or 40 percent of girls under the age of 18 are married; and (2) activities to-- (A) expand and replicate existing community-based programs that are successful in preventing the incidence of child marriage; (B) establish pilot projects to prevent child marriage; and (C) share evaluations of successful programs, program designs, experiences, and lessons. (c) Coordination.--Assistance authorized under subsection (a) shall be integrated with existing United States programs for advancing appropriate age and grade-level basic and secondary education through adolescence, ensure school enrollment and completion for girls, health, income generation, agriculture development, legal rights, and democracy building and human rights, including-- (1) support for community-based activities that encourage community members to address beliefs or practices that promote child marriage and to educate parents, community leaders, religious leaders, and adolescents of the health risks associated with child marriage and the benefits for adolescents, especially girls, of access to education, health care, livelihood skills, microfinance, and savings programs; (2) enrolling girls in primary and secondary school at the appropriate age and keeping them in age-appropriate grade levels through adolescence; (3) reducing education fees, and enhancing safe and supportive conditions in primary and secondary schools to meet the needs of girls, including-- (A) access to water and suitable hygiene facilities, including separate lavatories and latrines for girls; (B) assignment of female teachers; (C) safe routes to and from school; and (D) eliminating sexual harassment and other forms of violence and coercion; (4) ensuring access to health care services and proper nutrition for adolescent girls, which is essential to both their school performance and their economic productivity; (5) increasing training for adolescent girls and their parents in financial literacy and access to economic opportunities, including livelihood skills, savings, microfinance, and small-enterprise development; (6) supporting education, including through community and faith-based organizations and youth programs, that helps remove gender stereotypes and the bias against girls used to justify child marriage, especially efforts targeted at men and boys, promotes zero tolerance for violence, and promotes gender equality, which in turn help to increase the perceived value of girls; (7) creating peer support and female mentoring networks and safe social spaces specifically for girls; and (8) supporting local advocacy work to ensure that governments and law enforcement officials are meeting their obligations to prevent child and forced marriage as well as legal literacy programs at the community level. SEC. 5. STRATEGY TO PREVENT CHILD MARRIAGE IN DEVELOPING COUNTRIES. (a) Strategy Required.--The President, acting through the Administrator of the United States Agency for International Development, shall establish a multi-year strategy to prevent child marriage in developing countries and promote the empowerment of girls at risk of child marriage in developing countries, including by addressing the unique needs, vulnerabilities, and potential of girls ages eight to 18 in developing countries. (b) Consultation.--In establishing the strategy required by subsection (a), the President shall consult with Congress, relevant Federal departments and agencies, multilateral organizations, and representatives of civil society. (c) Elements.--The strategy required by subsection (a) shall-- (1) focus on areas in developing countries with high prevalence of child marriage; and (2) encompass diplomatic initiatives between the United States and governments of developing countries, with attention to human rights, legal reforms and the rule of law, and programmatic initiatives in the areas of education, health, income generation, changing social norms, human rights, and democracy building. (d) Report.--Not later than 180 days after the date of the enactment of this Act, the President shall transmit to Congress a report that includes-- (1) the strategy required by subsection (a); (2) an assessment, including data disaggregated by age and gender to the extent possible, of current United States-funded efforts to specifically assist girls in developing countries; and (3) examples of best practices or programs to prevent child marriage in developing countries that could be replicated. SEC. 6. DEPARTMENT OF STATE'S COUNTRY REPORTS ON HUMAN RIGHTS PRACTICES. The Foreign Assistance Act of 1961 is amended-- (1) in section 116 (22 U.S.C. 2151n), by adding at the end the following new subsection: ``(g) The report required by subsection (d) shall include for each country in which child marriage is prevalent at rates at or above 40 percent in at least one sub-national region, a description on the status of the practice of child marriage (as defined in section 7 of the International Protecting Girls by Preventing Child Marriage Act of 2007) in the country.''; and (2) in section 502B (22 U.S.C. 2304), by adding at the end the following new subsection: ``(i) The report required by subsection (b) shall include for each country in which child marriage is prevalent at rates at or above 40 percent in at least one sub-national region, a description on the status of the practice of child marriage (as defined in section 7 of the International Protecting Girls by Preventing Child Marriage Act of 2007) in the country.''. SEC. 7. DEFINITION. In this Act, the term ``child marriage'' means the marriage of a girl or boy, not yet the minimum age for marriage stipulated in law in the country in which the girl or boy is a resident. SEC. 8. AUTHORIZATION OF APPROPRIATIONS. To carry out this Act and the amendments made by this Act, there are authorized to be appropriated $25,000,000 for each of fiscal years 2008 through 2012.

International Protecting Girls by Preventing Child Marriage Act of 2007 - Authorizes the President to provide assistance, including through multilateral, nongovernmental, and faith-based organizations, to prevent child marriage in developing countries and to promote the educational, health, economic, social, and legal empowerment of girls and women. Sets forth priority assistance criteria. Directs the President, through the United States Agency for International Development (USAID), to establish a multi-year strategy to prevent child marriage in developing countries and to promote the empowerment of girls at risk of child marriage, including by addressing the unique needs and potentials of eight to 18 year old girls. Amends the Foreign Assistance Act of 1961 to require that Department of State country reports on human rights practices include a description of the status of child marriage for countries with specified rates of child marriage. Defines "child marriage."

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``International Protecting Girls by Preventing Child Marriage Act of 2007''. SEC. 2. FINDINGS. Congress makes the following findings: (1) Child marriage, also known as ``forced marriage'' or ``early marriage'', is a harmful traditional practice that deprives girls of their dignity and human rights. (2) Child marriage as a traditional practice, as well as through coercion or force, is a violation of Article 16 of the Universal Declaration of Human Rights, which states, ``Marriage shall be entered into only with the free and full consent of intending spouses.''. (3) An estimated 51 million girls in developing countries now ages 20-24 were married under the age of 18, and if present trends continue more than 100 million more girls in developing countries will be married as children over the next decade. (4) In developing countries, other than China, approximately one in seven girls marry before the age of 15 and one in three girls are married before the age of 18. (5) Child marriage ``treats young girls as property'' and ``poses grave risks not only to women's basic rights but also their health, economic independence, education, and status in society'', according to the Department of State. (6) In 2005, the Department of State conducted a world-wide survey and found child marriage to be a concern in 64 out of 182 countries surveyed, with child marriage most common in sub- Saharan Africa and parts of South Asia as well as the Middle East (7) In Ethiopia's Amhara region, about half of all girls are married by age 14 with 95 percent not knowing their husbands before marriage, 85 percent unaware they were to be married, and 70 percent reporting their first sexual initiation within marriage taking place before their first menstrual period, according to a 2004 survey. (8) In Afghanistan, where the legal age of marriage for girls is 16 years, 57 percent of marriages involve girls below the age of 16, including girls younger than 10 years, according to the United Nations Children's Fund (UNICEF). (9) In some areas of northern Nigeria, 45 percent of girls are married by age 15 and 73 percent by age 18, with age gaps between girls and the husbands averaging between 12 and 18 years. (10) Between half and three-quarters of all girls are married before the age of 18 in the following countries: Niger, Chad, Bangladesh, Mali, Guinea, the Central African Republic, Nepal, Mozambique, Uganda, Burkina Faso, and India, according to Demographic Health Survey data. (11) Factors perpetuating child marriage include poverty, a lack of educational or employment opportunities for girls, parental concerns to ensure sexual relations within marriage, the dowry system, and the perceived lack of value of girls. (12) Child marriage has negative effects on girls' health, including significantly increased risk of maternal death and morbidity, infant mortality, obstetric fistula, and sexually transmitted diseases, including HIV/AIDS. (13) In developing countries, girls ages 10 to 14 who become pregnant are five times more likely to die during a pregnancy or in childbirth than women ages 20 to 24. (14) Child marriage can result in bonded labor or enslavement, commercial sexual exploitation, and violence against the victims, according to UNICEF. (15) Out-of-school or unschooled girls are at greater risk of child marriage while girls in school face pressure to withdraw from school when secondary school requires monetary costs, travel, or other social costs, including lack of lavatories and supplies for menstruating girls and increased risk of sexual violence. (16) The World Bank reports in 2006 that it is estimated that ``about half of girls in Sub-Saharan Africa who drop out of primary school do so because of poor water and sanitation facilities''. (17) UNICEF reports that investments in improving school sanitation resulted in a 17 percent increase in school enrollment for girls in Guinea and an 11 percent increase for girls in Bangladesh. (18) Investments in girls' schooling, creating safe community spaces for girls, and programs for skills building for out-of-school girls are all effective and demonstrated strategies for preventing child marriage and creating a pathway to empower girls by addressing conditions of poverty, low status, and norms that contribute to child marriage. (19) Most countries with high rates of child marriage have a legally-established minimum age of marriage, yet child marriage persists due to strong traditional norms and the failure to enforce existing laws. SEC. 3. SENSE OF CONGRESS. It is the sense of Congress that-- (1) child marriage is a violation of human rights and the prevention and elimination of child marriage should be a foreign policy goal of the United States; (2) the practice of child marriage undermines United States investments in foreign assistance to promote education and skills building for girls, reduce maternal and child mortality, reduce maternal illness, halt the transmission of HIV/AIDS, prevent gender-based violence, and reduce poverty; and (3) expanding educational opportunities for girls, economic opportunities for women, and reducing maternal and child mortality are critical to achieving the Millennium Development Goals and the global health and development objectives of the United States, including efforts to prevent HIV/AIDS. SEC. 4. ASSISTANCE TO PREVENT THE INCIDENCE OF CHILDHOOD MARRIAGE IN DEVELOPING COUNTRIES. (a) Assistance Authorized.--The President is authorized to provide assistance, including through multilateral, nongovernmental, and faith- based organizations, to prevent the incidence of child marriage in developing countries and to promote the educational, health, economic, social, and legal empowerment of girls and women as part of the strategy to prevent child marriage in developing countries established pursuant to section 5. (b) Priority.--In providing assistance authorized under subsection (a), the President shall give priority to-- (1) areas or regions in developing countries in which 15 percent of girls under the age of 15 are married or 40 percent of girls under the age of 18 are married; and (2) activities to-- (A) expand and replicate existing community-based programs that are successful in preventing the incidence of child marriage; (B) establish pilot projects to prevent child marriage; and (C) share evaluations of successful programs, program designs, experiences, and lessons. (c) Coordination.--Assistance authorized under subsection (a) shall be integrated with existing United States programs for advancing appropriate age and grade-level basic and secondary education through adolescence, ensure school enrollment and completion for girls, health, income generation, agriculture development, legal rights, and democracy building and human rights, including-- (1) support for community-based activities that encourage community members to address beliefs or practices that promote child marriage and to educate parents, community leaders, religious leaders, and adolescents of the health risks associated with child marriage and the benefits for adolescents, especially girls, of access to education, health care, livelihood skills, microfinance, and savings programs; (2) enrolling girls in primary and secondary school at the appropriate age and keeping them in age-appropriate grade levels through adolescence; (3) reducing education fees, and enhancing safe and supportive conditions in primary and secondary schools to meet the needs of girls, including-- (A) access to water and suitable hygiene facilities, including separate lavatories and latrines for girls; (B) assignment of female teachers; (C) safe routes to and from school; and (D) eliminating sexual harassment and other forms of violence and coercion; (4) ensuring access to health care services and proper nutrition for adolescent girls, which is essential to both their school performance and their economic productivity; (5) increasing training for adolescent girls and their parents in financial literacy and access to economic opportunities, including livelihood skills, savings, microfinance, and small-enterprise development; (6) supporting education, including through community and faith-based organizations and youth programs, that helps remove gender stereotypes and the bias against girls used to justify child marriage, especially efforts targeted at men and boys, promotes zero tolerance for violence, and promotes gender equality, which in turn help to increase the perceived value of girls; (7) creating peer support and female mentoring networks and safe social spaces specifically for girls; and (8) supporting local advocacy work to ensure that governments and law enforcement officials are meeting their obligations to prevent child and forced marriage as well as legal literacy programs at the community level. SEC. 5. STRATEGY TO PREVENT CHILD MARRIAGE IN DEVELOPING COUNTRIES. (a) Strategy Required.--The President, acting through the Administrator of the United States Agency for International Development, shall establish a multi-year strategy to prevent child marriage in developing countries and promote the empowerment of girls at risk of child marriage in developing countries, including by addressing the unique needs, vulnerabilities, and potential of girls ages eight to 18 in developing countries. (b) Consultation.--In establishing the strategy required by subsection (a), the President shall consult with Congress, relevant Federal departments and agencies, multilateral organizations, and representatives of civil society. (c) Elements.--The strategy required by subsection (a) shall-- (1) focus on areas in developing countries with high prevalence of child marriage; and (2) encompass diplomatic initiatives between the United States and governments of developing countries, with attention to human rights, legal reforms and the rule of law, and programmatic initiatives in the areas of education, health, income generation, changing social norms, human rights, and democracy building. (d) Report.--Not later than 180 days after the date of the enactment of this Act, the President shall transmit to Congress a report that includes-- (1) the strategy required by subsection (a); (2) an assessment, including data disaggregated by age and gender to the extent possible, of current United States-funded efforts to specifically assist girls in developing countries; and (3) examples of best practices or programs to prevent child marriage in developing countries that could be replicated. SEC. 6. DEPARTMENT OF STATE'S COUNTRY REPORTS ON HUMAN RIGHTS PRACTICES. The Foreign Assistance Act of 1961 is amended-- (1) in section 116 (22 U.S.C. 2151n), by adding at the end the following new subsection: ``(g) The report required by subsection (d) shall include for each country in which child marriage is prevalent at rates at or above 40 percent in at least one sub-national region, a description on the status of the practice of child marriage (as defined in section 7 of the International Protecting Girls by Preventing Child Marriage Act of 2007) in the country.''; and (2) in section 502B (22 U.S.C. 2304), by adding at the end the following new subsection: ``(i) The report required by subsection (b) shall include for each country in which child marriage is prevalent at rates at or above 40 percent in at least one sub-national region, a description on the status of the practice of child marriage (as defined in section 7 of the International Protecting Girls by Preventing Child Marriage Act of 2007) in the country.''. SEC. 7. DEFINITION. In this Act, the term ``child marriage'' means the marriage of a girl or boy, not yet the minimum age for marriage stipulated in law in the country in which the girl or boy is a resident. SEC. 8. AUTHORIZATION OF APPROPRIATIONS. To carry out this Act and the amendments made by this Act, there are authorized to be appropriated $25,000,000 for each of fiscal years 2008 through 2012.[/INST]International Protecting Girls by Preventing Child Marriage Act of 2007 - Authorizes the President to provide assistance, including through multilateral, nongovernmental, and faith-based organizations, to prevent child marriage in developing countries and to promote the educational, health, economic, social, and legal empowerment of girls and women. Sets forth priority assistance criteria. Directs the President, through the United States Agency for International Development (USAID), to establish a multi-year strategy to prevent child marriage in developing countries and to promote the empowerment of girls at risk of child marriage, including by addressing the unique needs and potentials of eight to 18 year old girls. Amends the Foreign Assistance Act of 1961 to require that Department of State country reports on human rights practices include a description of the status of child marriage for countries with specified rates of child marriage. Defines "child marriage."</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Pornography Victims Protection Act of 1993''. SEC. 2. SECTION 2251 AMENDMENTS. Section 2251 of title 18, United States Code, is amended-- (1) in subsection (a), by striking out ``subsection (d)'' and inserting in lieu thereof ``subsection (e)'' and by inserting before the period at the end thereof the following: ``or if such person knows or has reason to know that the minor was transported in interstate or foreign commerce for the purpose of producing any such visual depiction of such conduct''; (2) in subsection (b), by striking out ``subsection (d)'' and inserting in lieu thereof ``subsection (e)'' and by inserting before the period at the end thereof the following: ``or if such person knows or has reason to know that the minor was transported in interstate or foreign commerce for the purpose of producing any such visual depiction of such conduct''; (3) by inserting immediately after subsection (b) the following: ``(c)(1) Any person who coerces, intimidates, or fraudulently induces an individual 18 years or older to engage in any sexually explicit conduct for the purpose of producing any visual depiction of such conduct shall be punished as provided under subsection (e), if such person knows or has reason to know that such visual depiction will be transported in interstate or foreign commerce or mailed, if such visual depiction has actually been transported in interstate or foreign commerce or mailed, or if such person knows or has reason to know that the individual 18 years or older was transported in interstate or foreign commerce for the purpose of producing any such visual depiction of such conduct. ``(2) Proof of one or more of the following facts or conditions shall not, without more, negate a finding of coercion under this subsection: ``(A) that the person is or has been a prostitute; ``(B) that the person is connected by blood or marriage to anyone involved in or related to the making of the pornography; ``(C) that the person has previously had, or been thought to have had, sexual relations with anyone, including anyone involved in or related to the making of the pornography; ``(D) that the person has previously posed for sexually explicit pictures for or with anyone, including anyone involved in or related to the making of the pornography at issue; ``(E) that anyone else, including a spouse or other relative, has given permission on the person's behalf; ``(F) that the person actually consented to a use of the performance that is changed into pornography; ``(G) that the person knew that the purpose of the acts or events in question was to make pornography; ``(H) that the person signed a contract to produce pornography; or ``(I) that the person was paid or otherwise compensated.''; (4) in subsection (c), by striking out ``(c)'' and inserting in lieu thereof ``(d)''; (5) in subsection (d), by striking out ``(d)'' and inserting in lieu thereof ``(e)''; and (6) by amending the heading to read as follows: ``Sec. 2251. Sexual exploitation''. SEC. 3. CIVIL REMEDIES AND PROCEDURE. (a) Modification of Existing Civil Remedies.--Section 2255 of title 18, United States Code, is amended to read as follows: ``Sec. 2255. Civil remedies. ``(a) The district courts of the United States shall have jurisdiction to prevent and restrain violations of section 2251 of this title by issuing appropriate orders, including-- ``(1) ordering any person to divest himself of any interest, direct or indirect, in any legal or business entity; ``(2) imposing reasonable restrictions on the future activities or investments of any person including prohibiting such person from engaging in the same type of legal or business endeavor; or ``(3) ordering dissolution or reorganization of any legal or business entity after making due provision for the rights of innocent persons. ``(b) The Attorney General or any person threatened with loss or damage by reason of a violation of section 2251 of this title may institute proceedings under subsection (a) of this section and, in the event that the party bringing suit prevails, such party shall recover the cost of the suit, including a reasonable attorney's fee. Pending final determination, the court may at any time enter such restraining orders or prohibitions, or take such other actions, including the acceptance of satisfactory performance bonds, as it shall deem proper. For purposes of this section, a violation of section 2251 of this title shall be determined by a preponderance of the evidence. ``(c) Any victim of a violation of section 2251 of this title who suffers physical injury, emotional distress, or property damage as a result of such violation may sue to recover damages in any appropriate United States district court and shall recover threefold the damages such person sustains as a result of such violation and the cost of the suit, including a reasonable attorney's fee. For purposes of this section, a violation of section 2251 of this title shall be determined by a preponderance of the evidence. ``(d) A final judgment or decree rendered in favor of the United States in any criminal proceeding brought by the United States under this chapter shall estop the defendant from denying the essential allegations of the criminal offense in any subsequent civil proceeding. ``(e) Nothing in this section shall be construed to authorize any order restraining the exhibition, distribution or dissemination of any visual material without a full adversary proceeding and a final judicial determination that such material contains a visual depiction of sexually explicit conduct, engaged in by a minor or by a person who was coerced, intimidated, or fraudulently induced to engage in such sexually explicit conduct.''. (b) Additional Remedies and Procedure.--Chapter 110 of title 18, United States Code, is amended by adding at the end the following: ``Sec. 2259. Civil penalties. ``(a) Any person found to violate section 2251 of this title by preponderance of the evidence shall be liable to the United States Government for a civil penalty of $100,000 and the forfeiture of any interest in property described in section 2254. The Attorney General may bring an action for recovery of any such civil penalty or forfeiture against any such person. If the Attorney General prevails he may also recover the cost of the suit, including a reasonable attorney's fee. ``(b) If the identity of any victim of an offense provided in section 2251 of this title is established before an award of a civil penalty made to the United States under this section, the victim shall be entitled to the award. If there is more than one victim, the court shall apportion the award among the victims on an equitable basis after considering the harm suffered by each such victim. ``Sec. 2260. Venue and process. ``(a) Any civil action or proceeding brought under this chapter may be instituted in the district court of the United States for any district in which the defendant resides, is found, has an agent, or transacts his affairs. ``(b) In any action under section 2255 or 2259 of this title in any district court of the United States in which it is shown that the ends of justice require that other parties residing in any other district be brought before the court, the court may cause such parties to be summoned, and process for that purpose may be served in any judicial district of the United States by the marshal of such judicial district. ``(c) In any civil or criminal action or proceeding under this chapter in the district court of the United States for any judicial district, a subpoena issued by such court to compel the attendance of witnesses may be served in any other judicial district except that no subpoena shall be issued for service upon any individual who resides in another district at a place more than one hundred miles from the place at which such court is held without approval given by a judge of such court upon a showing of good cause. ``(d) All other process in any action or proceeding under this chapter may be served on any person in any judicial district in which such person resides, is found, has an agent, or transacts his affairs. ``Sec. 2261. Expedition of actions. ``In any civil action instituted under this chapter by the United States in any district court of the United States, the Attorney General may file with the clerk of such court a certificate stating that in his opinion the case is of general public importance. A copy of that certificate shall be furnished immediately by such clerk to the chief judge or in his absence to the presiding district judge of the district in which such action is pending. Upon receipt of such copy, such judge shall designate immediately a judge of that district to hear and determine the action. The judge designated to hear and determine the action shall assign the action for hearing as soon as practicable and hold hearings and make a determination as expeditiously as possible. ``Sec. 2262. Evidence. ``In any proceeding ancillary to or in any civil action instituted under this chapter the proceedings may be opened or closed to the public at the discretion of the court after consideration of the rights of affected persons. ``Sec. 2263. Limitations. ``A civil action under section 2255 or 2259 of this title must be brought within six years from the date the violation is committed. In any such action brought by or on behalf of a person who was a minor at the date the violation was committed, the running of such six-year period shall be deemed to have been tolled during the period of such person's minority.''. SEC. 5. CLERICAL AMENDMENT. (a) Table of Sections.--The table of sections for chapter 110 of part I of title 18, United States Code, is amended to read as follows: ``CHAPTER 110--SEXUAL EXPLOITATION ``Sec. ``2251. Sexual exploitation. ``2252. Selling or buying of children. ``2253. Criminal forfeiture. ``2254. Civil forfeiture. ``2255. Civil remedies. ``2256. Definitions for chapter. ``2257. Record keeping requirements. ``2258. Failure to report child abuse. ``2259. Civil penalties. ``2260. Venue and process. ``2261. Expedition of actions. ``2262. Evidence. ``2263. Limitations.''. (b) Table of Chapters.--The table of chapters for part I of title 18, United States Code, is amended by striking the item relating to chapter 110 and inserting in lieu thereof the following: ``110. Sexual Exploitation.................................. 2251''.

Pornography Victims Protection Act of 1993 - Amends the Federal criminal code with respect to the prohibition against the sexual exploitation of children to add as a condition triggering Federal penalties that the person concerned knows that a minor was transported in interstate or foreign commerce for the purpose of producing pornography. Makes it a criminal offense for any person to coerce, intimidate, or fraudulently induce an individual 18 years or older to engage in any sexually explicit conduct for the purposes of producing any visual depiction of such conduct. Grants the U.S. district courts jurisdiction to prevent and restrain violations of this Act. Authorizes the Attorney General or any person threatened with loss or damage by such conduct to institute a civil suit. Provides for treble damages for a victim who suffers physical injury, emotional distress, or property damage. Imposes civil penalties for violation of the prohibition against sexual exploitation of children.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Pornography Victims Protection Act of 1993''. SEC. 2. SECTION 2251 AMENDMENTS. Section 2251 of title 18, United States Code, is amended-- (1) in subsection (a), by striking out ``subsection (d)'' and inserting in lieu thereof ``subsection (e)'' and by inserting before the period at the end thereof the following: ``or if such person knows or has reason to know that the minor was transported in interstate or foreign commerce for the purpose of producing any such visual depiction of such conduct''; (2) in subsection (b), by striking out ``subsection (d)'' and inserting in lieu thereof ``subsection (e)'' and by inserting before the period at the end thereof the following: ``or if such person knows or has reason to know that the minor was transported in interstate or foreign commerce for the purpose of producing any such visual depiction of such conduct''; (3) by inserting immediately after subsection (b) the following: ``(c)(1) Any person who coerces, intimidates, or fraudulently induces an individual 18 years or older to engage in any sexually explicit conduct for the purpose of producing any visual depiction of such conduct shall be punished as provided under subsection (e), if such person knows or has reason to know that such visual depiction will be transported in interstate or foreign commerce or mailed, if such visual depiction has actually been transported in interstate or foreign commerce or mailed, or if such person knows or has reason to know that the individual 18 years or older was transported in interstate or foreign commerce for the purpose of producing any such visual depiction of such conduct. ``(2) Proof of one or more of the following facts or conditions shall not, without more, negate a finding of coercion under this subsection: ``(A) that the person is or has been a prostitute; ``(B) that the person is connected by blood or marriage to anyone involved in or related to the making of the pornography; ``(C) that the person has previously had, or been thought to have had, sexual relations with anyone, including anyone involved in or related to the making of the pornography; ``(D) that the person has previously posed for sexually explicit pictures for or with anyone, including anyone involved in or related to the making of the pornography at issue; ``(E) that anyone else, including a spouse or other relative, has given permission on the person's behalf; ``(F) that the person actually consented to a use of the performance that is changed into pornography; ``(G) that the person knew that the purpose of the acts or events in question was to make pornography; ``(H) that the person signed a contract to produce pornography; or ``(I) that the person was paid or otherwise compensated.''; (4) in subsection (c), by striking out ``(c)'' and inserting in lieu thereof ``(d)''; (5) in subsection (d), by striking out ``(d)'' and inserting in lieu thereof ``(e)''; and (6) by amending the heading to read as follows: ``Sec. 2251. Sexual exploitation''. SEC. 3. CIVIL REMEDIES AND PROCEDURE. (a) Modification of Existing Civil Remedies.--Section 2255 of title 18, United States Code, is amended to read as follows: ``Sec. 2255. Civil remedies. ``(a) The district courts of the United States shall have jurisdiction to prevent and restrain violations of section 2251 of this title by issuing appropriate orders, including-- ``(1) ordering any person to divest himself of any interest, direct or indirect, in any legal or business entity; ``(2) imposing reasonable restrictions on the future activities or investments of any person including prohibiting such person from engaging in the same type of legal or business endeavor; or ``(3) ordering dissolution or reorganization of any legal or business entity after making due provision for the rights of innocent persons. ``(b) The Attorney General or any person threatened with loss or damage by reason of a violation of section 2251 of this title may institute proceedings under subsection (a) of this section and, in the event that the party bringing suit prevails, such party shall recover the cost of the suit, including a reasonable attorney's fee. Pending final determination, the court may at any time enter such restraining orders or prohibitions, or take such other actions, including the acceptance of satisfactory performance bonds, as it shall deem proper. For purposes of this section, a violation of section 2251 of this title shall be determined by a preponderance of the evidence. ``(c) Any victim of a violation of section 2251 of this title who suffers physical injury, emotional distress, or property damage as a result of such violation may sue to recover damages in any appropriate United States district court and shall recover threefold the damages such person sustains as a result of such violation and the cost of the suit, including a reasonable attorney's fee. For purposes of this section, a violation of section 2251 of this title shall be determined by a preponderance of the evidence. ``(d) A final judgment or decree rendered in favor of the United States in any criminal proceeding brought by the United States under this chapter shall estop the defendant from denying the essential allegations of the criminal offense in any subsequent civil proceeding. ``(e) Nothing in this section shall be construed to authorize any order restraining the exhibition, distribution or dissemination of any visual material without a full adversary proceeding and a final judicial determination that such material contains a visual depiction of sexually explicit conduct, engaged in by a minor or by a person who was coerced, intimidated, or fraudulently induced to engage in such sexually explicit conduct.''. (b) Additional Remedies and Procedure.--Chapter 110 of title 18, United States Code, is amended by adding at the end the following: ``Sec. 2259. Civil penalties. ``(a) Any person found to violate section 2251 of this title by preponderance of the evidence shall be liable to the United States Government for a civil penalty of $100,000 and the forfeiture of any interest in property described in section 2254. The Attorney General may bring an action for recovery of any such civil penalty or forfeiture against any such person. If the Attorney General prevails he may also recover the cost of the suit, including a reasonable attorney's fee. ``(b) If the identity of any victim of an offense provided in section 2251 of this title is established before an award of a civil penalty made to the United States under this section, the victim shall be entitled to the award. If there is more than one victim, the court shall apportion the award among the victims on an equitable basis after considering the harm suffered by each such victim. ``Sec. 2260. Venue and process. ``(a) Any civil action or proceeding brought under this chapter may be instituted in the district court of the United States for any district in which the defendant resides, is found, has an agent, or transacts his affairs. ``(b) In any action under section 2255 or 2259 of this title in any district court of the United States in which it is shown that the ends of justice require that other parties residing in any other district be brought before the court, the court may cause such parties to be summoned, and process for that purpose may be served in any judicial district of the United States by the marshal of such judicial district. ``(c) In any civil or criminal action or proceeding under this chapter in the district court of the United States for any judicial district, a subpoena issued by such court to compel the attendance of witnesses may be served in any other judicial district except that no subpoena shall be issued for service upon any individual who resides in another district at a place more than one hundred miles from the place at which such court is held without approval given by a judge of such court upon a showing of good cause. ``(d) All other process in any action or proceeding under this chapter may be served on any person in any judicial district in which such person resides, is found, has an agent, or transacts his affairs. ``Sec. 2261. Expedition of actions. ``In any civil action instituted under this chapter by the United States in any district court of the United States, the Attorney General may file with the clerk of such court a certificate stating that in his opinion the case is of general public importance. A copy of that certificate shall be furnished immediately by such clerk to the chief judge or in his absence to the presiding district judge of the district in which such action is pending. Upon receipt of such copy, such judge shall designate immediately a judge of that district to hear and determine the action. The judge designated to hear and determine the action shall assign the action for hearing as soon as practicable and hold hearings and make a determination as expeditiously as possible. ``Sec. 2262. Evidence. ``In any proceeding ancillary to or in any civil action instituted under this chapter the proceedings may be opened or closed to the public at the discretion of the court after consideration of the rights of affected persons. ``Sec. 2263. Limitations. ``A civil action under section 2255 or 2259 of this title must be brought within six years from the date the violation is committed. In any such action brought by or on behalf of a person who was a minor at the date the violation was committed, the running of such six-year period shall be deemed to have been tolled during the period of such person's minority.''. SEC. 5. CLERICAL AMENDMENT. (a) Table of Sections.--The table of sections for chapter 110 of part I of title 18, United States Code, is amended to read as follows: ``CHAPTER 110--SEXUAL EXPLOITATION ``Sec. ``2251. Sexual exploitation. ``2252. Selling or buying of children. ``2253. Criminal forfeiture. ``2254. Civil forfeiture. ``2255. Civil remedies. ``2256. Definitions for chapter. ``2257. Record keeping requirements. ``2258. Failure to report child abuse. ``2259. Civil penalties. ``2260. Venue and process. ``2261. Expedition of actions. ``2262. Evidence. ``2263. Limitations.''. (b) Table of Chapters.--The table of chapters for part I of title 18, United States Code, is amended by striking the item relating to chapter 110 and inserting in lieu thereof the following: ``110. Sexual Exploitation.................................. 2251''.[/INST]Pornography Victims Protection Act of 1993 - Amends the Federal criminal code with respect to the prohibition against the sexual exploitation of children to add as a condition triggering Federal penalties that the person concerned knows that a minor was transported in interstate or foreign commerce for the purpose of producing pornography. Makes it a criminal offense for any person to coerce, intimidate, or fraudulently induce an individual 18 years or older to engage in any sexually explicit conduct for the purposes of producing any visual depiction of such conduct. Grants the U.S. district courts jurisdiction to prevent and restrain violations of this Act. Authorizes the Attorney General or any person threatened with loss or damage by such conduct to institute a civil suit. Provides for treble damages for a victim who suffers physical injury, emotional distress, or property damage. Imposes civil penalties for violation of the prohibition against sexual exploitation of children.</s>

BUFFALO -- President Obama had a simple message Thursday for the Republicans who have tried to thwart his economic policies. I told you so. In a defense of the often unpopular actions his administration has taken to confront the economic crisis, Obama told employees of an expanding manufacturing company here that he was right and his critics were wrong. "Today, we are heading in the right direction," Obama said. "Those tough steps we took -- they're working. Despite all the naysayers -- who were predicting failure a year ago -- our economy is growing again." Standing in front of heavy equipment in a manufacturing bay at a company that has added workers, Obama said his critics should have to admit that the steps he took -- and they opposed -- ended the recession and have begun to add jobs, if slowly. "I knew that if we didn't act boldly and quickly -- if we didn't defy the politics of the moment and do what was necessary -- we would have risked an even greater disaster," he said, calling out the Republican Party as having been "in power when the crisis happened." The response from Republicans was swift. They pointed out that White House officials had predicted an unemployment rate of 7.7 percent by now when they were arguing for the president's stimulus package. And they pointed to polls suggesting that the public still does not believe the recovery act has helped them much. "Last year, the administration rushed a trillion-dollar stimulus bill through Congress because it said we needed it to create jobs," Senate Minority Leader Mitch McConnell (R-Ky.) said. "Well, more than a year later unemployment is hovering around 10 percent. And taxpayers want their money back." Obama's trip to Buffalo highlights one of the central dilemmas for any president presiding over a slow economic recovery: how to balance the good news and the bad news, the continuing misery and the hopeful signs. Just days ago, Obama stood in the Rose Garden at the White House to tout the best job numbers in years -- almost 300,000 jobs created in a single month. Flanked by his economic team, the president used the opportunity to remind Americans how far the country had come since the recession began. "At the height of the downturn, around the time that I took office, we were losing an average of 750,000 jobs per month," Obama told the people watching his announcement last Friday morning. But as he has done every time there is good news, the president quickly made a pivot, acknowledging the frustration undoubtedly felt by the unemployed every time they hear that the economy is improving and that the recession is over. ||||| Obama stopped at the local landmark in Cheektowaga, N.Y. and surprised the customers. The woman giving Obama the once-over was Luann Haley, 45. Sheryl Stolberg of the New York Times, the pool reporter, said Obama "replied by giving her a big hug. ("He gave me a squeeze,'' she said afterward.) She swooned and he said Michelle would be watching on television. "That's allright,'' Ms. Haley said as the cameras rolled."Hi Michelle, eat your heart out." President Obama stopped for lunch on an upstate New York swing on Thursday and got something not on the menu at Duff's Famous Wings: a steamy compliment from a female patron who told him, "you're a hottie with a smokin' little body." Pool report by Sheryl Stolberg, New York Times at Duff's Famous Wings in Cheektowaga, N.Y. 5-13-10 QUOTE OF THE DAY: "You're a hottie with a smokin' little body." Yes indeed, some people will say just about anything to get a hug from Barack Obama. Those words were spoken by Luann Haley, 45, to the president, during his unannounced visit to this local landmark. He replied by giving her a big hug. ("He gave me a squeeze,'' she said afterward.) She swooned and he said Michelle would be watching on television. "That's allright,'' Ms. Haley said as the cameras rolled."Hi Michelle, eat your heart out." To backtrack, POTUS surprised many of what looked to be about 100 employees and guests when he strode into the restaurant, jacketless. He leaned over the counter; the receptionist Mary DiGiacomo, told him they had a lunch special but he demurred, saying he was in the car. He quietly placed an order. She tried to tell him it would be on the house. "No, I've got to pay,'' he insisted, pulling out his wallet, which sported a $5 bill on top. Your pooler asked the obvious: what did he get? "Wings!'' the president declared. "This is the wing capital." And so it is. A painted sign on the Duffs wall says: Duff's Famous Wings. Medium is HOT. Medium hot IS VERY HOT. Hot IS VERY VERY HOT.'' Mr. Obama ordered his medium, but was told halfway through his meet-and-greet that he needed to get them extra spicy. So he called out to the restaurant staff that he would have five regular, five extra spicey. They cost $10.82. Your pool did not see him pay. Ms. Haley was part of a large crowd of Department of Education contractors, who work next door to the restaurant collecting money on federal student loans whose borrowers have defaulted. They saw the Secret Service and figured something was up, so arrived en masse at Duff's. Sheryl Stolberg New York Times ||||| (CNN) – Unemployment is part of everyday life for millions of Americans and one man finally decided to do something about it. He created a grassroots organization, "I need a freakin' job," to give a voice to the fifteen million unemployed. There's also a billboard on display in Buffalo with the same message directed at President Obama, and that's where he'll be today as part of his "White House to Main Street" tour. Jeff Baker, the creator of "I need a freakin' job," joined us on Thursday's American Morning. Read more: Obama's 'Main Street' tour heads to NY

– Generally speaking, this is not how to address the leader of the free world: "You're a hottie with a smokin' little body." And yet that's exactly what a Buffalo woman told President Obama when he visited a chicken wing joint today, reports the Chicago Sun-Times. The president responded by giving 45-year-old Luann Haley a hug. "Hi Michelle, eat your heart out," she said. On more substantive matters, Obama repeated the pitch that his administration's economic policies were working, reports the Washington Post. "Today, we are heading in the right direction," he said. "Those tough steps we took—they're working. Despite all the naysayers—who were predicting failure a year ago—our economy is growing again." Republicans disagreed, as did the Buffalo billboard with the message, "I need a freakin' job," notes CNN.

<s>[INST]BUFFALO -- President Obama had a simple message Thursday for the Republicans who have tried to thwart his economic policies. I told you so. In a defense of the often unpopular actions his administration has taken to confront the economic crisis, Obama told employees of an expanding manufacturing company here that he was right and his critics were wrong. "Today, we are heading in the right direction," Obama said. "Those tough steps we took -- they're working. Despite all the naysayers -- who were predicting failure a year ago -- our economy is growing again." Standing in front of heavy equipment in a manufacturing bay at a company that has added workers, Obama said his critics should have to admit that the steps he took -- and they opposed -- ended the recession and have begun to add jobs, if slowly. "I knew that if we didn't act boldly and quickly -- if we didn't defy the politics of the moment and do what was necessary -- we would have risked an even greater disaster," he said, calling out the Republican Party as having been "in power when the crisis happened." The response from Republicans was swift. They pointed out that White House officials had predicted an unemployment rate of 7.7 percent by now when they were arguing for the president's stimulus package. And they pointed to polls suggesting that the public still does not believe the recovery act has helped them much. "Last year, the administration rushed a trillion-dollar stimulus bill through Congress because it said we needed it to create jobs," Senate Minority Leader Mitch McConnell (R-Ky.) said. "Well, more than a year later unemployment is hovering around 10 percent. And taxpayers want their money back." Obama's trip to Buffalo highlights one of the central dilemmas for any president presiding over a slow economic recovery: how to balance the good news and the bad news, the continuing misery and the hopeful signs. Just days ago, Obama stood in the Rose Garden at the White House to tout the best job numbers in years -- almost 300,000 jobs created in a single month. Flanked by his economic team, the president used the opportunity to remind Americans how far the country had come since the recession began. "At the height of the downturn, around the time that I took office, we were losing an average of 750,000 jobs per month," Obama told the people watching his announcement last Friday morning. But as he has done every time there is good news, the president quickly made a pivot, acknowledging the frustration undoubtedly felt by the unemployed every time they hear that the economy is improving and that the recession is over. ||||| Obama stopped at the local landmark in Cheektowaga, N.Y. and surprised the customers. The woman giving Obama the once-over was Luann Haley, 45. Sheryl Stolberg of the New York Times, the pool reporter, said Obama "replied by giving her a big hug. ("He gave me a squeeze,'' she said afterward.) She swooned and he said Michelle would be watching on television. "That's allright,'' Ms. Haley said as the cameras rolled."Hi Michelle, eat your heart out." President Obama stopped for lunch on an upstate New York swing on Thursday and got something not on the menu at Duff's Famous Wings: a steamy compliment from a female patron who told him, "you're a hottie with a smokin' little body." Pool report by Sheryl Stolberg, New York Times at Duff's Famous Wings in Cheektowaga, N.Y. 5-13-10 QUOTE OF THE DAY: "You're a hottie with a smokin' little body." Yes indeed, some people will say just about anything to get a hug from Barack Obama. Those words were spoken by Luann Haley, 45, to the president, during his unannounced visit to this local landmark. He replied by giving her a big hug. ("He gave me a squeeze,'' she said afterward.) She swooned and he said Michelle would be watching on television. "That's allright,'' Ms. Haley said as the cameras rolled."Hi Michelle, eat your heart out." To backtrack, POTUS surprised many of what looked to be about 100 employees and guests when he strode into the restaurant, jacketless. He leaned over the counter; the receptionist Mary DiGiacomo, told him they had a lunch special but he demurred, saying he was in the car. He quietly placed an order. She tried to tell him it would be on the house. "No, I've got to pay,'' he insisted, pulling out his wallet, which sported a $5 bill on top. Your pooler asked the obvious: what did he get? "Wings!'' the president declared. "This is the wing capital." And so it is. A painted sign on the Duffs wall says: Duff's Famous Wings. Medium is HOT. Medium hot IS VERY HOT. Hot IS VERY VERY HOT.'' Mr. Obama ordered his medium, but was told halfway through his meet-and-greet that he needed to get them extra spicy. So he called out to the restaurant staff that he would have five regular, five extra spicey. They cost $10.82. Your pool did not see him pay. Ms. Haley was part of a large crowd of Department of Education contractors, who work next door to the restaurant collecting money on federal student loans whose borrowers have defaulted. They saw the Secret Service and figured something was up, so arrived en masse at Duff's. Sheryl Stolberg New York Times ||||| (CNN) – Unemployment is part of everyday life for millions of Americans and one man finally decided to do something about it. He created a grassroots organization, "I need a freakin' job," to give a voice to the fifteen million unemployed. There's also a billboard on display in Buffalo with the same message directed at President Obama, and that's where he'll be today as part of his "White House to Main Street" tour. Jeff Baker, the creator of "I need a freakin' job," joined us on Thursday's American Morning. Read more: Obama's 'Main Street' tour heads to NY[/INST]– Generally speaking, this is not how to address the leader of the free world: "You're a hottie with a smokin' little body." And yet that's exactly what a Buffalo woman told President Obama when he visited a chicken wing joint today, reports the Chicago Sun-Times. The president responded by giving 45-year-old Luann Haley a hug. "Hi Michelle, eat your heart out," she said. On more substantive matters, Obama repeated the pitch that his administration's economic policies were working, reports the Washington Post. "Today, we are heading in the right direction," he said. "Those tough steps we took—they're working. Despite all the naysayers—who were predicting failure a year ago—our economy is growing again." Republicans disagreed, as did the Buffalo billboard with the message, "I need a freakin' job," notes CNN.</s>

pain is an unpleasant sensory and emotional experience associated with actual or potential tissue damage [ 1 , 2 ] . extreme pressure , abnormal temperature , or ph elicits a pain sensation in the brain , following pain avoidance behavior . therefore , appropriate and prompt pain sensation is critical to adapt to the outside environment . transducers on primary afferent sensory nerve terminal , including transient receptor potential ( trp ) ion channels , convert painful chemical or mechanical stimuli into electrical signals , thereby initiating activation of sensory nerves [ 3 , 4 ] . action potential initiated in primary afferent nociceptors is transmitted to higher sensory brain cortex via multiple synaptic connections in the central nervous system . pain signal transmission is regulated by the vast complexity of excitatory and inhibitory neural networks and ligand - receptor pairs [ 57 ] , indicating the importance of proper regulation and adaptation of these sensory modalities to maintain homeostasis of our body response to external painful stimuli . in disease , prolonged tissue damage or inflammation induces alterations of gene expression and membrane protein modifications in such a way that aberrant activation of certain nociceptor occurs , even in the absence of noxious stimuli [ 810 ] . millions of people worldwide suffer from chronic pain with lack of proper analgesic treatment options . based upon our knowledge of cellular modalities including primary afferent nociceptors , immune cells , and glial cells and molecular entities including ion channels , g protein - coupled receptors , neurotransmitters , inflammatory mediators , kinases , and growth factors involved in pain transmission , several target - based pharmacological approaches and anti - inflammatory drugs have been partially successful in controlling several pain symptoms [ 5 , 6 , 8 , 11 ] . however , when pain is originated from dysfunction in relaying pain signals from the sensory nerve or neuron network to the central nervous system , it is difficult to control pain transmission with a conventional target - based approach . this is mainly because multigenic origin and multiple cellular and molecular targets are involved in the development of neuropathic pain . whole genome rna sequencing ( rnaseq ) or microarray explorations of neuropathic pain have revealed dramatic and extensive changes in gene expression profile during the disease process [ 1217 ] . the highly plastic nature of neurons and their surrounding environments could be an obstacle for conventional single target - based therapeutic strategy in controlling pain , necessitating the novel therapeutic approaches that are more selective and systemic in their effect . control of neural activity using light activated ion channels ( optogenetics ) or using designer receptor g protein - coupled receptors ( gpcrs ) , abbreviated dreadds , has become possible and has been tested in several animal models . since neuropathic pain is attributed largely to the abnormal activity of neurons or immune cells , it could be possible to employ these techniques in suppressing abnormal pain signal transmission . in this review , we discuss molecular and cellular changes in neuropathic pain development with the main focus on peripheral sensory nerve . this review highlights the use of optogenetics and dreadds in controlling neuronal activity and elaborates the advantage and possibility of their application in the treatment of neuropathic pain . pain is a subjective sensation in response to obnoxious stimuli that include toxic chemicals , mechanical stress , extreme temperature , and tissue damage . external pain stimuli are first detected at cellular levels at primary afferent sensory neurons in the dorsal root ganglion ( drg ) . they are termed nociceptive c fibers and are characterized by a small diameter cell body and unmyelinated axons . neuropathic pain is defined as a pain state arising from neuronal lesion , which alters the degree of pain [ 19 , 20 ] . complaints include spontaneous pain , burning pain , or tingling and exaggerated responses to innocuous and noxious mechanical or thermal stimuli that include allodynia , hyperalgesia , and hypersensitivity to heat or cold . neuropathic pain develops as a consequence of dramatic changes in multiple levels of nociceptive pain wires following formation of a nerve lesion . the cause of neural damage can be diverse and includes traumatic injury , inflammation , and metabolic diseases like diabetes , toxins , viral infections , or malignant cancer . the alterations in response to nerve lesions are extensive and encompass gene profile changes with novel receptor and ion channel presentation at the membranes , alterations of nociceptive signal processing in the peripheral and central nervous system , and finally pathologic synapse formation with neighboring neurons [ 9 , 10 , 2123 ] . substances released in the vicinity of spared fibers by wallerian degeneration ( e.g. , nerve growth factor ) or calcium influx into neurons may underlie substantial transcriptome remodeling in neuropathic pain development . hypersensitization of primary afferent nociceptors contributes to pathological pain sensation ( hyperalgesia or allodynia ) . hyperactivity input from peripheral neuropathic nociceptors in turn leads to central sensitization that interprets mild stimuli from periphery , such as touch or proprioception , as pain sensation . the remodeling can cause abnormal sensitivity and can generate pathological spontaneous activities ( figure 1 ) . expression of diverse membrane proteins is altered , which may contribute to hypersensitization of nociceptive neurons . several independent studies and a recent global rnaseq analysis revealed that pain sensing trp ion channel expression and voltage - gated sodium channel subtypes nav1.7 , nav1.8 , nav1.9 , and nav1.3 are increased in nociceptors in neuropathic pain models [ 6 , 14 , 16 , 23 ] . in the normal condition , functional potassium currents provide inhibitory control over neuronal activity and are critical for preventing ectopic activity of neurons . along with ion channel expression contributing to membrane depolarization , membrane stabilizing potassium channel kv1 and kv2 family subunits are impaired in pathological conditions , such as experimental diabetes [ 5 , 6 ] . moreover , kv7 ( kcnq ) contributes to generation and maintenance of neuropathic pain [ 24 , 25 ] . all of these changes lower the threshold for nociceptor activation . in this condition , even mild stimuli can be sufficient to elicit action potential in nociceptive neurons . in other words , activation of even a few nociceptors can be sufficient to transmit high frequency pain signal to the sensory cortex . together with nociceptors , several types of immune cells are involved in the development and maintenance of neuropathic pain . immune cells in peripheral injury sites include mast cells , neutrophils , monocytes , and macrophages . the role of immune cells in sensitizing nociceptors and their involvement in maintaining neuropathic pain are thoroughly reviewed elsewhere [ 9 , 26 ] . the inflammatory mediators released from immune cells can directly act on nociceptors initiating pain signaling cascade [ 9 , 10 ] . notably , diffusible inflammatory mediators and substances from damaged neurons affect adjacent uninjured neurons , spreading pathological changes to a broader area . experiments that restricted the recruitment of these immune cells to neuronal injury sites have shown protective effects against development of neuropathic pain in animals [ 11 , 27 ] , demonstrating the important role of immune cell - nociceptor interplay in the disease progression . imbalance between proinflammatory cytokines and anti - inflammatory cytokines has been found in neuropathic pain patients [ 28 , 29 ] . interestingly , animal models of neuropathic pain have demonstrated upregulation of proinflammatory cytokines , such as tnf- , il-1 , and tnf receptors [ 3032 ] . infusion of these cytokines is sufficient to induce neuropathic pain development [ 33 , 34 ] , indicating a role of immune cells in the early stage of neuropathic pain development . in contrast to short - acting ion channel function , gpcr can mediate long - lasting changes in gene expression or membrane excitability [ 35 , 36 ] . similar to ion channels , gpcrs also undergo substantial changes in expression during neuropathic pain development . nerve lesions lead to induction of 1 or 2 adrenoceptors on cutaneous afferent fibers , driving the development of neuropathic pain associated with and responding to sympathetic stimulation [ 37 , 38 ] . in some neuropathic patients , sympathetic efferent may cause excitation of nociceptors by noradrenaline or circulating catecholamines with additional expression of 1 receptors , initiating pain associated with sympathetic stimulation . immune cell activation involves many gpcrs for classic chemoattractants and chemokines [ 10 , 35 ] . notably , the activation of gpcr often leads to fundamental transcription changes or inflammatory mediator release through divergence of signaling cascades . during inflammation , a variety of gpcr agonists act on gpcrs on nociceptors leading to hypersensitivity ( figure 1 ) . bradykinin and some prostaglandins are upregulated during the initial stage of neuropathic pain through interaction with b1 and b2 bradykinin receptors or nine prostanoid receptors that are coupled with diverse g proteins . during nociceptor sensitization , gpcrs for prostaglandin or substance p mediate intracellular signaling cascades that result in posttranslational modification of sodium or n - methyl - d - aspartic acid ( nmda ) receptors leading to hypersensitization of nociception in drg and the cns [ 20 , 39 ] . as demonstrated by microarray and rnaseq whole transcriptome analysis , extensive changes of gene expression underlie structural and functional remodeling of nociceptors in pathological neuropathic pain [ 14 , 17 , 23 ] . in this regard , conventional strategies to inhibit individual ion channels or inflammatory processes have not been useful , due to the complex etiology of the pathological changes . moreover , commonly used pain medications including opioid analgesics or nsaids oftentimes develop side effects and tolerance . supporting the complicated molecular mechanism of neuropathic pain , nav1.3 or nav1.8 knockdown or knockout mouse models still develop neuropathic pain , although their contribution to hypersensitization of nociceptive neurons has been amply demonstrated in vitro [ 40 , 41 ] . considering the extensive isoforms of sodium channels or other receptor subtypes that are responsible for hypersensitization , selective inhibitors should be administered to minimize adverse side effects . however , the availability of those selective therapeutic ligands is limited . centrally acting drugs like antidepressants , anticonvulsants , and opioids provide partial pain relief , but the treatment of neuropathic pain is still unsatisfactory [ 8 , 19 ] . moreover , these centrally acting drugs are lipophilic and nonspecific with a narrow therapeutic window , further preventing their prolonged use for chronic pain treatment . treatment of chronic pain requires a novel approach regulating excitability of nociceptors as a final outcome , since it is clear that nociceptors and immune cells behave abnormally in neuropathic pain . genetic approaches that target these activated neurons in selective manner could be a potential therapeutic strategy . pharmacosynthetics and chemogenetic tools modulate transgenic receptors using artificial pharmacologic agents . currently , the most plausible pharmacosynthetic tool is the designer receptors exclusively activated by designer drug ( dreadd ) . dreadds are activated only by synthetic ligands like clozapine n - oxide ( cno ) , which are otherwise an inert pharmacological agent . dreadds are gpcrs capable of being pharmacologically modulated by synthetic chemicals , but not by endogenous gpcr ligands . a dreadd receptor can be engineered to be coupled with gs ( rm3ds ) , gi ( hm4di ) , or gq ( hm3dq ) to activate different secondary signaling pathways and different modulation of neuronal or cellular functions . transgenic expression of dreadds in specific cell types enables selective modulation of these dreadd expressing cells by ligands . except for the fact that they can be controlled with chemical ligands , dreadds behave like other endogenous gpcrs , interacting efficiently with downstream intracellular signaling components . for example , one study employed rm3ds dreadds to study the role of gs / camp / protein kinase k signaling cascades in the striatal medium spiny neurons for the hyperlocomotor response following psychostimulant treatment , such as methamphetamine or cocaine treatment . to establish dreadds in vivo , transgenic mice expressing rm3ds in medium spiny neuron ( msn ) were generated using the promoter adenosine a2a . with rm3ds expression in msn , cno treatment inhibited hyperlocomotor response even in the presence of amphetamine , thus demonstrating the important contribution of gpcr signaling in msn for this type of behavior . in addition , a novel gi - coupled dreadd has been recently developed by reengineering kappa - opioid receptor as a template . this inhibitory dreadd is activated pharmacologically by the inert ligand , salvinorin b ( salb ) . in addition , gpcrs have a diverse expression pattern in tissues and they are the most popular drug targets , representing 36% of currently approved drug targets . for this reason , dreadds draw attention for the potential in the treatment of pathological conditions that involve abnormal gpcr downstream signaling . gpcr is a naturally occurring metabotropic receptor that mediates diverse neuronal functions including gene expression . gpcr often collaborates with ion channels leading to activation or inhibition of ion channel activity . therefore , appropriate dreadd expression in neurons can counteract aberrant neuronal excitability through long - lasting secondary changes to an excitable membrane . for instance , the expression of hm3dq dreadd on neurons and activation by cno can lead to effective membrane depolarization , whereas hm4di expression inhibits neuronal action potential firing ( figures 1 and 2 ) . optogenetics utilizes channel rhodopsin that can be opened by certain light frequency stimulus , thus controlling neuronal firing . chimeric ion channels expressed in specific cell types by the conditional transgenic approach enable selective stimulation of certain neuronal population with fiber optics inserted into the desired site to deliver light to neurons . channelrhodopsin ( chr ) is engineered to be selective for cation entry whereas halorhodopsin ( nphr ) is selective for anion flux so that the activity of neuron can be effectively controlled by either stimulation or inhibition as intended . combined with the conditional transgenic approach that expresses it in specific neuronal circuit , optogenetics has been extensively used to delineate neuronal connection and pathways even in the control of emotion or behavior [ 46 , 47 ] . in terms of pain sensation , optogenetics has been employed to elicit pain with a stimulatory opsin expression in nav1.8 positive neurons in combination with transdermal optogenetic activation . in other cases , it also mitigate neuropathic pain with an inhibitory opsin expression in sensory nociceptive neuron population via adeno - associated virus ( aav ) serotype 6 infection and expression of opsin by neuron specific human synapsin-1 promoter . this delivery route allows very efficient access in small diameter nociceptive nerves salvaging large - diameter myelinated neurons that transduce touch and proprioception . optogenetic inhibition of action potential generation in nociceptors has been attempted using yellow light sensitive third - generation chloride pump halorhodopsin ( enphr3.0 ) . when delivered via aav6 intrasciatic injection , enphr3.0 activation in drg neurons with constant yellow light illumination strongly inhibits action potential initiation by membrane hyperpolarization . in vivo stimulation of this channel was sufficient to prevent painful behavior in neuropathic pain model , suggesting its therapeutic potential . the rationale of applying optogenetics or dreadds for control of abnormal pain perception in neuropathic pain is straightforward . in neuropathic pain , pain is heightened by the complicated modification of structure and gene expression in nociceptors . in this condition , neurons are easily activated to generate action potentials and transmit signals through an already built - in pain transmission network wired to the sensory cortex . as demonstrated by in vivo research discussed in the previous section , dampening of excitation in the pathologically sensitized nociceptors could be possible by expressing halorhodopsin for cl influx , thereby stabilizing membrane potential to prevent further high frequency action potential generation ( figure 1 ) . discrete expression of halorhodopsin in nociceptors is crucial to achieving selective inhibition in sensitized nociceptors . on the other hand , if interneurons are synapsed with pathological nociceptors , excitable opsins can be also employed together in the interneurons to enhance inhibitory capacity by flowing abundant inhibitory neurotransmitters , such as gaba and glycine , at certain levels . similarly , gi - coupled dreadds could be expressed in injured nociceptors to induce inhibitory changes on the membrane excitability . gi - coupled inhibition of adenylyl cyclase and resulting decrease of camp and pka signaling pathway can reverse pathological changes that have already occurred in neuropathic pain ( figure 1 ) . the difference between the optogenetics and dreadd approaches could be the duration of the effects and the extent of the downstream influence . optogenetic - mediated nociceptor inhibition can be directly achieved by fast - acting membrane potential stabilization , which occurs within a few milliseconds after light signal is applied . on the other hand , dreadds involve second messenger activation and , sometimes , alteration of gene expression changes [ 42 , 45 , 51 ] . this can cause longer latency time to achieve actual therapeutic effect , but this effect could be longer - lasting . many therapeutically effective chemicals are modulators rather than direct ligands , which inhibit or open ion channels . in this respect , the use of dreadds could be a relatively safer approach in actual human trials compared to optogenetic modulation of nociceptors , which could have potential adverse effects . extensive expression profiles with various physiologic involvements of gpcrs also favor application of dreadds in pain modulation . gpcr is involved in nociceptive neurons and in the activation and functioning of immune cells [ 9 , 10 ] . thus , dreadd expression in regions where neuropathic pain develops is able to control aberrant activation of immune cells , which ultimately induces and maintains the hypersensitivity of nociceptors . since immune cells propagate pathological chemokines and inflammatory mediators , pharmacological control of stimulated immune cells by dreadds , together with control of nociceptor activity , will facilitate more successful control of neuropathic pain transmission . a characteristic of neuropathic pain development is that the inflicted neurons and pain pathways are highly restricted . drug treatment in itself has intrinsic weakness in the lack of selectivity , which can cause unwanted adverse effect , especially at higher doses . in this respect , dreadds can be only activated by specific ligands that otherwise do not interact with other endogenous receptors at the therapeutic dosage range . as long as dreadds are expressed in the desired region , the intended effect can be exerted in specific site . in similar way conditional expression of chr can be achieved with tissue specific promoters or by delivery of channel genes via stereotaxic viral injection to target regions ( figure 2 ) . light - gated halorhodopsin or inhibitory dreadds can be also combined with conditional approaches to enhance cell type specific expression ( figure 2 ) . by combining double - floxed inverted opsins with aav expressing cre recombinase under the control of tissue specific promoter , it could be plausible to drive inhibitory opsin expression in desired neuronal or pathologically inflicted neurons to control pain signal transmission to higher structure of pain perception . as an exemplary application of cre - mediated dreadd expression in specific neuronal population , hm3d1 or hm4di dreadd has been expressed in agouti related protein ( agrp ) expressing neurons by using a cre - loxp system . when loxp - blocked hm3dq aav was injected into agrp - ires - cre mice , hm3dq expression was only confined to cell types expressing cre under control of the agrp promoter . interestingly , depending on g protein signaling modulated with cno ( 0.3 mg / kg ) administration , the eating behavior of the mice was reversibly controlled , demonstrating the role of g protein - coupled signaling in this type of neural circuit for food intake behavior . temporal regulation is also possible because dreadds or chrs can be only activated when the corresponding stimuli are given either by pharmacological application of ligands or by light stimuli in the vicinity . while the chr response upon withdrawal of light is immediate , dreadd activity will be gradually reduced following pharmacokinetic elimination of ligand resulting in longer - lasting changes . in this respect , the tet - on system is applied for controlled expression spatially and temporally by relaying actions of rtta acting on teto promoter . when rtta expression is driven by tissue specific promoter , teto - driven dreadd transgene expression can be restricted to specific tissue . reversible expression of dreadd receptor is achieved by doxycycline dependent activation of rtta action on teto promoter . by combining with dreadd - cno coupling , the tet - on system will provide additional safeguard to control dreadd expression as well as dreadd - mediated g protein signaling in targeted cell population ( figure 2 ) . viral delivery is a very efficient tool to deliver any gene of interest in vivo . although we are at mostly preclinical validation stages of viral gene therapy for neuropathy pain control , there has been great success in suppressing pain sensation by viral transfer of single gene in neuropathic animal models . due to the efficient delivery of therapeutic genes and promising preclinical results in several disease animal models , clinical trials for this method have been made for over 20 years . to increase safety and selectivity of clinical application of the viral vector - mediated gene therapy , firstly , the viral vector should be devoid of replication ability , genomic integration , and immunogenicity to be safely applied to human subjects . secondly , the neuropathic disease states are usually chronic , persisting for long period of time . this makes it necessary for the viral vector to maintain constitutive expression levels in therapeutic dosage . thirdly , gene delivery should be targeted to specific cells to prevent undesirable toxicity from transgene expression in other areas with optimal titer volume . some candidate viral vectors fall into the categories such as adeno - associated virus ( aav ) , herpes simplex virus ( hsv ) , and lentivirus . these viral vectors offer attractive features like less immunogenicity and genomic insertion possibility than other viral vectors . indeed there have been ongoing clinical trials with hsv and aav to treat inherited disease with defective gene expression [ 5761 ] . lentiviral vector has advantage to harbor larger transgene in the virus particle and it shows tropism for neuron transduction , but its genomic integration makes it relatively unsafe . its application is mostly confined to ex vivo gene transfer . but still there has been an attempt to apply this virus for neurodegenerative diseases such as parkinson 's disease . on the other hand , hsv and aav seldom integrate into host genome and they have tropism for neuron transduction depending on serotypes used for gene delivery . these features and others provide advantages in translational research and clinical application of the viral vectors for neuropathic pain modulation . the wild type aav is not causing any known disease in human , confirming safety in practice . small size of aav with diameter of 2025 nm enables highly robust diffusion even in application to solid tissues . it can still encompass up to 5 kb size of dna into virus particle which is sufficient to clone gene of interest for delivery . several reports have shown efficient transduction of several cell types including neurons in vivo animal studies and clinical trials . due to these attractive features of aav virus , aav - mediated gene therapy has been extensively studied , and long term expression of genes for therapeutic purpose has been achieved in a clinical setting especially for patients with inherited disorders such as retinal disorders and hemophilia b [ 57 , 59 ] . although successful application of viral gene therapy varied depending on target tissues and replacement genes of interest , there have been reports demonstrating safety and therapeutic efficacy of aav - mediated gene transfer to patients with inherited disease defective in certain genes . as mentioned above , aav can transduce dividing and postmitotic tissues with specificity depending on its serotypes . aav serotype 2 has been widely used since it shows relative selectivity for neuron transduction in comparison to glial transduction , while aav serotype 1 tends to infect both neurons and glial cells in nonspecific manner . thus , depending on target cells of interest , appropriate aav viral serotypes can be chosen for best result . actually , in animal model studies , aav has been successfully administered via intrathecal or direct injection to drg to achieve transduction of afferent sensory neurons and glial cells . serotype 1 aav , on the other hand , has tendency to transduce not only neurons but glial cell population ; it would be possible to transfer inhibitory dreadds to inflammatory glial cells that are highly activated in neuropathic pain environments . however , there are certainly disadvantages in aav application , too . even though its sizable capacity is up to 5 kb of dna into the virus particle , it would be difficult to package cell type specific promoter components that are usually bigger than 5 kb . therefore , it would be hard to purify aav virus expressing channel rhodopsin or dreadds via responsive promoter ( e.g. , tet promoter , or loxp flanked stop cassette containing cba promoter ) . it may be necessary to use combinatorial viral application using other viral vectors that can hold larger capacity to package bigger size of foreign dna like hsv vector . furthermore , aav clinical application could induce adverse immune reactions through aav viral capsid responsive t cell activation or transgene expression itself . replication - defective herpes simplex virus ( hsv ) , thus nonpathogenic , has been used for gene therapy in animal models and human clinical trials . the clinical trial of nonreplicating hsv expressing preproenkephalin treatment for intractable pain in cancer patients has shown to be safe with dose responsive therapeutic efficacy to relieve pain , providing proof of evidence for gene therapy with hsv virus [ 61 , 63 ] . different from aav approach , hsv has a tendency to transduce neurons in a retrograde manner , which makes this vector suitable for targeting afferent sensory nerves . hsv vectors expressing antinociceptive substances , such as endomorphin-1 , proenkephalin a , and il-4 , have been subcutaneously inoculated to selectively transduce drg in neuropathic animal models . most striking feature of hsv vector is that it has strong tropism for nerve cells and high capacity to contain sizable dna fragment . furthermore , once introduced into neurons via retrograde transport , the viral genes are stable and exert sustained expression of transgenes . there features are quite advantageous in clinical application for human neuropathy because conditional dreadds and halorhodopsin gene expression in disease specific manner requires selection and usage of tissue specific gene promoter that is usually big in size ranging around 10 kb . thus hsv viral vector is suitable to transfer neuropathic nociceptor specific promoter driving expression of cre or rtta into abnormally activated nociceptors with sustainable expression of transgenes ( figure 2 ) . despite some promising clinical application of viral vector - mediated gene therapy , caution should be taken because unexpected toxicity due to irreversible expression of therapeutic genes could be harmful to patients . in this respect , our proposed conditional viral model system to deliver either cre responsive or tetracycline responsive halorhodopsin or inhibitory dreadds provides additional safeguard . different from previously attempted constitutive expression of antinociceptive proteins , expression of halorhodopsin or inhibitory dreadds is switchable even after successful integration into neuropathic pain sites . as discussed above , channelrhodopsin and dreadds retain temporal resolution in their activation and function via lighting or cno ligand treatment , respectively . any unwanted adverse effects after clinical application can be immediately abolished by simply withdrawing the aforementioned gating stimuli . in addition , tet - off controlled expression of channelrhodopsin or dreadds ( figure 2(c ) ) allows stopping expression of this transgene itself . thus , if transgene expression initiates harmful immune response in clinical setting , the expression of therapeutic genes can be turned off by withdrawing doxycycline treatment . overall , the safety and efficacy of gene therapy mediated treatment for clinical neuropathy could be improved substantially by combining optogenetics / dreadds , conditional genetic tools , and appropriate viral vectors . tissue type selective expression and temporal control of chrs or dreadds may not be sufficient to pinpoint the damaged nociceptive neurons . to gain specific control over neuropathic pain , it is essential to understand which genetic program differential promoter activities between normal and neuropathic states can be exploited to construct transgenic viral vectors for dreadds or chrs to be expressed in more defined pathological cell types ( figure 2 ) . rather than affecting normal pain pathways , this approach will ensure disease specific control for drug treatment . as discussed above , normal sensation of pain is crucial to adapting to outside danger through proper response [ 18 , 64 ] . the selective expression of therapeutic modules in abnormally stimulated nociceptive neurons with altered gene expressions will attenuate abnormal pain sensation while preserving normal sensation of pain . to accomplish this , a complete understanding of global gene expression profiling is needed . previously , microarray with probes printed on slides was a representative method to obtain transcriptome profiling . microarray experiments are relatively easy to perform and are adequate for high - throughput data acquisition . there are many microarray databases pertaining to neuropathic pain that have provided insight into differentially regulated genes in neuropathic pain state [ 23 , 65 ] . these have shown that several neuropeptide messenger levels ( npy , galanin , and vip ) are highly elevated in drg of neuropathic pain models . inflammatory mediators such as complement proteins , allograft inflammatory factor-1 , alpha-2-macroglobulin , interferon - induced guanylate - binding protein 2 , and il-18 are also upregulated . notably , upregulated receptors include gaba receptor , nicotinic acetylcholine receptor 7 subunit , p2y1 purinoceptor , na channel 2 subunit , and ca channel 2-1 subunit [ 23 , 65 ] , providing ample promising promoter candidates for selective induction of dreadds or chrs . microarray - based transcriptome analysis often has shortcomings due to the limited pool of custom - designed probes for gene detection . furthermore , depending on probe and messenger pairing , absolute comparison of each gene expression level is almost impossible , only detecting relative changes of certain gene expression . on the other hand , rnaseq technology enables unprecedented global characterization of transcriptome changes in vitro and in vivo with greater sensitivity . due to its wide detection range , rnaseq provides quantitative values ( e.g. , reads / fragments per kilobase of transcript per million mapped reads ) that can be used to estimate gene abundance . it is also possible to do rnaseq transcriptome profiling if it is combined with bac - trap technology , even in brains with highly heterogeneous distribution of neuronal and glial cell types . rnaseq in drg neurons has been described in normal and pathological neuropathic pain condition . this global profiling can be used as a basis to identify neuropathic pain specific promoters that are highly activated in nociceptors . several genes with more than 10-fold enrichment in drg have been identified in this global rnaseq analysis . these data can be utilized to mine sensory neuron specific promoters for disease modifying transgene . even in ultraviolet - induced inflammatory pain , rnaseq analysis in damaged drg has successfully identified upregulated expression of reg3b , ccl2 , and vgf . application and comparison of rna whole transcriptome sequencing in defined neuropathic pain animal models or in patient samples will provide detailed and systemic molecular insights underlying the disease process . combined with the genetic engineering and functional expression of dreadds and chrs , better strategy for neuropathic pain control could be designed as compared to pan neuronal expression of these modules , which could shut down the overall pain sensation , possibly leading to adverse effects . since conventional therapies targeting single target genes including ion channels , receptors , or inflammatory mediators have been largely unsatisfactory , novel therapeutic strategies are needed . optogenetics and dreadds provide hope in controlling intractable pain in patients suffering from debilitating neuropathic pain . these tools can provide an effective means to control the disease process by artificial drugs through the modulation of distinct neuronal populations . based upon the underlying cause of neuropathic pain , it would be possible to improve the potential of pain management by combination therapies of these techniques and drugs targeting specific molecular targets . with continuing development and refinement of this technique in combination with viral vector - mediated safe and efficient gene therapy

chronic pain originating from neuronal damage remains an incurable symptom debilitating patients . proposed molecular modalities in neuropathic pain include ion channel expressions , immune reactions , and inflammatory substrate diffusions . recent advances in rna sequence analysis have discovered specific ion channel expressions in nociceptors such as transient receptor potential ( trp ) channels , voltage - gated potassium , and sodium channels . g protein - coupled receptors ( gpcrs ) also play an important role in triggering surrounding immune cells . the multiple protein expressions complicate therapeutic development for neuropathic pain . recent progress in optogenetics and pharmacogenetics may herald the development of novel therapeutics for the incurable pain . designer receptors exclusively activated by designer drugs ( dreadds ) facilitate the artificial manipulation of intracellular signaling through excitatory or inhibitory g protein subunits activated by biologically inert synthetic ligands . expression of excitatory channelrhodopsins and inhibitory halorhodopsins on injured neurons or surrounding cells can attenuate neuropathic pain precisely controlled by light stimulation . to achieve the discrete treatment of injured neurons , we can exploit the transcriptome database obtained by rna sequence analysis in specific neuropathies . this can recommend the suitable promoter information to target the injury sites circumventing intact neurons . therefore , novel strategies benefiting from pharmacogenetics , optogenetics , and rna sequencing might be promising for neuropathic pain treatment in future .

<s>[INST]pain is an unpleasant sensory and emotional experience associated with actual or potential tissue damage [ 1 , 2 ] . extreme pressure , abnormal temperature , or ph elicits a pain sensation in the brain , following pain avoidance behavior . therefore , appropriate and prompt pain sensation is critical to adapt to the outside environment . transducers on primary afferent sensory nerve terminal , including transient receptor potential ( trp ) ion channels , convert painful chemical or mechanical stimuli into electrical signals , thereby initiating activation of sensory nerves [ 3 , 4 ] . action potential initiated in primary afferent nociceptors is transmitted to higher sensory brain cortex via multiple synaptic connections in the central nervous system . pain signal transmission is regulated by the vast complexity of excitatory and inhibitory neural networks and ligand - receptor pairs [ 57 ] , indicating the importance of proper regulation and adaptation of these sensory modalities to maintain homeostasis of our body response to external painful stimuli . in disease , prolonged tissue damage or inflammation induces alterations of gene expression and membrane protein modifications in such a way that aberrant activation of certain nociceptor occurs , even in the absence of noxious stimuli [ 810 ] . millions of people worldwide suffer from chronic pain with lack of proper analgesic treatment options . based upon our knowledge of cellular modalities including primary afferent nociceptors , immune cells , and glial cells and molecular entities including ion channels , g protein - coupled receptors , neurotransmitters , inflammatory mediators , kinases , and growth factors involved in pain transmission , several target - based pharmacological approaches and anti - inflammatory drugs have been partially successful in controlling several pain symptoms [ 5 , 6 , 8 , 11 ] . however , when pain is originated from dysfunction in relaying pain signals from the sensory nerve or neuron network to the central nervous system , it is difficult to control pain transmission with a conventional target - based approach . this is mainly because multigenic origin and multiple cellular and molecular targets are involved in the development of neuropathic pain . whole genome rna sequencing ( rnaseq ) or microarray explorations of neuropathic pain have revealed dramatic and extensive changes in gene expression profile during the disease process [ 1217 ] . the highly plastic nature of neurons and their surrounding environments could be an obstacle for conventional single target - based therapeutic strategy in controlling pain , necessitating the novel therapeutic approaches that are more selective and systemic in their effect . control of neural activity using light activated ion channels ( optogenetics ) or using designer receptor g protein - coupled receptors ( gpcrs ) , abbreviated dreadds , has become possible and has been tested in several animal models . since neuropathic pain is attributed largely to the abnormal activity of neurons or immune cells , it could be possible to employ these techniques in suppressing abnormal pain signal transmission . in this review , we discuss molecular and cellular changes in neuropathic pain development with the main focus on peripheral sensory nerve . this review highlights the use of optogenetics and dreadds in controlling neuronal activity and elaborates the advantage and possibility of their application in the treatment of neuropathic pain . pain is a subjective sensation in response to obnoxious stimuli that include toxic chemicals , mechanical stress , extreme temperature , and tissue damage . external pain stimuli are first detected at cellular levels at primary afferent sensory neurons in the dorsal root ganglion ( drg ) . they are termed nociceptive c fibers and are characterized by a small diameter cell body and unmyelinated axons . neuropathic pain is defined as a pain state arising from neuronal lesion , which alters the degree of pain [ 19 , 20 ] . complaints include spontaneous pain , burning pain , or tingling and exaggerated responses to innocuous and noxious mechanical or thermal stimuli that include allodynia , hyperalgesia , and hypersensitivity to heat or cold . neuropathic pain develops as a consequence of dramatic changes in multiple levels of nociceptive pain wires following formation of a nerve lesion . the cause of neural damage can be diverse and includes traumatic injury , inflammation , and metabolic diseases like diabetes , toxins , viral infections , or malignant cancer . the alterations in response to nerve lesions are extensive and encompass gene profile changes with novel receptor and ion channel presentation at the membranes , alterations of nociceptive signal processing in the peripheral and central nervous system , and finally pathologic synapse formation with neighboring neurons [ 9 , 10 , 2123 ] . substances released in the vicinity of spared fibers by wallerian degeneration ( e.g. , nerve growth factor ) or calcium influx into neurons may underlie substantial transcriptome remodeling in neuropathic pain development . hypersensitization of primary afferent nociceptors contributes to pathological pain sensation ( hyperalgesia or allodynia ) . hyperactivity input from peripheral neuropathic nociceptors in turn leads to central sensitization that interprets mild stimuli from periphery , such as touch or proprioception , as pain sensation . the remodeling can cause abnormal sensitivity and can generate pathological spontaneous activities ( figure 1 ) . expression of diverse membrane proteins is altered , which may contribute to hypersensitization of nociceptive neurons . several independent studies and a recent global rnaseq analysis revealed that pain sensing trp ion channel expression and voltage - gated sodium channel subtypes nav1.7 , nav1.8 , nav1.9 , and nav1.3 are increased in nociceptors in neuropathic pain models [ 6 , 14 , 16 , 23 ] . in the normal condition , functional potassium currents provide inhibitory control over neuronal activity and are critical for preventing ectopic activity of neurons . along with ion channel expression contributing to membrane depolarization , membrane stabilizing potassium channel kv1 and kv2 family subunits are impaired in pathological conditions , such as experimental diabetes [ 5 , 6 ] . moreover , kv7 ( kcnq ) contributes to generation and maintenance of neuropathic pain [ 24 , 25 ] . all of these changes lower the threshold for nociceptor activation . in this condition , even mild stimuli can be sufficient to elicit action potential in nociceptive neurons . in other words , activation of even a few nociceptors can be sufficient to transmit high frequency pain signal to the sensory cortex . together with nociceptors , several types of immune cells are involved in the development and maintenance of neuropathic pain . immune cells in peripheral injury sites include mast cells , neutrophils , monocytes , and macrophages . the role of immune cells in sensitizing nociceptors and their involvement in maintaining neuropathic pain are thoroughly reviewed elsewhere [ 9 , 26 ] . the inflammatory mediators released from immune cells can directly act on nociceptors initiating pain signaling cascade [ 9 , 10 ] . notably , diffusible inflammatory mediators and substances from damaged neurons affect adjacent uninjured neurons , spreading pathological changes to a broader area . experiments that restricted the recruitment of these immune cells to neuronal injury sites have shown protective effects against development of neuropathic pain in animals [ 11 , 27 ] , demonstrating the important role of immune cell - nociceptor interplay in the disease progression . imbalance between proinflammatory cytokines and anti - inflammatory cytokines has been found in neuropathic pain patients [ 28 , 29 ] . interestingly , animal models of neuropathic pain have demonstrated upregulation of proinflammatory cytokines , such as tnf- , il-1 , and tnf receptors [ 3032 ] . infusion of these cytokines is sufficient to induce neuropathic pain development [ 33 , 34 ] , indicating a role of immune cells in the early stage of neuropathic pain development . in contrast to short - acting ion channel function , gpcr can mediate long - lasting changes in gene expression or membrane excitability [ 35 , 36 ] . similar to ion channels , gpcrs also undergo substantial changes in expression during neuropathic pain development . nerve lesions lead to induction of 1 or 2 adrenoceptors on cutaneous afferent fibers , driving the development of neuropathic pain associated with and responding to sympathetic stimulation [ 37 , 38 ] . in some neuropathic patients , sympathetic efferent may cause excitation of nociceptors by noradrenaline or circulating catecholamines with additional expression of 1 receptors , initiating pain associated with sympathetic stimulation . immune cell activation involves many gpcrs for classic chemoattractants and chemokines [ 10 , 35 ] . notably , the activation of gpcr often leads to fundamental transcription changes or inflammatory mediator release through divergence of signaling cascades . during inflammation , a variety of gpcr agonists act on gpcrs on nociceptors leading to hypersensitivity ( figure 1 ) . bradykinin and some prostaglandins are upregulated during the initial stage of neuropathic pain through interaction with b1 and b2 bradykinin receptors or nine prostanoid receptors that are coupled with diverse g proteins . during nociceptor sensitization , gpcrs for prostaglandin or substance p mediate intracellular signaling cascades that result in posttranslational modification of sodium or n - methyl - d - aspartic acid ( nmda ) receptors leading to hypersensitization of nociception in drg and the cns [ 20 , 39 ] . as demonstrated by microarray and rnaseq whole transcriptome analysis , extensive changes of gene expression underlie structural and functional remodeling of nociceptors in pathological neuropathic pain [ 14 , 17 , 23 ] . in this regard , conventional strategies to inhibit individual ion channels or inflammatory processes have not been useful , due to the complex etiology of the pathological changes . moreover , commonly used pain medications including opioid analgesics or nsaids oftentimes develop side effects and tolerance . supporting the complicated molecular mechanism of neuropathic pain , nav1.3 or nav1.8 knockdown or knockout mouse models still develop neuropathic pain , although their contribution to hypersensitization of nociceptive neurons has been amply demonstrated in vitro [ 40 , 41 ] . considering the extensive isoforms of sodium channels or other receptor subtypes that are responsible for hypersensitization , selective inhibitors should be administered to minimize adverse side effects . however , the availability of those selective therapeutic ligands is limited . centrally acting drugs like antidepressants , anticonvulsants , and opioids provide partial pain relief , but the treatment of neuropathic pain is still unsatisfactory [ 8 , 19 ] . moreover , these centrally acting drugs are lipophilic and nonspecific with a narrow therapeutic window , further preventing their prolonged use for chronic pain treatment . treatment of chronic pain requires a novel approach regulating excitability of nociceptors as a final outcome , since it is clear that nociceptors and immune cells behave abnormally in neuropathic pain . genetic approaches that target these activated neurons in selective manner could be a potential therapeutic strategy . pharmacosynthetics and chemogenetic tools modulate transgenic receptors using artificial pharmacologic agents . currently , the most plausible pharmacosynthetic tool is the designer receptors exclusively activated by designer drug ( dreadd ) . dreadds are activated only by synthetic ligands like clozapine n - oxide ( cno ) , which are otherwise an inert pharmacological agent . dreadds are gpcrs capable of being pharmacologically modulated by synthetic chemicals , but not by endogenous gpcr ligands . a dreadd receptor can be engineered to be coupled with gs ( rm3ds ) , gi ( hm4di ) , or gq ( hm3dq ) to activate different secondary signaling pathways and different modulation of neuronal or cellular functions . transgenic expression of dreadds in specific cell types enables selective modulation of these dreadd expressing cells by ligands . except for the fact that they can be controlled with chemical ligands , dreadds behave like other endogenous gpcrs , interacting efficiently with downstream intracellular signaling components . for example , one study employed rm3ds dreadds to study the role of gs / camp / protein kinase k signaling cascades in the striatal medium spiny neurons for the hyperlocomotor response following psychostimulant treatment , such as methamphetamine or cocaine treatment . to establish dreadds in vivo , transgenic mice expressing rm3ds in medium spiny neuron ( msn ) were generated using the promoter adenosine a2a . with rm3ds expression in msn , cno treatment inhibited hyperlocomotor response even in the presence of amphetamine , thus demonstrating the important contribution of gpcr signaling in msn for this type of behavior . in addition , a novel gi - coupled dreadd has been recently developed by reengineering kappa - opioid receptor as a template . this inhibitory dreadd is activated pharmacologically by the inert ligand , salvinorin b ( salb ) . in addition , gpcrs have a diverse expression pattern in tissues and they are the most popular drug targets , representing 36% of currently approved drug targets . for this reason , dreadds draw attention for the potential in the treatment of pathological conditions that involve abnormal gpcr downstream signaling . gpcr is a naturally occurring metabotropic receptor that mediates diverse neuronal functions including gene expression . gpcr often collaborates with ion channels leading to activation or inhibition of ion channel activity . therefore , appropriate dreadd expression in neurons can counteract aberrant neuronal excitability through long - lasting secondary changes to an excitable membrane . for instance , the expression of hm3dq dreadd on neurons and activation by cno can lead to effective membrane depolarization , whereas hm4di expression inhibits neuronal action potential firing ( figures 1 and 2 ) . optogenetics utilizes channel rhodopsin that can be opened by certain light frequency stimulus , thus controlling neuronal firing . chimeric ion channels expressed in specific cell types by the conditional transgenic approach enable selective stimulation of certain neuronal population with fiber optics inserted into the desired site to deliver light to neurons . channelrhodopsin ( chr ) is engineered to be selective for cation entry whereas halorhodopsin ( nphr ) is selective for anion flux so that the activity of neuron can be effectively controlled by either stimulation or inhibition as intended . combined with the conditional transgenic approach that expresses it in specific neuronal circuit , optogenetics has been extensively used to delineate neuronal connection and pathways even in the control of emotion or behavior [ 46 , 47 ] . in terms of pain sensation , optogenetics has been employed to elicit pain with a stimulatory opsin expression in nav1.8 positive neurons in combination with transdermal optogenetic activation . in other cases , it also mitigate neuropathic pain with an inhibitory opsin expression in sensory nociceptive neuron population via adeno - associated virus ( aav ) serotype 6 infection and expression of opsin by neuron specific human synapsin-1 promoter . this delivery route allows very efficient access in small diameter nociceptive nerves salvaging large - diameter myelinated neurons that transduce touch and proprioception . optogenetic inhibition of action potential generation in nociceptors has been attempted using yellow light sensitive third - generation chloride pump halorhodopsin ( enphr3.0 ) . when delivered via aav6 intrasciatic injection , enphr3.0 activation in drg neurons with constant yellow light illumination strongly inhibits action potential initiation by membrane hyperpolarization . in vivo stimulation of this channel was sufficient to prevent painful behavior in neuropathic pain model , suggesting its therapeutic potential . the rationale of applying optogenetics or dreadds for control of abnormal pain perception in neuropathic pain is straightforward . in neuropathic pain , pain is heightened by the complicated modification of structure and gene expression in nociceptors . in this condition , neurons are easily activated to generate action potentials and transmit signals through an already built - in pain transmission network wired to the sensory cortex . as demonstrated by in vivo research discussed in the previous section , dampening of excitation in the pathologically sensitized nociceptors could be possible by expressing halorhodopsin for cl influx , thereby stabilizing membrane potential to prevent further high frequency action potential generation ( figure 1 ) . discrete expression of halorhodopsin in nociceptors is crucial to achieving selective inhibition in sensitized nociceptors . on the other hand , if interneurons are synapsed with pathological nociceptors , excitable opsins can be also employed together in the interneurons to enhance inhibitory capacity by flowing abundant inhibitory neurotransmitters , such as gaba and glycine , at certain levels . similarly , gi - coupled dreadds could be expressed in injured nociceptors to induce inhibitory changes on the membrane excitability . gi - coupled inhibition of adenylyl cyclase and resulting decrease of camp and pka signaling pathway can reverse pathological changes that have already occurred in neuropathic pain ( figure 1 ) . the difference between the optogenetics and dreadd approaches could be the duration of the effects and the extent of the downstream influence . optogenetic - mediated nociceptor inhibition can be directly achieved by fast - acting membrane potential stabilization , which occurs within a few milliseconds after light signal is applied . on the other hand , dreadds involve second messenger activation and , sometimes , alteration of gene expression changes [ 42 , 45 , 51 ] . this can cause longer latency time to achieve actual therapeutic effect , but this effect could be longer - lasting . many therapeutically effective chemicals are modulators rather than direct ligands , which inhibit or open ion channels . in this respect , the use of dreadds could be a relatively safer approach in actual human trials compared to optogenetic modulation of nociceptors , which could have potential adverse effects . extensive expression profiles with various physiologic involvements of gpcrs also favor application of dreadds in pain modulation . gpcr is involved in nociceptive neurons and in the activation and functioning of immune cells [ 9 , 10 ] . thus , dreadd expression in regions where neuropathic pain develops is able to control aberrant activation of immune cells , which ultimately induces and maintains the hypersensitivity of nociceptors . since immune cells propagate pathological chemokines and inflammatory mediators , pharmacological control of stimulated immune cells by dreadds , together with control of nociceptor activity , will facilitate more successful control of neuropathic pain transmission . a characteristic of neuropathic pain development is that the inflicted neurons and pain pathways are highly restricted . drug treatment in itself has intrinsic weakness in the lack of selectivity , which can cause unwanted adverse effect , especially at higher doses . in this respect , dreadds can be only activated by specific ligands that otherwise do not interact with other endogenous receptors at the therapeutic dosage range . as long as dreadds are expressed in the desired region , the intended effect can be exerted in specific site . in similar way conditional expression of chr can be achieved with tissue specific promoters or by delivery of channel genes via stereotaxic viral injection to target regions ( figure 2 ) . light - gated halorhodopsin or inhibitory dreadds can be also combined with conditional approaches to enhance cell type specific expression ( figure 2 ) . by combining double - floxed inverted opsins with aav expressing cre recombinase under the control of tissue specific promoter , it could be plausible to drive inhibitory opsin expression in desired neuronal or pathologically inflicted neurons to control pain signal transmission to higher structure of pain perception . as an exemplary application of cre - mediated dreadd expression in specific neuronal population , hm3d1 or hm4di dreadd has been expressed in agouti related protein ( agrp ) expressing neurons by using a cre - loxp system . when loxp - blocked hm3dq aav was injected into agrp - ires - cre mice , hm3dq expression was only confined to cell types expressing cre under control of the agrp promoter . interestingly , depending on g protein signaling modulated with cno ( 0.3 mg / kg ) administration , the eating behavior of the mice was reversibly controlled , demonstrating the role of g protein - coupled signaling in this type of neural circuit for food intake behavior . temporal regulation is also possible because dreadds or chrs can be only activated when the corresponding stimuli are given either by pharmacological application of ligands or by light stimuli in the vicinity . while the chr response upon withdrawal of light is immediate , dreadd activity will be gradually reduced following pharmacokinetic elimination of ligand resulting in longer - lasting changes . in this respect , the tet - on system is applied for controlled expression spatially and temporally by relaying actions of rtta acting on teto promoter . when rtta expression is driven by tissue specific promoter , teto - driven dreadd transgene expression can be restricted to specific tissue . reversible expression of dreadd receptor is achieved by doxycycline dependent activation of rtta action on teto promoter . by combining with dreadd - cno coupling , the tet - on system will provide additional safeguard to control dreadd expression as well as dreadd - mediated g protein signaling in targeted cell population ( figure 2 ) . viral delivery is a very efficient tool to deliver any gene of interest in vivo . although we are at mostly preclinical validation stages of viral gene therapy for neuropathy pain control , there has been great success in suppressing pain sensation by viral transfer of single gene in neuropathic animal models . due to the efficient delivery of therapeutic genes and promising preclinical results in several disease animal models , clinical trials for this method have been made for over 20 years . to increase safety and selectivity of clinical application of the viral vector - mediated gene therapy , firstly , the viral vector should be devoid of replication ability , genomic integration , and immunogenicity to be safely applied to human subjects . secondly , the neuropathic disease states are usually chronic , persisting for long period of time . this makes it necessary for the viral vector to maintain constitutive expression levels in therapeutic dosage . thirdly , gene delivery should be targeted to specific cells to prevent undesirable toxicity from transgene expression in other areas with optimal titer volume . some candidate viral vectors fall into the categories such as adeno - associated virus ( aav ) , herpes simplex virus ( hsv ) , and lentivirus . these viral vectors offer attractive features like less immunogenicity and genomic insertion possibility than other viral vectors . indeed there have been ongoing clinical trials with hsv and aav to treat inherited disease with defective gene expression [ 5761 ] . lentiviral vector has advantage to harbor larger transgene in the virus particle and it shows tropism for neuron transduction , but its genomic integration makes it relatively unsafe . its application is mostly confined to ex vivo gene transfer . but still there has been an attempt to apply this virus for neurodegenerative diseases such as parkinson 's disease . on the other hand , hsv and aav seldom integrate into host genome and they have tropism for neuron transduction depending on serotypes used for gene delivery . these features and others provide advantages in translational research and clinical application of the viral vectors for neuropathic pain modulation . the wild type aav is not causing any known disease in human , confirming safety in practice . small size of aav with diameter of 2025 nm enables highly robust diffusion even in application to solid tissues . it can still encompass up to 5 kb size of dna into virus particle which is sufficient to clone gene of interest for delivery . several reports have shown efficient transduction of several cell types including neurons in vivo animal studies and clinical trials . due to these attractive features of aav virus , aav - mediated gene therapy has been extensively studied , and long term expression of genes for therapeutic purpose has been achieved in a clinical setting especially for patients with inherited disorders such as retinal disorders and hemophilia b [ 57 , 59 ] . although successful application of viral gene therapy varied depending on target tissues and replacement genes of interest , there have been reports demonstrating safety and therapeutic efficacy of aav - mediated gene transfer to patients with inherited disease defective in certain genes . as mentioned above , aav can transduce dividing and postmitotic tissues with specificity depending on its serotypes . aav serotype 2 has been widely used since it shows relative selectivity for neuron transduction in comparison to glial transduction , while aav serotype 1 tends to infect both neurons and glial cells in nonspecific manner . thus , depending on target cells of interest , appropriate aav viral serotypes can be chosen for best result . actually , in animal model studies , aav has been successfully administered via intrathecal or direct injection to drg to achieve transduction of afferent sensory neurons and glial cells . serotype 1 aav , on the other hand , has tendency to transduce not only neurons but glial cell population ; it would be possible to transfer inhibitory dreadds to inflammatory glial cells that are highly activated in neuropathic pain environments . however , there are certainly disadvantages in aav application , too . even though its sizable capacity is up to 5 kb of dna into the virus particle , it would be difficult to package cell type specific promoter components that are usually bigger than 5 kb . therefore , it would be hard to purify aav virus expressing channel rhodopsin or dreadds via responsive promoter ( e.g. , tet promoter , or loxp flanked stop cassette containing cba promoter ) . it may be necessary to use combinatorial viral application using other viral vectors that can hold larger capacity to package bigger size of foreign dna like hsv vector . furthermore , aav clinical application could induce adverse immune reactions through aav viral capsid responsive t cell activation or transgene expression itself . replication - defective herpes simplex virus ( hsv ) , thus nonpathogenic , has been used for gene therapy in animal models and human clinical trials . the clinical trial of nonreplicating hsv expressing preproenkephalin treatment for intractable pain in cancer patients has shown to be safe with dose responsive therapeutic efficacy to relieve pain , providing proof of evidence for gene therapy with hsv virus [ 61 , 63 ] . different from aav approach , hsv has a tendency to transduce neurons in a retrograde manner , which makes this vector suitable for targeting afferent sensory nerves . hsv vectors expressing antinociceptive substances , such as endomorphin-1 , proenkephalin a , and il-4 , have been subcutaneously inoculated to selectively transduce drg in neuropathic animal models . most striking feature of hsv vector is that it has strong tropism for nerve cells and high capacity to contain sizable dna fragment . furthermore , once introduced into neurons via retrograde transport , the viral genes are stable and exert sustained expression of transgenes . there features are quite advantageous in clinical application for human neuropathy because conditional dreadds and halorhodopsin gene expression in disease specific manner requires selection and usage of tissue specific gene promoter that is usually big in size ranging around 10 kb . thus hsv viral vector is suitable to transfer neuropathic nociceptor specific promoter driving expression of cre or rtta into abnormally activated nociceptors with sustainable expression of transgenes ( figure 2 ) . despite some promising clinical application of viral vector - mediated gene therapy , caution should be taken because unexpected toxicity due to irreversible expression of therapeutic genes could be harmful to patients . in this respect , our proposed conditional viral model system to deliver either cre responsive or tetracycline responsive halorhodopsin or inhibitory dreadds provides additional safeguard . different from previously attempted constitutive expression of antinociceptive proteins , expression of halorhodopsin or inhibitory dreadds is switchable even after successful integration into neuropathic pain sites . as discussed above , channelrhodopsin and dreadds retain temporal resolution in their activation and function via lighting or cno ligand treatment , respectively . any unwanted adverse effects after clinical application can be immediately abolished by simply withdrawing the aforementioned gating stimuli . in addition , tet - off controlled expression of channelrhodopsin or dreadds ( figure 2(c ) ) allows stopping expression of this transgene itself . thus , if transgene expression initiates harmful immune response in clinical setting , the expression of therapeutic genes can be turned off by withdrawing doxycycline treatment . overall , the safety and efficacy of gene therapy mediated treatment for clinical neuropathy could be improved substantially by combining optogenetics / dreadds , conditional genetic tools , and appropriate viral vectors . tissue type selective expression and temporal control of chrs or dreadds may not be sufficient to pinpoint the damaged nociceptive neurons . to gain specific control over neuropathic pain , it is essential to understand which genetic program differential promoter activities between normal and neuropathic states can be exploited to construct transgenic viral vectors for dreadds or chrs to be expressed in more defined pathological cell types ( figure 2 ) . rather than affecting normal pain pathways , this approach will ensure disease specific control for drug treatment . as discussed above , normal sensation of pain is crucial to adapting to outside danger through proper response [ 18 , 64 ] . the selective expression of therapeutic modules in abnormally stimulated nociceptive neurons with altered gene expressions will attenuate abnormal pain sensation while preserving normal sensation of pain . to accomplish this , a complete understanding of global gene expression profiling is needed . previously , microarray with probes printed on slides was a representative method to obtain transcriptome profiling . microarray experiments are relatively easy to perform and are adequate for high - throughput data acquisition . there are many microarray databases pertaining to neuropathic pain that have provided insight into differentially regulated genes in neuropathic pain state [ 23 , 65 ] . these have shown that several neuropeptide messenger levels ( npy , galanin , and vip ) are highly elevated in drg of neuropathic pain models . inflammatory mediators such as complement proteins , allograft inflammatory factor-1 , alpha-2-macroglobulin , interferon - induced guanylate - binding protein 2 , and il-18 are also upregulated . notably , upregulated receptors include gaba receptor , nicotinic acetylcholine receptor 7 subunit , p2y1 purinoceptor , na channel 2 subunit , and ca channel 2-1 subunit [ 23 , 65 ] , providing ample promising promoter candidates for selective induction of dreadds or chrs . microarray - based transcriptome analysis often has shortcomings due to the limited pool of custom - designed probes for gene detection . furthermore , depending on probe and messenger pairing , absolute comparison of each gene expression level is almost impossible , only detecting relative changes of certain gene expression . on the other hand , rnaseq technology enables unprecedented global characterization of transcriptome changes in vitro and in vivo with greater sensitivity . due to its wide detection range , rnaseq provides quantitative values ( e.g. , reads / fragments per kilobase of transcript per million mapped reads ) that can be used to estimate gene abundance . it is also possible to do rnaseq transcriptome profiling if it is combined with bac - trap technology , even in brains with highly heterogeneous distribution of neuronal and glial cell types . rnaseq in drg neurons has been described in normal and pathological neuropathic pain condition . this global profiling can be used as a basis to identify neuropathic pain specific promoters that are highly activated in nociceptors . several genes with more than 10-fold enrichment in drg have been identified in this global rnaseq analysis . these data can be utilized to mine sensory neuron specific promoters for disease modifying transgene . even in ultraviolet - induced inflammatory pain , rnaseq analysis in damaged drg has successfully identified upregulated expression of reg3b , ccl2 , and vgf . application and comparison of rna whole transcriptome sequencing in defined neuropathic pain animal models or in patient samples will provide detailed and systemic molecular insights underlying the disease process . combined with the genetic engineering and functional expression of dreadds and chrs , better strategy for neuropathic pain control could be designed as compared to pan neuronal expression of these modules , which could shut down the overall pain sensation , possibly leading to adverse effects . since conventional therapies targeting single target genes including ion channels , receptors , or inflammatory mediators have been largely unsatisfactory , novel therapeutic strategies are needed . optogenetics and dreadds provide hope in controlling intractable pain in patients suffering from debilitating neuropathic pain . these tools can provide an effective means to control the disease process by artificial drugs through the modulation of distinct neuronal populations . based upon the underlying cause of neuropathic pain , it would be possible to improve the potential of pain management by combination therapies of these techniques and drugs targeting specific molecular targets . with continuing development and refinement of this technique in combination with viral vector - mediated safe and efficient gene therapy[/INST]chronic pain originating from neuronal damage remains an incurable symptom debilitating patients . proposed molecular modalities in neuropathic pain include ion channel expressions , immune reactions , and inflammatory substrate diffusions . recent advances in rna sequence analysis have discovered specific ion channel expressions in nociceptors such as transient receptor potential ( trp ) channels , voltage - gated potassium , and sodium channels . g protein - coupled receptors ( gpcrs ) also play an important role in triggering surrounding immune cells . the multiple protein expressions complicate therapeutic development for neuropathic pain . recent progress in optogenetics and pharmacogenetics may herald the development of novel therapeutics for the incurable pain . designer receptors exclusively activated by designer drugs ( dreadds ) facilitate the artificial manipulation of intracellular signaling through excitatory or inhibitory g protein subunits activated by biologically inert synthetic ligands . expression of excitatory channelrhodopsins and inhibitory halorhodopsins on injured neurons or surrounding cells can attenuate neuropathic pain precisely controlled by light stimulation . to achieve the discrete treatment of injured neurons , we can exploit the transcriptome database obtained by rna sequence analysis in specific neuropathies . this can recommend the suitable promoter information to target the injury sites circumventing intact neurons . therefore , novel strategies benefiting from pharmacogenetics , optogenetics , and rna sequencing might be promising for neuropathic pain treatment in future .</s>

with the recent observational discovery of magnetars , which are assumed to be strongly magnetized young neutron stars and also the possible sources of soft gamma - ray repeaters ( sgr ) and anomalous x - ray pulsars ( axp ) @xcite , the study on the effect of strong magnetic fields on dense stellar matter has got a new dimension . in the recent years a lot of work have been done on the effect of strong magnetic field on the equation of state of dense stellar matter @xcite . some studies have also been done on the effect of strong magnetic field on elementary processes ( e.g. , weak and electromagnetic processes ) occurring at the core region as well as at the envelope of strongly magnetized neutron stars @xcite . during the past few years , in a number of publications we have reported our thorough investigations on the effect of strong magnetic field on the stability of dense quark matter and quark - hadron phase transition ( both first order and second order ) at the core of a strongly magnetized neutron star @xcite . we have also studied the effect of strong magnetic field on dense neutron matter with properly modifying the @xmath0-meson type mean - field theory . in those work we have developed the relativistic version of mean field theory in presence of strong quantizing magnetic field using hartree and hartree - fock model with @xmath1 mesons exchange interaction @xcite . in the recent years the transport coefficients in particular , the electrical conductivity of electrons at the crustal region of neutron stars have also been calculated in presence of strong magnetic fields @xcite . unfortunately , in none of these studies the dense core region of the star is taken into account . now from the observational data of sgr and axp , the strength of surface magnetic field of magnetars are predicted to be @xmath2 g . then it is very easy to show by scalar virial theorem that the magnetic field strength at the core region may go up to @xmath3 g . this is of course strong enough to affect most of the physical processes occurring at the core region . as a consequence , one of the most important physical phenomena , the transport properties of dense core matter , in particular , the electrical conductivity of electrons and transport properties of emitted neutrinos will be affected significantly by the strong magnetic field . to investigate the transport properties of dense matter at the core of a neutron star , we use the standard form of boltzmann kinetic equation with relaxation time approximation . since protons are too heavy compared to electrons , we have assumed that the electric current is solely due to the motion of electrons . now the relaxation time is directly related to the rates of the relevant ( weak and electromagnetic ) processes . these processes are strongly affected by the presence of quantizing magnetic field . as a consequence , both qualitative and the quantitative nature of transport coefficients , e.g. , electrical conductivity , viscosity and heat conductivity should change significantly in presence of strong magnetic field . in a future publication we shall report the effect of strong magnetic field on the transport properties of neutrinos at the core region @xcite . in the present article , we shall investigate the effect of strong magnetic field on the electrical conductivity at the core region of strongly magnetized neutron stars or magnetars . the paper is organized in the following manner : in section 2 , we obtain the rates of the relevant processes in presence of strong magnetic field . in section 3 , we shall derive an expression for the electrical conductivity from boltzmann kinetic equation using relaxation time approximation . in the last section , we have given the conclusion and discussed the future perspective of the work . to obtain electrical conductivity at the core of a magnetar , we have considered the following two electromagnetic processes relevant for electron transport : electron - electron scattering @xmath4 and electron - proton scattering @xmath5 where @xmath6 and @xmath7 are the initial and final four momenta . since the rate of the electron - neutrino weak scattering , given by @xmath8 is several orders of magnitude less than the electromagnetic processes , it has almost no significance in the electrical conductivity calculation . of course , this is one of the most important neutrino transport processes . for the same reason , we have neglected @xmath9 weak scattering . to obtain electrical conductivity at the core of a magnetar , we first consider e - e scattering . for this process , both the direct as well as exchange diagrams are considered . from the definition , the transition matrix element is given by @xmath10 where @xmath11 is the electric current produced by the scattered electron and @xmath12}{q^2 } j^\mu ( x')d^4x'\ ] ] is the electromagnetic field induced by the current @xmath13 of the other electron and @xmath14 is the transferred four momentum . now in the case , when only the zeroth landau levels are occupied by the electrons the positive energy dirac spinor is given by @xmath15\nonumber \\ & & \left ( \frac{eb}{\pi}\right ) ^{1/4 } \exp \left [ -\frac{1}{2 } eb \left ( x-\ \frac{p}{eb}\right ) ^2\right ] \left ( \begin{array}{c } \varepsilon_0+m\\ 0\\ p_z\\ 0 \end{array } \right ) \end{aligned}\ ] ] where @xmath16 and @xmath17 are the lengths along @xmath18 and @xmath19 directions , @xmath20 is the modified form of single particle energy , @xmath21 and @xmath22 are @xmath18 and @xmath19 components of electron momentum , @xmath23 is the strength of magnetic field , assumed to be along positive @xmath19-direction ( we have chosen the gauge @xmath24 ) . the counter part of this spinor has no contribution when only the zeroth landau level is occupied . whereas , for low temperature case ( the chemical potential @xmath25 , where @xmath26 is the temperature of the system . in the numerical calculation , we have taken @xmath27mev and found that the results are almost temperature independent for @xmath28 ) the negative energy spinor solutions may be neglected . combining eqns.(4)-(6 ) and after integrating over @xmath29 , @xmath30 , @xmath31 ( which result three @xmath32-functions ) , we have the transition matrix element for the direct @xmath9 scattering diagram @xmath33}{q^2}\frac{\exp[-i q_x x']}{l_y^2 l_z^2}\frac{e^2}{[16 p_1 ^ 0 p_2 ^ 0 k_1 ^ 0 k_2 ^ 0 ( p_1 ^ 0+m)(k_1 ^ 0+m)(p_2 ^ 0+m)(k_2 ^ 0+m)]^{1/2}}\nonumber \\ & & \exp[-i\{(p_2 ^ 0-k_2 ^ 0)t-(p_{2y}-k_{2y})y-(p_{2z}-k_{2z})z\ } ] [ j_\mu(x')]_{p_1,k_1 } [ j_\mu(x)]_{p_2,k_2 } dx'\end{aligned}\ ] ] where @xmath34_{p , k}=\bar u(k)\gamma^\mu u(p ) i_{0;k_y , k_z}(x ) i_{0;p_y , p_z}(x),\ ] ] @xmath35 and @xmath36 are respectively the positive energy spinor and the corresponding adjoint and @xmath37\ ] ] the integrals over @xmath38 and @xmath39 can very easily be evaluated by changing the variables to @xmath40 and @xmath41 , given by @xmath42 and @xmath43 . the integration over @xmath41 the gives @xmath44\ ] ] similarly , the integration over @xmath40 is given by @xmath45 erfc [ -(2eb)^{1/2}x_{(dir)}]\ ] ] where @xmath46 , @xmath47 and @xmath48 is the complementary error function . after evaluating the integrals over @xmath49 with the help of @xmath32-functions we have the transition matrix element for direct @xmath9 scattering @xmath50^{1/2}}\nonumber \\ & & [ j_\mu(p_1,k_1)][j_\mu(p_2,k_2)]\frac{1}{4l_y^2l_z^2eb } \nonumber \\ & & \exp\left [ \frac{1}{2eb}(p_{1y}+p_{2y})^2\right ] \exp(-2ebx_{(dir)}^2)\nonumber \\ & & erfc ( -(2eb)^{1/2 } x_{(dir ) } ) \frac{1}{2k_{(dir)}}(2\pi)^3 \delta(p_1 ^ 0+p_2 ^ 0-k_1 ^ 0-k_2 ^ 0)\nonumber \\ & & \delta(p_{1y}+p_{2y}-k_{1y}-k_{2y } ) \delta(p_{1z}+p_{2z}-k_{1z}-k_{2z})\end{aligned}\ ] ] which may be written as @xmath51 the transition matrix element for @xmath9 exchange interaction can very easily be obtained from the direct one just by exchanging @xmath52 and @xmath53 ( @xmath54 ) . then we have @xmath55^{1/2}}\nonumber \\ & & [ j_\mu(p_1,k_2)][j_2(p_2,k_1)]\frac{1}{4 l_y^2 l_z^2 eb}\nonumber \\ & & \exp\left [ \frac{1}{2eb}(p_{1y}+p_{2y})^2\right ] \exp(-2ebx_{(ex)}^2 ) erfc[-(2eb)^{1/2}x_{ex)}]\frac{1}{2k_{(ex ) } } ( 2\pi)^3 \nonumber \\ & & \delta(p_1 ^ 0+p_2 ^ 0-k_1 ^ 0-k_2 ^ 0)\delta(p_{1y}+p_{2y}-k_{1y}-k_{2y } ) \delta(p_{1z } + p_{2z}-k_{1z}-k_{2z})\end{aligned}\ ] ] where @xmath56 and @xmath57 . which may also be written in the form @xmath58 now from the elementary definition of rate per unit volume for the scattering process , we have the differential rate for @xmath9 scattering @xmath59 hence to obtain the differential rate @xmath60 of the processes we have to calculate @xmath61 , @xmath62 and the cross term . further , to compute these quantities , we have to evaluate the traces of the products of @xmath63-matrices . using the standard techniques , we have computed the traces of the products of @xmath63-matrices . then we have @xmath64 \exp(-4ebx_{(dir)}^2 ) \nonumber \\ & & \{erfc[-(2eb)^{1/2 } x_{(dir)}]\}^2 [ ( p_1.p_2)(k_1.k_2)+(p_1.k_2)(k_1.p_2)-m^2(p_2.k_2)-m^2(p_1,k_1 ) \nonumber\\ & & + 2m^4 ] \frac{1}{8 \pi^2 k_{(dir)}^2 } \frac{1}{(2\pi)^3 } \delta(p_1 ^ 0+p_2 ^ 0-k_1 ^ 0-k_2 ^ 0)\delta(p_{1y}+p_{2y}-k_{1y}-k_{2y } ) \nonumber\\ & & \delta(p_{1z } + p_{2z}-k_{1z}-k_{2z } ) dk_{1y } dk_{1z } dk_{2y } dk_{2z } dp_{2y } dp_{2z}\end{aligned}\ ] ] similarly , the exchange term is obtained by @xmath65 and is given by @xmath66\exp(-4ebx_{(ex)}^2 ) { erfc[-(2eb)^{1/2}x_{(ex)}]}^2 \nonumber \\ & & [ ( p_1.p_2)(k_1.k_2)+(p_1.k_1)(p_2.k_2)-m^2(p_2.k_1)-m^2 ( p_1.k_2)+2m^4]\frac{1}{8\pi^2 k_{(ex)}^2}\nonumber \\ & & \frac{1}{(2\pi)^3 } \delta(p_1 ^ 0+p_2 ^ 0-k_1 ^ 0-k_2 ^ 0)\delta(p_{1y}+p_{2y}-k_{1y}-k_{2y } ) \delta(p_{1z } + p_{2z}-k_{1z}-k_{2z})\nonumber \\ & & dk_{1y } dk_{1z } dk_{2y } dk_{2z } dp_{2y } dp_{2z}\end{aligned}\ ] ] finally the cross term whose evaluation is a bit lengthy , but straight - forward , is given by @xmath67 \exp[-2eb(x_{(dir)}^2 + x_{(ex)}^2)]\nonumber \\ & & erfc[-(2eb)^{1/2}x_{(dir)}]erfc[-(2eb)^{1/2}x_{(ex)}]\nonumber \\ & & [ -2(k_1.k_2)(p_1.p_2)+m^2(p_2.k_2)+m^2(p_2.k_1)+m^2(p_2.p_1)+\nonumber \\ & & m^2(p_1.k_1)+m^2(p_1.k_2)+m^2(k_1.k_2)-2m^4 ] \nonumber \\ & & \frac{1}{8\pi^2 k_{(dir)}k_{(ex)}}\frac{1}{(2\pi^3 ) } \delta(p_1 ^ 0+p_2 ^ 0-k_1 ^ 0-k_2 ^ 0)\delta(p_{1y}+p_{2y}-k_{1y}-k_{2y } ) \delta(p_{1z } + p_{2z}-k_{1z}-k_{2z})\nonumber \\ & & dk_{1y } dk_{1z } dk_{2y } dk_{2z } dp_{2y } dp_{2z}\end{aligned}\ ] ] the simplified form of these rates can very easily be obtained by integrating over the momentum components @xmath68 , @xmath69 , @xmath70 and @xmath71 with the help of @xmath32-functions . then we have after some simple algebraic manipulation @xmath72 \exp\left [ \frac{1}{eb}(k_{2y}-k_{1y}-k_{(dir)})\right ] \nonumber \\ & & \left [ erfc\left \{-\frac{1}{(2eb)^{1/2}}(k_{2y}-k_{1y}-k_{(dir)})\right \}\right]^2 [ ( p_1 ^ 0p_2 ^ 0-p_{1z}p_{2z})(k_1 ^ 0k_2 ^ 0-k_{1z}k_{2z})+ \nonumber \\ & & ( p_1 ^ 0k_2 ^ 0-p_{1z}k_{2z})(k_1 ^ 0p_2 ^ 0-k_{1z}p_{2z } ) -m^2(p_2 ^ 0k_2 ^ 0-p_{2z}k_{2z } ) -m^2(p_1 ^ 0k_1 ^ 0 -p_{1z}k_{1z } ) + 2m^4 ] \nonumber \\ & & \frac{1}{8\pi^2k_{(dir)}^2}\frac{1}{(2\pi)^3}dk_{1y}dk_{2y}\huge |_{k_{1z } = p_f , k_{2z}=k_{2z}^{(r ) } , p_{2z}=p_{1z}+k_{1z}-k_{2z}}\nonumber \\ & & \frac{p_f}{\mid f'(k_{2z})\mid_{k_{2z}=k_{2z}^{(r)}}}\end{aligned}\ ] ] where @xmath73 , @xmath74 and @xmath75 are the electron chemical potential and fermi momentum respectively , @xmath76^{1/2}}\ ] ] is the root of the transcendental equation @xmath77 and @xmath78 where @xmath79 similarly , for the exchange interaction we have @xmath80 \exp\left [ -\frac{1}{eb}(k_{1y}-k_{2y}-k_{(ex)})^2 \right ] \nonumber \\ & & \left \{erfc\left [ -\frac{k_{1y}-k_{2y}-k_{(ex)}}{(2eb)^{1/2 } } \right ] \right \}^2 [ ( p_1.p_2)(k_1.k_2 ) + ( p_1.k_1)(p_2.k_2)\nonumber \\ & & -m^2 ( p_2.k_1)-m^2(p_1.k_2 ) + 2m^4 ] \frac{1}{8\pi^2 k_{(ex)}^2 } \frac{1}{(2\pi)^3 } \nonumber \\ & & dk_{1y}dk_{2y}\huge |_{k_{2z}=k_f , k_{1z}=k_{1z}^{(r ) } , k_{2z}= k_{1z}+ p_{1z } -k_{2z } } \frac{p_f}{\left | f'(k_{2z})\right |_{k_{2z } = k_{2z}^{(r ) } } } \end{aligned}\ ] ] where @xmath81 . finally for the mixed term , we have @xmath82 \exp\left [ -\frac{1}{2eb}(k_{2y}-k_{1y}-k_{(dir)})^2 \right ] \nonumber \\ & & \exp\left [ -\frac{1}{2eb}(k_{1y}-k_{2y}-k_{(ex)})^2 \right ] erfc\left [ -\frac{k_{2y}-k_{1y}-k_{(dir)}}{(2eb)^{1/2 } } \right ] \nonumber \\ & & erfc\left [ -\frac{k_{1y}-k_{2y}-k_{(ex)}}{(2eb)^{1/2 } } \right ] [ -2(p_1.p_2)(k_1.k_2 ) + m^2(p_2.k_2 ) + m^2 ( p_2.k_1)+\nonumber \\ & & m^2(p_1.p_2)+m^2(p_1.k_1 ) + m^2(p_1.k_2 ) + m^2(k_1.k_2)-2m^4 ] \nonumber \\ & & \frac{1}{8\pi^2 k_{(dir)}k_{(ex ) } } \frac{1}{(2\pi)^3 } \nonumber \\ & & dk_{1y}dk_{2y}\huge |_{k_{2z}=k_f , k_{1z}=k_{1z}^{(r ) } , k_{2z}= k_{1z}+ p_{1z } -k_{2z } } \frac{p_f}{\left | f'(k_{1z})\right |_{k_{1z } = k_{1z}^{(r ) } } } \end{aligned}\ ] ] in the case of @xmath83 scattering , given by eqn.(2 ) the direct diagram only contributes and the form of trace term will be slightly different from that of @xmath9 direct term , given by @xmath84\end{aligned}\ ] ] where @xmath85 is the effective proton mass in the hartree type mean field model in presence of strong magnetic field @xcite . in this case we have to use @xmath86 and @xmath87 and make necessary changes in eqn.(20 ) of @xmath88 for @xmath9 scattering to obtain @xmath89 . in the next section we shall use these differential rates ( eqns.(20 ) , ( 23 ) , ( 24 ) and @xmath89 ) to obtain the electrical conductivity . to compute the electrical conductivity of the magnetized stellar matter , we consider the simplest form of boltzmann kinetic equation for electrons which are assumed to be slightly out of local thermodynamic equilibrium . the kinetic equation is then given by @xcite @xmath90 where @xmath91 is the non - equilibrium distribution function and @xmath92 is the collision term , given by @xmath93 where @xmath94 $ ] , and @xmath95 s are the pauli blocking factors . replacing collision term by the relaxation time approximation , we have the relevant portion of the kinetic equation needed to obtain the electrical conductivity . @xmath96 where @xmath97 is the local equilibrium distribution function for electrons ( fermi distribution ) , given by @xmath98 here @xmath22 is the longitudinal momentum and @xmath99 is the corresponding transverse part for the electrons , @xmath100=@xmath101 and @xmath102 are the local temperature and chemical potential . when only the zeroth landau levels ( @xmath103 ) are occupied by the electrons , the transverse momentum becomes exactly zero . we now consider the first order approximation , i.e. , the system is very close to its local equilibrium configuration , then we can write @xmath104 where @xmath105 is a measure of its deviation from local statistical equilibrium configuration . then we have @xmath106 , where @xmath107 s are the equilibrium distribution function for the @xmath108th component ( fermi distribution ) . the we can write @xmath109 expressing the force term in the form , @xmath110 we have after using eqn.(3 ) @xmath111 then just by inspection , it is very easy to realize that the relaxation time is obtained by evaluating the integrals over @xmath112 and @xmath113 in the expressions for the rates and the relation with the total rate of the processes is given by @xmath114 where @xmath115 therefore , @xmath116 the well know matthiessen s rule @xcite . now the expression for electric current is given by @xmath117 because of randomness in the system , the local current vanishes at equilibrium . then the nonzero part of electric current is obtained by using the first order deviation @xmath118 and is given by @xmath119 in presence of a strong magnetic field of strength @xmath120 , the quantum limit of magnetic field , where @xmath121 g , we have @xmath122 . then writing ohm s law in the form @xmath123 , we have @xmath124 which is second rank tensor with the components @xmath125 , @xmath126 , @xmath127 and @xmath128 . since we are interested for @xmath129 case only , i.e. , when the lowest landau levels are populated , we have @xmath130 and @xmath131 which is the only non - zero component . the electron transport in this special case becomes essentially one dimensional- along the direction of magnetic field . in fig.(1 ) we have plotted the variation of @xmath125 with electron density for ( a)@xmath132 , ( b)@xmath133 , ( c)@xmath134 , ( d)@xmath135 and ( e ) @xmath136 , where @xmath137 g , the quantum limit for electrons . in fig.(2 ) we have shown the variation of the nonzero component of electrical conductivity @xmath125 with magnetic field strength for ( a)@xmath138 , ( b)@xmath139 , ( c)@xmath140 , and ( d)@xmath141 , where @xmath142@xmath143 , the typical electron density in a non - magnetic neutron star . in both these cases we have not taken @xmath144 equilibrium condition into account . the density of electron is in some sense arbitrary . therefore , we now consider an interacting @xmath145 system in @xmath144-equilibrium , which is the real physical picture at the core region of a neutron star . then we have @xmath146 , the charge neutrality condition , @xmath147 , the @xmath144-equilibrium condition ( we assume that the neutrinos are non - degenerate , leave the system as soon as they are produced ) and baryon number density @xmath148 remains invariant in electromagnetic and weak interaction processes . solving these constraints self - consistently at the core of a magnetar , we obtain the chemical potential of the constituents and hence the density of electrons for various baryon densities and magnetic field strengths . we have assumed a fixed temperature @xmath27mev . in fig.(3 ) we have shown the variation of @xmath125 with the strength of magnetic field for a fixed baryon number density ( in the numerical computation we have taken @xmath149 , @xmath150@xmath143 ) assuming that the system is in @xmath144-equilibrium . in fig.(4 ) we have plotted @xmath125 against the electron density for a fixed magnetic field strength ( @xmath151 ) in @xmath144-equilibrium condition . we have studied the electrical conductivity at the core of a magnetar using boltzmann kinetic equation with the relaxation time approximation . the latter is obtained from the rates of the electromagnetic processes , which essentially control the electron transport in the medium . we have further noticed that the electrical conductivity behaves like a second rank tensor above the critical value ( quantum limit ) of magnetic field strength . however , only @xmath125 components is non - zero when the lowest landau levels are occupied by the charged particles . the system effectively becomes one - dimensional in presence of quantizing magnetic field- electrons can move along the field direction . the electric current vanishes in the plane transverse to the direction of magnetic field . since it is impossible to compute the rates analytically ( even it is very difficult to obtain numerically ) with the non - zero values of landau quantum numbers for all the four charged particles , we have assumed that only the zeroth landau levels are occupied . this makes our like much simpler . the assumption of only zero landau quantum number is also justified by the presence of intense magnetic field at the core region of magnetars . fig.(1 ) shows that there exist cut off densities , beyond which , the pauli blocking factor supresses the electron scattering and as a result the conductivity becomes zero . this figure also shows that the cut off density increases with the increas of magnetic field strength . as the magnetic field increases , for a given baryon number density , the chemical potential of electrons decreases , which further reduces the pauli suppression factor . similarly , we have noticed from fig.(2 ) that there is a minimum value for magnetic field strength for a particular baryon number density below which the conductivity again becomes zero because of same reason as discussed above . on the other hand , in the case of @xmath144-equilibrium condition , electrons are generated self - consistently . so there are no such cut off values for the density or magnetic field and the variation is smooth . 99 c. kouveliotou , et al . , nature * 393 * , 235 ( 1998 ) . k. hurley , et al . , astrophys . * 442 * , l111 ( 1999 ) . s. mereghetti and l. stella , astrophys . jour . * 442 * , l17 ( 1999 ) . j. van paradihs , r.e . taam and e.p.j . van den heuvel , astron . astrophys . * 299 * , l41 ( 1995 ) ; s. mereghetti , astro - ph/99111252 ; see also a. reisenegger , astro - ph/01003010 . cardall , m. prakash and j.m . lattimer , astro - ph/0011148 . in - saeng suh and g.j . mathews , astro - ph/9912301 . f. @xmath152zel , astro - ph/0103227 ; t. ghosh , ph.d . thesis , univ . of kalyani ( unpublished ) . a.y . potekhin and d.g . yakovlev , astro - ph/0105261 and references therein . s. chakrabarty , astrophys . space sci . * 213 * , 121 ( 1994 ) ; s. chakrabarty and a. goyal , mod . * a9 * , 3611 ( 1994 ) ; s. chakrabarty , phys . rev . * d51 * , 4591 ( 1995 ) . s. chakrabarty and p. k. sahu , phys . rev . * d54 * , 1306 ( 1996 ) ; s. chakrabarty , d. bandopadhyay and s. pal , int . mod . phys . * a13 * , 295 ( 1998 ) ; d. bandopadhyaya , s. chakrabarty , p. dey and s. pal , phys . rev . * d58 * , 121301 ( 1998 ) . t. ghosh and s. chakrabarty , phys . rev . * d63 * , 0403006 ( 2001 ) ; t. ghosh and s. chakrabarty , int . mod . phys . * d10 * , 89 ( 2001 ) . s. chakrabarty , d. bandopadhyay and s. pal , phys . * 78 * , 2898 ( 1997 ) . d. bandopadhyay , s. chakrabarty and s. pal , phys . * 79 * , 2176 ( 1997 ) . k. huang , statistical mechanics , 2nd . ed . , john wiley and sons , new york ( 1987 ) . e.m . lifshitz and l.p . pitaevskii , statistical physics , part 2 , pergamon , oxford ( 1980 ) . sanchayita ghosh , sutapa ghosh and s. chakrabary ( in preparation ) . solid state physics , n.w . ashcroft and n.d . mermin , saunders college publ . new york , ( 1976 ) .

an expression for the electrical conductivity at the core of a magnetar is derived using boltzmann kinetic equation with the relaxation time approximation . the rates for the relevant scattering processes , e.g. , electron - electron and electron - proton are evaluated in presence of strong quantizing magnetic fields using tree level diagrams . it is found that in presence of a strong quantizing magnetic field , electrical conductivity behaves like a second rank tensor . however , if the zeroth landau levels are only occupied by the charged particles , it again behaves like a scaler of a one dimensional system . pacs:05.20.dd , 72.10.-d , 72.15.lh , 79.60.jd

<s>[INST]with the recent observational discovery of magnetars , which are assumed to be strongly magnetized young neutron stars and also the possible sources of soft gamma - ray repeaters ( sgr ) and anomalous x - ray pulsars ( axp ) @xcite , the study on the effect of strong magnetic fields on dense stellar matter has got a new dimension . in the recent years a lot of work have been done on the effect of strong magnetic field on the equation of state of dense stellar matter @xcite . some studies have also been done on the effect of strong magnetic field on elementary processes ( e.g. , weak and electromagnetic processes ) occurring at the core region as well as at the envelope of strongly magnetized neutron stars @xcite . during the past few years , in a number of publications we have reported our thorough investigations on the effect of strong magnetic field on the stability of dense quark matter and quark - hadron phase transition ( both first order and second order ) at the core of a strongly magnetized neutron star @xcite . we have also studied the effect of strong magnetic field on dense neutron matter with properly modifying the @xmath0-meson type mean - field theory . in those work we have developed the relativistic version of mean field theory in presence of strong quantizing magnetic field using hartree and hartree - fock model with @xmath1 mesons exchange interaction @xcite . in the recent years the transport coefficients in particular , the electrical conductivity of electrons at the crustal region of neutron stars have also been calculated in presence of strong magnetic fields @xcite . unfortunately , in none of these studies the dense core region of the star is taken into account . now from the observational data of sgr and axp , the strength of surface magnetic field of magnetars are predicted to be @xmath2 g . then it is very easy to show by scalar virial theorem that the magnetic field strength at the core region may go up to @xmath3 g . this is of course strong enough to affect most of the physical processes occurring at the core region . as a consequence , one of the most important physical phenomena , the transport properties of dense core matter , in particular , the electrical conductivity of electrons and transport properties of emitted neutrinos will be affected significantly by the strong magnetic field . to investigate the transport properties of dense matter at the core of a neutron star , we use the standard form of boltzmann kinetic equation with relaxation time approximation . since protons are too heavy compared to electrons , we have assumed that the electric current is solely due to the motion of electrons . now the relaxation time is directly related to the rates of the relevant ( weak and electromagnetic ) processes . these processes are strongly affected by the presence of quantizing magnetic field . as a consequence , both qualitative and the quantitative nature of transport coefficients , e.g. , electrical conductivity , viscosity and heat conductivity should change significantly in presence of strong magnetic field . in a future publication we shall report the effect of strong magnetic field on the transport properties of neutrinos at the core region @xcite . in the present article , we shall investigate the effect of strong magnetic field on the electrical conductivity at the core region of strongly magnetized neutron stars or magnetars . the paper is organized in the following manner : in section 2 , we obtain the rates of the relevant processes in presence of strong magnetic field . in section 3 , we shall derive an expression for the electrical conductivity from boltzmann kinetic equation using relaxation time approximation . in the last section , we have given the conclusion and discussed the future perspective of the work . to obtain electrical conductivity at the core of a magnetar , we have considered the following two electromagnetic processes relevant for electron transport : electron - electron scattering @xmath4 and electron - proton scattering @xmath5 where @xmath6 and @xmath7 are the initial and final four momenta . since the rate of the electron - neutrino weak scattering , given by @xmath8 is several orders of magnitude less than the electromagnetic processes , it has almost no significance in the electrical conductivity calculation . of course , this is one of the most important neutrino transport processes . for the same reason , we have neglected @xmath9 weak scattering . to obtain electrical conductivity at the core of a magnetar , we first consider e - e scattering . for this process , both the direct as well as exchange diagrams are considered . from the definition , the transition matrix element is given by @xmath10 where @xmath11 is the electric current produced by the scattered electron and @xmath12}{q^2 } j^\mu ( x')d^4x'\ ] ] is the electromagnetic field induced by the current @xmath13 of the other electron and @xmath14 is the transferred four momentum . now in the case , when only the zeroth landau levels are occupied by the electrons the positive energy dirac spinor is given by @xmath15\nonumber \\ & & \left ( \frac{eb}{\pi}\right ) ^{1/4 } \exp \left [ -\frac{1}{2 } eb \left ( x-\ \frac{p}{eb}\right ) ^2\right ] \left ( \begin{array}{c } \varepsilon_0+m\\ 0\\ p_z\\ 0 \end{array } \right ) \end{aligned}\ ] ] where @xmath16 and @xmath17 are the lengths along @xmath18 and @xmath19 directions , @xmath20 is the modified form of single particle energy , @xmath21 and @xmath22 are @xmath18 and @xmath19 components of electron momentum , @xmath23 is the strength of magnetic field , assumed to be along positive @xmath19-direction ( we have chosen the gauge @xmath24 ) . the counter part of this spinor has no contribution when only the zeroth landau level is occupied . whereas , for low temperature case ( the chemical potential @xmath25 , where @xmath26 is the temperature of the system . in the numerical calculation , we have taken @xmath27mev and found that the results are almost temperature independent for @xmath28 ) the negative energy spinor solutions may be neglected . combining eqns.(4)-(6 ) and after integrating over @xmath29 , @xmath30 , @xmath31 ( which result three @xmath32-functions ) , we have the transition matrix element for the direct @xmath9 scattering diagram @xmath33}{q^2}\frac{\exp[-i q_x x']}{l_y^2 l_z^2}\frac{e^2}{[16 p_1 ^ 0 p_2 ^ 0 k_1 ^ 0 k_2 ^ 0 ( p_1 ^ 0+m)(k_1 ^ 0+m)(p_2 ^ 0+m)(k_2 ^ 0+m)]^{1/2}}\nonumber \\ & & \exp[-i\{(p_2 ^ 0-k_2 ^ 0)t-(p_{2y}-k_{2y})y-(p_{2z}-k_{2z})z\ } ] [ j_\mu(x')]_{p_1,k_1 } [ j_\mu(x)]_{p_2,k_2 } dx'\end{aligned}\ ] ] where @xmath34_{p , k}=\bar u(k)\gamma^\mu u(p ) i_{0;k_y , k_z}(x ) i_{0;p_y , p_z}(x),\ ] ] @xmath35 and @xmath36 are respectively the positive energy spinor and the corresponding adjoint and @xmath37\ ] ] the integrals over @xmath38 and @xmath39 can very easily be evaluated by changing the variables to @xmath40 and @xmath41 , given by @xmath42 and @xmath43 . the integration over @xmath41 the gives @xmath44\ ] ] similarly , the integration over @xmath40 is given by @xmath45 erfc [ -(2eb)^{1/2}x_{(dir)}]\ ] ] where @xmath46 , @xmath47 and @xmath48 is the complementary error function . after evaluating the integrals over @xmath49 with the help of @xmath32-functions we have the transition matrix element for direct @xmath9 scattering @xmath50^{1/2}}\nonumber \\ & & [ j_\mu(p_1,k_1)][j_\mu(p_2,k_2)]\frac{1}{4l_y^2l_z^2eb } \nonumber \\ & & \exp\left [ \frac{1}{2eb}(p_{1y}+p_{2y})^2\right ] \exp(-2ebx_{(dir)}^2)\nonumber \\ & & erfc ( -(2eb)^{1/2 } x_{(dir ) } ) \frac{1}{2k_{(dir)}}(2\pi)^3 \delta(p_1 ^ 0+p_2 ^ 0-k_1 ^ 0-k_2 ^ 0)\nonumber \\ & & \delta(p_{1y}+p_{2y}-k_{1y}-k_{2y } ) \delta(p_{1z}+p_{2z}-k_{1z}-k_{2z})\end{aligned}\ ] ] which may be written as @xmath51 the transition matrix element for @xmath9 exchange interaction can very easily be obtained from the direct one just by exchanging @xmath52 and @xmath53 ( @xmath54 ) . then we have @xmath55^{1/2}}\nonumber \\ & & [ j_\mu(p_1,k_2)][j_2(p_2,k_1)]\frac{1}{4 l_y^2 l_z^2 eb}\nonumber \\ & & \exp\left [ \frac{1}{2eb}(p_{1y}+p_{2y})^2\right ] \exp(-2ebx_{(ex)}^2 ) erfc[-(2eb)^{1/2}x_{ex)}]\frac{1}{2k_{(ex ) } } ( 2\pi)^3 \nonumber \\ & & \delta(p_1 ^ 0+p_2 ^ 0-k_1 ^ 0-k_2 ^ 0)\delta(p_{1y}+p_{2y}-k_{1y}-k_{2y } ) \delta(p_{1z } + p_{2z}-k_{1z}-k_{2z})\end{aligned}\ ] ] where @xmath56 and @xmath57 . which may also be written in the form @xmath58 now from the elementary definition of rate per unit volume for the scattering process , we have the differential rate for @xmath9 scattering @xmath59 hence to obtain the differential rate @xmath60 of the processes we have to calculate @xmath61 , @xmath62 and the cross term . further , to compute these quantities , we have to evaluate the traces of the products of @xmath63-matrices . using the standard techniques , we have computed the traces of the products of @xmath63-matrices . then we have @xmath64 \exp(-4ebx_{(dir)}^2 ) \nonumber \\ & & \{erfc[-(2eb)^{1/2 } x_{(dir)}]\}^2 [ ( p_1.p_2)(k_1.k_2)+(p_1.k_2)(k_1.p_2)-m^2(p_2.k_2)-m^2(p_1,k_1 ) \nonumber\\ & & + 2m^4 ] \frac{1}{8 \pi^2 k_{(dir)}^2 } \frac{1}{(2\pi)^3 } \delta(p_1 ^ 0+p_2 ^ 0-k_1 ^ 0-k_2 ^ 0)\delta(p_{1y}+p_{2y}-k_{1y}-k_{2y } ) \nonumber\\ & & \delta(p_{1z } + p_{2z}-k_{1z}-k_{2z } ) dk_{1y } dk_{1z } dk_{2y } dk_{2z } dp_{2y } dp_{2z}\end{aligned}\ ] ] similarly , the exchange term is obtained by @xmath65 and is given by @xmath66\exp(-4ebx_{(ex)}^2 ) { erfc[-(2eb)^{1/2}x_{(ex)}]}^2 \nonumber \\ & & [ ( p_1.p_2)(k_1.k_2)+(p_1.k_1)(p_2.k_2)-m^2(p_2.k_1)-m^2 ( p_1.k_2)+2m^4]\frac{1}{8\pi^2 k_{(ex)}^2}\nonumber \\ & & \frac{1}{(2\pi)^3 } \delta(p_1 ^ 0+p_2 ^ 0-k_1 ^ 0-k_2 ^ 0)\delta(p_{1y}+p_{2y}-k_{1y}-k_{2y } ) \delta(p_{1z } + p_{2z}-k_{1z}-k_{2z})\nonumber \\ & & dk_{1y } dk_{1z } dk_{2y } dk_{2z } dp_{2y } dp_{2z}\end{aligned}\ ] ] finally the cross term whose evaluation is a bit lengthy , but straight - forward , is given by @xmath67 \exp[-2eb(x_{(dir)}^2 + x_{(ex)}^2)]\nonumber \\ & & erfc[-(2eb)^{1/2}x_{(dir)}]erfc[-(2eb)^{1/2}x_{(ex)}]\nonumber \\ & & [ -2(k_1.k_2)(p_1.p_2)+m^2(p_2.k_2)+m^2(p_2.k_1)+m^2(p_2.p_1)+\nonumber \\ & & m^2(p_1.k_1)+m^2(p_1.k_2)+m^2(k_1.k_2)-2m^4 ] \nonumber \\ & & \frac{1}{8\pi^2 k_{(dir)}k_{(ex)}}\frac{1}{(2\pi^3 ) } \delta(p_1 ^ 0+p_2 ^ 0-k_1 ^ 0-k_2 ^ 0)\delta(p_{1y}+p_{2y}-k_{1y}-k_{2y } ) \delta(p_{1z } + p_{2z}-k_{1z}-k_{2z})\nonumber \\ & & dk_{1y } dk_{1z } dk_{2y } dk_{2z } dp_{2y } dp_{2z}\end{aligned}\ ] ] the simplified form of these rates can very easily be obtained by integrating over the momentum components @xmath68 , @xmath69 , @xmath70 and @xmath71 with the help of @xmath32-functions . then we have after some simple algebraic manipulation @xmath72 \exp\left [ \frac{1}{eb}(k_{2y}-k_{1y}-k_{(dir)})\right ] \nonumber \\ & & \left [ erfc\left \{-\frac{1}{(2eb)^{1/2}}(k_{2y}-k_{1y}-k_{(dir)})\right \}\right]^2 [ ( p_1 ^ 0p_2 ^ 0-p_{1z}p_{2z})(k_1 ^ 0k_2 ^ 0-k_{1z}k_{2z})+ \nonumber \\ & & ( p_1 ^ 0k_2 ^ 0-p_{1z}k_{2z})(k_1 ^ 0p_2 ^ 0-k_{1z}p_{2z } ) -m^2(p_2 ^ 0k_2 ^ 0-p_{2z}k_{2z } ) -m^2(p_1 ^ 0k_1 ^ 0 -p_{1z}k_{1z } ) + 2m^4 ] \nonumber \\ & & \frac{1}{8\pi^2k_{(dir)}^2}\frac{1}{(2\pi)^3}dk_{1y}dk_{2y}\huge |_{k_{1z } = p_f , k_{2z}=k_{2z}^{(r ) } , p_{2z}=p_{1z}+k_{1z}-k_{2z}}\nonumber \\ & & \frac{p_f}{\mid f'(k_{2z})\mid_{k_{2z}=k_{2z}^{(r)}}}\end{aligned}\ ] ] where @xmath73 , @xmath74 and @xmath75 are the electron chemical potential and fermi momentum respectively , @xmath76^{1/2}}\ ] ] is the root of the transcendental equation @xmath77 and @xmath78 where @xmath79 similarly , for the exchange interaction we have @xmath80 \exp\left [ -\frac{1}{eb}(k_{1y}-k_{2y}-k_{(ex)})^2 \right ] \nonumber \\ & & \left \{erfc\left [ -\frac{k_{1y}-k_{2y}-k_{(ex)}}{(2eb)^{1/2 } } \right ] \right \}^2 [ ( p_1.p_2)(k_1.k_2 ) + ( p_1.k_1)(p_2.k_2)\nonumber \\ & & -m^2 ( p_2.k_1)-m^2(p_1.k_2 ) + 2m^4 ] \frac{1}{8\pi^2 k_{(ex)}^2 } \frac{1}{(2\pi)^3 } \nonumber \\ & & dk_{1y}dk_{2y}\huge |_{k_{2z}=k_f , k_{1z}=k_{1z}^{(r ) } , k_{2z}= k_{1z}+ p_{1z } -k_{2z } } \frac{p_f}{\left | f'(k_{2z})\right |_{k_{2z } = k_{2z}^{(r ) } } } \end{aligned}\ ] ] where @xmath81 . finally for the mixed term , we have @xmath82 \exp\left [ -\frac{1}{2eb}(k_{2y}-k_{1y}-k_{(dir)})^2 \right ] \nonumber \\ & & \exp\left [ -\frac{1}{2eb}(k_{1y}-k_{2y}-k_{(ex)})^2 \right ] erfc\left [ -\frac{k_{2y}-k_{1y}-k_{(dir)}}{(2eb)^{1/2 } } \right ] \nonumber \\ & & erfc\left [ -\frac{k_{1y}-k_{2y}-k_{(ex)}}{(2eb)^{1/2 } } \right ] [ -2(p_1.p_2)(k_1.k_2 ) + m^2(p_2.k_2 ) + m^2 ( p_2.k_1)+\nonumber \\ & & m^2(p_1.p_2)+m^2(p_1.k_1 ) + m^2(p_1.k_2 ) + m^2(k_1.k_2)-2m^4 ] \nonumber \\ & & \frac{1}{8\pi^2 k_{(dir)}k_{(ex ) } } \frac{1}{(2\pi)^3 } \nonumber \\ & & dk_{1y}dk_{2y}\huge |_{k_{2z}=k_f , k_{1z}=k_{1z}^{(r ) } , k_{2z}= k_{1z}+ p_{1z } -k_{2z } } \frac{p_f}{\left | f'(k_{1z})\right |_{k_{1z } = k_{1z}^{(r ) } } } \end{aligned}\ ] ] in the case of @xmath83 scattering , given by eqn.(2 ) the direct diagram only contributes and the form of trace term will be slightly different from that of @xmath9 direct term , given by @xmath84\end{aligned}\ ] ] where @xmath85 is the effective proton mass in the hartree type mean field model in presence of strong magnetic field @xcite . in this case we have to use @xmath86 and @xmath87 and make necessary changes in eqn.(20 ) of @xmath88 for @xmath9 scattering to obtain @xmath89 . in the next section we shall use these differential rates ( eqns.(20 ) , ( 23 ) , ( 24 ) and @xmath89 ) to obtain the electrical conductivity . to compute the electrical conductivity of the magnetized stellar matter , we consider the simplest form of boltzmann kinetic equation for electrons which are assumed to be slightly out of local thermodynamic equilibrium . the kinetic equation is then given by @xcite @xmath90 where @xmath91 is the non - equilibrium distribution function and @xmath92 is the collision term , given by @xmath93 where @xmath94 $ ] , and @xmath95 s are the pauli blocking factors . replacing collision term by the relaxation time approximation , we have the relevant portion of the kinetic equation needed to obtain the electrical conductivity . @xmath96 where @xmath97 is the local equilibrium distribution function for electrons ( fermi distribution ) , given by @xmath98 here @xmath22 is the longitudinal momentum and @xmath99 is the corresponding transverse part for the electrons , @xmath100=@xmath101 and @xmath102 are the local temperature and chemical potential . when only the zeroth landau levels ( @xmath103 ) are occupied by the electrons , the transverse momentum becomes exactly zero . we now consider the first order approximation , i.e. , the system is very close to its local equilibrium configuration , then we can write @xmath104 where @xmath105 is a measure of its deviation from local statistical equilibrium configuration . then we have @xmath106 , where @xmath107 s are the equilibrium distribution function for the @xmath108th component ( fermi distribution ) . the we can write @xmath109 expressing the force term in the form , @xmath110 we have after using eqn.(3 ) @xmath111 then just by inspection , it is very easy to realize that the relaxation time is obtained by evaluating the integrals over @xmath112 and @xmath113 in the expressions for the rates and the relation with the total rate of the processes is given by @xmath114 where @xmath115 therefore , @xmath116 the well know matthiessen s rule @xcite . now the expression for electric current is given by @xmath117 because of randomness in the system , the local current vanishes at equilibrium . then the nonzero part of electric current is obtained by using the first order deviation @xmath118 and is given by @xmath119 in presence of a strong magnetic field of strength @xmath120 , the quantum limit of magnetic field , where @xmath121 g , we have @xmath122 . then writing ohm s law in the form @xmath123 , we have @xmath124 which is second rank tensor with the components @xmath125 , @xmath126 , @xmath127 and @xmath128 . since we are interested for @xmath129 case only , i.e. , when the lowest landau levels are populated , we have @xmath130 and @xmath131 which is the only non - zero component . the electron transport in this special case becomes essentially one dimensional- along the direction of magnetic field . in fig.(1 ) we have plotted the variation of @xmath125 with electron density for ( a)@xmath132 , ( b)@xmath133 , ( c)@xmath134 , ( d)@xmath135 and ( e ) @xmath136 , where @xmath137 g , the quantum limit for electrons . in fig.(2 ) we have shown the variation of the nonzero component of electrical conductivity @xmath125 with magnetic field strength for ( a)@xmath138 , ( b)@xmath139 , ( c)@xmath140 , and ( d)@xmath141 , where @xmath142@xmath143 , the typical electron density in a non - magnetic neutron star . in both these cases we have not taken @xmath144 equilibrium condition into account . the density of electron is in some sense arbitrary . therefore , we now consider an interacting @xmath145 system in @xmath144-equilibrium , which is the real physical picture at the core region of a neutron star . then we have @xmath146 , the charge neutrality condition , @xmath147 , the @xmath144-equilibrium condition ( we assume that the neutrinos are non - degenerate , leave the system as soon as they are produced ) and baryon number density @xmath148 remains invariant in electromagnetic and weak interaction processes . solving these constraints self - consistently at the core of a magnetar , we obtain the chemical potential of the constituents and hence the density of electrons for various baryon densities and magnetic field strengths . we have assumed a fixed temperature @xmath27mev . in fig.(3 ) we have shown the variation of @xmath125 with the strength of magnetic field for a fixed baryon number density ( in the numerical computation we have taken @xmath149 , @xmath150@xmath143 ) assuming that the system is in @xmath144-equilibrium . in fig.(4 ) we have plotted @xmath125 against the electron density for a fixed magnetic field strength ( @xmath151 ) in @xmath144-equilibrium condition . we have studied the electrical conductivity at the core of a magnetar using boltzmann kinetic equation with the relaxation time approximation . the latter is obtained from the rates of the electromagnetic processes , which essentially control the electron transport in the medium . we have further noticed that the electrical conductivity behaves like a second rank tensor above the critical value ( quantum limit ) of magnetic field strength . however , only @xmath125 components is non - zero when the lowest landau levels are occupied by the charged particles . the system effectively becomes one - dimensional in presence of quantizing magnetic field- electrons can move along the field direction . the electric current vanishes in the plane transverse to the direction of magnetic field . since it is impossible to compute the rates analytically ( even it is very difficult to obtain numerically ) with the non - zero values of landau quantum numbers for all the four charged particles , we have assumed that only the zeroth landau levels are occupied . this makes our like much simpler . the assumption of only zero landau quantum number is also justified by the presence of intense magnetic field at the core region of magnetars . fig.(1 ) shows that there exist cut off densities , beyond which , the pauli blocking factor supresses the electron scattering and as a result the conductivity becomes zero . this figure also shows that the cut off density increases with the increas of magnetic field strength . as the magnetic field increases , for a given baryon number density , the chemical potential of electrons decreases , which further reduces the pauli suppression factor . similarly , we have noticed from fig.(2 ) that there is a minimum value for magnetic field strength for a particular baryon number density below which the conductivity again becomes zero because of same reason as discussed above . on the other hand , in the case of @xmath144-equilibrium condition , electrons are generated self - consistently . so there are no such cut off values for the density or magnetic field and the variation is smooth . 99 c. kouveliotou , et al . , nature * 393 * , 235 ( 1998 ) . k. hurley , et al . , astrophys . * 442 * , l111 ( 1999 ) . s. mereghetti and l. stella , astrophys . jour . * 442 * , l17 ( 1999 ) . j. van paradihs , r.e . taam and e.p.j . van den heuvel , astron . astrophys . * 299 * , l41 ( 1995 ) ; s. mereghetti , astro - ph/99111252 ; see also a. reisenegger , astro - ph/01003010 . cardall , m. prakash and j.m . lattimer , astro - ph/0011148 . in - saeng suh and g.j . mathews , astro - ph/9912301 . f. @xmath152zel , astro - ph/0103227 ; t. ghosh , ph.d . thesis , univ . of kalyani ( unpublished ) . a.y . potekhin and d.g . yakovlev , astro - ph/0105261 and references therein . s. chakrabarty , astrophys . space sci . * 213 * , 121 ( 1994 ) ; s. chakrabarty and a. goyal , mod . * a9 * , 3611 ( 1994 ) ; s. chakrabarty , phys . rev . * d51 * , 4591 ( 1995 ) . s. chakrabarty and p. k. sahu , phys . rev . * d54 * , 1306 ( 1996 ) ; s. chakrabarty , d. bandopadhyay and s. pal , int . mod . phys . * a13 * , 295 ( 1998 ) ; d. bandopadhyaya , s. chakrabarty , p. dey and s. pal , phys . rev . * d58 * , 121301 ( 1998 ) . t. ghosh and s. chakrabarty , phys . rev . * d63 * , 0403006 ( 2001 ) ; t. ghosh and s. chakrabarty , int . mod . phys . * d10 * , 89 ( 2001 ) . s. chakrabarty , d. bandopadhyay and s. pal , phys . * 78 * , 2898 ( 1997 ) . d. bandopadhyay , s. chakrabarty and s. pal , phys . * 79 * , 2176 ( 1997 ) . k. huang , statistical mechanics , 2nd . ed . , john wiley and sons , new york ( 1987 ) . e.m . lifshitz and l.p . pitaevskii , statistical physics , part 2 , pergamon , oxford ( 1980 ) . sanchayita ghosh , sutapa ghosh and s. chakrabary ( in preparation ) . solid state physics , n.w . ashcroft and n.d . mermin , saunders college publ . new york , ( 1976 ) .[/INST] an expression for the electrical conductivity at the core of a magnetar is derived using boltzmann kinetic equation with the relaxation time approximation . the rates for the relevant scattering processes , e.g. , electron - electron and electron - proton are evaluated in presence of strong quantizing magnetic fields using tree level diagrams . it is found that in presence of a strong quantizing magnetic field , electrical conductivity behaves like a second rank tensor . however , if the zeroth landau levels are only occupied by the charged particles , it again behaves like a scaler of a one dimensional system . pacs:05.20.dd , 72.10.-d , 72.15.lh , 79.60.jd </s>

salmonellosis is a broad term applied to enteric infections caused by a group of gram - negative bacteria of the genus salmonella , belonging to the family enterobacteriaceae . salmonella enterica , the causative agent of salmonellosis , is known to be a primary inhabitant of the gastrointestinal tract of numerous animal species including humans and mostly affects a wide host range with the exception of a few salmonella serovars that are host - specific : salmonella typhi in humans , s. gallinarum and s. pullorum in poultry , and s. dublin in cattle . they are common contaminants of wide range of food , eggs , vegetables , and water and are therefore considered as the most common causes of foodborne zoonotic infection worldwide . consequently , they are recognized as a major public health problem in both developed and developing countries . feaces of nearly all - animal species including dogs may serve as a potential source of salmonella infection to humans and even to other animals . several studies have documented the isolation of salmonella spp . from healthy dogs and subsequent transmission of the infection to humans [ 47 ] . other studies have recognized shedding of salmonella by dogs as a possible source of infection for dog owners and their communities [ 8 , 9 ] . dogs generally remain resistant to salmonella infections and infected ones may remain carriers and feacal shedding therefore may serve as sources of infection to man and other animals . due to the increase in dog keeping among the elites especially those living within the metropolitan cities in nigeria , there is an increased risk of transmission of salmonella infection to humans . there is paucity of information regarding the role of dogs as sources of salmonella infection to humans in maiduguri metropolis and therefore this study aims to determine the carrier status of salmonella in dogs and their role as potential sources of infection to humans . maiduguri is located in the sahel savannah region of northeastern nigeria at 115011.83 north latitude and 130913.15 east longitude . it shares an extensive border with niger to the north , chad to the northeast , and cameroon to the east . its altitude is about 350 metres above sea level and has an area of 75,540.9 km . its population is about 4,171,104 with a population density of 60 people per km ( 2006 census figures ) . the climate is favourable , with a mean annual rainfall and temperature of about 650 mm and 32c , respectively . the months of march and april are the hottest periods of the year with temperatures ranging between 30c and 40c . it is usually cold and dry during the harmattan , november to january being the coldest months ( http://en.wikipedia.org/wiki/maiduguri ) . samples were obtained only from dogs kept at home for security / guard or other purposes and from dogs at the veterinary teaching hospital ( n = 20 ) , university of maiduguri staff quarters ( n = 11 ) , mairi village ( n = 23 ) , gwange ward ( n = 15 ) , bulunkutu polo ( n = 18 ) , custom area ( n = 10 ) , gommari ( n = 13 ) , and ummalari ( n = 9 ) wards . a total of 119 feacal samples , comprising 70 males and 49 females , were collected from three breeds of dogs ( nigerian local breed mongrel , alsatian , and terrier breed ) . the age of the dogs was determined by dental eruption at the time of sample collection . a total of 97 nigerian local breed mongrel and 12 alsatian and 10 terrier breeds were sampled . all the ages of the sampled dogs ranged from <3 months to older than 2 years . all the dogs were apparently healthy dogs with only 5 ( 4.2% ) having diarrhoea as at the time of sample collection . rectal swabs were collected aseptically using sterile swab sticks ( oxoid ) and placed in tubes containing carry - blair transport medium ( oxoid , basingstoke , uk ) . the samples were immediately transported ice cooled within 8 hours of collection to the microbiology laboratory , faculty of veterinary medicine , university of maiduguri , for further processing and analysis . all the samples collected were then inoculated into 2 ml of selenite - feaces - broth ( oxoid , biotec , suffolk , uk ) for enrichment and incubated aerobically at 37c for 24 hours . subcultures were then made from each broth culture by streaking onto brilliant green agar ( bga ) ( oxoid ) , mcconkey agar ( oxoid ) , salmonella - shigella agar ( ssa ) ( oxoid ) , and xylose lysine deoxycholate ( xld ) agar ( oxoid ) . the cultured plates were then examined for the presence of typical colonies of salmonella based on cultural and morphological characteristics : presumptive salmonella colonies appearing colourless and nonlactose fermenting on mcconkey agar , dome - shaped colonies with central black spot on xld agar , transparent colonies with black centre on ssa , and pink colonies surrounded by a red medium were selected as presumptive salmonella colonies and subjected to further biochemical tests and gram staining as described by barrow and feltham . antibiotic susceptibility pattern of isolates to various routine antibiotics was carried out using the kirby - bauer disk diffusion method on mueller - hinton agar ( oxoid ) as recommended by anonymous . the susceptibility of the isolates to the following antimicrobials was determined : tetracycline ( 30 g ) , gentamycin ( 30 g ) , chloramphenicol ( 30 g ) , ciprofloxacin ( 10 g ) , ofloxacin ( 5 g ) , streptomycin ( 10 g ) , ampicillin ( 30 g ) , amoxicillin - clavulanic acid ( amc ) ( 5 g ) , vancomycin ( 30 g ) , neomycin ( 25 g ) , trimethoprim ( 25 g ) , and erythromycin ( 15 g ) . prevalence of salmonella infection was expressed in percentages and proportions in microsoft excel version 2010 before finally importing the data into statistical package for social sciences ( spss ) software version 16.0 to determine the statistical association between dependent and independent variables . the association between infection and other risk factors was determined using chi - square test at 5% significance level . of the 119 sampled dogs , 70 ( 58.8% ) and 49 ( 41.2% ) were males and females , respectively ; 97 ( 81.5% ) , 12 ( 10.1% ) , and 10 ( 8.4% ) were nigerian local breed mongrel , alsatian , and terrier , respectively ; 2 ( 1.2% ) , 22 ( 18.5% ) , 17 ( 14.3% ) , 17 ( 14.3% ) , 20 ( 16.8% ) , and 40 ( 34.5% ) were from dogs aged < 3 , 36 , 79 , 1012 , 1324 , and older than 24 months , respectively ( table 1 ) . of these ( 52 ) , 50.0% and 34.7% were the male and female infection rates , respectively ( table 2 ) . there was significant difference ( p < 0.05 ) in the prevalence of salmonella infection in either sex . highest prevalence was observed in dogs aged older than 24 months with 61.0% ( 25/41 ) and except for dogs < 3 months , the lowest was seen in dogs 1324 months with 15.0% ( 3/20 ) . while the prevalence of 31.8% , 41.2% , and 58.8% was observed in dogs aged 36 , 1012 , and 79 months in this order of infection rates ( table 2 ) . there was statistically significant difference ( p < 0.05 ) in the prevalence of salmonella infection across the age groups . highest prevalence of 49.5% ( 48/97 ) was observed in the nigerian local breed mongrel , while terrier and alsatian breeds had 30.0% ( 3/10 ) and 8.3% ( 1/12 ) , respectively ( table 2 ) . the antimicrobial sensitivity testing of the salmonella isolates reveals that salmonella isolates from the terrier and alsatian breeds had high susceptibility to all the antimicrobials used , with small pockets of resistance ( table 3 ) . while a higher percentage of the salmonella isolates from the mongrels showed susceptibility to ciprofloxacin ( 89.7% ) , amoxicillin ( 87.6% ) , vancomycin ( 86.6% ) , chloramphenicol ( 84.5% ) , trimethoprim ( 81.4% ) , ampicillin ( 80.4% ) , neomycin ( 77.3% ) , and gentamycin ( 71.1% ) ( table 3 ) , however , about 50% of the isolates from mongrels were resistant to ofloxacin . dogs as carriers of salmonella spp . worldwide have been incriminated as the potential sources of salmonella infection to humans especially children due to close contact and interaction that exists between them . cases of salmonella transmission from dogs to humans resulting into severe infection in humans have been documented . it was also reported that the intestinal carriage of salmonella by dogs is more common than the prevalence of clinical disease . the frequency of feacal isolation of salmonella spp . from clinically healthy dogs was reported to be between 0.0% and 43.0% [ 9 , 15 ] , while other studies reported prevalence of salmonella in feacal samples from clinically healthy or hospitalized dogs to range from 1% to 36% . however , recent studies suggested that the prevalence is probably decreasing because more pets are fed commercially processed foods . in the present study , this prevalence is within the reported 0.0% and 43.0% range of prevalence of salmonella isolated from clinically healthy dogs [ 9 , 15 ] . however , this finding is consequently higher than the results obtained from other parts of nigeria and other countries in the world . in similar studies by britt et al . in vom , another study by khan in sudan reveals that about 23.5% of 442 dogs were positive for salmonella . the differences in the sample sizes , period of study , type of feacal samples , geographical areas , and isolation methods employed in the various studies above may account for the differences in the prevalence and may all affect the prevalence . the high prevalence of 43.7% in dogs in maiduguri metropolis might be associated with poor management conditions , compromised good and hygienic environmental standards , contaminated kennels , and food sources . mongrels in the study area are mostly kept under less restraint and are left to wander and scavenge for food . this makes them highly exposed to salmonella contaminated food materials in the environment ( table 2 ) . the absence of salmonella in dogs within the age of <3 months could be attributed to the small number of dogs from which samples were obtained ( table 2 ) . it could also result probably from the protection by the maternal antibodies in dogs within this age bracket . there is seemingly high prevalence of salmonella in dogs within the age groups of 36 , 79 , and 1012 months . this is in concordance with the works of britt et al . in vom , plateau state , that salmonella infections are acquired during the early stages of life in dogs this could result from the low resistance of the immune system to infection by salmonella during this stage of life in dogs . the low prevalence of 15.0% observed in dogs within 1324 months could be the result of risen immunity and possibly good environmental and management conditions provided by the pet owners . morse et al . reported that feacal shedding could last for a period of 6 weeks and this could possibly be the reason why the prevalence was lower in dogs within this age bracket . a high prevalence of 61.0% observed in dogs within the age of > 24 months might possibly be attributed to the fact that older dogs are usually immunosuppressed and therefore at high risk of infection . this renders dogs asymptomatic carriers of the infection and consequently contaminates human environment , food , and water resulting in outbreaks of human salmonellosis . males had higher prevalence of salmonella infection compared with females ( 50.0% versus 34.7% ) . this could be due to the differing number of samples in each sex ( table 2 ) . according to breeds , this is in agreement with the work of britt et al . who highlighted the fact that due to the poor management and compromised sanitary conditions , a large number of mongrels tend to acquire the infection and shed the organism in the environment . a large population of the mongrels in the study area is normally kept under less restraint and left to wander around wider range of distances scavenging for food and therefore get exposed to many contaminated materials compared with the terrier and alsatian breeds kept under good hygienic conditions . scavengers are likely to harbor more salmonella serovars than nonscavengers kept under strict restraint and good hygienic conditions . compromised sanitary conditions could lead to feacal contamination of the food and water of the mongrels in the environment and therefore could serve as a source of infection in this breed . also observed that when dogs are fed with salmonella - contaminated feed , raw food , and commercially prepared dry foods , they can become infected and consequently shed the organism in their feaces to contaminate the environment , domestic animals , other dogs , and even man . the local breed mongrels are provided with poor environmental conditions and are less cared for compared with the exotic breeds of terrier and alsatian . the alsatian and terrier breeds are kept at home mostly by the elites ( restrained ) and fed with commercial food and this makes them less exposed to salmonella infection compared with the mongrels ( table 2 ) . the antimicrobial sensitivity testing results reveal that high percentages of the salmonella isolates from the alsatian and terrier breeds were susceptible to the antimicrobials used , while a high percentage of the isolates from mongrels showed susceptibility to ciprofloxacin ( 89.7% ) , amoxicillin - clavulanic acid ( amc ) ( 87.6% ) , vancomycin ( 86.6% ) , and chloramphenicol ( 84.5% ) . however , about 50% of these isolates were resistant to ofloxacin ( table 3 ) . in the past decades , the emergence of antibiotic resistant strains of salmonella has become a major public health concern . mongrels are more likely to harbor salmonella serovars due to their scavenging nature and therefore are more likely to be treated with antibiotics than the exotic breeds in the study area . alsatian and terrier breeds are mostly restricted and fed at home and are not allowed to scavenge or stray in the environment . this makes them less likely to acquire salmonella infection and therefore not likely to be treated with antibiotics . indiscriminate use of antibiotics in animals could be responsible for the emergence of antimicrobial resistant strains of bacteria . therefore , the use of antibiotics should be well regulated and used only when it is indicated . ciprofloxacin and amoxicillin - clavulanic acid ( amc ) could be useful antibiotics in the treatment of majority of salmonellosis cases as revealed by their effectiveness against a high percentage of salmonella isolates from the study area . in conclusion , this study revealed a high salmonella carrier status in dogs kept in households in maiduguri metropolis , nigeria . mongrels had high salmonella carrier status compared with the other breeds in the study area . most of the households visited keep mongrels , where they are left to wander and scavenge for food in the environment and only return back home in the evening . this has public health significance as dogs may pose a risk to humans where close contact between dogs and their owners occurs in households and children and immunosuppressed individuals may be particularly at risk . as the infection is acquired during the early stage of their life , pet keepers or dog keepers should maintain a high personal and environmental standard hygiene of the dogs to mitigate the potential zoonotic transmission to humans . properly cooked and uncontaminated feed should be fed to dogs and scavenging and straying of dogs should be discouraged . it is recommended that complete bacteriological identification be carried out on the isolates to determine the serotypes found in the study area .

the prevalence and antimicrobial sensitivity of salmonella from dogs in maiduguri metropolis were determined using standard bacteriological methods to assess the risk of possible transmission of salmonella infection from dogs to humans . of 119 samples , salmonella was isolated from 52 ( 43.7% ) . males had higher prevalence of 50.0% compared with 34.7% in females ( p < 0.05 ) . dogs older than 24 months had higher prevalence of 61.0% and the lowest was seen in dogs aged 1324 months ( p < 0.05 ) . the prevalence of 31.8% , 41.2% , and 58.8% was observed in dogs aged 36 , 1012 , and 79 months , respectively . high prevalence of 49.5% was observed in mongrels , while terrier and alsatian breeds had 30.0% and 8.3% , respectively . salmonella isolates from alsatian and terrier breeds showed about 100% susceptibility to all the tested antimicrobials . higher percentage of the salmonella isolates from mongrels also showed susceptibility to ciprofloxacin ( 89.7% ) , amoxicillin ( 87.6% ) , vancomycin ( 86.6% ) , and chloramphenicol ( 84.5% ) . however about 50% of these isolates showed resistance to ofloxacin . the carrier status of salmonella is high among dogs especially mongrels . therefore good environmental hygiene , discouraging straying coupled with feeding of dogs with properly cooked and uncontaminated feeds was recommended to mitigate risk of human salmonellosis .

<s>[INST]salmonellosis is a broad term applied to enteric infections caused by a group of gram - negative bacteria of the genus salmonella , belonging to the family enterobacteriaceae . salmonella enterica , the causative agent of salmonellosis , is known to be a primary inhabitant of the gastrointestinal tract of numerous animal species including humans and mostly affects a wide host range with the exception of a few salmonella serovars that are host - specific : salmonella typhi in humans , s. gallinarum and s. pullorum in poultry , and s. dublin in cattle . they are common contaminants of wide range of food , eggs , vegetables , and water and are therefore considered as the most common causes of foodborne zoonotic infection worldwide . consequently , they are recognized as a major public health problem in both developed and developing countries . feaces of nearly all - animal species including dogs may serve as a potential source of salmonella infection to humans and even to other animals . several studies have documented the isolation of salmonella spp . from healthy dogs and subsequent transmission of the infection to humans [ 47 ] . other studies have recognized shedding of salmonella by dogs as a possible source of infection for dog owners and their communities [ 8 , 9 ] . dogs generally remain resistant to salmonella infections and infected ones may remain carriers and feacal shedding therefore may serve as sources of infection to man and other animals . due to the increase in dog keeping among the elites especially those living within the metropolitan cities in nigeria , there is an increased risk of transmission of salmonella infection to humans . there is paucity of information regarding the role of dogs as sources of salmonella infection to humans in maiduguri metropolis and therefore this study aims to determine the carrier status of salmonella in dogs and their role as potential sources of infection to humans . maiduguri is located in the sahel savannah region of northeastern nigeria at 115011.83 north latitude and 130913.15 east longitude . it shares an extensive border with niger to the north , chad to the northeast , and cameroon to the east . its altitude is about 350 metres above sea level and has an area of 75,540.9 km . its population is about 4,171,104 with a population density of 60 people per km ( 2006 census figures ) . the climate is favourable , with a mean annual rainfall and temperature of about 650 mm and 32c , respectively . the months of march and april are the hottest periods of the year with temperatures ranging between 30c and 40c . it is usually cold and dry during the harmattan , november to january being the coldest months ( http://en.wikipedia.org/wiki/maiduguri ) . samples were obtained only from dogs kept at home for security / guard or other purposes and from dogs at the veterinary teaching hospital ( n = 20 ) , university of maiduguri staff quarters ( n = 11 ) , mairi village ( n = 23 ) , gwange ward ( n = 15 ) , bulunkutu polo ( n = 18 ) , custom area ( n = 10 ) , gommari ( n = 13 ) , and ummalari ( n = 9 ) wards . a total of 119 feacal samples , comprising 70 males and 49 females , were collected from three breeds of dogs ( nigerian local breed mongrel , alsatian , and terrier breed ) . the age of the dogs was determined by dental eruption at the time of sample collection . a total of 97 nigerian local breed mongrel and 12 alsatian and 10 terrier breeds were sampled . all the ages of the sampled dogs ranged from <3 months to older than 2 years . all the dogs were apparently healthy dogs with only 5 ( 4.2% ) having diarrhoea as at the time of sample collection . rectal swabs were collected aseptically using sterile swab sticks ( oxoid ) and placed in tubes containing carry - blair transport medium ( oxoid , basingstoke , uk ) . the samples were immediately transported ice cooled within 8 hours of collection to the microbiology laboratory , faculty of veterinary medicine , university of maiduguri , for further processing and analysis . all the samples collected were then inoculated into 2 ml of selenite - feaces - broth ( oxoid , biotec , suffolk , uk ) for enrichment and incubated aerobically at 37c for 24 hours . subcultures were then made from each broth culture by streaking onto brilliant green agar ( bga ) ( oxoid ) , mcconkey agar ( oxoid ) , salmonella - shigella agar ( ssa ) ( oxoid ) , and xylose lysine deoxycholate ( xld ) agar ( oxoid ) . the cultured plates were then examined for the presence of typical colonies of salmonella based on cultural and morphological characteristics : presumptive salmonella colonies appearing colourless and nonlactose fermenting on mcconkey agar , dome - shaped colonies with central black spot on xld agar , transparent colonies with black centre on ssa , and pink colonies surrounded by a red medium were selected as presumptive salmonella colonies and subjected to further biochemical tests and gram staining as described by barrow and feltham . antibiotic susceptibility pattern of isolates to various routine antibiotics was carried out using the kirby - bauer disk diffusion method on mueller - hinton agar ( oxoid ) as recommended by anonymous . the susceptibility of the isolates to the following antimicrobials was determined : tetracycline ( 30 g ) , gentamycin ( 30 g ) , chloramphenicol ( 30 g ) , ciprofloxacin ( 10 g ) , ofloxacin ( 5 g ) , streptomycin ( 10 g ) , ampicillin ( 30 g ) , amoxicillin - clavulanic acid ( amc ) ( 5 g ) , vancomycin ( 30 g ) , neomycin ( 25 g ) , trimethoprim ( 25 g ) , and erythromycin ( 15 g ) . prevalence of salmonella infection was expressed in percentages and proportions in microsoft excel version 2010 before finally importing the data into statistical package for social sciences ( spss ) software version 16.0 to determine the statistical association between dependent and independent variables . the association between infection and other risk factors was determined using chi - square test at 5% significance level . of the 119 sampled dogs , 70 ( 58.8% ) and 49 ( 41.2% ) were males and females , respectively ; 97 ( 81.5% ) , 12 ( 10.1% ) , and 10 ( 8.4% ) were nigerian local breed mongrel , alsatian , and terrier , respectively ; 2 ( 1.2% ) , 22 ( 18.5% ) , 17 ( 14.3% ) , 17 ( 14.3% ) , 20 ( 16.8% ) , and 40 ( 34.5% ) were from dogs aged < 3 , 36 , 79 , 1012 , 1324 , and older than 24 months , respectively ( table 1 ) . of these ( 52 ) , 50.0% and 34.7% were the male and female infection rates , respectively ( table 2 ) . there was significant difference ( p < 0.05 ) in the prevalence of salmonella infection in either sex . highest prevalence was observed in dogs aged older than 24 months with 61.0% ( 25/41 ) and except for dogs < 3 months , the lowest was seen in dogs 1324 months with 15.0% ( 3/20 ) . while the prevalence of 31.8% , 41.2% , and 58.8% was observed in dogs aged 36 , 1012 , and 79 months in this order of infection rates ( table 2 ) . there was statistically significant difference ( p < 0.05 ) in the prevalence of salmonella infection across the age groups . highest prevalence of 49.5% ( 48/97 ) was observed in the nigerian local breed mongrel , while terrier and alsatian breeds had 30.0% ( 3/10 ) and 8.3% ( 1/12 ) , respectively ( table 2 ) . the antimicrobial sensitivity testing of the salmonella isolates reveals that salmonella isolates from the terrier and alsatian breeds had high susceptibility to all the antimicrobials used , with small pockets of resistance ( table 3 ) . while a higher percentage of the salmonella isolates from the mongrels showed susceptibility to ciprofloxacin ( 89.7% ) , amoxicillin ( 87.6% ) , vancomycin ( 86.6% ) , chloramphenicol ( 84.5% ) , trimethoprim ( 81.4% ) , ampicillin ( 80.4% ) , neomycin ( 77.3% ) , and gentamycin ( 71.1% ) ( table 3 ) , however , about 50% of the isolates from mongrels were resistant to ofloxacin . dogs as carriers of salmonella spp . worldwide have been incriminated as the potential sources of salmonella infection to humans especially children due to close contact and interaction that exists between them . cases of salmonella transmission from dogs to humans resulting into severe infection in humans have been documented . it was also reported that the intestinal carriage of salmonella by dogs is more common than the prevalence of clinical disease . the frequency of feacal isolation of salmonella spp . from clinically healthy dogs was reported to be between 0.0% and 43.0% [ 9 , 15 ] , while other studies reported prevalence of salmonella in feacal samples from clinically healthy or hospitalized dogs to range from 1% to 36% . however , recent studies suggested that the prevalence is probably decreasing because more pets are fed commercially processed foods . in the present study , this prevalence is within the reported 0.0% and 43.0% range of prevalence of salmonella isolated from clinically healthy dogs [ 9 , 15 ] . however , this finding is consequently higher than the results obtained from other parts of nigeria and other countries in the world . in similar studies by britt et al . in vom , another study by khan in sudan reveals that about 23.5% of 442 dogs were positive for salmonella . the differences in the sample sizes , period of study , type of feacal samples , geographical areas , and isolation methods employed in the various studies above may account for the differences in the prevalence and may all affect the prevalence . the high prevalence of 43.7% in dogs in maiduguri metropolis might be associated with poor management conditions , compromised good and hygienic environmental standards , contaminated kennels , and food sources . mongrels in the study area are mostly kept under less restraint and are left to wander and scavenge for food . this makes them highly exposed to salmonella contaminated food materials in the environment ( table 2 ) . the absence of salmonella in dogs within the age of <3 months could be attributed to the small number of dogs from which samples were obtained ( table 2 ) . it could also result probably from the protection by the maternal antibodies in dogs within this age bracket . there is seemingly high prevalence of salmonella in dogs within the age groups of 36 , 79 , and 1012 months . this is in concordance with the works of britt et al . in vom , plateau state , that salmonella infections are acquired during the early stages of life in dogs this could result from the low resistance of the immune system to infection by salmonella during this stage of life in dogs . the low prevalence of 15.0% observed in dogs within 1324 months could be the result of risen immunity and possibly good environmental and management conditions provided by the pet owners . morse et al . reported that feacal shedding could last for a period of 6 weeks and this could possibly be the reason why the prevalence was lower in dogs within this age bracket . a high prevalence of 61.0% observed in dogs within the age of > 24 months might possibly be attributed to the fact that older dogs are usually immunosuppressed and therefore at high risk of infection . this renders dogs asymptomatic carriers of the infection and consequently contaminates human environment , food , and water resulting in outbreaks of human salmonellosis . males had higher prevalence of salmonella infection compared with females ( 50.0% versus 34.7% ) . this could be due to the differing number of samples in each sex ( table 2 ) . according to breeds , this is in agreement with the work of britt et al . who highlighted the fact that due to the poor management and compromised sanitary conditions , a large number of mongrels tend to acquire the infection and shed the organism in the environment . a large population of the mongrels in the study area is normally kept under less restraint and left to wander around wider range of distances scavenging for food and therefore get exposed to many contaminated materials compared with the terrier and alsatian breeds kept under good hygienic conditions . scavengers are likely to harbor more salmonella serovars than nonscavengers kept under strict restraint and good hygienic conditions . compromised sanitary conditions could lead to feacal contamination of the food and water of the mongrels in the environment and therefore could serve as a source of infection in this breed . also observed that when dogs are fed with salmonella - contaminated feed , raw food , and commercially prepared dry foods , they can become infected and consequently shed the organism in their feaces to contaminate the environment , domestic animals , other dogs , and even man . the local breed mongrels are provided with poor environmental conditions and are less cared for compared with the exotic breeds of terrier and alsatian . the alsatian and terrier breeds are kept at home mostly by the elites ( restrained ) and fed with commercial food and this makes them less exposed to salmonella infection compared with the mongrels ( table 2 ) . the antimicrobial sensitivity testing results reveal that high percentages of the salmonella isolates from the alsatian and terrier breeds were susceptible to the antimicrobials used , while a high percentage of the isolates from mongrels showed susceptibility to ciprofloxacin ( 89.7% ) , amoxicillin - clavulanic acid ( amc ) ( 87.6% ) , vancomycin ( 86.6% ) , and chloramphenicol ( 84.5% ) . however , about 50% of these isolates were resistant to ofloxacin ( table 3 ) . in the past decades , the emergence of antibiotic resistant strains of salmonella has become a major public health concern . mongrels are more likely to harbor salmonella serovars due to their scavenging nature and therefore are more likely to be treated with antibiotics than the exotic breeds in the study area . alsatian and terrier breeds are mostly restricted and fed at home and are not allowed to scavenge or stray in the environment . this makes them less likely to acquire salmonella infection and therefore not likely to be treated with antibiotics . indiscriminate use of antibiotics in animals could be responsible for the emergence of antimicrobial resistant strains of bacteria . therefore , the use of antibiotics should be well regulated and used only when it is indicated . ciprofloxacin and amoxicillin - clavulanic acid ( amc ) could be useful antibiotics in the treatment of majority of salmonellosis cases as revealed by their effectiveness against a high percentage of salmonella isolates from the study area . in conclusion , this study revealed a high salmonella carrier status in dogs kept in households in maiduguri metropolis , nigeria . mongrels had high salmonella carrier status compared with the other breeds in the study area . most of the households visited keep mongrels , where they are left to wander and scavenge for food in the environment and only return back home in the evening . this has public health significance as dogs may pose a risk to humans where close contact between dogs and their owners occurs in households and children and immunosuppressed individuals may be particularly at risk . as the infection is acquired during the early stage of their life , pet keepers or dog keepers should maintain a high personal and environmental standard hygiene of the dogs to mitigate the potential zoonotic transmission to humans . properly cooked and uncontaminated feed should be fed to dogs and scavenging and straying of dogs should be discouraged . it is recommended that complete bacteriological identification be carried out on the isolates to determine the serotypes found in the study area .[/INST]the prevalence and antimicrobial sensitivity of salmonella from dogs in maiduguri metropolis were determined using standard bacteriological methods to assess the risk of possible transmission of salmonella infection from dogs to humans . of 119 samples , salmonella was isolated from 52 ( 43.7% ) . males had higher prevalence of 50.0% compared with 34.7% in females ( p < 0.05 ) . dogs older than 24 months had higher prevalence of 61.0% and the lowest was seen in dogs aged 1324 months ( p < 0.05 ) . the prevalence of 31.8% , 41.2% , and 58.8% was observed in dogs aged 36 , 1012 , and 79 months , respectively . high prevalence of 49.5% was observed in mongrels , while terrier and alsatian breeds had 30.0% and 8.3% , respectively . salmonella isolates from alsatian and terrier breeds showed about 100% susceptibility to all the tested antimicrobials . higher percentage of the salmonella isolates from mongrels also showed susceptibility to ciprofloxacin ( 89.7% ) , amoxicillin ( 87.6% ) , vancomycin ( 86.6% ) , and chloramphenicol ( 84.5% ) . however about 50% of these isolates showed resistance to ofloxacin . the carrier status of salmonella is high among dogs especially mongrels . therefore good environmental hygiene , discouraging straying coupled with feeding of dogs with properly cooked and uncontaminated feeds was recommended to mitigate risk of human salmonellosis .</s>

we describe measurements and searches performed using a data sample of photonic events with large missing transverse energy collected with the opal detector in 1999 and 2000 , the final two years of lep operation . the events result from @xmath9 collisions in the centre - of - mass energy range of about @xmath1 gev with a combined integrated luminosity of 426.5 pb@xmath94 . when deriving cross - section limits on new physics processes , these data are combined with previously published data@xcite taken at 189 gev and corresponding to 177.3 pb@xmath94 . the present paper builds on past publications based on data samples collected at lower centre - of - mass energies@xcite . the new data samples , taken at the highest energies achieved by lep , provide discovery potential in a new kinematic regime with a large increase in integrated luminosity . similar searches have been made by the other lep collaborations @xcite . the analysis presented here is designed to select events with two photons and significant missing transverse energy in the final state , indicating the presence of at least one neutrino - like invisible particle which interacts only weakly with matter . the event selection for this search topology is identical to that used in our most recent publication@xcite . within the standard model , such events are expected from the @xmath2 process . the selection is designed to retain acceptance for events with an additional photon , provided that the system formed by the three photons is consistent with the presence of significant missing transverse energy . this final - state topology is also sensitive to several new physics scenarios . in the context of the search for new physics , the emphasis in this publication is on general searches applicable to a broad class of models . to this end , a generic classification is used : @xmath95 where @xmath96 is neutral and can decay radiatively ( @xmath97 ) and @xmath4 is stable and only weakly interacting . the limits presented for this generic process are applicable to a variety of physics searches . for the general case of massive @xmath96 and @xmath4 this includes conventional supersymmetric processes @xmath98 . there is particularly good sensitivity for the special case of @xmath99 . this is applicable both to the production of excited neutrinos @xmath100 and to supersymmetric models in which the lightest supersymmetric particle ( lsp ) is a light gravitino and @xmath101 is the next - to - lightest supersymmetric particle ( nlsp ) which decays to a gravitino and a photon ( @xmath102 ) . in the latter case , we also set limits on an example light - gravitino model@xcite . the neutralino lifetime in such models is a free parameter . in this paper we address only the case of promptly decaying @xmath96 . this search topology also has sensitivity to the production of two particles , one invisible , or with an invisible decay mode , and the other decaying into two photons . such events might arise from the production of a higgs - like scalar particle , @xmath103 : @xmath104 , followed by s@xmath105@xmath106 , @xmath107 . the results of an opal search for this process , including the hadronic and leptonic @xmath108 decays , have been separately reported @xcite . finally , this search topology can also probe ww@xmath109 quartic couplings in the @xmath110 process . the opal quartic gauge coupling measurements are described in @xcite . this paper first describes the opal detector and the monte carlo samples used . a brief summary of the event selection will then be given , followed by cross - section measurements and comparisons with standard model expectations . the new physics search results will then be discussed . the opal detector , which is described in detail in @xcite , contained a silicon micro - vertex detector surrounded by a pressurized central tracking system operating inside a solenoid with a magnetic field of 0.435 t. the barrel and endcap regions of the detector were instrumented with scintillation counters , presamplers and a lead - glass electromagnetic calorimeter ( ecal ) . the magnet return yoke was instrumented for hadron calorimetry and was surrounded by muon chambers . electromagnetic calorimeters close to the beam axis measured luminosity and completed the acceptance . the measurements presented here are based mainly on the observation of clusters of energy deposited in the lead - glass electromagnetic calorimeter . this consisted of an array of 9,440 lead - glass blocks in the barrel region , @xmath111 , with a quasi - pointing geometry and two endcap arrays , each of 1,132 lead - glass blocks , covering the polar angle axis points along the direction of the @xmath112 beam . the polar angle @xmath113 is defined with respect to the @xmath112 beam direction and @xmath114 is the azimuthal angle measured from the @xmath115 axis . ] range , @xmath116 . hermetic electromagnetic calorimeter coverage was achieved beyond the end of the ecal down to 33 mrad in polar angle with the use of the gamma - catcher calorimeter , the forward calorimeter and the silicon - tungsten calorimeter . scintillators in the barrel and endcap regions were used to reject backgrounds from cosmic - ray interactions by providing time measurements for the large fraction ( @xmath117 80% ) of photons which converted in the material in front of the ecal . the barrel time - of - flight ( tof ) scintillator bars were located outside the solenoid in front of the barrel ecal and matched its geometrical acceptance @xmath111 . tile endcap ( te ) scintillator arrays were located in front of the endcap ecal at @xmath118 . additional scintillating - tile arrays , referred to as the mip plug , were located at more forward angles . in the region from 125 to 200 mrad these detectors were used to provide redundancy in the rejection of events with significant electromagnetic activity in the forward region . the integrated luminosities of the data samples are determined to better than 1% from small - angle bhabha scattering events in the silicon - tungsten calorimeter . triggers based on electromagnetic energy deposits in either the barrel or endcap electromagnetic calorimeters lead to full trigger efficiency for photonic events passing the event selection criteria used in this analysis . the nunugpv98 @xcite and kk2f @xcite monte carlo generators were used to simulate the standard model signal process , @xmath2 . for other expected standard model processes , a number of different generators were used : radcor @xcite for @xmath119 ; bhwide @xcite and teegg @xcite for @xmath120 ; koralw @xcite using ` grc4f ` @xcite matrix elements for @xmath121 and @xmath122 , and koralz@xcite for @xmath123 and @xmath124 . the bdk program@xcite was used for @xmath125 , except for @xmath126 which was generated using the vermaseren program@xcite . the expected contribution from each of these standard model processes was evaluated using a total equivalent integrated luminosity at least five times larger than the integrated luminosity of the data sample . to simulate possible new physics processes of the type @xmath95 where @xmath96 decays to @xmath127 and @xmath4 escapes detection , a modified version of the susygen @xcite monte carlo generator was used to produce neutralino pair events of the type @xmath128 , @xmath129 , with isotropic angular distributions for the production and decay of @xmath130 and including the effects of initial - state radiation . for @xmath131 206 gev , monte carlo events were generated at 49 points in the kinematically accessible region of the ( @xmath132 , @xmath133 ) plane . monte carlo events at 42 points in ( @xmath132 , @xmath133 ) with @xmath131 189 gev were generated for our previous publication@xcite . using these two samples , the selection efficiency was determined for each generated point and then parametrized as a function of ( @xmath132 , @xmath133 ) and centre - of - mass energy . the efficiency varies slowly with energy and for energies above 206 gev , the 206 gev values were used . all monte carlo samples described above were processed through the full opal detector simulation @xcite . a detailed description of the event selection is given in our previous publications@xcite . in brief , photons are identified as energy deposits in the electromagnetic calorimeter . events are required to have no other significant activity , except for the possibility of additional photons . information from the tracking chambers is used to reject electromagnetic clusters associated with prompt charged tracks while retaining sensitivity for photons which converted in the material between the interaction point and the calorimeter . timing information is used to reject backgrounds from cosmic - ray events . events with activity beyond the acceptance of the ecal are vetoed using information from the gamma catcher , the forward calorimeter , the silicon - tungsten calorimeter and the mip plug.the kinematic acceptance of the selection is defined by requiring : * at least two photons , each with @xmath134 and @xmath135 , or one photon with @xmath136 gev and @xmath137 and a second photon with @xmath136 gev and @xmath135 ; here @xmath138 is the photon energy , @xmath113 is the photon polar angle and @xmath139 is the photon scaled energy @xmath140 * that the two - photon system consisting of the two highest - energy photons have momentum transverse to the beamline ( @xmath141 ) satifying @xmath142 the selection is designed to retain acceptance for events with additional photons in which the resulting photonic system is still consistent with the presence of significant missing energy . this reduces the sensitivity of the measurement to the modelling of higher - order contributions . the data described in this paper were taken during the final two years of lep operation , at centre - of - mass energies between 192 and 209 gev . for the purposes of this publication the data have been binned into six samples with mean centre - of - mass energies of approximately 192 , 196 , 200 , 202 , 205 and 207 gev . the energy ranges and luminosity breakdown are summarized in table [ tab : g2_xsec_new ] . applied to the entire sample , the selection yields a total of @xmath143 events , in good agreement with the kk2f prediction of @xmath144 events for the standard model @xmath2 contribution . the expected contribution from other standard model processes and from cosmic ray and beam - related backgrounds is @xmath145 events , dominated by contributions from low - angle radiative bhabha events and radiative four - fermion final states . the selection results are included in table [ tab : g2_xsec_new ] . the selection efficiency for @xmath2 events within the kinematic acceptance of the selection is ( @xmath146)% , independent of energy . the cross - section within the kinematic acceptance of the selection is also shown in table [ tab : g2_xsec_new ] as are the corresponding predictions obtained using the kk2f monte carlo generator . the predictions of the nunugpv98 monte carlo generator were also examined and agreed well with those of kk2f . small differences are accounted for in the systematic uncertainties . the dominant sources of systematic uncertainties arise from modelling of the event selection efficiency , especially the simulation of the detector material and consequent photon conversion probabilities . the effects of these uncertainties and of uncertainties on the efficiency of timing cuts used to suppress cosmic - ray events are calculated accounting for different event topologies ( both photons in the barrel region , both in the endcap , or one in each ) . this total uncertainty is 1.7% . other sources arise from uncertainties on the integrated luminosity measurement ( 0.5% ) , on detector occupancy estimates ( 1% ) obtained from the analysis of randomly triggered events , on comparisons of different monte carlo event generators for the process @xmath2(1% ) . the total systematic uncertainty common to each energy bin is 2.3% . in individual energy bins , monte carlo statistics account for an additional systematic uncertainty of @xmath147% . the kinematic properties of the selected events , summed over all energies , are displayed in figure [ f : g2_kine_all ] where they are compared with the predicted distributions for @xmath2 obtained using the kk2f generator normalized to the integrated luminosity of the data . plot ( a ) shows the recoil mass distribution of the selected events ( for the two most energetic photons in the case of events with three or more photons ) . the distribution is peaked near the mass of the @xmath148 as is expected for contributions from @xmath2 . the resolution of the recoil mass is typically @xmath149 gev for @xmath150 . events with a negative recoil - mass squared are plotted in the zero bin of the distribution . plot ( b ) shows the distribution of the scaled energy of the second most energetic photon . plot ( c ) shows the @xmath151 invariant - mass distribution for which the mass resolution is typically @xmath152 gev . plot ( d ) shows the distribution in scaled transverse momentum of the selected two - photon system . there are 3 selected events having a third photon with deposited energy above 300 mev and within the polar - angle acceptance of the selection . the corresponding expectation from kk2f is @xmath153 events . the results of this selection are used to test the standard model and to search for new physics contributions . in the absence of an excess of events beyond the standard model expectation , we set 95% cl upper limits on the quantity @xmath3 for the general case of massive @xmath96 and @xmath4 , and separately for the special case of @xmath99 . efficiencies were evaluated under the assumption that @xmath96 decays promptly . monte carlo samples were generated for a variety of mass points in the kinematically accessible region of the @xmath154 plane . to set limits for arbitrary @xmath132 and @xmath133 , the efficiency over the entire @xmath154 plane was parameterized using the efficiencies calculated at the generated mass points . for @xmath132 values below @xmath155/2 , search results based on lep1 data have been previously reported @xcite . in this low - mass region , events with radiative return to the @xmath148 followed by @xmath156 would yield very different kinematics than those used here to generate the signal monte carlo samples . for this reason , the search is restricted to the mass region @xmath157 . [ sec : g2_results_allmy ] the searches for @xmath95 , @xmath97 , both for the general case discussed here and the special case of @xmath99 discussed in section 5.2 , use the methods described in our previous publications@xcite . selected events are classified as consistent with a given value of @xmath132 and @xmath133 if the energy of each of the photons falls within the region kinematically accessible to photons from the process @xmath95 , @xmath97 , including resolution effects . selection efficiencies at some of the generated grid points for the @xmath95 , @xmath97 @xmath159 gev monte carlo events are shown in table [ tab : g2_eff_206 ] . these values include the efficiency of the kinematic consistency requirement which is higher than 95% at each generated point in the region of the @xmath154 plane . for @xmath160 values lower than 5 gev the efficiency begins to fall off rapidly and is thus difficult to model accurately . for this reason , we place limits only in the region of the @xmath161 plane satisfying @xmath162 gev . efficiencies at lower centre - of - mass energies are obtained from an interpolation between these efficiencies and the equivalent efficiencies at 189 gev , which are given in our previous publication @xcite . for data taken at centre - of - mass energies above 206 gev , the 206 gev efficiencies are used . events from @xmath2 are typically characterized by a high - energy photon from the radiative return to the @xmath108 and a second lower energy photon . the kinematic consistency requirement is such that the two photons must have energies within the same ( kinematically accessible ) region . thus , as @xmath132 and @xmath133 increase , the allowed range of energy for the photons narrows , and fewer @xmath163 events will be accepted . for the 54 selected events , the distribution of the number of events consistent with a given mass point ( @xmath132,@xmath133 ) is consistent with the expectation from @xmath2 monte carlo , over the full ( @xmath132,@xmath133 ) plane . upper limits are placed on @xmath3 accounting for the number of selected events and the expected number of background events from the process @xmath2 . other backgrounds are not subtracted . for each of the energy bins , table [ tab : limits ] shows the maximum and minimum limits obtained in the region of the ( @xmath164 plane described above . figure [ mxmy_207_combined ] shows the 95% cl lower limits on @xmath3 at @xmath165 gev , obtained from all opal data with @xmath166 gev , under the assumption that @xmath167 scales with centre - of - mass energy as @xmath168 . these limits range from @xmath169 fb . systematic uncertainties arise from the sources described in section 4 . however there are additional contributions due to limited monte carlo statistics at each of the generated ( @xmath170 ) points and from uncertainties on the efficiency parameterization across the ( @xmath170 ) plane and as a function of energy . the combined relative uncertainty on the efficiency varies from about 3% to 6% across the plane ( for @xmath171 gev ) . the uncertainty on the expected sm background contribution is 2.6% . in calculating the limits , systematic uncertainties are accounted for in the manner advocated in reference@xcite . this also applies to the limits for the @xmath99 case , presented in the next section . [ sec : g2_results_my0 ] for the special case of @xmath99 the applied kinematic consistency requirements differ from those used for the general case . one can calculate@xcite the maximum mass , @xmath172 , which is consistent with the measured three - momenta of the two photons , assuming a massless @xmath4 . a cut on @xmath172 provides further suppression of the @xmath163 background while retaining high efficiency for the signal hypothesis . this is discussed in more detail in reference @xcite . to allow for resolution effects , we require that the maximum kinematically allowed mass be greater than @xmath173 gev . this has better than 96% relative efficiency for signal at all values of @xmath132 while suppressing much of the remaining @xmath163 background . the @xmath172 distributions for all selected events , divided into the @xmath174 gev and @xmath175 gev data samples , are shown in figure [ g2_mxmax_206 ] . in each case , the points with error bars show the opal data while the unshaded histogram shows the expected contribution from the @xmath2 , from kk2f monte carlo , normalized to the luminosity of the data . shown as a shaded histgram in the @xmath175 gev plot is the expected distribution from signal monte carlo events generated with @xmath176 gev ( with arbitrary normalization ) . for this @xmath99 case , the signal reconstruction efficiencies calculated from monte carlo events generated at @xmath159 gev are shown in table [ tab : g2_eff_my0_206 ] after application of the event selection criteria and then after the cut on @xmath172 . also shown in table [ tab : g2_eff_my0_206 ] are the numbers of events selected from the @xmath175 gev data sample which are consistent with each value of @xmath132 as well as the expected number of @xmath2 events . the number of selected events ( from the @xmath175 gev sample ) consistent with a given value of @xmath132 varies from 10 , for @xmath177 45 gev , to 2 at the kinematic limit . the expected number of events decreases from @xmath178 at @xmath179 gev to @xmath180 consistent with @xmath181 gev . based on the efficiencies and the number of selected events , we calculate 95% cl upper limits on @xmath3 for @xmath99 as a function of @xmath132 , in each region of centre - of - mass energy . the last two columns of table [ tab : limits ] show the range of limits obtained from each of the data samples , for @xmath132 values from 45 gev up to the kinematic limit . figure [ my0_207_combined ] shows the limit obtained from the 207 gev data sample , as well as the combined limit obtained from the entire data sample with @xmath166 gev assuming that the cross - section scales as @xmath168 . for the mass range of interest ( @xmath182 gev ) the model - independent limits range between 45 and 70 fb while the combined limits range between 20 and 45 gev . these limits gev region the limits are actually slightly worse than those along the @xmath133=0 axis of figure [ mxmy_207_combined ] despite the more efficient background suppression of the @xmath172 cut , relative to the kinematic consistency cuts applied in the general case . this is due to a deficit of selected events in this region , compared to the expected background when using the general kinematic consistency requirements . ] can be used to set model - dependent limits on the mass of the lightest neutralino in supersymmetric models in which the nlsp is the lightest neutralino and the lsp is a light gravitino ( @xmath102 ) . shown in figure [ my0_207_combined ] , as a dotted line , is the ( born - level ) cross - section prediction from a specific light gravitino lsp model@xcite in which the neutralino composition is purely bino , with @xmath183 and @xmath184 . within the framework of this model , @xmath101 masses between 45 and 99.0 gev are excluded at 95% cl . as described in section 2 , the efficiencies over the full angular range have been obtained using isotropic angular distributions for the production and decay of @xmath96 . the validity of this model has been examined based on the angular distributions calculated for photino pair production in reference@xcite . for models proposed in reference@xcite , the production angular distributions are more central and so this procedure is conservative . for a @xmath185 production angular distribution expected for t - channel exchange of a very heavy particle according to reference@xcite , the relative efficiency reduction would be less than 2% at all points in the ( @xmath170 ) plane . we have searched for events with a final state consisting of two or three photons and large missing energy , in data taken with the opal detector at lep , at centre - of - mass energies in the range of @xmath1 gev . the selection requires at least two photons with scaled energy @xmath186 within the polar angle region @xmath187 or at least two photons with energy @xmath188 gev with one satisfying @xmath137 and the other satisfying @xmath187 . in each case , the requirement @xmath142 is also applied . there are 54 events selected . the kk2f prediction for the contribution from @xmath2 is @xmath144 events ; expected contributions from other sources sum to @xmath189 events . the number of events observed in the data and their kinematic distributions are consistent with standard model expectations . limits on new physics processes of the form are set separately at energies of 192 , 196 , 200 , 202 , 205 and 207 gev . in addition , combined limits are set at @xmath190 gev , assuming a @xmath168 scaling of the production cross - section . from the full opal data sample with @xmath166 gev , we derive 95% cl upper limits on @xmath3 ranging from 10 to 60 fb for the general case of massive @xmath96 and @xmath4 . for the special case of @xmath99 , the 95% cl upper limits on @xmath3 range from 20 to 45 fb , for @xmath182 gev . these results are used to place model - dependent lower limits on the @xmath101 mass in a specific light gravitino lsp model@xcite . masses between 45 and 99 gev are excluded at 95% cl . all limits assume that particle @xmath96 decays promptly . we particularly wish to thank the sl division for the efficient operation of the lep accelerator at all energies and for their close cooperation with our experimental group . in addition to the support staff at our own institutions we are pleased to acknowledge the + department of energy , usa , + national science foundation , usa , + particle physics and astronomy research council , uk , + natural sciences and engineering research council , canada , + israel science foundation , administered by the israel academy of science and humanities , + benoziyo center for high energy physics , + japanese ministry of education , culture , sports , science and technology ( mext ) and a grant under the mext international science research program , + japanese society for the promotion of science ( jsps ) , + german israeli bi - national science foundation ( gif ) , + bundesministerium fr bildung und forschung , germany , + national research council of canada , + hungarian foundation for scientific research , otka t-038240 , and t-042864 , + the nwo / nato fund for scientific research , the netherlands . + 99 opal collab . , g. abbiendi et al . , eur . j. * c18 * ( 2000 ) 253 . opal collab . , g. abbiendi et al . j. * c8 * ( 1999 ) 23 . opal collab . , k. ackerstaff et al . j. * c2 * ( 1998 ) 607 . aleph collab . , r. barate et al . , j. * c28 * ( 2003 ) 1 . ; delphi collab . , p. abreu et al . , cern - ep-2003 - 093 . submitted to eur . j. ; l3 collab . , j. abdallah et al . , phys . lett . * b587 * ( 2004 ) 16 . c.y . chang and g.a . snow , umd / pp/97 - 57;k . s. babu , c. kolda and f. wilczek , phys . * 77 * ( 1996 ) 3070 . opal collab . , g. abbiendi et al . , phys b544 * ( 2002 ) 44 . opal collab . , g. abbiendi et al . , cern - ep-2004 - 003 submitted to phys . d opal collab . , k. ahmet et al . , nucl . . methods * a305 * ( 1991 ) 275 ; s. anderson et al . . methods * a403 * ( 1998 ) 326 ; b.e . anderson et al . , ieee transactions on nuclear science * 41 * ( 1994 ) 845 . g. montagna , m. moretti , o. nicrosini and f. piccinini , nucl . b541 * ( 1999 ) 31 . s. jadach , b.f.l . ward and z. was , phys . lett . * b449 * ( 1999 ) 97 ; + s. jadach , b.f.l . ward and z. was , comp . 130 ( 2000 ) 260 . berends and r. kleiss , nucl . * b186 * ( 1981 ) 22 . s. jadach , w. placzek and b.f.l . ward , phys . * b390 * ( 1997 ) 298 . d. karlen , nucl . * b289 * ( 1987 ) 23 . s. jadach et al . , comp . * 119 * ( 1999 ) 272 . j. fujimoto et al . , comp . . comm . * 100 * ( 1997 ) 128 . s. jadach , b.f.l . ward and z. was , comp . * 79 * ( 1994 ) 503.version 4.02 was used including a recommended correction to the ndist0 subroutine . berends , p.h . daverveldt and r. kleiss , nucl . * b253 * ( 1985 ) 421 ; + f.a . berends , p.h . daverveldt and r. kleiss , comput . phys . commun . * 40 * ( 1986 ) 271 , 285 and 309 . j. a. m. vermaseren , nucl b229 * ( 1983 ) 347 . s. katsanevas and s. melachronios , in physics at lep2 , edited by g. alterelli , t. sjstrand and f. zwirner , cern/96 - 01 , vol.2 ( 1996 ) 328 . j. allison et al . , nucl . instrum . methods * a317 * ( 1992 ) 47 . opal collab . akrawy et al . , phys . lett . * b248 * ( 1990 ) 211 ; aleph collab . , d. decamp et al . , phys . * 216 * ( 1992 ) 253 ; l3 collab . , m. acciarri et al . , phys . lett . * b350 * ( 1995 ) 109 . r.d . cousins and v.l . highland , nucl . instrum . methods * a320 * ( 1992 ) 331 . j.l . lopez and d.v . nanopoulos , mod . * a11 * ( 1996 ) 2473;phys . rev . * d55 * ( 1997 ) 4450 . j. ellis and j.s . hagelin , phys . lett . * b122 * ( 1983 ) 303 . s. dimopoulos et al . , phys . * 76 * ( 1996 ) 3494;d.r . stump , m. wiest , c.p . yuan , phys . rev . * d54 * ( 1996 ) 1936;s . ambrosanio et al . , phys . rev . * d54 * ( 1996 ) 5395 . .results of the selection applied to the opal 1999 and 2000 data samples . shown for each sub - sample are the integrated luminosity @xmath191 , the centre - of - mass energy range , the luminosity - weighted mean centre - of - mass energy , the numbers of events observed and expected , and the measured and predicted cross - section for the process @xmath2 , within the kinematic acceptance of the selection . predicted values were obtained using the kk2f monte carlo generator . the errors shown are the sum of the statistical and systematic uncertainties . [ cols="^,^,^,^,>,>,^,^",options="header " , ] system and d ) the scaled transverse momentum distribution for the @xmath192 system . the data points with error bars represent the selected opal data events . in each case the histogram shows the expected contribution from @xmath2 events , from kk2f , normalized to the integrated luminosity of the data . the expected background from other sources ( @xmath189 events ) is not shown . , scaledwidth=95.0% ] at @xmath190 gev obtained from all opal data with @xmath193 189 gev , under the assumption that the cross - section scales as @xmath168 . no limit is set for mass - difference values @xmath194 gev , defined by the lower line above the shaded regions . the upper line is for @xmath195 . , scaledwidth=95.0% ] for events selected from a ) the @xmath174 gev data sample and b ) the @xmath175 gev sample . in each case the data points show the opal data and the unshaded histogram shows the expected distribution from the standard model process @xmath2 , evaluated using kk2f and normalized to the integrated luminosity of the data sample . in b ) the shaded histogram shows the expected distribution for the signal process @xmath95 , @xmath97 for @xmath176 gev with arbitrary production cross - section.,scaledwidth=95.0% ] at 207 gev for @xmath99 obtained from all opal data with @xmath196 189 gev . the lightly shaded region shows the excluded region obtained using only the opal 207 gev data sample . the darker region shows the exclusion region obtained using all opal data with @xmath166 gev , assuming that the cross - section scales as @xmath168 . the line shows the prediction of an example light gravitino lsp model@xcite . within that model , @xmath101 masses between 45 and 99 gev are excluded at 95% cl . these limits assume that particle x decays promptly.,scaledwidth=95.0% ]

events with a final state consisting of two or more photons and large missing transverse energy have been observed in @xmath0 collisions at centre - of - mass energies in the range @xmath1 gev using the opal detector at lep . cross - section measurements are performed within the kinematic acceptance of the selection and compared with the expectations from the standard model process @xmath2 . no evidence for new physics contributions to this final state is observed . upper limits on @xmath3 are derived for the case of stable and invisible @xmath4 . in the case of massive @xmath4 the combined limits obtained from all the data range from 10 fb to 60 fb , while for the special case of massless @xmath4 the range is 20 fb to 40 fb . the limits apply to pair production of excited neutrinos ( @xmath5 ) , to neutralino production ( @xmath6 ) and to supersymmetric models in which @xmath7 and @xmath8 is a light gravitino . european organization for nuclear research cern - ph - ep-2004 - 035 + 12 july 2004 + * multi - photon events with large missing energy + in @xmath9 collisions at @xmath10 gev * the opal collaboration to be submitted to physics letters b the opal collaboration g.abbiendi@xmath11 , c.ainsley@xmath12 , p.f.kesson@xmath13 , g.alexander@xmath14 , j.allison@xmath15 , p.amaral@xmath16 , g.anagnostou@xmath17 , k.j.anderson@xmath16 , s.arcelli@xmath11 , s.asai@xmath18 , d.axen@xmath19 , g.azuelos@xmath20 , i.bailey@xmath21 , e.barberio@xmath22 , t.barillari@xmath23 , r.j.barlow@xmath15 , r.j.batley@xmath12 , p.bechtle@xmath24 , t.behnke@xmath24 , k.w.bell@xmath25 , p.j.bell@xmath17 , g.bella@xmath14 , a.bellerive@xmath26 , g.benelli@xmath27 , s.bethke@xmath23 , o.biebel@xmath28 , o.boeriu@xmath29 , p.bock@xmath30 , m.boutemeur@xmath28 , s.braibant@xmath31 , l.brigliadori@xmath11 , r.m.brown@xmath25 , k.buesser@xmath24 , h.j.burckhart@xmath31 , s.campana@xmath27 , r.k.carnegie@xmath26 , a.a.carter@xmath32 , j.r.carter@xmath12 , c.y.chang@xmath33 , d.g.charlton@xmath17 , c.ciocca@xmath11 , a.csilling@xmath34 , m.cuffiani@xmath11 , s.dado@xmath35 , a.de roeck@xmath31 , e.a.de wolf@xmath36 , k.desch@xmath24 , b.dienes@xmath37 , m.donkers@xmath26 , j.dubbert@xmath28 , e.duchovni@xmath38 , g.duckeck@xmath28 , i.p.duerdoth@xmath15 , e.etzion@xmath14 , f.fabbri@xmath11 , l.feld@xmath29 , p.ferrari@xmath31 , f.fiedler@xmath28 , i.fleck@xmath29 , m.ford@xmath12 , a.frey@xmath31 , p.gagnon@xmath39 , j.w.gary@xmath27 , g.gaycken@xmath24 , c.geich-gimbel@xmath40 , g.giacomelli@xmath11 , p.giacomelli@xmath11 , m.giunta@xmath27 , j.goldberg@xmath35 , e.gross@xmath38 , j.grunhaus@xmath14 , m.gruw@xmath31 , p.o.gnther@xmath40 , a.gupta@xmath16 , c.hajdu@xmath34 , m.hamann@xmath24 , g.g.hanson@xmath27 , a.harel@xmath35 , m.hauschild@xmath31 , c.m.hawkes@xmath17 , r.hawkings@xmath31 , r.j.hemingway@xmath26 , g.herten@xmath29 , r.d.heuer@xmath24 , j.c.hill@xmath12 , k.hoffman@xmath16 , d.horvth@xmath41 , p.igo-kemenes@xmath30 , k.ishii@xmath18 , h.jeremie@xmath42 , p.jovanovic@xmath17 , t.r.junk@xmath43 , n.kanaya@xmath21 , j.kanzaki@xmath44 , d.karlen@xmath21 , k.kawagoe@xmath18 , t.kawamoto@xmath18 , r.k.keeler@xmath21 , r.g.kellogg@xmath33 , b.w.kennedy@xmath25 , s.kluth@xmath23 , t.kobayashi@xmath18 , m.kobel@xmath40 , s.komamiya@xmath18 , t.krmer@xmath24 , p.krieger@xmath45 , j.von krogh@xmath30 , k.kruger@xmath31 , t.kuhl@xmath46 , m.kupper@xmath38 , g.d.lafferty@xmath15 , h.landsman@xmath35 , d.lanske@xmath47 , j.g.layter@xmath27 , d.lellouch@xmath38 , j.letts@xmath48 , l.levinson@xmath38 , j.lillich@xmath29 , s.l.lloyd@xmath32 , f.k.loebinger@xmath15 , j.lu@xmath49 , a.ludwig@xmath40 , j.ludwig@xmath29 , w.mader@xmath40 , s.marcellini@xmath11 , a.j.martin@xmath32 , g.masetti@xmath11 , t.mashimo@xmath18 , p.mttig@xmath50 , j.mckenna@xmath19 , r.a.mcpherson@xmath21 , f.meijers@xmath31 , w.menges@xmath24 , f.s.merritt@xmath16 , h.mes@xmath51 , n.meyer@xmath24 , a.michelini@xmath11 , s.mihara@xmath18 , g.mikenberg@xmath38 , d.j.miller@xmath52 , s.moed@xmath35 , w.mohr@xmath29 , t.mori@xmath18 , a.mutter@xmath29 , k.nagai@xmath32 , i.nakamura@xmath53 , h.nanjo@xmath18 , h.a.neal@xmath54 , r.nisius@xmath23 , s.w.oneale@xmath55 , a.oh@xmath31 , m.j.oreglia@xmath16 , s.orito@xmath56 , c.pahl@xmath23 , g.psztor@xmath57 , j.r.pater@xmath15 , j.e.pilcher@xmath16 , j.pinfold@xmath58 , d.e.plane@xmath31 , b.poli@xmath11 , o.pooth@xmath47 , m.przybycie@xmath59 , a.quadt@xmath40 , k.rabbertz@xmath60 , c.rembser@xmath31 , p.renkel@xmath38 , j.m.roney@xmath21 , y.rozen@xmath35 , k.runge@xmath29 , k.sachs@xmath26 , t.saeki@xmath18 , e.k.g.sarkisyan@xmath61 , a.d.schaile@xmath28 , o.schaile@xmath28 , p.scharff-hansen@xmath31 , j.schieck@xmath23 , t.schrner-sadenius@xmath62 , m.schrder@xmath31 , m.schumacher@xmath40 , w.g.scott@xmath25 , r.seuster@xmath63 , t.g.shears@xmath64 , b.c.shen@xmath27 , p.sherwood@xmath52 , a.skuja@xmath33 , a.m.smith@xmath31 , r.sobie@xmath21 , s.sldner-rembold@xmath52 , f.spano@xmath16 , a.stahl@xmath65 , d.strom@xmath66 , r.strhmer@xmath28 , s.tarem@xmath35 , m.tasevsky@xmath36 , r.teuscher@xmath16 , m.a.thomson@xmath12 , e.torrence@xmath66 , d.toya@xmath18 , p.tran@xmath27 , i.trigger@xmath31 , z.trcsnyi@xmath67 , e.tsur@xmath14 , m.f.turner-watson@xmath17 , i.ueda@xmath18 , b.ujvri@xmath67 , c.f.vollmer@xmath28 , p.vannerem@xmath29 , r.vrtesi@xmath68 , m.verzocchi@xmath33 , h.voss@xmath69 , j.vossebeld@xmath70 , c.p.ward@xmath12 , d.r.ward@xmath12 , p.m.watkins@xmath17 , a.t.watson@xmath17 , n.k.watson@xmath17 , p.s.wells@xmath31 , t.wengler@xmath31 , n.wermes@xmath40 , g.w.wilson@xmath71 , j.a.wilson@xmath17 , g.wolf@xmath38 , t.r.wyatt@xmath15 , s.yamashita@xmath18 , d.zer-zion@xmath27 , l.zivkovic@xmath38 @xmath17school of physics and astronomy , university of birmingham , birmingham b15 2tt , uk @xmath11dipartimento di fisica dell universit di bologna and infn , i-40126 bologna , italy @xmath40physikalisches institut , universitt bonn , d-53115 bonn , germany @xmath27department of physics , university of california , riverside ca 92521 , usa @xmath12cavendish laboratory , cambridge cb3 0he , uk @xmath26ottawa - carleton institute for physics , department of physics , carleton university , ottawa , ontario k1s 5b6 , canada @xmath31cern , european organisation for nuclear research , ch-1211 geneva 23 , switzerland @xmath16enrico fermi institute and department of physics , university of chicago , chicago il 60637 , usa @xmath29fakultt fr physik , albert - ludwigs - universitt freiburg , d-79104 freiburg , germany @xmath30physikalisches institut , universitt heidelberg , d-69120 heidelberg , germany @xmath39indiana university , department of physics , bloomington in 47405 , usa @xmath32queen mary and westfield college , university of london , london e1 4ns , uk @xmath47technische hochschule aachen , iii physikalisches institut , sommerfeldstrasse 26 - 28 , d-52056 aachen , germany @xmath52university college london , london wc1e 6bt , uk @xmath15department of physics , schuster laboratory , the university , manchester m13 9pl , uk @xmath33department of physics , university of maryland , college park , md 20742 , usa @xmath42laboratoire de physique nuclaire , universit de montral , montral , qubec h3c 3j7 , canada @xmath66university of oregon , department of physics , eugene or 97403 , usa @xmath25cclrc rutherford appleton laboratory , chilton , didcot , oxfordshire ox11 0qx , uk @xmath35department of physics , technion - israel institute of technology , haifa 32000 , israel @xmath14department of physics and astronomy , tel aviv university , tel aviv 69978 , israel @xmath18international centre for elementary particle physics and department of physics , university of tokyo , tokyo 113 - 0033 , and kobe university , kobe 657 - 8501 , japan @xmath38particle physics department , weizmann institute of science , rehovot 76100 , israel @xmath24universitt hamburg / desy , institut fr experimentalphysik , notkestrasse 85 , d-22607 hamburg , germany @xmath21university of victoria , department of physics , p o box 3055 , victoria bc v8w 3p6 , canada @xmath19university of british columbia , department of physics , vancouver bc v6 t 1z1 , canada @xmath58university of alberta , department of physics , edmonton ab t6 g 2j1 , canada @xmath34research institute for particle and nuclear physics , h-1525 budapest , p o box 49 , hungary @xmath37institute of nuclear research , h-4001 debrecen , p o box 51 , hungary @xmath28ludwig - maximilians - universitt mnchen , sektion physik , am coulombwall 1 , d-85748 garching , germany @xmath23max - planck - institute fr physik , fhringer ring 6 , d-80805 mnchen , germany @xmath54yale university , department of physics , new haven , ct 06520 , usa @xmath72 and at triumf , vancouver , canada v6 t 2a3 @xmath73 and institute of nuclear research , debrecen , hungary @xmath74 and department of experimental physics , university of debrecen , hungary @xmath75 and mpi mnchen @xmath76 and research institute for particle and nuclear physics , budapest , hungary @xmath77 now at university of liverpool , dept of physics , liverpool l69 3bx , u.k . @xmath78 now at dept . physics , university of illinois at urbana - champaign , u.s.a . @xmath79 and manchester university @xmath80 now at university of kansas , dept of physics and astronomy , lawrence , ks 66045 , u.s.a . @xmath81 now at university of toronto , dept of physics , toronto , canada @xmath50 current address bergische universitt , wuppertal , germany @xmath82 now at university of mining and metallurgy , cracow , poland @xmath48 now at university of california , san diego , u.s.a . @xmath83 now at the university of melbourne , victoria , australia @xmath84 now at iphe universit de lausanne , ch-1015 lausanne , switzerland @xmath85 now at iekp universitt karlsruhe , germany @xmath86 now at university of antwerpen , physics department , b-2610 antwerpen , belgium ; supported by interuniversity attraction poles programme belgian science policy @xmath87 and high energy accelerator research organisation ( kek ) , tsukuba , ibaraki , japan @xmath88 now at university of pennsylvania , philadelphia , pennsylvania , usa @xmath89 now at triumf , vancouver , canada @xmath90 now at desy zeuthen @xmath91 now at cern @xmath92 now at desy @xmath93 deceased

<s>[INST]we describe measurements and searches performed using a data sample of photonic events with large missing transverse energy collected with the opal detector in 1999 and 2000 , the final two years of lep operation . the events result from @xmath9 collisions in the centre - of - mass energy range of about @xmath1 gev with a combined integrated luminosity of 426.5 pb@xmath94 . when deriving cross - section limits on new physics processes , these data are combined with previously published data@xcite taken at 189 gev and corresponding to 177.3 pb@xmath94 . the present paper builds on past publications based on data samples collected at lower centre - of - mass energies@xcite . the new data samples , taken at the highest energies achieved by lep , provide discovery potential in a new kinematic regime with a large increase in integrated luminosity . similar searches have been made by the other lep collaborations @xcite . the analysis presented here is designed to select events with two photons and significant missing transverse energy in the final state , indicating the presence of at least one neutrino - like invisible particle which interacts only weakly with matter . the event selection for this search topology is identical to that used in our most recent publication@xcite . within the standard model , such events are expected from the @xmath2 process . the selection is designed to retain acceptance for events with an additional photon , provided that the system formed by the three photons is consistent with the presence of significant missing transverse energy . this final - state topology is also sensitive to several new physics scenarios . in the context of the search for new physics , the emphasis in this publication is on general searches applicable to a broad class of models . to this end , a generic classification is used : @xmath95 where @xmath96 is neutral and can decay radiatively ( @xmath97 ) and @xmath4 is stable and only weakly interacting . the limits presented for this generic process are applicable to a variety of physics searches . for the general case of massive @xmath96 and @xmath4 this includes conventional supersymmetric processes @xmath98 . there is particularly good sensitivity for the special case of @xmath99 . this is applicable both to the production of excited neutrinos @xmath100 and to supersymmetric models in which the lightest supersymmetric particle ( lsp ) is a light gravitino and @xmath101 is the next - to - lightest supersymmetric particle ( nlsp ) which decays to a gravitino and a photon ( @xmath102 ) . in the latter case , we also set limits on an example light - gravitino model@xcite . the neutralino lifetime in such models is a free parameter . in this paper we address only the case of promptly decaying @xmath96 . this search topology also has sensitivity to the production of two particles , one invisible , or with an invisible decay mode , and the other decaying into two photons . such events might arise from the production of a higgs - like scalar particle , @xmath103 : @xmath104 , followed by s@xmath105@xmath106 , @xmath107 . the results of an opal search for this process , including the hadronic and leptonic @xmath108 decays , have been separately reported @xcite . finally , this search topology can also probe ww@xmath109 quartic couplings in the @xmath110 process . the opal quartic gauge coupling measurements are described in @xcite . this paper first describes the opal detector and the monte carlo samples used . a brief summary of the event selection will then be given , followed by cross - section measurements and comparisons with standard model expectations . the new physics search results will then be discussed . the opal detector , which is described in detail in @xcite , contained a silicon micro - vertex detector surrounded by a pressurized central tracking system operating inside a solenoid with a magnetic field of 0.435 t. the barrel and endcap regions of the detector were instrumented with scintillation counters , presamplers and a lead - glass electromagnetic calorimeter ( ecal ) . the magnet return yoke was instrumented for hadron calorimetry and was surrounded by muon chambers . electromagnetic calorimeters close to the beam axis measured luminosity and completed the acceptance . the measurements presented here are based mainly on the observation of clusters of energy deposited in the lead - glass electromagnetic calorimeter . this consisted of an array of 9,440 lead - glass blocks in the barrel region , @xmath111 , with a quasi - pointing geometry and two endcap arrays , each of 1,132 lead - glass blocks , covering the polar angle axis points along the direction of the @xmath112 beam . the polar angle @xmath113 is defined with respect to the @xmath112 beam direction and @xmath114 is the azimuthal angle measured from the @xmath115 axis . ] range , @xmath116 . hermetic electromagnetic calorimeter coverage was achieved beyond the end of the ecal down to 33 mrad in polar angle with the use of the gamma - catcher calorimeter , the forward calorimeter and the silicon - tungsten calorimeter . scintillators in the barrel and endcap regions were used to reject backgrounds from cosmic - ray interactions by providing time measurements for the large fraction ( @xmath117 80% ) of photons which converted in the material in front of the ecal . the barrel time - of - flight ( tof ) scintillator bars were located outside the solenoid in front of the barrel ecal and matched its geometrical acceptance @xmath111 . tile endcap ( te ) scintillator arrays were located in front of the endcap ecal at @xmath118 . additional scintillating - tile arrays , referred to as the mip plug , were located at more forward angles . in the region from 125 to 200 mrad these detectors were used to provide redundancy in the rejection of events with significant electromagnetic activity in the forward region . the integrated luminosities of the data samples are determined to better than 1% from small - angle bhabha scattering events in the silicon - tungsten calorimeter . triggers based on electromagnetic energy deposits in either the barrel or endcap electromagnetic calorimeters lead to full trigger efficiency for photonic events passing the event selection criteria used in this analysis . the nunugpv98 @xcite and kk2f @xcite monte carlo generators were used to simulate the standard model signal process , @xmath2 . for other expected standard model processes , a number of different generators were used : radcor @xcite for @xmath119 ; bhwide @xcite and teegg @xcite for @xmath120 ; koralw @xcite using ` grc4f ` @xcite matrix elements for @xmath121 and @xmath122 , and koralz@xcite for @xmath123 and @xmath124 . the bdk program@xcite was used for @xmath125 , except for @xmath126 which was generated using the vermaseren program@xcite . the expected contribution from each of these standard model processes was evaluated using a total equivalent integrated luminosity at least five times larger than the integrated luminosity of the data sample . to simulate possible new physics processes of the type @xmath95 where @xmath96 decays to @xmath127 and @xmath4 escapes detection , a modified version of the susygen @xcite monte carlo generator was used to produce neutralino pair events of the type @xmath128 , @xmath129 , with isotropic angular distributions for the production and decay of @xmath130 and including the effects of initial - state radiation . for @xmath131 206 gev , monte carlo events were generated at 49 points in the kinematically accessible region of the ( @xmath132 , @xmath133 ) plane . monte carlo events at 42 points in ( @xmath132 , @xmath133 ) with @xmath131 189 gev were generated for our previous publication@xcite . using these two samples , the selection efficiency was determined for each generated point and then parametrized as a function of ( @xmath132 , @xmath133 ) and centre - of - mass energy . the efficiency varies slowly with energy and for energies above 206 gev , the 206 gev values were used . all monte carlo samples described above were processed through the full opal detector simulation @xcite . a detailed description of the event selection is given in our previous publications@xcite . in brief , photons are identified as energy deposits in the electromagnetic calorimeter . events are required to have no other significant activity , except for the possibility of additional photons . information from the tracking chambers is used to reject electromagnetic clusters associated with prompt charged tracks while retaining sensitivity for photons which converted in the material between the interaction point and the calorimeter . timing information is used to reject backgrounds from cosmic - ray events . events with activity beyond the acceptance of the ecal are vetoed using information from the gamma catcher , the forward calorimeter , the silicon - tungsten calorimeter and the mip plug.the kinematic acceptance of the selection is defined by requiring : * at least two photons , each with @xmath134 and @xmath135 , or one photon with @xmath136 gev and @xmath137 and a second photon with @xmath136 gev and @xmath135 ; here @xmath138 is the photon energy , @xmath113 is the photon polar angle and @xmath139 is the photon scaled energy @xmath140 * that the two - photon system consisting of the two highest - energy photons have momentum transverse to the beamline ( @xmath141 ) satifying @xmath142 the selection is designed to retain acceptance for events with additional photons in which the resulting photonic system is still consistent with the presence of significant missing energy . this reduces the sensitivity of the measurement to the modelling of higher - order contributions . the data described in this paper were taken during the final two years of lep operation , at centre - of - mass energies between 192 and 209 gev . for the purposes of this publication the data have been binned into six samples with mean centre - of - mass energies of approximately 192 , 196 , 200 , 202 , 205 and 207 gev . the energy ranges and luminosity breakdown are summarized in table [ tab : g2_xsec_new ] . applied to the entire sample , the selection yields a total of @xmath143 events , in good agreement with the kk2f prediction of @xmath144 events for the standard model @xmath2 contribution . the expected contribution from other standard model processes and from cosmic ray and beam - related backgrounds is @xmath145 events , dominated by contributions from low - angle radiative bhabha events and radiative four - fermion final states . the selection results are included in table [ tab : g2_xsec_new ] . the selection efficiency for @xmath2 events within the kinematic acceptance of the selection is ( @xmath146)% , independent of energy . the cross - section within the kinematic acceptance of the selection is also shown in table [ tab : g2_xsec_new ] as are the corresponding predictions obtained using the kk2f monte carlo generator . the predictions of the nunugpv98 monte carlo generator were also examined and agreed well with those of kk2f . small differences are accounted for in the systematic uncertainties . the dominant sources of systematic uncertainties arise from modelling of the event selection efficiency , especially the simulation of the detector material and consequent photon conversion probabilities . the effects of these uncertainties and of uncertainties on the efficiency of timing cuts used to suppress cosmic - ray events are calculated accounting for different event topologies ( both photons in the barrel region , both in the endcap , or one in each ) . this total uncertainty is 1.7% . other sources arise from uncertainties on the integrated luminosity measurement ( 0.5% ) , on detector occupancy estimates ( 1% ) obtained from the analysis of randomly triggered events , on comparisons of different monte carlo event generators for the process @xmath2(1% ) . the total systematic uncertainty common to each energy bin is 2.3% . in individual energy bins , monte carlo statistics account for an additional systematic uncertainty of @xmath147% . the kinematic properties of the selected events , summed over all energies , are displayed in figure [ f : g2_kine_all ] where they are compared with the predicted distributions for @xmath2 obtained using the kk2f generator normalized to the integrated luminosity of the data . plot ( a ) shows the recoil mass distribution of the selected events ( for the two most energetic photons in the case of events with three or more photons ) . the distribution is peaked near the mass of the @xmath148 as is expected for contributions from @xmath2 . the resolution of the recoil mass is typically @xmath149 gev for @xmath150 . events with a negative recoil - mass squared are plotted in the zero bin of the distribution . plot ( b ) shows the distribution of the scaled energy of the second most energetic photon . plot ( c ) shows the @xmath151 invariant - mass distribution for which the mass resolution is typically @xmath152 gev . plot ( d ) shows the distribution in scaled transverse momentum of the selected two - photon system . there are 3 selected events having a third photon with deposited energy above 300 mev and within the polar - angle acceptance of the selection . the corresponding expectation from kk2f is @xmath153 events . the results of this selection are used to test the standard model and to search for new physics contributions . in the absence of an excess of events beyond the standard model expectation , we set 95% cl upper limits on the quantity @xmath3 for the general case of massive @xmath96 and @xmath4 , and separately for the special case of @xmath99 . efficiencies were evaluated under the assumption that @xmath96 decays promptly . monte carlo samples were generated for a variety of mass points in the kinematically accessible region of the @xmath154 plane . to set limits for arbitrary @xmath132 and @xmath133 , the efficiency over the entire @xmath154 plane was parameterized using the efficiencies calculated at the generated mass points . for @xmath132 values below @xmath155/2 , search results based on lep1 data have been previously reported @xcite . in this low - mass region , events with radiative return to the @xmath148 followed by @xmath156 would yield very different kinematics than those used here to generate the signal monte carlo samples . for this reason , the search is restricted to the mass region @xmath157 . [ sec : g2_results_allmy ] the searches for @xmath95 , @xmath97 , both for the general case discussed here and the special case of @xmath99 discussed in section 5.2 , use the methods described in our previous publications@xcite . selected events are classified as consistent with a given value of @xmath132 and @xmath133 if the energy of each of the photons falls within the region kinematically accessible to photons from the process @xmath95 , @xmath97 , including resolution effects . selection efficiencies at some of the generated grid points for the @xmath95 , @xmath97 @xmath159 gev monte carlo events are shown in table [ tab : g2_eff_206 ] . these values include the efficiency of the kinematic consistency requirement which is higher than 95% at each generated point in the region of the @xmath154 plane . for @xmath160 values lower than 5 gev the efficiency begins to fall off rapidly and is thus difficult to model accurately . for this reason , we place limits only in the region of the @xmath161 plane satisfying @xmath162 gev . efficiencies at lower centre - of - mass energies are obtained from an interpolation between these efficiencies and the equivalent efficiencies at 189 gev , which are given in our previous publication @xcite . for data taken at centre - of - mass energies above 206 gev , the 206 gev efficiencies are used . events from @xmath2 are typically characterized by a high - energy photon from the radiative return to the @xmath108 and a second lower energy photon . the kinematic consistency requirement is such that the two photons must have energies within the same ( kinematically accessible ) region . thus , as @xmath132 and @xmath133 increase , the allowed range of energy for the photons narrows , and fewer @xmath163 events will be accepted . for the 54 selected events , the distribution of the number of events consistent with a given mass point ( @xmath132,@xmath133 ) is consistent with the expectation from @xmath2 monte carlo , over the full ( @xmath132,@xmath133 ) plane . upper limits are placed on @xmath3 accounting for the number of selected events and the expected number of background events from the process @xmath2 . other backgrounds are not subtracted . for each of the energy bins , table [ tab : limits ] shows the maximum and minimum limits obtained in the region of the ( @xmath164 plane described above . figure [ mxmy_207_combined ] shows the 95% cl lower limits on @xmath3 at @xmath165 gev , obtained from all opal data with @xmath166 gev , under the assumption that @xmath167 scales with centre - of - mass energy as @xmath168 . these limits range from @xmath169 fb . systematic uncertainties arise from the sources described in section 4 . however there are additional contributions due to limited monte carlo statistics at each of the generated ( @xmath170 ) points and from uncertainties on the efficiency parameterization across the ( @xmath170 ) plane and as a function of energy . the combined relative uncertainty on the efficiency varies from about 3% to 6% across the plane ( for @xmath171 gev ) . the uncertainty on the expected sm background contribution is 2.6% . in calculating the limits , systematic uncertainties are accounted for in the manner advocated in reference@xcite . this also applies to the limits for the @xmath99 case , presented in the next section . [ sec : g2_results_my0 ] for the special case of @xmath99 the applied kinematic consistency requirements differ from those used for the general case . one can calculate@xcite the maximum mass , @xmath172 , which is consistent with the measured three - momenta of the two photons , assuming a massless @xmath4 . a cut on @xmath172 provides further suppression of the @xmath163 background while retaining high efficiency for the signal hypothesis . this is discussed in more detail in reference @xcite . to allow for resolution effects , we require that the maximum kinematically allowed mass be greater than @xmath173 gev . this has better than 96% relative efficiency for signal at all values of @xmath132 while suppressing much of the remaining @xmath163 background . the @xmath172 distributions for all selected events , divided into the @xmath174 gev and @xmath175 gev data samples , are shown in figure [ g2_mxmax_206 ] . in each case , the points with error bars show the opal data while the unshaded histogram shows the expected contribution from the @xmath2 , from kk2f monte carlo , normalized to the luminosity of the data . shown as a shaded histgram in the @xmath175 gev plot is the expected distribution from signal monte carlo events generated with @xmath176 gev ( with arbitrary normalization ) . for this @xmath99 case , the signal reconstruction efficiencies calculated from monte carlo events generated at @xmath159 gev are shown in table [ tab : g2_eff_my0_206 ] after application of the event selection criteria and then after the cut on @xmath172 . also shown in table [ tab : g2_eff_my0_206 ] are the numbers of events selected from the @xmath175 gev data sample which are consistent with each value of @xmath132 as well as the expected number of @xmath2 events . the number of selected events ( from the @xmath175 gev sample ) consistent with a given value of @xmath132 varies from 10 , for @xmath177 45 gev , to 2 at the kinematic limit . the expected number of events decreases from @xmath178 at @xmath179 gev to @xmath180 consistent with @xmath181 gev . based on the efficiencies and the number of selected events , we calculate 95% cl upper limits on @xmath3 for @xmath99 as a function of @xmath132 , in each region of centre - of - mass energy . the last two columns of table [ tab : limits ] show the range of limits obtained from each of the data samples , for @xmath132 values from 45 gev up to the kinematic limit . figure [ my0_207_combined ] shows the limit obtained from the 207 gev data sample , as well as the combined limit obtained from the entire data sample with @xmath166 gev assuming that the cross - section scales as @xmath168 . for the mass range of interest ( @xmath182 gev ) the model - independent limits range between 45 and 70 fb while the combined limits range between 20 and 45 gev . these limits gev region the limits are actually slightly worse than those along the @xmath133=0 axis of figure [ mxmy_207_combined ] despite the more efficient background suppression of the @xmath172 cut , relative to the kinematic consistency cuts applied in the general case . this is due to a deficit of selected events in this region , compared to the expected background when using the general kinematic consistency requirements . ] can be used to set model - dependent limits on the mass of the lightest neutralino in supersymmetric models in which the nlsp is the lightest neutralino and the lsp is a light gravitino ( @xmath102 ) . shown in figure [ my0_207_combined ] , as a dotted line , is the ( born - level ) cross - section prediction from a specific light gravitino lsp model@xcite in which the neutralino composition is purely bino , with @xmath183 and @xmath184 . within the framework of this model , @xmath101 masses between 45 and 99.0 gev are excluded at 95% cl . as described in section 2 , the efficiencies over the full angular range have been obtained using isotropic angular distributions for the production and decay of @xmath96 . the validity of this model has been examined based on the angular distributions calculated for photino pair production in reference@xcite . for models proposed in reference@xcite , the production angular distributions are more central and so this procedure is conservative . for a @xmath185 production angular distribution expected for t - channel exchange of a very heavy particle according to reference@xcite , the relative efficiency reduction would be less than 2% at all points in the ( @xmath170 ) plane . we have searched for events with a final state consisting of two or three photons and large missing energy , in data taken with the opal detector at lep , at centre - of - mass energies in the range of @xmath1 gev . the selection requires at least two photons with scaled energy @xmath186 within the polar angle region @xmath187 or at least two photons with energy @xmath188 gev with one satisfying @xmath137 and the other satisfying @xmath187 . in each case , the requirement @xmath142 is also applied . there are 54 events selected . the kk2f prediction for the contribution from @xmath2 is @xmath144 events ; expected contributions from other sources sum to @xmath189 events . the number of events observed in the data and their kinematic distributions are consistent with standard model expectations . limits on new physics processes of the form are set separately at energies of 192 , 196 , 200 , 202 , 205 and 207 gev . in addition , combined limits are set at @xmath190 gev , assuming a @xmath168 scaling of the production cross - section . from the full opal data sample with @xmath166 gev , we derive 95% cl upper limits on @xmath3 ranging from 10 to 60 fb for the general case of massive @xmath96 and @xmath4 . for the special case of @xmath99 , the 95% cl upper limits on @xmath3 range from 20 to 45 fb , for @xmath182 gev . these results are used to place model - dependent lower limits on the @xmath101 mass in a specific light gravitino lsp model@xcite . masses between 45 and 99 gev are excluded at 95% cl . all limits assume that particle @xmath96 decays promptly . we particularly wish to thank the sl division for the efficient operation of the lep accelerator at all energies and for their close cooperation with our experimental group . in addition to the support staff at our own institutions we are pleased to acknowledge the + department of energy , usa , + national science foundation , usa , + particle physics and astronomy research council , uk , + natural sciences and engineering research council , canada , + israel science foundation , administered by the israel academy of science and humanities , + benoziyo center for high energy physics , + japanese ministry of education , culture , sports , science and technology ( mext ) and a grant under the mext international science research program , + japanese society for the promotion of science ( jsps ) , + german israeli bi - national science foundation ( gif ) , + bundesministerium fr bildung und forschung , germany , + national research council of canada , + hungarian foundation for scientific research , otka t-038240 , and t-042864 , + the nwo / nato fund for scientific research , the netherlands . + 99 opal collab . , g. abbiendi et al . , eur . j. * c18 * ( 2000 ) 253 . opal collab . , g. abbiendi et al . j. * c8 * ( 1999 ) 23 . opal collab . , k. ackerstaff et al . j. * c2 * ( 1998 ) 607 . aleph collab . , r. barate et al . , j. * c28 * ( 2003 ) 1 . ; delphi collab . , p. abreu et al . , cern - ep-2003 - 093 . submitted to eur . j. ; l3 collab . , j. abdallah et al . , phys . lett . * b587 * ( 2004 ) 16 . c.y . chang and g.a . snow , umd / pp/97 - 57;k . s. babu , c. kolda and f. wilczek , phys . * 77 * ( 1996 ) 3070 . opal collab . , g. abbiendi et al . , phys b544 * ( 2002 ) 44 . opal collab . , g. abbiendi et al . , cern - ep-2004 - 003 submitted to phys . d opal collab . , k. ahmet et al . , nucl . . methods * a305 * ( 1991 ) 275 ; s. anderson et al . . methods * a403 * ( 1998 ) 326 ; b.e . anderson et al . , ieee transactions on nuclear science * 41 * ( 1994 ) 845 . g. montagna , m. moretti , o. nicrosini and f. piccinini , nucl . b541 * ( 1999 ) 31 . s. jadach , b.f.l . ward and z. was , phys . lett . * b449 * ( 1999 ) 97 ; + s. jadach , b.f.l . ward and z. was , comp . 130 ( 2000 ) 260 . berends and r. kleiss , nucl . * b186 * ( 1981 ) 22 . s. jadach , w. placzek and b.f.l . ward , phys . * b390 * ( 1997 ) 298 . d. karlen , nucl . * b289 * ( 1987 ) 23 . s. jadach et al . , comp . * 119 * ( 1999 ) 272 . j. fujimoto et al . , comp . . comm . * 100 * ( 1997 ) 128 . s. jadach , b.f.l . ward and z. was , comp . * 79 * ( 1994 ) 503.version 4.02 was used including a recommended correction to the ndist0 subroutine . berends , p.h . daverveldt and r. kleiss , nucl . * b253 * ( 1985 ) 421 ; + f.a . berends , p.h . daverveldt and r. kleiss , comput . phys . commun . * 40 * ( 1986 ) 271 , 285 and 309 . j. a. m. vermaseren , nucl b229 * ( 1983 ) 347 . s. katsanevas and s. melachronios , in physics at lep2 , edited by g. alterelli , t. sjstrand and f. zwirner , cern/96 - 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section for the process @xmath2 , within the kinematic acceptance of the selection . predicted values were obtained using the kk2f monte carlo generator . the errors shown are the sum of the statistical and systematic uncertainties . [ cols="^,^,^,^,>,>,^,^",options="header " , ] system and d ) the scaled transverse momentum distribution for the @xmath192 system . the data points with error bars represent the selected opal data events . in each case the histogram shows the expected contribution from @xmath2 events , from kk2f , normalized to the integrated luminosity of the data . the expected background from other sources ( @xmath189 events ) is not shown . , scaledwidth=95.0% ] at @xmath190 gev obtained from all opal data with @xmath193 189 gev , under the assumption that the cross - section scales as @xmath168 . no limit is set for mass - difference values @xmath194 gev , defined by the lower line above the shaded regions . the upper line is for @xmath195 . , scaledwidth=95.0% ] for events selected from a ) the @xmath174 gev data sample and b ) the @xmath175 gev sample . in each case the data points show the opal data and the unshaded histogram shows the expected distribution from the standard model process @xmath2 , evaluated using kk2f and normalized to the integrated luminosity of the data sample . in b ) the shaded histogram shows the expected distribution for the signal process @xmath95 , @xmath97 for @xmath176 gev with arbitrary production cross - section.,scaledwidth=95.0% ] at 207 gev for @xmath99 obtained from all opal data with @xmath196 189 gev . the lightly shaded region shows the excluded region obtained using only the opal 207 gev data sample . the darker region shows the exclusion region obtained using all opal data with @xmath166 gev , assuming that the cross - section scales as @xmath168 . the line shows the prediction of an example light gravitino lsp model@xcite . within that model , @xmath101 masses between 45 and 99 gev are excluded at 95% cl . these limits assume that particle x decays promptly.,scaledwidth=95.0% ][/INST] events with a final state consisting of two or more photons and large missing transverse energy have been observed in @xmath0 collisions at centre - of - mass energies in the range @xmath1 gev using the opal detector at lep . cross - section measurements are performed within the kinematic acceptance of the selection and compared with the expectations from the standard model process @xmath2 . no evidence for new physics contributions to this final state is observed . upper limits on @xmath3 are derived for the case of stable and invisible @xmath4 . in the case of massive @xmath4 the combined limits obtained from all the data range from 10 fb to 60 fb , while for the special case of massless @xmath4 the range is 20 fb to 40 fb . the limits apply to pair production of excited neutrinos ( @xmath5 ) , to neutralino production ( @xmath6 ) and to supersymmetric models in which @xmath7 and @xmath8 is a light gravitino . european organization for nuclear research cern - ph - ep-2004 - 035 + 12 july 2004 + * multi - photon events with large missing energy + in @xmath9 collisions at @xmath10 gev * the opal collaboration to be submitted to physics letters b the opal collaboration g.abbiendi@xmath11 , c.ainsley@xmath12 , p.f.kesson@xmath13 , g.alexander@xmath14 , j.allison@xmath15 , p.amaral@xmath16 , g.anagnostou@xmath17 , k.j.anderson@xmath16 , s.arcelli@xmath11 , s.asai@xmath18 , d.axen@xmath19 , g.azuelos@xmath20 , i.bailey@xmath21 , e.barberio@xmath22 , t.barillari@xmath23 , r.j.barlow@xmath15 , r.j.batley@xmath12 , p.bechtle@xmath24 , t.behnke@xmath24 , k.w.bell@xmath25 , p.j.bell@xmath17 , g.bella@xmath14 , a.bellerive@xmath26 , g.benelli@xmath27 , s.bethke@xmath23 , o.biebel@xmath28 , o.boeriu@xmath29 , p.bock@xmath30 , m.boutemeur@xmath28 , s.braibant@xmath31 , l.brigliadori@xmath11 , r.m.brown@xmath25 , k.buesser@xmath24 , h.j.burckhart@xmath31 , s.campana@xmath27 , r.k.carnegie@xmath26 , a.a.carter@xmath32 , j.r.carter@xmath12 , c.y.chang@xmath33 , d.g.charlton@xmath17 , c.ciocca@xmath11 , a.csilling@xmath34 , m.cuffiani@xmath11 , s.dado@xmath35 , a.de roeck@xmath31 , e.a.de wolf@xmath36 , k.desch@xmath24 , b.dienes@xmath37 , m.donkers@xmath26 , j.dubbert@xmath28 , e.duchovni@xmath38 , g.duckeck@xmath28 , i.p.duerdoth@xmath15 , e.etzion@xmath14 , f.fabbri@xmath11 , l.feld@xmath29 , p.ferrari@xmath31 , f.fiedler@xmath28 , i.fleck@xmath29 , m.ford@xmath12 , a.frey@xmath31 , p.gagnon@xmath39 , j.w.gary@xmath27 , g.gaycken@xmath24 , c.geich-gimbel@xmath40 , g.giacomelli@xmath11 , p.giacomelli@xmath11 , m.giunta@xmath27 , j.goldberg@xmath35 , e.gross@xmath38 , j.grunhaus@xmath14 , m.gruw@xmath31 , p.o.gnther@xmath40 , a.gupta@xmath16 , c.hajdu@xmath34 , m.hamann@xmath24 , g.g.hanson@xmath27 , a.harel@xmath35 , m.hauschild@xmath31 , c.m.hawkes@xmath17 , r.hawkings@xmath31 , r.j.hemingway@xmath26 , g.herten@xmath29 , r.d.heuer@xmath24 , j.c.hill@xmath12 , k.hoffman@xmath16 , d.horvth@xmath41 , p.igo-kemenes@xmath30 , k.ishii@xmath18 , h.jeremie@xmath42 , p.jovanovic@xmath17 , t.r.junk@xmath43 , n.kanaya@xmath21 , j.kanzaki@xmath44 , d.karlen@xmath21 , k.kawagoe@xmath18 , t.kawamoto@xmath18 , r.k.keeler@xmath21 , r.g.kellogg@xmath33 , b.w.kennedy@xmath25 , s.kluth@xmath23 , t.kobayashi@xmath18 , m.kobel@xmath40 , s.komamiya@xmath18 , t.krmer@xmath24 , p.krieger@xmath45 , j.von krogh@xmath30 , k.kruger@xmath31 , t.kuhl@xmath46 , m.kupper@xmath38 , g.d.lafferty@xmath15 , h.landsman@xmath35 , d.lanske@xmath47 , j.g.layter@xmath27 , d.lellouch@xmath38 , j.letts@xmath48 , l.levinson@xmath38 , j.lillich@xmath29 , s.l.lloyd@xmath32 , f.k.loebinger@xmath15 , j.lu@xmath49 , a.ludwig@xmath40 , j.ludwig@xmath29 , w.mader@xmath40 , s.marcellini@xmath11 , a.j.martin@xmath32 , g.masetti@xmath11 , t.mashimo@xmath18 , p.mttig@xmath50 , j.mckenna@xmath19 , r.a.mcpherson@xmath21 , f.meijers@xmath31 , w.menges@xmath24 , f.s.merritt@xmath16 , h.mes@xmath51 , n.meyer@xmath24 , a.michelini@xmath11 , s.mihara@xmath18 , g.mikenberg@xmath38 , d.j.miller@xmath52 , s.moed@xmath35 , w.mohr@xmath29 , t.mori@xmath18 , a.mutter@xmath29 , k.nagai@xmath32 , i.nakamura@xmath53 , h.nanjo@xmath18 , h.a.neal@xmath54 , r.nisius@xmath23 , s.w.oneale@xmath55 , a.oh@xmath31 , m.j.oreglia@xmath16 , s.orito@xmath56 , c.pahl@xmath23 , g.psztor@xmath57 , j.r.pater@xmath15 , j.e.pilcher@xmath16 , j.pinfold@xmath58 , d.e.plane@xmath31 , b.poli@xmath11 , o.pooth@xmath47 , m.przybycie@xmath59 , a.quadt@xmath40 , k.rabbertz@xmath60 , c.rembser@xmath31 , p.renkel@xmath38 , j.m.roney@xmath21 , y.rozen@xmath35 , k.runge@xmath29 , k.sachs@xmath26 , t.saeki@xmath18 , e.k.g.sarkisyan@xmath61 , a.d.schaile@xmath28 , o.schaile@xmath28 , p.scharff-hansen@xmath31 , j.schieck@xmath23 , t.schrner-sadenius@xmath62 , m.schrder@xmath31 , m.schumacher@xmath40 , w.g.scott@xmath25 , r.seuster@xmath63 , t.g.shears@xmath64 , b.c.shen@xmath27 , p.sherwood@xmath52 , a.skuja@xmath33 , a.m.smith@xmath31 , r.sobie@xmath21 , s.sldner-rembold@xmath52 , f.spano@xmath16 , a.stahl@xmath65 , d.strom@xmath66 , r.strhmer@xmath28 , s.tarem@xmath35 , m.tasevsky@xmath36 , r.teuscher@xmath16 , m.a.thomson@xmath12 , e.torrence@xmath66 , d.toya@xmath18 , p.tran@xmath27 , i.trigger@xmath31 , z.trcsnyi@xmath67 , e.tsur@xmath14 , m.f.turner-watson@xmath17 , i.ueda@xmath18 , b.ujvri@xmath67 , c.f.vollmer@xmath28 , p.vannerem@xmath29 , r.vrtesi@xmath68 , m.verzocchi@xmath33 , h.voss@xmath69 , j.vossebeld@xmath70 , c.p.ward@xmath12 , d.r.ward@xmath12 , p.m.watkins@xmath17 , a.t.watson@xmath17 , n.k.watson@xmath17 , p.s.wells@xmath31 , t.wengler@xmath31 , n.wermes@xmath40 , g.w.wilson@xmath71 , j.a.wilson@xmath17 , g.wolf@xmath38 , t.r.wyatt@xmath15 , s.yamashita@xmath18 , d.zer-zion@xmath27 , l.zivkovic@xmath38 @xmath17school of physics and astronomy , university of birmingham , birmingham b15 2tt , uk @xmath11dipartimento di fisica dell universit di bologna and infn , i-40126 bologna , italy @xmath40physikalisches institut , universitt bonn , d-53115 bonn , germany @xmath27department of physics , university of california , riverside ca 92521 , usa @xmath12cavendish laboratory , cambridge cb3 0he , uk @xmath26ottawa - carleton institute for physics , department of physics , carleton university , ottawa , ontario k1s 5b6 , canada @xmath31cern , european organisation for nuclear research , ch-1211 geneva 23 , switzerland @xmath16enrico fermi institute and department of physics , university of chicago , chicago il 60637 , usa @xmath29fakultt fr physik , albert - ludwigs - universitt freiburg , d-79104 freiburg , germany @xmath30physikalisches institut , universitt heidelberg , d-69120 heidelberg , germany @xmath39indiana university , department of physics , bloomington in 47405 , usa @xmath32queen mary and westfield college , university of london , london e1 4ns , uk @xmath47technische hochschule aachen , iii physikalisches institut , sommerfeldstrasse 26 - 28 , d-52056 aachen , germany @xmath52university college london , london wc1e 6bt , uk @xmath15department of physics , schuster laboratory , the university , manchester m13 9pl , uk @xmath33department of physics , university of maryland , college park , md 20742 , usa @xmath42laboratoire de physique nuclaire , universit de montral , montral , qubec h3c 3j7 , canada @xmath66university of oregon , department of physics , eugene or 97403 , usa @xmath25cclrc rutherford appleton laboratory , chilton , didcot , oxfordshire ox11 0qx , uk @xmath35department of physics , technion - israel institute of technology , haifa 32000 , israel @xmath14department of physics and astronomy , tel aviv university , tel aviv 69978 , israel @xmath18international centre for elementary particle physics and department of physics , university of tokyo , tokyo 113 - 0033 , and kobe university , kobe 657 - 8501 , japan @xmath38particle physics department , weizmann institute of science , rehovot 76100 , israel @xmath24universitt hamburg / desy , institut fr experimentalphysik , notkestrasse 85 , d-22607 hamburg , germany @xmath21university of victoria , department of physics , p o box 3055 , victoria bc v8w 3p6 , canada @xmath19university of british columbia , department of physics , vancouver bc v6 t 1z1 , canada @xmath58university of alberta , department of physics , edmonton ab t6 g 2j1 , canada @xmath34research institute for particle and nuclear physics , h-1525 budapest , p o box 49 , hungary @xmath37institute of nuclear research , h-4001 debrecen , p o box 51 , hungary @xmath28ludwig - maximilians - universitt mnchen , sektion physik , am coulombwall 1 , d-85748 garching , germany @xmath23max - planck - institute fr physik , fhringer ring 6 , d-80805 mnchen , germany @xmath54yale university , department of physics , new haven , ct 06520 , usa @xmath72 and at triumf , vancouver , canada v6 t 2a3 @xmath73 and institute of nuclear research , debrecen , hungary @xmath74 and department of experimental physics , university of debrecen , hungary @xmath75 and mpi mnchen @xmath76 and research institute for particle and nuclear physics , budapest , hungary @xmath77 now at university of liverpool , dept of physics , liverpool l69 3bx , u.k . @xmath78 now at dept . physics , university of illinois at urbana - champaign , u.s.a . @xmath79 and manchester university @xmath80 now at university of kansas , dept of physics and astronomy , lawrence , ks 66045 , u.s.a . @xmath81 now at university of toronto , dept of physics , toronto , canada @xmath50 current address bergische universitt , wuppertal , germany @xmath82 now at university of mining and metallurgy , cracow , poland @xmath48 now at university of california , san diego , u.s.a . @xmath83 now at the university of melbourne , victoria , australia @xmath84 now at iphe universit de lausanne , ch-1015 lausanne , switzerland @xmath85 now at iekp universitt karlsruhe , germany @xmath86 now at university of antwerpen , physics department , b-2610 antwerpen , belgium ; supported by interuniversity attraction poles programme belgian science policy @xmath87 and high energy accelerator research organisation ( kek ) , tsukuba , ibaraki , japan @xmath88 now at university of pennsylvania , philadelphia , pennsylvania , usa @xmath89 now at triumf , vancouver , canada @xmath90 now at desy zeuthen @xmath91 now at cern @xmath92 now at desy @xmath93 deceased </s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Check Cashing Consumer Protection Act of 1994''. SEC. 2. UNIFORM STATE LICENSING AND REGULATION OF CHECK CASHING SERVICES. (a) Uniform Laws and Enforcement.--For purposes of protecting the consumers of check cashing services from fraud and abuse, it is the sense of the Congress that the several States should-- (1) establish uniform laws for licensing and regulating businesses which-- (A) provide check cashing services, transmit money, or issue or redeem money orders, travelers' checks, and other similar instruments; and (B) are not depository institutions (as defined in section 19(b)(1)(A) of the Federal Reserve Act); and (2) provide sufficient resources to the appropriate State agency to enforce such laws and regulations prescribed pursuant to such laws. (b) Model Statute.--It is the sense of the Congress that the several States should develop, through the auspices of the National Conference of Commissioners on Uniform State Laws, the American Law Institute, or such other forum as the States may determine to be appropriate, a model statute to carry out the goals described in subsection (a) which would include the following: (1) Licensing requirements.--A requirement that any issuer, redeemer, or cashier of travelers' checks, checks, money orders, or similar instruments, and any transmitter of money, other than a depository institution (as defined in section 19(b)(1)(A) of the Federal Reserve Act), be licensed and regulated by an appropriate State agency in order to engage in any such activity within the State. (2) Licensing standards.--A requirement that-- (A) in order for any issuer, redeemer, or cashier of travelers' checks, checks, money orders, or similar instruments, and any transmitter of money to be licensed in the State, the appropriate State agency shall review and approve-- (i) the business record and the capital adequacy of the business seeking the license; and (ii) the competence, experience, integrity, and financial ability of any individual who-- (I) is a director, officer, or supervisory employee of such business; or (II) owns or controls such business; (B) as a condition for the issuance and continued validity of the license the business may not impose, charge, or collect any fee for cashing or redeeming any travelers' check, check, money order or similar instrument in excess of the amount which is equal to the greater of-- (i) an amount equal to 1.5 percent of the face amount of such check or money order (not to exceed $8); or (ii) 50 cents; and (C) any record, on the part of any business seeking the license or any person referred to in subparagraph (A)(ii), of-- (i) any criminal activity; (ii) any fraud or other act of personal dishonesty; (iii) any act, omission, or practice which constitutes a breach of a fiduciary duty; or (iv) any suspension or removal, by any agency or department of the United States or any State, from participation in the conduct of any federally or State licensed or regulated business, be grounds for the denial of any such license by the appropriate State agency. (3) Procedures to ensure compliance with federal cash transaction reporting requirements.--A civil or criminal penalty for operating any business referred to in paragraph (1) without establishing and complying with appropriate procedures to ensure compliance with subchapter II of chapter 53 of title 31, United States Code (relating to records and reports on monetary instruments transactions). (4) Criminal penalties for operation of business without a license.--A criminal penalty for operating, within the State, any business referred to in paragraph (1) after the effective date of the model statute without a license issued by the State. (c) Study Required.--The Secretary of the Treasury shall conduct a study of-- (1) the progress made by the several States in developing and enacting a model statute which-- (A) meets the requirements of subsection (b); and (B) furthers the goals of-- (i) preventing money laundering by businesses which are required to be licensed under any such statute; and (ii) protecting the payment system, including the receipt, payment, collection, and clearing of checks, from fraud and abuse by such businesses; and (2) the adequacy of-- (A) the activity of the several States in enforcing the requirements of such statute; and (B) the resources made available to the appropriate State agencies for such enforcement activity. (d) Report Required.--Before the end of the 3-year period beginning on the date of the enactment of this Act and by the end of each 1-year period beginning after the end of such period, the Secretary of the Treasury shall submit a report to the Congress containing the findings and recommendations of the Secretary in connection with the study under subsection (c), together with such recommendations for legislative and administrative action as the Secretary may determine to be appropriate, including any recommendation pursuant to subsection (e). (e) Recommendations for Incentives or Sanctions in Cases of Inadequate Regulation and Enforcement by States.--If the Secretary of the Treasury determines that any State has failed-- (1) to enact a statute which meets the requirements described in subsection (b); (2) to undertake adequate activity to enforce such statute; or (3) to make adequate resources available to the appropriate State agency for such enforcement activity, the report submitted pursuant to subsection (d) shall contain recommendations for legislation establishing incentives which may be provided or sanctions which may be imposed to remedy such failure.

Check Cashing Consumer Protection Act of 1994 - Expresses the sense of the Congress that States should: (1) establish uniform laws for licensing and regulating businesses which are not depository institutions and which provide check cashing services, transmit money, or issue or redeem money orders, travelers' checks, and similar instruments; and (2) provide sufficient resources to the appropriate State agency to enforce such laws and regulations. Asks the States to develop a model statute which includes, with respect to such businesses: (1) licensing requirements and standards; (2) procedures to ensure compliance with Federal cash transaction reporting requirements; and (3) criminal penalties for operation of such a business without a license. Directs the Secretary of the Treasury to study and report to the Congress on the States' progress in developing and enacting a model statute meeting appropriate requirements and recommendations for appropriate legislative and administrative action, including possible incentives or sanctions for States failing to enact an appropriate model statute or failing to enforce such statute.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Check Cashing Consumer Protection Act of 1994''. SEC. 2. UNIFORM STATE LICENSING AND REGULATION OF CHECK CASHING SERVICES. (a) Uniform Laws and Enforcement.--For purposes of protecting the consumers of check cashing services from fraud and abuse, it is the sense of the Congress that the several States should-- (1) establish uniform laws for licensing and regulating businesses which-- (A) provide check cashing services, transmit money, or issue or redeem money orders, travelers' checks, and other similar instruments; and (B) are not depository institutions (as defined in section 19(b)(1)(A) of the Federal Reserve Act); and (2) provide sufficient resources to the appropriate State agency to enforce such laws and regulations prescribed pursuant to such laws. (b) Model Statute.--It is the sense of the Congress that the several States should develop, through the auspices of the National Conference of Commissioners on Uniform State Laws, the American Law Institute, or such other forum as the States may determine to be appropriate, a model statute to carry out the goals described in subsection (a) which would include the following: (1) Licensing requirements.--A requirement that any issuer, redeemer, or cashier of travelers' checks, checks, money orders, or similar instruments, and any transmitter of money, other than a depository institution (as defined in section 19(b)(1)(A) of the Federal Reserve Act), be licensed and regulated by an appropriate State agency in order to engage in any such activity within the State. (2) Licensing standards.--A requirement that-- (A) in order for any issuer, redeemer, or cashier of travelers' checks, checks, money orders, or similar instruments, and any transmitter of money to be licensed in the State, the appropriate State agency shall review and approve-- (i) the business record and the capital adequacy of the business seeking the license; and (ii) the competence, experience, integrity, and financial ability of any individual who-- (I) is a director, officer, or supervisory employee of such business; or (II) owns or controls such business; (B) as a condition for the issuance and continued validity of the license the business may not impose, charge, or collect any fee for cashing or redeeming any travelers' check, check, money order or similar instrument in excess of the amount which is equal to the greater of-- (i) an amount equal to 1.5 percent of the face amount of such check or money order (not to exceed $8); or (ii) 50 cents; and (C) any record, on the part of any business seeking the license or any person referred to in subparagraph (A)(ii), of-- (i) any criminal activity; (ii) any fraud or other act of personal dishonesty; (iii) any act, omission, or practice which constitutes a breach of a fiduciary duty; or (iv) any suspension or removal, by any agency or department of the United States or any State, from participation in the conduct of any federally or State licensed or regulated business, be grounds for the denial of any such license by the appropriate State agency. (3) Procedures to ensure compliance with federal cash transaction reporting requirements.--A civil or criminal penalty for operating any business referred to in paragraph (1) without establishing and complying with appropriate procedures to ensure compliance with subchapter II of chapter 53 of title 31, United States Code (relating to records and reports on monetary instruments transactions). (4) Criminal penalties for operation of business without a license.--A criminal penalty for operating, within the State, any business referred to in paragraph (1) after the effective date of the model statute without a license issued by the State. (c) Study Required.--The Secretary of the Treasury shall conduct a study of-- (1) the progress made by the several States in developing and enacting a model statute which-- (A) meets the requirements of subsection (b); and (B) furthers the goals of-- (i) preventing money laundering by businesses which are required to be licensed under any such statute; and (ii) protecting the payment system, including the receipt, payment, collection, and clearing of checks, from fraud and abuse by such businesses; and (2) the adequacy of-- (A) the activity of the several States in enforcing the requirements of such statute; and (B) the resources made available to the appropriate State agencies for such enforcement activity. (d) Report Required.--Before the end of the 3-year period beginning on the date of the enactment of this Act and by the end of each 1-year period beginning after the end of such period, the Secretary of the Treasury shall submit a report to the Congress containing the findings and recommendations of the Secretary in connection with the study under subsection (c), together with such recommendations for legislative and administrative action as the Secretary may determine to be appropriate, including any recommendation pursuant to subsection (e). (e) Recommendations for Incentives or Sanctions in Cases of Inadequate Regulation and Enforcement by States.--If the Secretary of the Treasury determines that any State has failed-- (1) to enact a statute which meets the requirements described in subsection (b); (2) to undertake adequate activity to enforce such statute; or (3) to make adequate resources available to the appropriate State agency for such enforcement activity, the report submitted pursuant to subsection (d) shall contain recommendations for legislation establishing incentives which may be provided or sanctions which may be imposed to remedy such failure.[/INST]Check Cashing Consumer Protection Act of 1994 - Expresses the sense of the Congress that States should: (1) establish uniform laws for licensing and regulating businesses which are not depository institutions and which provide check cashing services, transmit money, or issue or redeem money orders, travelers' checks, and similar instruments; and (2) provide sufficient resources to the appropriate State agency to enforce such laws and regulations. Asks the States to develop a model statute which includes, with respect to such businesses: (1) licensing requirements and standards; (2) procedures to ensure compliance with Federal cash transaction reporting requirements; and (3) criminal penalties for operation of such a business without a license. Directs the Secretary of the Treasury to study and report to the Congress on the States' progress in developing and enacting a model statute meeting appropriate requirements and recommendations for appropriate legislative and administrative action, including possible incentives or sanctions for States failing to enact an appropriate model statute or failing to enforce such statute.</s>

traumatic injuries related to muscles and tendons of the shoulder girdle are common among athletes ; however , injury to the latissimus dorsi ( ld ) muscle is quite rare . in this case report , we will present acute traumatic tear of the ld muscle close to the myotendinous junction in a female track and field athlete ( 100 m hurdler ) . ld tears related to a sports activity have been reported in rock climbers , rodeo steer wrestlers , golfers , skiers , body builders , baseball players , tennis players , gymnasts , volleyball and basketball players ; but , extensive literature search has not revealed any track athletes . this is the first ld tear ever reported in a track athlete . unlike other cases , ultrasound ( us ) was used to depict the ld tear in detail and the tear was managed non - surgically in a conservative manner . the patient was a 27-year old female elite track and field athlete ( 100 m hurdler ) who has been competing for the last 10 years in many games , including the olympic games . she felt contraction around the right axillary region during a weight - training workout ( snatch ) and a week later , she felt sudden tearing pain after a vigorous start from the crouched position in the blocks . pain , ecchymosis and swelling at the axilla were the most apparent complaints when she visited a physician 4 days later . however her symptoms continued and she was referred to sports medicine department of a tertiary medical center with the presumptive diagnosis of axillary lymphadenopathy 6 weeks after the injury . a soft tissue swelling ( 35 cm ) with a gap in the mid portion and ecchymosis along the right posterolateral axillary region was noted on physical examination ( figure 1 ) . us revealed a complete ( 17 mm long ) tear of ld muscle close to the myotendinous junction on the right axillary region . ld muscle is a large fan - shaped muscle that covers the whole posterolateral aspect of the trunk . the fan - shaped edge originates from multiple sites such as the thoracic , lumbar and sacral spinous processes and the iliac crest then tapers superiorly to insert as a single long tendon to the intertubercular groove of the humerus . therefore , injuries often occur close to the insertion site ( figure 3 ) . in our case , a mild grade i muscle sprain to ld , which occurred during snatch exercises , most likely predisposed the muscle to consequent tearing injury . the actual tear ( grade ii ) occurred later when the patient was trying to generate power to run from the crouched position in the block by pushing her trunk forcibly forward while arms were extended , adducted and fixed on the ground . similar mechanisms were described for slam - dunking in basketball and vaulting in gymnastics . on the basis of patient preference , a conservative approach was preferred rather than surgery ; because competitions were close and requiring immediate treatment plan . presence of an intramuscular tear in an auxiliary muscle , not actively and dominantly involved in running , increased the likelihood of a successful conservative treatment . this was a late admittance case in which 6 weeks had already passed from the time of initial injury ; therefore classic physical treatment modalities [ protection , rest , ice , compression and elevation ( price ) ] were not closely followed . three - plane shoulder range of motion ( rom ) exercises were initiated ( 10 - 15 times 2 sets per day ) . within a week , complaints subsided , rom was full and movements were pain free . the patient resumed full athletic activity after two weeks of treatment , which made 8 weeks in total after the initial injury . the patient did not have any complaint in the follow - up exam 6 weeks later . latissimus dorsi muscle is one of the largest and strongest muscles of the back , having the main function of adduction , internal rotation and extension of the shoulder . the muscle is used to pull the trunk up or to lift or to pull an object forcefully towards the body and it is these exercises that render the muscle prone to traumatic injuries combined with overtraining , incompetent technique and inadequate rehabilitation . ld is used widely as a free flap for reconstructive surgery and a mild decrease ( a decrease of approximately 15 - 25% ) in strength is noted if harvested in the normal population . most probably , injuries to ld muscle are either misdiagnosed or neglected due to lack of serious functional disturbance and problems . but in elite athletes of competitive sports , such mild decreases of strength may become important . the main difference of our case from others is that this is an intramuscular tear close to the myotendinious junction in a field / track athlete . myotendinous junction involvement has been reported by parks et al . in a tennis player . tears involving the muscle belly are quite rare , reported in a series of traumatic injuries related to baseball and as a complication of anterior spinal surgery . intramuscular tears tend to respond well to conservative treatment whereas surgery is often reserved for tears involving the tendon , for complete tears and avulsions in elite athletes ; however , case series suggest that conservative treatment may also be a successful option in this setting . whether ld muscle is actively involved or not , as in pitchers , also affects the recovery and indications for surgery . ld is often an auxiliary muscle working synergistically with teres major , posterior muscles of the deltoid and long head of triceps brachii . spinner et al . reported an ld and teres major muscle tendon tear in a 38-year old golf player that eventually resumed full activity in one month with conservative treatment . butterwick reported a steer wrestler who resumed to competition successfully after two weeks of conservative treatment involving exercises and immobilization . in two separate case series consisting of 10 patients with teres major and latissimus dorsi injuries , including elite baseball pitchers , successful recoveries were reported with a conservative treatment of approximately 2 to 3 months . henry and scerpella et al . reported an acute traumatic avulsion tear of ld muscle tendon in a water skier who returned to sports activities within 6 months after surgery . return to physical activity tends to take longer time after surgery ( 4 - 6 months ) in comparison to the conservative treatment ( 1 - 3 months ) . outcomes of surgical and nonsurgical management are both good . surgical treatment may be opted in patients when full recovery of muscle function is intended and if the patient is willing to devote time to surgery and rehabilitation away from activities . in our case , the patient opted for conservative treatment including anti - inflammatory , analgesic management and physical therapy . most ld tears present a burning sensation and axillary pain along the posteromedial region of the arm , lasting for days . generally , trauma and a shearing sensation are present and injury mechanism has sudden and forceful resisted arm adduction . hurdling technique in athletics requires a strong pull down of contralateral arm of leading leg . starting from the block , a strong - arm action provides inertia for an effective forward rush and ld muscle plays an important role in both actions . anderson et al . have analyzed 5 cases with us , between the years 1998 - 2002 , which were perceived as sarcoma or as a lymphadenopathy as in our case . magnetic resonance imaging is widely used to diagnose ld rupture , has a larger field of view ( fov ) , can better differentiate the teres major and ld tendons from each other , may better depict avulsion injuries with large bone fragments and may also rule out bone edema , tumors of the humerus or scapula ( osteosarcoma or osteoid osteoma ) or additional injuries on the shoulder girdle . us is a useful diagnostic tool in the imaging of soft tissue anatomy , especially for tears and hematomas and it allows dynamic imaging while it is highly operator - dependent with a relatively small fov . ld tears may occasionally be seen in track / field athletes and may go unrecognized . conservative treatment is quite successful especially if ld maintains auxiliary function and if the tear is intramuscular .

soft tissue injuries constitute 30 - 50% of all sports related injuries ; however , injury to the latissimus dorsi muscle is quite rare with only a few cases reported in the literature . herein , we describe an acute traumatic tear of the latissimus dorsi muscle in an elite track athlete , which has not been reported in the track and field sports before . the injury was caused by forceful resisted arm adduction that took place at hurdling and starting from the block . a pseudotumor appearance in the axillary region was misdiagnosed as a mass . the diagnosis was made by ultrasound alone and the patient was managed conservatively .

<s>[INST]traumatic injuries related to muscles and tendons of the shoulder girdle are common among athletes ; however , injury to the latissimus dorsi ( ld ) muscle is quite rare . in this case report , we will present acute traumatic tear of the ld muscle close to the myotendinous junction in a female track and field athlete ( 100 m hurdler ) . ld tears related to a sports activity have been reported in rock climbers , rodeo steer wrestlers , golfers , skiers , body builders , baseball players , tennis players , gymnasts , volleyball and basketball players ; but , extensive literature search has not revealed any track athletes . this is the first ld tear ever reported in a track athlete . unlike other cases , ultrasound ( us ) was used to depict the ld tear in detail and the tear was managed non - surgically in a conservative manner . the patient was a 27-year old female elite track and field athlete ( 100 m hurdler ) who has been competing for the last 10 years in many games , including the olympic games . she felt contraction around the right axillary region during a weight - training workout ( snatch ) and a week later , she felt sudden tearing pain after a vigorous start from the crouched position in the blocks . pain , ecchymosis and swelling at the axilla were the most apparent complaints when she visited a physician 4 days later . however her symptoms continued and she was referred to sports medicine department of a tertiary medical center with the presumptive diagnosis of axillary lymphadenopathy 6 weeks after the injury . a soft tissue swelling ( 35 cm ) with a gap in the mid portion and ecchymosis along the right posterolateral axillary region was noted on physical examination ( figure 1 ) . us revealed a complete ( 17 mm long ) tear of ld muscle close to the myotendinous junction on the right axillary region . ld muscle is a large fan - shaped muscle that covers the whole posterolateral aspect of the trunk . the fan - shaped edge originates from multiple sites such as the thoracic , lumbar and sacral spinous processes and the iliac crest then tapers superiorly to insert as a single long tendon to the intertubercular groove of the humerus . therefore , injuries often occur close to the insertion site ( figure 3 ) . in our case , a mild grade i muscle sprain to ld , which occurred during snatch exercises , most likely predisposed the muscle to consequent tearing injury . the actual tear ( grade ii ) occurred later when the patient was trying to generate power to run from the crouched position in the block by pushing her trunk forcibly forward while arms were extended , adducted and fixed on the ground . similar mechanisms were described for slam - dunking in basketball and vaulting in gymnastics . on the basis of patient preference , a conservative approach was preferred rather than surgery ; because competitions were close and requiring immediate treatment plan . presence of an intramuscular tear in an auxiliary muscle , not actively and dominantly involved in running , increased the likelihood of a successful conservative treatment . this was a late admittance case in which 6 weeks had already passed from the time of initial injury ; therefore classic physical treatment modalities [ protection , rest , ice , compression and elevation ( price ) ] were not closely followed . three - plane shoulder range of motion ( rom ) exercises were initiated ( 10 - 15 times 2 sets per day ) . within a week , complaints subsided , rom was full and movements were pain free . the patient resumed full athletic activity after two weeks of treatment , which made 8 weeks in total after the initial injury . the patient did not have any complaint in the follow - up exam 6 weeks later . latissimus dorsi muscle is one of the largest and strongest muscles of the back , having the main function of adduction , internal rotation and extension of the shoulder . the muscle is used to pull the trunk up or to lift or to pull an object forcefully towards the body and it is these exercises that render the muscle prone to traumatic injuries combined with overtraining , incompetent technique and inadequate rehabilitation . ld is used widely as a free flap for reconstructive surgery and a mild decrease ( a decrease of approximately 15 - 25% ) in strength is noted if harvested in the normal population . most probably , injuries to ld muscle are either misdiagnosed or neglected due to lack of serious functional disturbance and problems . but in elite athletes of competitive sports , such mild decreases of strength may become important . the main difference of our case from others is that this is an intramuscular tear close to the myotendinious junction in a field / track athlete . myotendinous junction involvement has been reported by parks et al . in a tennis player . tears involving the muscle belly are quite rare , reported in a series of traumatic injuries related to baseball and as a complication of anterior spinal surgery . intramuscular tears tend to respond well to conservative treatment whereas surgery is often reserved for tears involving the tendon , for complete tears and avulsions in elite athletes ; however , case series suggest that conservative treatment may also be a successful option in this setting . whether ld muscle is actively involved or not , as in pitchers , also affects the recovery and indications for surgery . ld is often an auxiliary muscle working synergistically with teres major , posterior muscles of the deltoid and long head of triceps brachii . spinner et al . reported an ld and teres major muscle tendon tear in a 38-year old golf player that eventually resumed full activity in one month with conservative treatment . butterwick reported a steer wrestler who resumed to competition successfully after two weeks of conservative treatment involving exercises and immobilization . in two separate case series consisting of 10 patients with teres major and latissimus dorsi injuries , including elite baseball pitchers , successful recoveries were reported with a conservative treatment of approximately 2 to 3 months . henry and scerpella et al . reported an acute traumatic avulsion tear of ld muscle tendon in a water skier who returned to sports activities within 6 months after surgery . return to physical activity tends to take longer time after surgery ( 4 - 6 months ) in comparison to the conservative treatment ( 1 - 3 months ) . outcomes of surgical and nonsurgical management are both good . surgical treatment may be opted in patients when full recovery of muscle function is intended and if the patient is willing to devote time to surgery and rehabilitation away from activities . in our case , the patient opted for conservative treatment including anti - inflammatory , analgesic management and physical therapy . most ld tears present a burning sensation and axillary pain along the posteromedial region of the arm , lasting for days . generally , trauma and a shearing sensation are present and injury mechanism has sudden and forceful resisted arm adduction . hurdling technique in athletics requires a strong pull down of contralateral arm of leading leg . starting from the block , a strong - arm action provides inertia for an effective forward rush and ld muscle plays an important role in both actions . anderson et al . have analyzed 5 cases with us , between the years 1998 - 2002 , which were perceived as sarcoma or as a lymphadenopathy as in our case . magnetic resonance imaging is widely used to diagnose ld rupture , has a larger field of view ( fov ) , can better differentiate the teres major and ld tendons from each other , may better depict avulsion injuries with large bone fragments and may also rule out bone edema , tumors of the humerus or scapula ( osteosarcoma or osteoid osteoma ) or additional injuries on the shoulder girdle . us is a useful diagnostic tool in the imaging of soft tissue anatomy , especially for tears and hematomas and it allows dynamic imaging while it is highly operator - dependent with a relatively small fov . ld tears may occasionally be seen in track / field athletes and may go unrecognized . conservative treatment is quite successful especially if ld maintains auxiliary function and if the tear is intramuscular .[/INST]soft tissue injuries constitute 30 - 50% of all sports related injuries ; however , injury to the latissimus dorsi muscle is quite rare with only a few cases reported in the literature . herein , we describe an acute traumatic tear of the latissimus dorsi muscle in an elite track athlete , which has not been reported in the track and field sports before . the injury was caused by forceful resisted arm adduction that took place at hurdling and starting from the block . a pseudotumor appearance in the axillary region was misdiagnosed as a mass . the diagnosis was made by ultrasound alone and the patient was managed conservatively .</s>

light sterile neutrinos were invoked to explain the results of the lsnd experiment which reported oscillation events in the @xmath8 mode corresponding to a mass squared difference @xmath6 ev@xmath9 @xcite . adding one sterile neutrino to the standard 3 generation framework gives rise to two possible mass spectra the 2 + 2 in which two pairs of mass states are separated by a difference @xmath6 ev@xmath9 and 3 + 1 in which a single predominantly sterile state differs by @xmath6 ev@xmath9 from the three active states @xcite . subsequently the 2 + 2 schemes were found to be incompatible with the solar and atmospheric neutrino data @xcite . the miniboone experiment was designed to test this and its antineutrino data confirmed the lsnd anomaly @xcite . both 3 + 1 and 3 + 2 sterile neutrino schemes have been considered to explain these results @xcite . such global fits aim to explain the non - observance of ev@xmath9 oscillations in the disappearance channel in other short baseline experiments as well as the reported evidence in lsnd / miniboone experiments . the relevant probabilities for 3 + 1 case is governed by a single mass squared difference and hence is independent of the cp phase . in the 3 + 2 scheme , dependence on cp phase comes into play and one gets a slightly better fit . other evidences in support of sterile neutrinos include the reactor and the ga anomaly . the first one refers to the deficit in the measured electron antineutrino flux in several experiments when the theoretical predictions of reactor neutrino fluxes were reevaluated @xcite . the second one implies shortfall of electron neutrinos observed in the solar neutrino detectors gallex and sage using radioactive sources @xcite . both these can be explained by adding light sub - ev sterile neutrinos in the three generation framework . there has also been some hint in favour of sterile neutrinos from cosmological observations of a `` dark radiation '' which is weakly interacting and relativistic . attributing this to sterile neutrinos one gets the bound on the number of neutrinos as @xmath10 at 68% c.l @xcite . the plank satellite experiment which has very recently declared its first results @xcite , on the other hand , gives @xmath11 at 68% c.l . which allows for an extra sterile neutrino at 95% c.l . , although its mixing with active species can be very tightly constrained @xcite within the framework of standard cosmology . thus the sterile neutrinos continue to be intriguing and many new experiments are planned proposed to test this @xcite . theoretically , sterile neutrinos are naturally included in type - i seesaw model @xcite . but their mass scale is usually very high to account for the small mass of the neutrinos . light sub - ev sterile neutrinos as suggested by the data can arise in many models @xcite . irrespective of the mechanism for generation of neutrino masses the low energy majorana mass matrix in presence of an extra sterile neutrino will be of dimension @xmath12 with ten independent entries and is given as , @xmath13 where , @xmath14 and @xmath15 denotes the leptonic mixing matrix in a basis where the charged lepton mass matrix is diagonal . one of the important aspects in the study of neutrino physics is to explore the structure of the neutrino mass matrices . at the fundamental level these are governed by yukawa couplings which are essentially free parameters in most models . these motivated the study of texture zeros which means one or more elements are relatively small compared to the others . texture zeros in the low energy mass matrices in the context of three generations have been extensively explored both in the quark and lepton sector @xcite , @xcite . such studies help in understanding the underlying parameter space and the nature of the mass spectrum involved and often predict correlations between various parameters which can be experimentally tested . for three generation scenario it is well known that the number of maximum texture zeros in low energy mass matrix is two @xcite . in the context of the 4-neutrino case however more than two zeros can be allowed @xcite . two zero textures of sterile neutrinos have been studied recently in @xcite and three zero cases have been considered in @xcite . in this paper we concentrate on the textures where one of the mass matrix elements is vanishing . for the @xmath12 symmetric mass matrix it gives total 10 different cases which needs to be investigated . we study the implications of one zero textures and the possible correlations between the parameters . we also compare our results with the 1 zero textures for three active neutrinos @xcite . the plan of the paper goes as follows . in section ii we discuss the possible mass spectra and the mixing matrix in the 3 + 1 scenario . in the next section we present our study regarding the implications of one vanishing entry in the low energy neutrino mass matrix . we conclude in section iv . there are two ways in which one can add a predominantly sterile state separated by @xmath6 ev@xmath9 from the standard 3 neutrino mass states . in the first case the additional neutrino can be of higher mass than the other three while in the second case the the fourth neutrino is the lightest state . the later turns out to be incompatible with cosmology since in this case three active neutrinos , each with mass @xmath6 ev results in an enhanced cosmological energy density . thus it suffices to consider only the first case which admits two possibilities displayed in fig . 1 . [ fig1 ] * snh : in this @xmath16 corresponding to a normal hierarchy ( nh ) among the active neutrinos which implies , + @xmath17 * sih : this corresponds to @xmath18 implying an inverted ordering among the active neutrinos with masses expressed as , + @xmath19 here , @xmath20 . we define the ratio of the mass squared differences @xmath21 and @xmath22 as @xmath23 @xmath24 in the extreme cases and using @xmath25 , these masses can be written in terms of @xmath21 and @xmath22 as + snh : |m_4| |m_3| |m_2| |m_1| [ xnh ] sih : |m_4| |m_2| |m_1| |m_3| [ xih ] sqd : |m_4||m_1||m_2||m_3|m_0 . [ qd ] the first two cases correspond to complete hierarchy among the active neutrinos while the last one is the quasi - degenerate ( qd ) regime where the three active neutrinos have approximately equal masses . .@xmath26 ranges of neutrino oscillation parameters @xcite . the current constraints on sterile neutrino parameters are from @xcite , @xcite , where @xmath27 or @xmath28 . also given are the @xmath29 ranges of the mass ratios @xmath30 and @xmath21 . [ cols="<,^,^,^",options="header " , ] in the 3 + 1 scenario , the neutrino mixing matrix , @xmath15 in the flavor basis will be a @xmath31 unitary matrix . in general a n @xmath32 n unitary mixing matrix contains @xmath33 mixing angles and @xmath34 dirac type cp violating phases . it will also have ( n-1 ) number of additional majorana phases if neutrinos are majorana particles . so in our case v can be parametrized in terms of sixteen parameters . in addition to the three mixing angles between the active flavors , ( @xmath35 , @xmath36 , @xmath37 ) we now have three more mixing angles from sterile and active mixing , ( @xmath38 , @xmath39 , @xmath40 ) . there are six cp violating phases , three dirac ( @xmath41 , @xmath42 , @xmath43 ) and three additional majorana phases as ( @xmath44 , @xmath45 , @xmath46 ) as neutrinos here are considered to be majorana particles . then , there are four masses of neutrino @xmath47 , @xmath48 , @xmath49 corresponding to three active states and @xmath50 which is predominantly the mass of heavy sterile neutrino . the mixing matrix @xmath15 can be expressed as @xmath51 @xcite where @xmath52 where @xmath53 denotes rotation matrices in the _ ij _ generation space and is expressed as , @xmath54=@xmath55 , @xmath56=@xmath57 + here we use the abbreviations @xmath58 and @xmath59 . the phase matrix is diagonal and is expressed as , @xmath60 . the best - fit values and the 3@xmath61 ranges of the oscillation parameters in the 3 + 1 scenario are given in table i where in addition to the masses and mixing angles we also present the mass ratios @xmath22 and @xmath21 which would be useful in our analysis . note that the constraints on the three - neutrino parameters may change slightly once a full four - neutrino fit combining all global data is done . however since the sterile mixing angles are small the change is not expected to be significant . therefore in absence of a full four - neutrino global fit we use three - neutrino parameter values as obtained from three generation analyses @xcite . [ sigmam ] + figure 2 : plots of sum of light neutrino masses ( @xmath62 ) vs the lowest mass in the 3 + 1 scenario . also shown are the the cosmological upper bound on neutrino mass from the analysis of cmb data plus matter power spectrum information ( sdss ) and a prior on @xmath63(hst ) and from the analysis of cmb data only from reference @xcite for 3 + 1 scheme . in fig . 2 we have plotted the sum of neutrino masses against the lowest neutrino mass for both nh and ih . the band corresponds to variation of the mass squared differences in their current 3@xmath61 range . we also show the cosmological upper bound on neutrino masses in 3 + 1 scenario from @xcite . the combined analysis of cmb + sdss + hst seems to rule out the mass spectrum of 3 + 1 scenario in the framework of standard cosmology . however , if only cmb data is taken then region for the lowest mass @xmath64 ev gets allowed for both the hierarchies . note that the analysis in @xcite does not incorporate the planck results @xcite which can constrain the sum of masses further . in our analysis we have varied the lowest mass up to 0.5 ev . in this section we study the implication of the condition of vanishing @xmath0 for the 3 + 1 scenario , where @xmath65 . since @xmath0 is complex the above condition implies both real and imaginary parts are zero . therefore to study the 1-zero textures we consider @xmath66 . in our analysis we have varied the three dirac phases in the range 0 to @xmath67 and the three majorana phases from 0 to @xmath68 . the matrix element @xmath69 in the 3 + 1 scenario is given as , m_ee = m_1 c_14 ^ 2 c_13 ^ 2c_12 ^ 2+m_2 s_12 ^ 2c_14 ^ 2c_13 ^ 2e^2i+m_3 s_13 ^ 2 c_14 ^ 2 e^2i+m_4s_14 ^ 2 e^2i . [ mee ] this is of the form [ meenh ] m_ee= c_14 ^ 2 ( m_ee)_3+e^2is_14 ^ 2 m_4 , where @xmath70 corresponds to the matrix element in the 3 active neutrino case . the contribution of the sterile neutrino to the element @xmath69 depends on the mass @xmath50 and the active - sterile mixing angle @xmath38 . of all the mass matrix element @xmath69 has the simplest form because of the chosen parametrization and can be understood quite well . using approximation in eq . ( [ xnh ] ) for the case of extreme hierarchy one can write this for nh as , [ meenh ] m_ee c_14 ^ 2 ( m_ee)_3+e^2is_14 ^ 2 , where @xmath71 and @xmath22 is defined in eq . [ zeta ] . [ meefig ] + figure 3 : plot of @xmath72 versus the lowest mass . the panel ( a ) corresponds to the three generation case while panel ( b ) is for 3 + 1 case . in panel ( b ) all the mixing angles are varied in their 3@xmath61 range and the majorana cp violating phases are varied in their full range ( 0-@xmath68 ) . the panel ( c ) and ( d ) are for specific values of @xmath38 with all other parameters covering their full range . the modulus of @xmath69 is the effective mass that can be extracted from half life measurements in neutrinoless double beta decay . in fig . 3 we plot the effective mass as a function of the smallest mass by varying @xmath38 in its complete 3@xmath61 range from table i as well as for specific values of the mixing angle @xmath38 . the majorana phases are varied randomly in the range 0 to @xmath68 in all the plots . the first panel is for @xmath73 i.e the three generation case . it is seen that for present values of the oscillation parameters the cancellation condition is not satisfied for @xmath74 for nh . however , as one increases @xmath47 , complete cancellation can be achieved . for ih the complete cancellation is never possible . these results change when we include the sterile contribution as is evident from the panel ( b ) in fig . 3 which shows the effective mass for nh and ih by varying all the parameters in their full 3@xmath61 allowed range . the behaviour can be understood from the expressions of @xmath72 in various limiting cases . for nh , in the hierarchical limit of @xmath74 the major contributor will be the additional term due to the sterile neutrinos because of higher value of @xmath50 . complete cancellation is only possible for smaller values of @xmath38 so that this contribution is suppressed . the typical value of @xmath38 required for cancellation can be obtained by putting @xmath75 ( which would maximize the three neutrino contribution ) and @xmath76 , as ^2_14 10 ^ -3 , which lies outside the allowed range of @xmath38 given in table i. as we increase @xmath47 , @xmath70 increases and can be of the same order of magnitude of the sterile term . hence one can get cancellation regions . the cancellation is mainly controlled by the value of @xmath38 . for higher values of @xmath77 one needs a higher value of @xmath47 for cancellation to occur . this correlation between @xmath47 and @xmath38 is brought out by the panels ( c ) and ( d ) in fig . 3 . for ih case , in the limit of vanishing @xmath49 using approximation in eq . ( [ xih ] ) , @xmath69 in a 3 + 1 scenario can be written as |m_ee| |c_14 ^ 2 c_13 ^ 2 ( c_12 ^ 2+s_12 ^ 2 e^2i)+s_14 ^ 2 e^2i| . the maximum value of this is achieved for @xmath78 which is slightly lower than that of nh in this limit . the element vanishes in the limit @xmath79 0 ev when @xmath80 and @xmath76 provided [ meeih ] ^2_14 0.05 this is well within the allowed range . this behaviour is in stark contrast to that in the 3 neutrino case @xcite . there is no significant change in this behaviour as the smallest mass @xmath49 is increased since this contribution is suppressed by the @xmath81 term and the dominant contribution to @xmath70 comes from the first two terms in eq . ( [ mee ] ) . therefore in this case we do not observe any correlation between @xmath49 and @xmath77 . while moving towards the quasi - degenerate regime of @xmath82 we find that effective mass can still be zero . however , when the lightest mass approaches a larger value ~ 0.3 ev we need very large values of active sterile mixing angle @xmath38 , outside the allowed range , for cancellation . hence the effective mass can not vanish for such values of masses . also shown is the current limit on effective mass from combined kamland - zen and exo 200 results on the half - life of @xmath83 in @xmath84xe @xcite . when translated in terms of effective mass this corresponds to the bound @xmath85 ev including nuclear matrix element uncertainties . for the three generation case , the hierarchical neutrinos can not saturate this bound . but in the 3 + 1 scenario this bound can be reached even for very small values of @xmath49 for ih and for some parameter values it can even exceed the current limit . thus from the present limits on neutrinoless double beta decay searches a part of the parameter space for smaller values of @xmath49 can be disfavoured for ih . for nh , the kamland - zen + exo 200 combined bound is reached for @xmath86 ev and again some part of the parameter space can be disfavoured by this bound . the mass matrix element @xmath87 in the presence of extra sterile neutrino is given as m_e & = & c_14(e^i ( _ 14-_24 + 2 ) m_4s_14s_24+e^i(_13 + 2 ) m_3s_13(c_13c_24s_23-e^i ( _ 14-_13-_24 ) + & & s_13s_14s_24 ) + c_12c_13m_1(-c_23c_24s_12+c_12(-e^i _ 13c_24s_13s_23-e^i ( _ 14-_24)c_13s_14s_24 ) ) + & + & e^2i m_2c_13s_12 ( c_12c_23c_24+s_12(-e^i _ 13c_24s_13s_23-e^i ( _ 14-_24)c_13s_14s_24 ) ) ) . unlike @xmath69 here the expression is complicated and an analytic understanding is difficult from the full expression . the expression for @xmath88 in the limit of vanishing active sterile mixing angle @xmath39 becomes m_e = c_14(m_e ) _ 3 . since the active sterile mixing is small , in order to simplify these expressions we introduce a quantity @xmath890.2 and define these small angles to be of the form @xmath90 . thus a systematic expansion in terms of @xmath91 can be done . for sterile mixing angle [ chi1 ] _ 14 _ 14 _ 14 , + _ 24 _ 24 _ 24 , and the reactor mixing angle as [ chi2 ] _ 13 _ 13 _ 13 . here are parameters of @xmath7(1 ) and their @xmath26 range from the current constraint on the mixing angles is given by @xmath93 note that for the sterile mixing angle @xmath40 we do not adopt the above approximation because this angle can be large compared to other two sterile mixing angles and hence the small parameter approximation will not be valid . using the approximation in eqs . ( [ xnh ] ) , ( [ chi1 ] ) and ( [ chi2 ] ) we get the expression for @xmath94 for normal hierarchy as & + & ^2 e^i(_14-_24)(e^2i -e^2i s_12 ^ 2)_14_24}| . to see the order of magnitude of the different terms we choose vanishing majorana phases while dirac cp phases are taken as @xmath68 . the mass matrix element @xmath88 vanishes when [ mem ] s_12c_12c_23-(1-s_12 ^ 2)s_23_13 + ^2(-s_12 ^ 2)_14_24=0 . + the three generation limit is recovered for @xmath95 and in panel ( a ) of fig . 4 we show @xmath94 as a function of @xmath47 of this case , for nh . panel ( b ) ( red / light region ) of fig . 4 shows @xmath94 for the 3 + 1 case , with all parameters varied randomly within their @xmath26 range . the figures show that @xmath96 can be achieved over the whole range of the smallest mass for both 3 and 3 + 1 cases . however , we find that in the hierarchical limit cancellation is not achieved for large values of @xmath39 , since in that case the third term of eq . ( [ mem ] ) will be of the @xmath7 ( 10@xmath97 ) compared to the leading order term which is of the @xmath7 ( 10@xmath98 ) and hence there will be no cancellation of these terms . this can be seen from panel ( b ) ( green / dark region ) of fig . 4 for @xmath99 . in the qd limit the contribution from the active terms are large enough to cancel the sterile contribution and thus @xmath100 can be achieved . [ fig4 ] figure 4 : plots of @xmath94 as a function of the lowest mass @xmath47 for nh . panel ( a ) correspond to the three generation case while ( b ) ( red / light region ) is for 3 + 1 case and also for @xmath101 ( green / dark region ) . all the parameters are varied in their full 3@xmath61 allowed range , the cp violating dirac phases are varied from 0 to @xmath102 and the majorana phases are varied from 0 to @xmath68 unless otherwise stated . + + figure 5 : plots of @xmath94 vs @xmath49 for inverted hierarchy for ( a ) three generation case ( b ) 3 + 1 case with all parameters varied randomly in their full range . panel ( c ) , ( d ) and ( e ) are for specific values of @xmath103 and @xmath44 . the panel ( f ) shows the correlation between @xmath44 and @xmath103 when all other parameters are randomly varied . [ fig5 ] for ih using the approximation eq . ( [ xih ] ) for the hierarchical limit we get the expression [ memih ] |m_e | & & & - & e^i(_14-_24)^2 _ 14_24(c_12 ^ 2 -e^2i+e^2is_12 ^ 2)}| . to see the order of magnitude of the various terms we consider the case when majorana phases vanish and the dirac phases assume the value @xmath68 . then we get for vanishing @xmath87 , s_23_13-^2(1-)_14_24=0 . in panel ( a ) of fig . 5 we display the plot of @xmath94 with @xmath49 for the 3 generation scenario i.e for @xmath104 for ih . in panel ( b ) we consider the 3 + 1 case with all the parameters varying in their allowed range . note that in the small @xmath49 limit ( cf . 3.13 ) for @xmath105 the leading order term vanishes . for this case , for large active sterile mixing angle @xmath39 , the @xmath106 term becomes large @xmath7 ( 10@xmath97 ) and the cancellation with @xmath91 term is not be possible . when cp violating phase @xmath44 is non zero , the leading order term can cancel the @xmath106 term even for large values of @xmath103 . these features are reflected in panel ( c ) where we plot @xmath94 for @xmath101 and @xmath107 ( blue / dark region ) and by varying @xmath44 in its full range ( cyan / light region ) . as expected , for @xmath80 , cancellation is not achieved for smaller values of @xmath49 . thus the condition @xmath96 implies some correlation between @xmath49 and @xmath44 for ih . even if @xmath44 is varied in its full range , the absolute value of the matrix element @xmath94 can vanish only if the product @xmath108 is small , i.e. @xmath77 and @xmath103 are simultaneously small . this is because if they are large the @xmath106 term becomes of the @xmath7 ( 10@xmath97 ) and hence cancellation will not be possible . this is seen from panel ( d ) where for @xmath109 and @xmath101 the region where @xmath49 is small gets disallowed . taking cp violating phase @xmath110 makes the magnitude of leading order term ( @xmath111 ) quite large and smaller values of @xmath39 can not give cancellation even for large values of @xmath49 which can be seen from panel ( e ) of fig . 5 . for the occurrence of cancellation @xmath103 has to be @xmath112 0.01 for @xmath110 as can be seen from panel ( f ) where we have plotted the correlation between @xmath44 and @xmath103 for @xmath100 . the mass matrix element @xmath113 in the presence of an extra sterile neutrino is given by m_e&=&c_14c_24e^i(2 + _ 14)m_4s_14s_34+m_3c_14s_13e^i(2+_13)(-c_24s_13s_14s_34 e^i(_14-_13 ) + & + & c_13(c_23c_34-e^i_24s_23s_24s_34))+m_2s_12c_13c_14e^2i(c_12(-c_34s_23-c_23s_24s_34e^i_24 ) + & + & s_12(-c_13c_24s_14s_34e^i_14-e^i_13s_13(c_23c_34-e^i_24s_23s_24s_34 ) ) ) + & + & m_1c_12c_13c_14(-s_12(-c_34s_23-c_23s_24s_34e^i_24)+c_12(-c_13c_24s_14s_34e^i_14 -e^i_13s_13 + & & ( c_23c_34-e^i_24s_23s_24s_34 ) ) ) . the elements @xmath113 and @xmath87 are related by @xmath114 permutation symmetry @xmath115 , in such a way that @xmath116 for three active neutrino case the mixing angle @xmath37 in the partner textures linked by @xmath114 symmetry are related as @xmath117 . however , in the 3 + 1 case the relation of @xmath37 between two textures related by this symmetry is not simple . the active sterile mixing angles @xmath39 and @xmath40 are also different in the textures connected by @xmath114 symmetry and are related as @xcite @xmath118 @xmath119 @xmath120 @xmath121 due to these relations the behaviour of @xmath87 is different from that of @xmath113 unlike in three active neutrino case where the plots of these two elements were same except for @xmath37 which differed in octant for the two cases . + it is found that in the limit of small @xmath39 the two active sterile mixing angles @xmath122 from eq ( [ mutau1 ] ) . the same can be seen from eq ( [ mutau2 ] ) which gives @xmath123 for smaller values of the mixing angle @xmath40 . thus , for these cases the behaviour shown by @xmath39 in @xmath87 ( @xmath124 ) is same as shown by @xmath40 in @xmath113 ( @xmath125 ) . in the limit of vanishing active sterile mixing angle @xmath40 this element becomes m_e = c_14(m_e ) _ 3 . using the approximation in eq ( [ xnh ] ) for nh the above element can be expressed as , |m_e| & & |\{- s_12s_23c_12c_34e^2i+(c_23c_34e^i(2+_13)_13-c_23c_34s_12 ^ 2 + & & _ 13e^i(2+_13)+e^i(2+_14)s_34_14- e^i(2+_14)s_12 ^ 2s_34_14-c_12c_23 + & & e^i(2+_24)s_12s_34_24 ) -e^i(_13+_24)(e^2i - e^2is_12 ^ 2)s_23s_34_13_24 ^ 2}| . for the case of vanishing majorana phases and dirac phases having the value @xmath68 , this element can vanish when [ metau : fixedphase ] & -&c_12c_34s_12s_23-(1-s_12 ^ 2)s_23s_34 ^ 2_13_24+(-c_23c_34_13 + + & & c_23s_12(c_34s_12_13+c_12s_34_24)+s_12 ^ 2s_34_14-s_34_14 ) = 0 . for a vanishing active sterile mixing angle @xmath40 one recovers the 3 generation case . in this limit , from eq . ( [ metau : fixedphase ] ) one observes that the leading order term and the term with @xmath91 are of the same order @xmath126 ( 10@xmath98 ) while the @xmath106 term vanishes and hence cancellation is possible excepting for very low values of the lightest mass . we can see this in panel ( a ) of fig . 6 . in panel ( b ) ( red / light region ) all the parameters are varied randomly ( 3 + 1 case ) and cancellation is seen to be possible over the whole range of @xmath47 . figure 6 : plots of @xmath127 for normal hierarchy with lowest mass @xmath47 . the panel ( a ) corresponds to three generation case . in ( b ) ( red / light region ) all the parameters are varied in their full allowed range and the green / dark region is for @xmath128 with all the other parameters covering their full range . [ fig6 ] in panel ( b ) ( green / dark region ) we also plot the element @xmath127 for the upper limit of @xmath128 . in this case there is no cancellation for very low values of the smallest mass . this is because when @xmath129 is large , the @xmath91 term containing @xmath21 becomes large @xmath7 ( 1 ) and there will be no cancellation . + for inverted hierarchy the element @xmath113 using the approximation in eq ( [ xih ] ) becomes |m_e| & & ( c_12 ^ 2+e^2is_12 ^ 2)s_23s_34 ^ 2_13_24 + & - & ( c_23c_34_13e^i_13(c_12 ^ 2+e^2is_12 ^ 2)+e^i_14s_34_14(c_12 ^ 2+e^is_12 ^ 2 ) + & - & e^i(2+_14)s_34_14+c_12c_23s_12s_34_24e^i_24(e^2i-1))}| in the limit of vanishing majorana phases and dirac cp violating phases equal to @xmath68 this element becomes negligible when ( c_23c_34_13+s_34_14-s_34_14 ) + s_23s_34_13_24 ^ 2 = 0 . in panel ( a ) of fig . 7 the three generation case is reproduced by putting @xmath130 and in ( b ) all the parameters are varied in their allowed range ( 3 + 1 case ) . in both the figures we can see that cancellation is permissible over the whole range of @xmath49 considered . when the cp violating phase @xmath80 we see that the leading order term ( @xmath131 ) vanishes and as a result for large values of @xmath129 the cancellation is not possible because the term with coefficient @xmath91 becomes large ( @xmath7(10@xmath97 ) ) . + + figure 7 : plots of @xmath127 for inverted hierarchy with lowest mass @xmath49 . the panel ( a ) corresponds to three generation case . in ( b ) all the parameters are varied in their full allowed range ( 3 + 1 ) . the panel ( c ) , ( d ) is for specific value of @xmath40 and @xmath44 with all the other parameters covering their full range . the panel ( f ) shows correlation between @xmath44 and @xmath103 . [ fig7 ] for non zero values of the cp violating phase @xmath44 this leading order term is non zero and its contribution will be significant . so in this case high values of @xmath40 are also allowed because now the leading order and the term with coefficient @xmath91 will be of same magnitude . when we fix @xmath132 and @xmath133 the region where @xmath49 is small is disallowed ( panel ( c ) blue / dark region ) but when @xmath44 varies within its full range the disallowed regions become allowed ( panel ( c ) cyan / light region ) . when @xmath129 approaches its upper limit , the @xmath91 term having @xmath21 becomes very large and cancellation is not possible even for non zero values of @xmath44 which can be seen from panel ( d ) . however , when @xmath110 , very small values of @xmath129 can not give cancellation as the leading order term becomes large ( panel ( e ) ) . @xmath129 has to be @xmath112 0.01 for the term to vanish which can be seen from panel ( f ) where we plotted the correlation between @xmath44 and @xmath129 for @xmath134 . the ( 2,2 ) diagonal entry in neutrino mass matrix is given as m _ & = & e^2 i(_14 - _ 24 + ) c_14 ^ 2 m_4 s_24 ^ 2 + & + & e^2 i ( _ 13 + ) m_3(c_13 c_24 s_23 - e^i(_14 - _ 13 -_24 ) s_13 s_14 s_24)^2 + & + & m_1 \{-c_23 c_24 s_12 + c_12(-e^i _ 13 c_24 s_13 s_23 - e^i(_14 - _ 24 ) c_13 s_14 s_24)}^2 + & + & e^2 i m_2 \{c_12 c_23 c_24 + s_12(-e^i _ 13 c_24 s_13 s_23 - e^i(_14 - _ 24 ) c_13 s_14 s_24)}^2 this expression reduces to its three generation case if the mixing angle @xmath39 vanishes . also we can see from the expression that there is no dependence on the mixing angle @xmath40 . using the approximation in eqs . ( [ xnh ] ) this element can be simplified to the form |m_| & & |\ { c_12 ^ 2 c_23 ^ 2 e^2 i + e^i(_13 + 2 ) s_23 ^ 2 + & - & 2 c_12 c_23 e^i(_13 + 2 ) s_12 s_23 _ 13 + & + & ^2\{e^2i(_13 + ) s_12 ^ 2s_23 ^ 2 ^ 2_13+e^i(_14-_24)(e^i(2 + _ 14 -_24)_24 + & - & 2 e^2ic_12c_23s_12_14)_24}}| . for the case of majorana cp phases having the value 0 and the dirac phases having the value @xmath68 , this element vanishes when [ mmmphase ] & & s_23 ^ 2 + c_12 ^ 2 c_23 ^ 2 + c_12 s_12 2 _ 23 _ 13 + & + & ^2(s_12 ^ 2s_23 ^ 2_13 ^ 2-c_232_12_14_24+_24 ^ 2)=0 . + figure 8 : plots of vanishing @xmath124 for normal hierarchy for different values of @xmath39 when all other mixing angles are varied in their 3@xmath61 ranges , dirac cp phases are varied from 0 to @xmath102 and majorana phases from 0 to @xmath68 . [ fig8 ] we know that for the case of 3 generations , the elements in the @xmath135 block are quite large and can not vanish for normal hierarchy . in panel ( a ) of fig . 8 we can see that @xmath136 can not vanish in small @xmath47 region for @xmath95 which is indeed the 3 generation case . this is because the magnitude of the first two terms in eq . ( [ mmmphase ] ) is quite large in this case , @xmath126 ( 10@xmath97 ) and for cancellation to occur the term with coefficient @xmath106 has to be of the same order . this is not possible when @xmath103 is small . however when @xmath137 is varied in its full allowed range the contribution of the sterile part is enhanced and this can cancel the active part as can be seen from panel ( b ) . now to understand the dependence of @xmath138 with @xmath39 we note that if we increase @xmath103 from its lower bound then the two terms become of the same order . so there will be regions in the limit of small @xmath47 for which this element vanishes ( panel ( c ) ) . we see in panel ( d ) of fig . 8 that when @xmath39 acquires very large values , the magnitude of the @xmath106 ( @xmath139 ) term becomes large , thus leading to non cancellation of the terms with the leading order first two terms . hence , the region with very small @xmath47 is not allowed . using the approximation for inverted hierarchy the element @xmath124 becomes |m_| & & & + & ^2[2_12 c_23 e^i(_14 - _ 24)(1 - e^2 i ) _ 14 _ 24 + s_23 ^ 2 e^2 i _ 13(c_12 ^ 2 + e^ 2 i s_12 ^ 2 ) _ 13 ^ 2 + & + & e^2i(+ _ 14 - _ 24 ) _ 24 ^ 2]}| . assuming majorana phases to be zero and dirac phases having value @xmath68 , this element can vanish when & & c_23 ^ 2+^2(s_23 ^ 2_13 ^ 2+_24 ^ 2)=0 . in panel ( a ) of fig . 9 we plotted @xmath136 for @xmath95 to reproduce 3 generation case whereas in panel ( b ) all the parameters are varied in their allowed range in 3 + 1 scenario . in both cases we can see that cancellation is possible for full range of @xmath49 . it can be noticed that unlike normal hierarchy , here cancellation is possible for small values of @xmath103 because in this case all the terms are of same order and there can always be cancellations . however , if we put @xmath133 then the term @xmath91 ( @xmath140 ) drops out from the equation and the leading order term can not be canceled for small values of @xmath103 . it can be seen from panel ( c ) that for @xmath141 and @xmath133 the regions where @xmath49 is small is not allowed . as the value of @xmath39 increases there is the possibility of cancellation of terms for all the values of @xmath44 as can be seen from panel ( d ) where we plot @xmath142 with the lowest mass for @xmath143 when all the other mixing angles are varied in 3@xmath61 range and cp violating phases are varied in full range . now if we keep increasing @xmath103 then @xmath106 term will become large and the chance of cancellation will be less . + figure 9 : plots of vanishing @xmath124 for inverted hierarchy with lowest mass @xmath49 . panel ( a ) for 3 generation case ( b ) all the parameters are varied in full allowed range ( 3 + 1 ) . panel ( c ) and ( d ) are for specific values of @xmath44 and @xmath103 are taken with all other parameters covering their full range . the ( 2,3 ) element of @xmath145 in the flavor basis becomes quite complicated in the presence of an extra sterile neutrino . the expression is m _ & = & e^i(2 _ 14 - _ 24 + 2 ) c_14 ^ 2 c_24 m_4 s_24 s_34 + & + & e^2 i ( _ 13 + ) m_3 ( c_13 c_24 s_23 - e^i(_14 - _ 24 - _ 13 ) s_13 s_14 s_24 ) + & & \{-e^i(_14 - _ 13 ) c_24 s_13 s_14 s_34 + c_13 ( c_23 c_34 - e^i _ 24 s_23 s_24 s_34 ) } + & + & m_1\{- c_23 c_24 s_12 + c_12(-e^i _ 13 c_24 s_13 s_23 - e^i(_14 - _ 24 ) c_13 s_14 s_24 ) } + & & [ -s_12 ( -c_34 s_23 - e^i _ 24 c_23 s_24 s_34 ) + & + & c_12 \ { -e^i _ 14 c_13 c_24 s_14 s_34 - e^i _ 13 s_13(c_23 c_34 - e^i_24 s_23 s_24 s_34 ) } ] + & + & e^2 i m_2\{c_12 c_23 c_24 + s_12(-e^i _ 13 c_24 s_13 s_23 - e^i(_14 - _ 24 ) c_13 s_14 s_24 ) } + & & [ c_12(-c_34 s_23 - e^i _ 24 c_23 s_24 s_34 ) + & + & s_12\{-e^i _ 14 c_13 c_24 s_14 s_34 - e^i _ 13 s_13(c_23 c_34 - e^i _ 24 s_23 s_24 s_34 ) } ] . it reduces to the 3 generation case when @xmath146 . in the normal hierarchical region where @xmath47 can assume very small values and can be neglected , using approximations in eqs . ( [ xnh ] , [ chi1 ] , [ chi2 ] ) we get & - & + & + & ^2 [ e^i(2 + _ 13)(e^i _ 14 s_12 _ 14 + 2 c_12 c_23 e^i _ 24 _ 24)s_12 s_23 s_34 _ 13 + & + & e^i _ 14(e^i(2 - _ 24 ) c_12 c_34 s_12 _ 24 - e^i(2 + _ 13 ) _ 13 s_34 ) _ 14 s_23 + & + & c_23 c_34 e^2i(+ _ 13 ) s_12 ^ 2 _ 13 ^ 2 s_23]}| . to see the order of the terms we consider the case where majorana cp phases vanish and dirac phases have the value @xmath68 . in this limit the element becomes negligible when & & c_23 c_34s_23(1-c_12 ^ 2)+\{(c_12c_34s_12_13)2_23 + & + & _ 24s_34(s_23 ^ 2+c_12 ^ 2c_23 ^ 2)+s_34(_24+c_12c_23s_12_14 ) } + & + & ^2\{s_12_13s_23s_34(s_12_14 + 2c_12c_23_24)+_14s_23(c_12c_34s_12 ^ 2s_23_13 ^ 2)}=0 . being an element of @xmath147 block , @xmath148 shows the same behaviour that of @xmath138 in normal hierarchy . in panel ( a ) of fig . 10 we plotted @xmath149 for @xmath150 which coincides with the 3 generation case and we can see that cancellation is not possible in hierarchical region . however , when all the parameters are varied in their allowed range in panel ( b ) it get contribution from the sterile part and cancellation is always possible . it can also be seen from panel ( c ) of fig . 10 that for @xmath151 there is no cancellation in the region when @xmath47 is small and the figure is quite similar to that of 3 generation case . however , as this active sterile mixing angle becomes larger there is always a possibility of allowed region towards the lower values of @xmath47 as is evident from panel ( d ) . this is because for the vanishing value of @xmath40 the terms with @xmath91 and @xmath106 become very small and can not cancel the leading term @xmath7 ( 10@xmath97 ) . it can also be seen that in this case ( i.e @xmath151 ) , there is no @xmath152 term in eq . ( 3.31 ) and this is why the figure is somewhat similar to the 3 generation case . however , when @xmath40 increases these two contributions become large and cancellation becomes possible . + figure 10 : plots of vanishing @xmath144 for normal hierarchy ( a ) for vanishing @xmath40 and @xmath39 . in panel ( b ) all parameters are varied in their full allowed range . panel(c , d ) are for specific values of @xmath40 when all other mixing angles are varied in their full range . [ fig10 ] for the case of inverted hierarchy where @xmath49 can have very small values , @xmath144 becomes |m_| & & |\ { -c_23 c_34 s_23(c_12 ^ 2 e^2 i + s_12 ^ 2 ) + & + & + & + & ^2 [ c_23 c_34 s_23 e^ 2 i _ 13(c_12 ^ 2 + e^2 i s_12 ^ 2 ) _ 13 ^ 2 + & + & c_12 s_12 s_23 ( e^2 i - 1)(c_34 e^i(_14 - _ 24 ) _ 14 + 2 s_34 c_23 e^i(_13 + _ 24 ) _ 13)_24]}| . to get an idea about the magnitude of the terms we take vanishing majorana phases and dirac cp phases to be of the order @xmath68 . the expression in this case for vanishing @xmath148 becomes & & -c_23c_34s_23+(s_34_24(c_23 ^ 2-))-^2(-s_34_13_14-c_23c_34_13 ^ 2)=0 in panel ( a ) of fig . 11 , where @xmath149 for 3 generation is plotted , we can see that unlike @xmath138 there is no cancellation in small @xmath49 region but when plotted for the full range it gets contribution from the sterile part and there is cancellation for the full range of @xmath49 ( panel ( b ) ) . clearly the cancellation of the terms do not become possible for small values of @xmath40 in strict hierarchical region . this case is similar to the three generation case in ih ( cyan / light region , panel ( c ) ) . this is because for @xmath151 the contribution of @xmath103 comes from the @xmath106 term . if we put the cp violating phase @xmath44 as zero then cancellation is not possible for whole range of @xmath49 ( blue / dark region panel ( c ) ) . however , as the value of @xmath129 increases all the terms in the above equation becomes of the same order and cancellation for very small values of @xmath49 is possible ( panel ( d ) ) . + figure 11 : plots of vanishing @xmath144 for inverted hierarchy ( a ) for vanishing @xmath40 and @xmath39 ( 3 generation ) . in panel ( b ) all parameters are varied in their full allowed range ( 3 + 1 ) . panel ( c ) and ( d ) are for specific values of @xmath40 and @xmath44 when all other mixing angles are varied in their full range . [ fig11 ] this element is related to @xmath124 by the @xmath114 symmetry . as discussed earlier , in the limit when @xmath39 and @xmath40 are not very large , the two mixing angles @xmath40 and @xmath39 will behave in the same way in the textures related by @xmath114 symmetry . the ( 3,3 ) element of the neutrino mass matrix in the presence of one sterile neutrino is given as m _ & = & e^2i(_14 + ) c_14 ^ 2 c_24 ^ 2 m_4 s_34 ^ 2 + & + & e^2i(_13 + ) m_3 \{e^i(_14 - _ 13 ) c_24 s_13 s_14 s_34 + c_13(c_23 c_34 - e^i _ 24 s_23 s_24 s_34)}^2 + & + & m_1[-s_12(-c_34 s_23 - e^i _ 24 c_23 s_24 s_34 ) + & + & c_12\{-e^i_14 c_13 c_24 s_14 s_34 - e^i _ 13 s_13(c_23 c_34 - e^i _ 24 s_23 s_24 s_34)}]^2 + & + & e^2 i m_2 [ c_12(-c_34 s_23 - e^i _ 24 c_23 s_24 s_34 ) + & + & s_12\{-e^i _ 14 c_13 c_24 s_14 s_34 - e^i _ 13 s_13(c_23 c_34 - e^i _ 24 s_23 s_24 s_34)}]^2 . it reduces to the 3 generation case for @xmath153 . using the approximation for normal hierarchy in eqs . ( [ xnh ] , [ chi1 ] , [ chi2 ] ) this becomes |m_| & & & & s_12c_12c_342_23_13-c_12c_23s_34e^2i(s_12_14e^i_14 + c_12c_23_24 e^2i_24)+s_34_24(-s_23 ^ 2e^2i(+ _ 13)+ i_24 + & -&e^2i(+ _ 14)-i_24)}+^2\ { s_12 ^ 2s_23_13e^i(2 + _ 13)(c_23c_34_13e^i_13+s_34_14e^i_14 ) + & + & c_12s_12s_23_24e^2i(2c_23s_34_13e^i(_13+_24)+c_34_14e^i(_14-_24 ) ) + & -&s_23s_34_13_14e^i(2+_13+_14)}}| . to get an idea of the order of the terms we consider the vanishing majorana phases and the dirac phases having the value equal to @xmath68 . this element vanishes when & & c_23c_34s_23(1-c_12 ^ 2)+\{s_12c_12c_342_23_13 + c_12c_23s_34(s_12_14 + & + & c_12c_23_24)-s_34_24(s_23 ^ 2-)}+^2\ { s_12 ^ 2s_23_13(c_23c_34_13+s_34_14 ) + & + & c_12s_12s_23_24(2c_23s_34_13+c_34_14)+s_23s_34_13_14}=0 . + figure 12 : plots of vanishing @xmath125 for normal hierarchy with lowest mass @xmath47 . panel ( a ) correspond to three generation case . in panel ( b ) all the mixing angles are varied in their full allowed range of parameters ( 3 + 1 ) . panel ( c ) and ( d ) are for some specific values of @xmath40 . [ fig12 ] for vanishing @xmath40 , which is the case for 3 generation , @xmath154 is disallowed for small @xmath47 as can be seen from panel ( a ) of fig . this is the generic behaviour of a element belonging to the @xmath135 block in normal hierarchy which we mentioned previously . this is because for @xmath40 equal to zero the leading order term is large ( @xmath7 ( 10@xmath97 ) ) . here the term with @xmath106 is quite small ( 10@xmath155 - 10@xmath156 ) and hence will not have very significant role to play . thus , only terms with coefficient @xmath91 can cancel the leading order term . however , for vanishing @xmath40 this term is small @xmath7 ( 10@xmath155 ) , and can not cancel the leading order term . in panel ( b ) when all the parameters are varied in their @xmath26 range we can see that cancellation is possible over the whole range of @xmath47 ( 3 + 1 case ) . now , when @xmath40 starts increasing from its lowest value there exist a region for intermediate values where both the terms become approximately of the same order and hence there can be cancellations ( panel ( c ) ) . towards very large values of @xmath40 the term with coefficient @xmath91 becomes larger than the leading order term due to which this element can not vanish . for the cancellation very large values of @xmath47 is required as can be seen from panel ( d ) of fig 12 . + figure 13 : plots of vanishing @xmath125 for inverted hierarchy with lowest mass @xmath49 . panel ( a ) correspond to three generation case . in panel ( b ) all the mixing angles are varied in their full allowed range of parameters ( 3 + 1 ) . panel ( c ) and ( d ) are for some specific values of @xmath40 and @xmath44 . [ fig13 ] for the case of inverted hierarchy where @xmath49 approaches small values we get the expression m _ & & c_34 ^ 2 s_23 ^ 2(c_12 ^ 2 e^2 i + s_12 ^ 2 ) + e^2 i ( _ 14 + ) s_34 ^ 2 + & + & 2 + & + & ^2[(c_12 ^ 2 + e^ 2 i s_12 ^ 2)\{c_23 c_34 _ 13 e^ i _ _ 13 e^ i _ 13 + 2 _ 14 s_34 e^ i _ 14 ) + e^ 2 i _ 14 _ 14 ^ 2 s_34 ^ 2 } + & + & ( c_12 ^ 2 e^ 2 i + s_12 ^ 2)c_23 ^ 2 e^ 2 i _ 24 _ 24 ^ 2 s_34 ^ 2 + & + & 2 s_12(e^2 i - 1 ) e^ i _ 24(c_34 _ 13 2_23 e^ i _ 13 + c_12 c_23 _ 14 s_34 ) s_34 _ 24 ] . for vanishing majorana cp phases and dirac phases having the value equal to @xmath68 this expression becomes m _ & & -c_23c_34s_23+s_34_24(c_23 ^ 2-)+^2s_23_13(c_23c_34_13+s_34_14 ) in panel ( a ) of fig . 13 we reproduced the 3 generation behaviour by plotting @xmath157 for @xmath151 and in panel ( b ) all the parameters are varied randomly ( 3 + 1 ) . in both the cases we can see that cancellations are possible for the whole range of @xmath49 . for @xmath151 all the terms are of same order and cancellations are always possible . but if we put @xmath133 then one term with coefficient @xmath91 and another term with coefficient @xmath106 drops out from the equation and then small values of @xmath129 can not cancel the leading order term any more . this can be seen from panel ( c ) where cancellation is not possible for lower @xmath49 region . however when @xmath129 increases to a value of about 0.02 this element can vanish ( panel ( d ) the cyan region ) . we see that when @xmath40 increase towards its upper bound the @xmath91 term becomes large @xmath158 . hence , the other terms are not able to cancel this term and we do not get small @xmath49 region allowed ( panel ( d ) , blue region ) . the elements @xmath2 , @xmath3 , @xmath4 and @xmath5 are present in the fourth row and fourth column in the neutrino mass matrix . they are the new elements that arises in 3 + 1 scenario due to the addition of one light sterile neutrino . the expressions for @xmath2 and @xmath3 are given by m_es & = & e^i(2 + _ 14 ) c_14 c_24 c_34 m_4 s_14 + & + & e^i(2 + _ 13 ) c_14 m_3 s_13\{-e^i(_14 - _ 13 ) c_24 c_34 s_13 s_14 + c_13(-e^ i _ 14 c_34 s_23 s_24 - c_23 s_34 ) } + & + & c_12 c_13 c_14 m_1[-s_12(-e^i _ 24 c_23 c_34 s_24 + s_23 s_34 ) + & + & c_12\{-e^i _ 14 c_13 c_24 c_34 s_14 - e^i _ 13 s_13(-e^i _ 24 c_34 s_23 s_24 - c_23 s_34 ) } ] + & + & e^ 2 i c_13 c_14 m_2 s_12[c_12(-e^ i _ 24 c_23 c_34 s_24+s_23s_34 ) + & + & s_12 \{- e^i _ 14 c_13 c_24 c_34 s_14 - e^i _ 13 s_13(-e^i _ 24 c_34 s_23 s_24 - c_23 s_34 ) } ] . + + + figure 14 : correlation plots for vanishing @xmath159 for both normal and inverted hierarchy . in these plots all the mixing angles are varied in their 3 @xmath61 allowed range , dirac cp phases are varied from 0 to @xmath102 and majorana phases from 0 to @xmath68 . [ fig14 ] @xmath160 \\ \nonumber & + & e^{2 i \alpha } m_2 \{c_{12 } c_{23 } c_{24 } + s_{12}(-e^{i \delta_{13 } } c_{24 } s_{13 } s_{23 } - e^{i(\delta_{14 } - \delta_{24 } } c_{13 } s_{14 } s_{24})\ } \\ \nonumber & & [ c_{12}(-e^{i \delta_{24 } } c_{23 } c_{34 } s_{24 } + s_{23 } s_{34 } ) \\ \nonumber & + & s_{12}\{-e^{i \delta_{14 } } c_{13 } c_{24 } c_{34 } s_{14 } - e^{i \delta_{13 } } s_{13}(-e^ { i \delta_{24 } } c_{34 } s_{23 } s_{24 } - c_{23 } s_{34})\ } ] . \end{aligned}\ ] ] though the equations seem very complex , one can easily understand the properties of these elements by just looking at the @xmath50 terms . the @xmath50 term in @xmath2 is proportional to @xmath161 . so in general it is quite large ( @xmath162 ) . for this element to become negligible very small values of @xmath77 is required . but as this angle is bounded by the sbl experiments , complete cancellations never occurs for both normal and inverted hierarchy ( panel ( a ) , ( b ) of fig . similar predictions are obtained for @xmath3 element which can not vanish since @xmath103 has to be negligible which is not allowed by the data . this can be seen from panel ( c ) , ( d ) of fig . 14 . for the element @xmath4 the scenario is quite different . m_s & = & c_14 ^ 2 c_24 ^ 2 c_34 e^ 2 i(_14 + ) m_4 s_34 + & + & e^2 i ( + _ 13 ) m_3\{-c_24 c_34 e^i(_14 - _ 13 ) s_13 s_14 + c_13(-c_23 s_34 - c_34 e^ i _ 24 s_23 s_24 ) } + & & \{-c_24 e^i(_14 - _ 13 ) s_13 s_14 s_34 + c_13(c_23 c_34 - e^i _ 24 s_23 s_34s_24 ) } + & + & m_1[-s_12(-c_23 c_34 e^i _ 24 s_24 + s_23 s_34 ) + & + & c_12\{-c_13 c_24 c_34 e^ i _ 14 s_14 - e^ i _ 13 s_13(-c_23 s_34 - c_34 e^i _ 24 s_23 s_34 ) } ] + & & [ -s_12(-c_34 s_23 - c_23 e^i _ 24 s_34s_24 ) + & + & c_12\{-c_13 c_24 e^ i _ 14 s_14 s_34 - e^i _ 13 s_13(c_23 c_34 - e^ i _ 24 s_23 s_34s_24 ) } ] + & + & e^ 2 i m_2[c_12(-c_23 c_34 e^i _ 24 s_34 + s_23 s_34 ) + & + & s_12\{-c_13 c_24 c_34 e^ i _ 14 s_14 - e^ i _ 13 s_13(-c_23 s_34 - c_34 e^ i _ 24 s_23 s_24 ) } ] + & & [ c_12(-c_34 s_23 - c_23 e^ i _ 24 s_34s_24 ) + & + & s_12\{-c_13 c_24 e^ i _ 14 s_14 s_34 - e^ i _ 13 s_13(c_23 c_34 - e^i _ 24 s_23 s_34s_14 ) } ] . in this case the @xmath50 term is proportional to @xmath40 and there is no lower bound on it from the sbl experiments i.e. it can approach smaller values . as a result the term with @xmath50 can be very small . thus this matrix element can possibly vanish in both hierarchies for whole range of the lowest mass ( panel ( e ) , ( f ) ) . + the ( 4,4 ) element of the neutrino mass matrix is given as m_ss & = & c_14 ^ 2 c_24 ^ 2 c_34 ^ 2 e^2 i ( + _ 14 ) m_4 + & + & e^2 i(+ _ 13 ) m_3\{-c_24 c_34 e^i(_14 - _ 13 ) s_13 s_14 + c_13(-c_23 s_34 - c_34 e^ i _ 24 s_23 s_24)}^2 + & + & m_1[-s_12(-c_23 c_34 e^ i _ 24 s_24 + s_23 s_34 ) + & + & c_12\{-c_13 c_24 c_34 e^ i _ 14 s_14 - e^ i _ 13 s_13(-c_23 s_34 - c_34 e^ i _ 24 s_23 s_24)}]^2 + & + & e^ 2 i m_2[c_12(-c_23 c_34 e^ i _ 24 s_24 + s_23 s_34 ) + & + & s_12\{-c_13 c_24 c_34 e^ i _ 14 s_14 - e^i _ 13 s_13(-c_23 s_34 - c_34 e^i _ 24 s_23 s_34)}]^2 the @xmath50 term for @xmath5 is proportional to @xmath163 . one can see that this term is of order one as a result this element can never vanish as is evident from panel ( g , h ) . in this paper we analyze systematically the one - zero textures of the @xmath12 mass matrix in presence of a sterile neutrino . assuming neutrinos to be majorana particles , this is a symmetric matrix with 10 independent entries . we use the information on the active sterile mixing angles from the short baseline experiments . we analyze if the current constraints on oscillation parameters allow each of these entries to assume a vanishing value . we also study the implications and correlations among the parameters when each matrix element is zero . we expand the mass matrix element in terms of a parameter @xmath91 with suitable coefficients @xmath164 and @xmath152 corresponding to the mixing angles @xmath35 , @xmath38 and @xmath39 . this is motivated by the observation that these angles are of same order with @xmath165 . these expressions facilitate the analytic understanding of the numerical results presented in the different plots . we study the vanishing condition as a function of the lowest mass @xmath47 ( nh ) or @xmath49 ( ih ) by varying the lightest mass in the range 0.0001 - 0.5 ev . we find that @xmath166 is possible for nh only for higher values of the smallest mass @xmath47 while for ih it is possible even for lower values . this is in sharp contrast with the 3 generation case where complete cancellation can never take place for ih . the current and upcoming @xmath83 experiments like gerda , cuore , majorana , exo , supernemo , kamland - zen , sno+ @xcite can lower the present sensitivity by one order of magnitude ( @xmath60.012 - 0.06 ev ) and hence can probe the ih region for the three neutrino scheme @xcite . however for 3 + 1 scenario , @xmath69 can be in the range of the expected sensitivity of the future @xmath83 experiments , even for nh . thus if the existence of sterile neutrinos is confirmed by future experiments @xcite then it may be difficult to probe the hierarchy from @xmath83 alone . @xmath94 can vanish over the whole range of the smallest mass for both 3 and 3 + 1 neutrino scenarios . however for larger values of the mixing angle @xmath103 , cancellation is not achieved for smaller @xmath47 for nh . for ih the cancellation condition depend on the majorana phase @xmath44 and the mixing angle @xmath39 . we obtain the correlations between these two parameters required for making this element vanishingly small . cancellation is achieved for the element @xmath113 for the full range of the lowest mass in the 3 + 1 scenario . the element @xmath87 is related to the element @xmath113 by @xmath114 symmetry . however unlike three generation case @xmath37 in these textures are not related simply by @xmath167 . the mixing angles @xmath39 and @xmath40 are also different in these two textures in general . however for small values of @xmath39 we get @xmath168 in these textures . consequently the role played by @xmath39 for @xmath87 is played by @xmath40 in @xmath169 in this limit . thus in this case cancellation is not achieved for larger values of @xmath129 in the hierarchical regime for nh . for ih we obtain correlations between @xmath44 and @xmath170 for fulfilling the condition for cancellations . the elements @xmath138 and @xmath171 are related by @xmath114 symmetry . for these cases , cancellation is not possible in the hierarchical zone for ih , in the 3 generation case . however the extra contribution coming from the sterile part helps in achieving cancellation in this region . for ih one can obtain correlations between the majorana phase @xmath44 and the mixing angle @xmath39(@xmath40 ) for @xmath172(@xmath173 ) . for @xmath148 element cancellation was possible for three generation case only for higher values of the lightest mass . however if one includes the sterile neutrino then this element can vanish over the whole range of the lightest neutrino mass considered . with the current constraints on sterile parameters it is not possible to obtain @xmath174 while @xmath2 and @xmath3 can only vanish in the qd regime of the active neutrinos . however , the element @xmath4 can be vanishingly small in the whole mass range . this is because the angle @xmath40 can take very small values and hence cancellation is possible even for smaller values of the lowest mass . the above results can be useful for building models for light sterile neutrinos and shed light on the underlying new physics if future experiments and analyses reconfirm the explanation of the present anomalies in terms of sterile neutrinos . the work of c. s. k and s. g. is supported by the national research foundation of korea ( nrf ) grant funded by korea government of the ministry of education , science and technology ( mest ) ( grant no . 2011 - 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in this paper we study the phenomenological implications of the one zero textures of low energy neutrino mass matrices in presence of a sterile neutrino . we consider the 3 + 1 scheme and use the results from global fit for short baseline neutrino oscillation data which provides the bounds on the three additional mixing angles . we find that the mass matrix elements @xmath0 ( @xmath1 ) involving only the active states can assume vanishing values in the allowed parameter space for all the mass spectrum . among the mass matrix elements connecting the active and sterile states , @xmath2 and @xmath3 can become small only for the quasi - degenerate neutrinos . the element @xmath4 on the other hand can vanish even for lower values of masses since the 3 - 4 mixing angle only has an upper bound from current data . the mass matrix element ( @xmath5 ) involving only the sterile state stays @xmath6 @xmath7(1 ) ev in the whole parameter region . we study the possible correlations between the sterile mixing angles and the majorana phases to give a zero element in the mass matrix .

<s>[INST]light sterile neutrinos were invoked to explain the results of the lsnd experiment which reported oscillation events in the @xmath8 mode corresponding to a mass squared difference @xmath6 ev@xmath9 @xcite . adding one sterile neutrino to the standard 3 generation framework gives rise to two possible mass spectra the 2 + 2 in which two pairs of mass states are separated by a difference @xmath6 ev@xmath9 and 3 + 1 in which a single predominantly sterile state differs by @xmath6 ev@xmath9 from the three active states @xcite . subsequently the 2 + 2 schemes were found to be incompatible with the solar and atmospheric neutrino data @xcite . the miniboone experiment was designed to test this and its antineutrino data confirmed the lsnd anomaly @xcite . both 3 + 1 and 3 + 2 sterile neutrino schemes have been considered to explain these results @xcite . such global fits aim to explain the non - observance of ev@xmath9 oscillations in the disappearance channel in other short baseline experiments as well as the reported evidence in lsnd / miniboone experiments . the relevant probabilities for 3 + 1 case is governed by a single mass squared difference and hence is independent of the cp phase . in the 3 + 2 scheme , dependence on cp phase comes into play and one gets a slightly better fit . other evidences in support of sterile neutrinos include the reactor and the ga anomaly . the first one refers to the deficit in the measured electron antineutrino flux in several experiments when the theoretical predictions of reactor neutrino fluxes were reevaluated @xcite . the second one implies shortfall of electron neutrinos observed in the solar neutrino detectors gallex and sage using radioactive sources @xcite . both these can be explained by adding light sub - ev sterile neutrinos in the three generation framework . there has also been some hint in favour of sterile neutrinos from cosmological observations of a `` dark radiation '' which is weakly interacting and relativistic . attributing this to sterile neutrinos one gets the bound on the number of neutrinos as @xmath10 at 68% c.l @xcite . the plank satellite experiment which has very recently declared its first results @xcite , on the other hand , gives @xmath11 at 68% c.l . which allows for an extra sterile neutrino at 95% c.l . , although its mixing with active species can be very tightly constrained @xcite within the framework of standard cosmology . thus the sterile neutrinos continue to be intriguing and many new experiments are planned proposed to test this @xcite . theoretically , sterile neutrinos are naturally included in type - i seesaw model @xcite . but their mass scale is usually very high to account for the small mass of the neutrinos . light sub - ev sterile neutrinos as suggested by the data can arise in many models @xcite . irrespective of the mechanism for generation of neutrino masses the low energy majorana mass matrix in presence of an extra sterile neutrino will be of dimension @xmath12 with ten independent entries and is given as , @xmath13 where , @xmath14 and @xmath15 denotes the leptonic mixing matrix in a basis where the charged lepton mass matrix is diagonal . one of the important aspects in the study of neutrino physics is to explore the structure of the neutrino mass matrices . at the fundamental level these are governed by yukawa couplings which are essentially free parameters in most models . these motivated the study of texture zeros which means one or more elements are relatively small compared to the others . texture zeros in the low energy mass matrices in the context of three generations have been extensively explored both in the quark and lepton sector @xcite , @xcite . such studies help in understanding the underlying parameter space and the nature of the mass spectrum involved and often predict correlations between various parameters which can be experimentally tested . for three generation scenario it is well known that the number of maximum texture zeros in low energy mass matrix is two @xcite . in the context of the 4-neutrino case however more than two zeros can be allowed @xcite . two zero textures of sterile neutrinos have been studied recently in @xcite and three zero cases have been considered in @xcite . in this paper we concentrate on the textures where one of the mass matrix elements is vanishing . for the @xmath12 symmetric mass matrix it gives total 10 different cases which needs to be investigated . we study the implications of one zero textures and the possible correlations between the parameters . we also compare our results with the 1 zero textures for three active neutrinos @xcite . the plan of the paper goes as follows . in section ii we discuss the possible mass spectra and the mixing matrix in the 3 + 1 scenario . in the next section we present our study regarding the implications of one vanishing entry in the low energy neutrino mass matrix . we conclude in section iv . there are two ways in which one can add a predominantly sterile state separated by @xmath6 ev@xmath9 from the standard 3 neutrino mass states . in the first case the additional neutrino can be of higher mass than the other three while in the second case the the fourth neutrino is the lightest state . the later turns out to be incompatible with cosmology since in this case three active neutrinos , each with mass @xmath6 ev results in an enhanced cosmological energy density . thus it suffices to consider only the first case which admits two possibilities displayed in fig . 1 . [ fig1 ] * snh : in this @xmath16 corresponding to a normal hierarchy ( nh ) among the active neutrinos which implies , + @xmath17 * sih : this corresponds to @xmath18 implying an inverted ordering among the active neutrinos with masses expressed as , + @xmath19 here , @xmath20 . we define the ratio of the mass squared differences @xmath21 and @xmath22 as @xmath23 @xmath24 in the extreme cases and using @xmath25 , these masses can be written in terms of @xmath21 and @xmath22 as + snh : |m_4| |m_3| |m_2| |m_1| [ xnh ] sih : |m_4| |m_2| |m_1| |m_3| [ xih ] sqd : |m_4||m_1||m_2||m_3|m_0 . [ qd ] the first two cases correspond to complete hierarchy among the active neutrinos while the last one is the quasi - degenerate ( qd ) regime where the three active neutrinos have approximately equal masses . .@xmath26 ranges of neutrino oscillation parameters @xcite . the current constraints on sterile neutrino parameters are from @xcite , @xcite , where @xmath27 or @xmath28 . also given are the @xmath29 ranges of the mass ratios @xmath30 and @xmath21 . [ cols="<,^,^,^",options="header " , ] in the 3 + 1 scenario , the neutrino mixing matrix , @xmath15 in the flavor basis will be a @xmath31 unitary matrix . in general a n @xmath32 n unitary mixing matrix contains @xmath33 mixing angles and @xmath34 dirac type cp violating phases . it will also have ( n-1 ) number of additional majorana phases if neutrinos are majorana particles . so in our case v can be parametrized in terms of sixteen parameters . in addition to the three mixing angles between the active flavors , ( @xmath35 , @xmath36 , @xmath37 ) we now have three more mixing angles from sterile and active mixing , ( @xmath38 , @xmath39 , @xmath40 ) . there are six cp violating phases , three dirac ( @xmath41 , @xmath42 , @xmath43 ) and three additional majorana phases as ( @xmath44 , @xmath45 , @xmath46 ) as neutrinos here are considered to be majorana particles . then , there are four masses of neutrino @xmath47 , @xmath48 , @xmath49 corresponding to three active states and @xmath50 which is predominantly the mass of heavy sterile neutrino . the mixing matrix @xmath15 can be expressed as @xmath51 @xcite where @xmath52 where @xmath53 denotes rotation matrices in the _ ij _ generation space and is expressed as , @xmath54=@xmath55 , @xmath56=@xmath57 + here we use the abbreviations @xmath58 and @xmath59 . the phase matrix is diagonal and is expressed as , @xmath60 . the best - fit values and the 3@xmath61 ranges of the oscillation parameters in the 3 + 1 scenario are given in table i where in addition to the masses and mixing angles we also present the mass ratios @xmath22 and @xmath21 which would be useful in our analysis . note that the constraints on the three - neutrino parameters may change slightly once a full four - neutrino fit combining all global data is done . however since the sterile mixing angles are small the change is not expected to be significant . therefore in absence of a full four - neutrino global fit we use three - neutrino parameter values as obtained from three generation analyses @xcite . [ sigmam ] + figure 2 : plots of sum of light neutrino masses ( @xmath62 ) vs the lowest mass in the 3 + 1 scenario . also shown are the the cosmological upper bound on neutrino mass from the analysis of cmb data plus matter power spectrum information ( sdss ) and a prior on @xmath63(hst ) and from the analysis of cmb data only from reference @xcite for 3 + 1 scheme . in fig . 2 we have plotted the sum of neutrino masses against the lowest neutrino mass for both nh and ih . the band corresponds to variation of the mass squared differences in their current 3@xmath61 range . we also show the cosmological upper bound on neutrino masses in 3 + 1 scenario from @xcite . the combined analysis of cmb + sdss + hst seems to rule out the mass spectrum of 3 + 1 scenario in the framework of standard cosmology . however , if only cmb data is taken then region for the lowest mass @xmath64 ev gets allowed for both the hierarchies . note that the analysis in @xcite does not incorporate the planck results @xcite which can constrain the sum of masses further . in our analysis we have varied the lowest mass up to 0.5 ev . in this section we study the implication of the condition of vanishing @xmath0 for the 3 + 1 scenario , where @xmath65 . since @xmath0 is complex the above condition implies both real and imaginary parts are zero . therefore to study the 1-zero textures we consider @xmath66 . in our analysis we have varied the three dirac phases in the range 0 to @xmath67 and the three majorana phases from 0 to @xmath68 . the matrix element @xmath69 in the 3 + 1 scenario is given as , m_ee = m_1 c_14 ^ 2 c_13 ^ 2c_12 ^ 2+m_2 s_12 ^ 2c_14 ^ 2c_13 ^ 2e^2i+m_3 s_13 ^ 2 c_14 ^ 2 e^2i+m_4s_14 ^ 2 e^2i . [ mee ] this is of the form [ meenh ] m_ee= c_14 ^ 2 ( m_ee)_3+e^2is_14 ^ 2 m_4 , where @xmath70 corresponds to the matrix element in the 3 active neutrino case . the contribution of the sterile neutrino to the element @xmath69 depends on the mass @xmath50 and the active - sterile mixing angle @xmath38 . of all the mass matrix element @xmath69 has the simplest form because of the chosen parametrization and can be understood quite well . using approximation in eq . ( [ xnh ] ) for the case of extreme hierarchy one can write this for nh as , [ meenh ] m_ee c_14 ^ 2 ( m_ee)_3+e^2is_14 ^ 2 , where @xmath71 and @xmath22 is defined in eq . [ zeta ] . [ meefig ] + figure 3 : plot of @xmath72 versus the lowest mass . the panel ( a ) corresponds to the three generation case while panel ( b ) is for 3 + 1 case . in panel ( b ) all the mixing angles are varied in their 3@xmath61 range and the majorana cp violating phases are varied in their full range ( 0-@xmath68 ) . the panel ( c ) and ( d ) are for specific values of @xmath38 with all other parameters covering their full range . the modulus of @xmath69 is the effective mass that can be extracted from half life measurements in neutrinoless double beta decay . in fig . 3 we plot the effective mass as a function of the smallest mass by varying @xmath38 in its complete 3@xmath61 range from table i as well as for specific values of the mixing angle @xmath38 . the majorana phases are varied randomly in the range 0 to @xmath68 in all the plots . the first panel is for @xmath73 i.e the three generation case . it is seen that for present values of the oscillation parameters the cancellation condition is not satisfied for @xmath74 for nh . however , as one increases @xmath47 , complete cancellation can be achieved . for ih the complete cancellation is never possible . these results change when we include the sterile contribution as is evident from the panel ( b ) in fig . 3 which shows the effective mass for nh and ih by varying all the parameters in their full 3@xmath61 allowed range . the behaviour can be understood from the expressions of @xmath72 in various limiting cases . for nh , in the hierarchical limit of @xmath74 the major contributor will be the additional term due to the sterile neutrinos because of higher value of @xmath50 . complete cancellation is only possible for smaller values of @xmath38 so that this contribution is suppressed . the typical value of @xmath38 required for cancellation can be obtained by putting @xmath75 ( which would maximize the three neutrino contribution ) and @xmath76 , as ^2_14 10 ^ -3 , which lies outside the allowed range of @xmath38 given in table i. as we increase @xmath47 , @xmath70 increases and can be of the same order of magnitude of the sterile term . hence one can get cancellation regions . the cancellation is mainly controlled by the value of @xmath38 . for higher values of @xmath77 one needs a higher value of @xmath47 for cancellation to occur . this correlation between @xmath47 and @xmath38 is brought out by the panels ( c ) and ( d ) in fig . 3 . for ih case , in the limit of vanishing @xmath49 using approximation in eq . ( [ xih ] ) , @xmath69 in a 3 + 1 scenario can be written as |m_ee| |c_14 ^ 2 c_13 ^ 2 ( c_12 ^ 2+s_12 ^ 2 e^2i)+s_14 ^ 2 e^2i| . the maximum value of this is achieved for @xmath78 which is slightly lower than that of nh in this limit . the element vanishes in the limit @xmath79 0 ev when @xmath80 and @xmath76 provided [ meeih ] ^2_14 0.05 this is well within the allowed range . this behaviour is in stark contrast to that in the 3 neutrino case @xcite . there is no significant change in this behaviour as the smallest mass @xmath49 is increased since this contribution is suppressed by the @xmath81 term and the dominant contribution to @xmath70 comes from the first two terms in eq . ( [ mee ] ) . therefore in this case we do not observe any correlation between @xmath49 and @xmath77 . while moving towards the quasi - degenerate regime of @xmath82 we find that effective mass can still be zero . however , when the lightest mass approaches a larger value ~ 0.3 ev we need very large values of active sterile mixing angle @xmath38 , outside the allowed range , for cancellation . hence the effective mass can not vanish for such values of masses . also shown is the current limit on effective mass from combined kamland - zen and exo 200 results on the half - life of @xmath83 in @xmath84xe @xcite . when translated in terms of effective mass this corresponds to the bound @xmath85 ev including nuclear matrix element uncertainties . for the three generation case , the hierarchical neutrinos can not saturate this bound . but in the 3 + 1 scenario this bound can be reached even for very small values of @xmath49 for ih and for some parameter values it can even exceed the current limit . thus from the present limits on neutrinoless double beta decay searches a part of the parameter space for smaller values of @xmath49 can be disfavoured for ih . for nh , the kamland - zen + exo 200 combined bound is reached for @xmath86 ev and again some part of the parameter space can be disfavoured by this bound . the mass matrix element @xmath87 in the presence of extra sterile neutrino is given as m_e & = & c_14(e^i ( _ 14-_24 + 2 ) m_4s_14s_24+e^i(_13 + 2 ) m_3s_13(c_13c_24s_23-e^i ( _ 14-_13-_24 ) + & & s_13s_14s_24 ) + c_12c_13m_1(-c_23c_24s_12+c_12(-e^i _ 13c_24s_13s_23-e^i ( _ 14-_24)c_13s_14s_24 ) ) + & + & e^2i m_2c_13s_12 ( c_12c_23c_24+s_12(-e^i _ 13c_24s_13s_23-e^i ( _ 14-_24)c_13s_14s_24 ) ) ) . unlike @xmath69 here the expression is complicated and an analytic understanding is difficult from the full expression . the expression for @xmath88 in the limit of vanishing active sterile mixing angle @xmath39 becomes m_e = c_14(m_e ) _ 3 . since the active sterile mixing is small , in order to simplify these expressions we introduce a quantity @xmath890.2 and define these small angles to be of the form @xmath90 . thus a systematic expansion in terms of @xmath91 can be done . for sterile mixing angle [ chi1 ] _ 14 _ 14 _ 14 , + _ 24 _ 24 _ 24 , and the reactor mixing angle as [ chi2 ] _ 13 _ 13 _ 13 . here are parameters of @xmath7(1 ) and their @xmath26 range from the current constraint on the mixing angles is given by @xmath93 note that for the sterile mixing angle @xmath40 we do not adopt the above approximation because this angle can be large compared to other two sterile mixing angles and hence the small parameter approximation will not be valid . using the approximation in eqs . ( [ xnh ] ) , ( [ chi1 ] ) and ( [ chi2 ] ) we get the expression for @xmath94 for normal hierarchy as & + & ^2 e^i(_14-_24)(e^2i -e^2i s_12 ^ 2)_14_24}| . to see the order of magnitude of the different terms we choose vanishing majorana phases while dirac cp phases are taken as @xmath68 . the mass matrix element @xmath88 vanishes when [ mem ] s_12c_12c_23-(1-s_12 ^ 2)s_23_13 + ^2(-s_12 ^ 2)_14_24=0 . + the three generation limit is recovered for @xmath95 and in panel ( a ) of fig . 4 we show @xmath94 as a function of @xmath47 of this case , for nh . panel ( b ) ( red / light region ) of fig . 4 shows @xmath94 for the 3 + 1 case , with all parameters varied randomly within their @xmath26 range . the figures show that @xmath96 can be achieved over the whole range of the smallest mass for both 3 and 3 + 1 cases . however , we find that in the hierarchical limit cancellation is not achieved for large values of @xmath39 , since in that case the third term of eq . ( [ mem ] ) will be of the @xmath7 ( 10@xmath97 ) compared to the leading order term which is of the @xmath7 ( 10@xmath98 ) and hence there will be no cancellation of these terms . this can be seen from panel ( b ) ( green / dark region ) of fig . 4 for @xmath99 . in the qd limit the contribution from the active terms are large enough to cancel the sterile contribution and thus @xmath100 can be achieved . [ fig4 ] figure 4 : plots of @xmath94 as a function of the lowest mass @xmath47 for nh . panel ( a ) correspond to the three generation case while ( b ) ( red / light region ) is for 3 + 1 case and also for @xmath101 ( green / dark region ) . all the parameters are varied in their full 3@xmath61 allowed range , the cp violating dirac phases are varied from 0 to @xmath102 and the majorana phases are varied from 0 to @xmath68 unless otherwise stated . + + figure 5 : plots of @xmath94 vs @xmath49 for inverted hierarchy for ( a ) three generation case ( b ) 3 + 1 case with all parameters varied randomly in their full range . panel ( c ) , ( d ) and ( e ) are for specific values of @xmath103 and @xmath44 . the panel ( f ) shows the correlation between @xmath44 and @xmath103 when all other parameters are randomly varied . [ fig5 ] for ih using the approximation eq . ( [ xih ] ) for the hierarchical limit we get the expression [ memih ] |m_e | & & & - & e^i(_14-_24)^2 _ 14_24(c_12 ^ 2 -e^2i+e^2is_12 ^ 2)}| . to see the order of magnitude of the various terms we consider the case when majorana phases vanish and the dirac phases assume the value @xmath68 . then we get for vanishing @xmath87 , s_23_13-^2(1-)_14_24=0 . in panel ( a ) of fig . 5 we display the plot of @xmath94 with @xmath49 for the 3 generation scenario i.e for @xmath104 for ih . in panel ( b ) we consider the 3 + 1 case with all the parameters varying in their allowed range . note that in the small @xmath49 limit ( cf . 3.13 ) for @xmath105 the leading order term vanishes . for this case , for large active sterile mixing angle @xmath39 , the @xmath106 term becomes large @xmath7 ( 10@xmath97 ) and the cancellation with @xmath91 term is not be possible . when cp violating phase @xmath44 is non zero , the leading order term can cancel the @xmath106 term even for large values of @xmath103 . these features are reflected in panel ( c ) where we plot @xmath94 for @xmath101 and @xmath107 ( blue / dark region ) and by varying @xmath44 in its full range ( cyan / light region ) . as expected , for @xmath80 , cancellation is not achieved for smaller values of @xmath49 . thus the condition @xmath96 implies some correlation between @xmath49 and @xmath44 for ih . even if @xmath44 is varied in its full range , the absolute value of the matrix element @xmath94 can vanish only if the product @xmath108 is small , i.e. @xmath77 and @xmath103 are simultaneously small . this is because if they are large the @xmath106 term becomes of the @xmath7 ( 10@xmath97 ) and hence cancellation will not be possible . this is seen from panel ( d ) where for @xmath109 and @xmath101 the region where @xmath49 is small gets disallowed . taking cp violating phase @xmath110 makes the magnitude of leading order term ( @xmath111 ) quite large and smaller values of @xmath39 can not give cancellation even for large values of @xmath49 which can be seen from panel ( e ) of fig . 5 . for the occurrence of cancellation @xmath103 has to be @xmath112 0.01 for @xmath110 as can be seen from panel ( f ) where we have plotted the correlation between @xmath44 and @xmath103 for @xmath100 . the mass matrix element @xmath113 in the presence of an extra sterile neutrino is given by m_e&=&c_14c_24e^i(2 + _ 14)m_4s_14s_34+m_3c_14s_13e^i(2+_13)(-c_24s_13s_14s_34 e^i(_14-_13 ) + & + & c_13(c_23c_34-e^i_24s_23s_24s_34))+m_2s_12c_13c_14e^2i(c_12(-c_34s_23-c_23s_24s_34e^i_24 ) + & + & s_12(-c_13c_24s_14s_34e^i_14-e^i_13s_13(c_23c_34-e^i_24s_23s_24s_34 ) ) ) + & + & m_1c_12c_13c_14(-s_12(-c_34s_23-c_23s_24s_34e^i_24)+c_12(-c_13c_24s_14s_34e^i_14 -e^i_13s_13 + & & ( c_23c_34-e^i_24s_23s_24s_34 ) ) ) . the elements @xmath113 and @xmath87 are related by @xmath114 permutation symmetry @xmath115 , in such a way that @xmath116 for three active neutrino case the mixing angle @xmath37 in the partner textures linked by @xmath114 symmetry are related as @xmath117 . however , in the 3 + 1 case the relation of @xmath37 between two textures related by this symmetry is not simple . the active sterile mixing angles @xmath39 and @xmath40 are also different in the textures connected by @xmath114 symmetry and are related as @xcite @xmath118 @xmath119 @xmath120 @xmath121 due to these relations the behaviour of @xmath87 is different from that of @xmath113 unlike in three active neutrino case where the plots of these two elements were same except for @xmath37 which differed in octant for the two cases . + it is found that in the limit of small @xmath39 the two active sterile mixing angles @xmath122 from eq ( [ mutau1 ] ) . the same can be seen from eq ( [ mutau2 ] ) which gives @xmath123 for smaller values of the mixing angle @xmath40 . thus , for these cases the behaviour shown by @xmath39 in @xmath87 ( @xmath124 ) is same as shown by @xmath40 in @xmath113 ( @xmath125 ) . in the limit of vanishing active sterile mixing angle @xmath40 this element becomes m_e = c_14(m_e ) _ 3 . using the approximation in eq ( [ xnh ] ) for nh the above element can be expressed as , |m_e| & & |\{- s_12s_23c_12c_34e^2i+(c_23c_34e^i(2+_13)_13-c_23c_34s_12 ^ 2 + & & _ 13e^i(2+_13)+e^i(2+_14)s_34_14- e^i(2+_14)s_12 ^ 2s_34_14-c_12c_23 + & & e^i(2+_24)s_12s_34_24 ) -e^i(_13+_24)(e^2i - e^2is_12 ^ 2)s_23s_34_13_24 ^ 2}| . for the case of vanishing majorana phases and dirac phases having the value @xmath68 , this element can vanish when [ metau : fixedphase ] & -&c_12c_34s_12s_23-(1-s_12 ^ 2)s_23s_34 ^ 2_13_24+(-c_23c_34_13 + + & & c_23s_12(c_34s_12_13+c_12s_34_24)+s_12 ^ 2s_34_14-s_34_14 ) = 0 . for a vanishing active sterile mixing angle @xmath40 one recovers the 3 generation case . in this limit , from eq . ( [ metau : fixedphase ] ) one observes that the leading order term and the term with @xmath91 are of the same order @xmath126 ( 10@xmath98 ) while the @xmath106 term vanishes and hence cancellation is possible excepting for very low values of the lightest mass . we can see this in panel ( a ) of fig . 6 . in panel ( b ) ( red / light region ) all the parameters are varied randomly ( 3 + 1 case ) and cancellation is seen to be possible over the whole range of @xmath47 . figure 6 : plots of @xmath127 for normal hierarchy with lowest mass @xmath47 . the panel ( a ) corresponds to three generation case . in ( b ) ( red / light region ) all the parameters are varied in their full allowed range and the green / dark region is for @xmath128 with all the other parameters covering their full range . [ fig6 ] in panel ( b ) ( green / dark region ) we also plot the element @xmath127 for the upper limit of @xmath128 . in this case there is no cancellation for very low values of the smallest mass . this is because when @xmath129 is large , the @xmath91 term containing @xmath21 becomes large @xmath7 ( 1 ) and there will be no cancellation . + for inverted hierarchy the element @xmath113 using the approximation in eq ( [ xih ] ) becomes |m_e| & & ( c_12 ^ 2+e^2is_12 ^ 2)s_23s_34 ^ 2_13_24 + & - & ( c_23c_34_13e^i_13(c_12 ^ 2+e^2is_12 ^ 2)+e^i_14s_34_14(c_12 ^ 2+e^is_12 ^ 2 ) + & - & e^i(2+_14)s_34_14+c_12c_23s_12s_34_24e^i_24(e^2i-1))}| in the limit of vanishing majorana phases and dirac cp violating phases equal to @xmath68 this element becomes negligible when ( c_23c_34_13+s_34_14-s_34_14 ) + s_23s_34_13_24 ^ 2 = 0 . in panel ( a ) of fig . 7 the three generation case is reproduced by putting @xmath130 and in ( b ) all the parameters are varied in their allowed range ( 3 + 1 case ) . in both the figures we can see that cancellation is permissible over the whole range of @xmath49 considered . when the cp violating phase @xmath80 we see that the leading order term ( @xmath131 ) vanishes and as a result for large values of @xmath129 the cancellation is not possible because the term with coefficient @xmath91 becomes large ( @xmath7(10@xmath97 ) ) . + + figure 7 : plots of @xmath127 for inverted hierarchy with lowest mass @xmath49 . the panel ( a ) corresponds to three generation case . in ( b ) all the parameters are varied in their full allowed range ( 3 + 1 ) . the panel ( c ) , ( d ) is for specific value of @xmath40 and @xmath44 with all the other parameters covering their full range . the panel ( f ) shows correlation between @xmath44 and @xmath103 . [ fig7 ] for non zero values of the cp violating phase @xmath44 this leading order term is non zero and its contribution will be significant . so in this case high values of @xmath40 are also allowed because now the leading order and the term with coefficient @xmath91 will be of same magnitude . when we fix @xmath132 and @xmath133 the region where @xmath49 is small is disallowed ( panel ( c ) blue / dark region ) but when @xmath44 varies within its full range the disallowed regions become allowed ( panel ( c ) cyan / light region ) . when @xmath129 approaches its upper limit , the @xmath91 term having @xmath21 becomes very large and cancellation is not possible even for non zero values of @xmath44 which can be seen from panel ( d ) . however , when @xmath110 , very small values of @xmath129 can not give cancellation as the leading order term becomes large ( panel ( e ) ) . @xmath129 has to be @xmath112 0.01 for the term to vanish which can be seen from panel ( f ) where we plotted the correlation between @xmath44 and @xmath129 for @xmath134 . the ( 2,2 ) diagonal entry in neutrino mass matrix is given as m _ & = & e^2 i(_14 - _ 24 + ) c_14 ^ 2 m_4 s_24 ^ 2 + & + & e^2 i ( _ 13 + ) m_3(c_13 c_24 s_23 - e^i(_14 - _ 13 -_24 ) s_13 s_14 s_24)^2 + & + & m_1 \{-c_23 c_24 s_12 + c_12(-e^i _ 13 c_24 s_13 s_23 - e^i(_14 - _ 24 ) c_13 s_14 s_24)}^2 + & + & e^2 i m_2 \{c_12 c_23 c_24 + s_12(-e^i _ 13 c_24 s_13 s_23 - e^i(_14 - _ 24 ) c_13 s_14 s_24)}^2 this expression reduces to its three generation case if the mixing angle @xmath39 vanishes . also we can see from the expression that there is no dependence on the mixing angle @xmath40 . using the approximation in eqs . ( [ xnh ] ) this element can be simplified to the form |m_| & & |\ { c_12 ^ 2 c_23 ^ 2 e^2 i + e^i(_13 + 2 ) s_23 ^ 2 + & - & 2 c_12 c_23 e^i(_13 + 2 ) s_12 s_23 _ 13 + & + & ^2\{e^2i(_13 + ) s_12 ^ 2s_23 ^ 2 ^ 2_13+e^i(_14-_24)(e^i(2 + _ 14 -_24)_24 + & - & 2 e^2ic_12c_23s_12_14)_24}}| . for the case of majorana cp phases having the value 0 and the dirac phases having the value @xmath68 , this element vanishes when [ mmmphase ] & & s_23 ^ 2 + c_12 ^ 2 c_23 ^ 2 + c_12 s_12 2 _ 23 _ 13 + & + & ^2(s_12 ^ 2s_23 ^ 2_13 ^ 2-c_232_12_14_24+_24 ^ 2)=0 . + figure 8 : plots of vanishing @xmath124 for normal hierarchy for different values of @xmath39 when all other mixing angles are varied in their 3@xmath61 ranges , dirac cp phases are varied from 0 to @xmath102 and majorana phases from 0 to @xmath68 . [ fig8 ] we know that for the case of 3 generations , the elements in the @xmath135 block are quite large and can not vanish for normal hierarchy . in panel ( a ) of fig . 8 we can see that @xmath136 can not vanish in small @xmath47 region for @xmath95 which is indeed the 3 generation case . this is because the magnitude of the first two terms in eq . ( [ mmmphase ] ) is quite large in this case , @xmath126 ( 10@xmath97 ) and for cancellation to occur the term with coefficient @xmath106 has to be of the same order . this is not possible when @xmath103 is small . however when @xmath137 is varied in its full allowed range the contribution of the sterile part is enhanced and this can cancel the active part as can be seen from panel ( b ) . now to understand the dependence of @xmath138 with @xmath39 we note that if we increase @xmath103 from its lower bound then the two terms become of the same order . so there will be regions in the limit of small @xmath47 for which this element vanishes ( panel ( c ) ) . we see in panel ( d ) of fig . 8 that when @xmath39 acquires very large values , the magnitude of the @xmath106 ( @xmath139 ) term becomes large , thus leading to non cancellation of the terms with the leading order first two terms . hence , the region with very small @xmath47 is not allowed . using the approximation for inverted hierarchy the element @xmath124 becomes |m_| & & & + & ^2[2_12 c_23 e^i(_14 - _ 24)(1 - e^2 i ) _ 14 _ 24 + s_23 ^ 2 e^2 i _ 13(c_12 ^ 2 + e^ 2 i s_12 ^ 2 ) _ 13 ^ 2 + & + & e^2i(+ _ 14 - _ 24 ) _ 24 ^ 2]}| . assuming majorana phases to be zero and dirac phases having value @xmath68 , this element can vanish when & & c_23 ^ 2+^2(s_23 ^ 2_13 ^ 2+_24 ^ 2)=0 . in panel ( a ) of fig . 9 we plotted @xmath136 for @xmath95 to reproduce 3 generation case whereas in panel ( b ) all the parameters are varied in their allowed range in 3 + 1 scenario . in both cases we can see that cancellation is possible for full range of @xmath49 . it can be noticed that unlike normal hierarchy , here cancellation is possible for small values of @xmath103 because in this case all the terms are of same order and there can always be cancellations . however , if we put @xmath133 then the term @xmath91 ( @xmath140 ) drops out from the equation and the leading order term can not be canceled for small values of @xmath103 . it can be seen from panel ( c ) that for @xmath141 and @xmath133 the regions where @xmath49 is small is not allowed . as the value of @xmath39 increases there is the possibility of cancellation of terms for all the values of @xmath44 as can be seen from panel ( d ) where we plot @xmath142 with the lowest mass for @xmath143 when all the other mixing angles are varied in 3@xmath61 range and cp violating phases are varied in full range . now if we keep increasing @xmath103 then @xmath106 term will become large and the chance of cancellation will be less . + figure 9 : plots of vanishing @xmath124 for inverted hierarchy with lowest mass @xmath49 . panel ( a ) for 3 generation case ( b ) all the parameters are varied in full allowed range ( 3 + 1 ) . panel ( c ) and ( d ) are for specific values of @xmath44 and @xmath103 are taken with all other parameters covering their full range . the ( 2,3 ) element of @xmath145 in the flavor basis becomes quite complicated in the presence of an extra sterile neutrino . the expression is m _ & = & e^i(2 _ 14 - _ 24 + 2 ) c_14 ^ 2 c_24 m_4 s_24 s_34 + & + & e^2 i ( _ 13 + ) m_3 ( c_13 c_24 s_23 - e^i(_14 - _ 24 - _ 13 ) s_13 s_14 s_24 ) + & & \{-e^i(_14 - _ 13 ) c_24 s_13 s_14 s_34 + c_13 ( c_23 c_34 - e^i _ 24 s_23 s_24 s_34 ) } + & + & m_1\{- c_23 c_24 s_12 + c_12(-e^i _ 13 c_24 s_13 s_23 - e^i(_14 - _ 24 ) c_13 s_14 s_24 ) } + & & [ -s_12 ( -c_34 s_23 - e^i _ 24 c_23 s_24 s_34 ) + & + & c_12 \ { -e^i _ 14 c_13 c_24 s_14 s_34 - e^i _ 13 s_13(c_23 c_34 - e^i_24 s_23 s_24 s_34 ) } ] + & + & e^2 i m_2\{c_12 c_23 c_24 + s_12(-e^i _ 13 c_24 s_13 s_23 - e^i(_14 - _ 24 ) c_13 s_14 s_24 ) } + & & [ c_12(-c_34 s_23 - e^i _ 24 c_23 s_24 s_34 ) + & + & s_12\{-e^i _ 14 c_13 c_24 s_14 s_34 - e^i _ 13 s_13(c_23 c_34 - e^i _ 24 s_23 s_24 s_34 ) } ] . it reduces to the 3 generation case when @xmath146 . in the normal hierarchical region where @xmath47 can assume very small values and can be neglected , using approximations in eqs . ( [ xnh ] , [ chi1 ] , [ chi2 ] ) we get & - & + & + & ^2 [ e^i(2 + _ 13)(e^i _ 14 s_12 _ 14 + 2 c_12 c_23 e^i _ 24 _ 24)s_12 s_23 s_34 _ 13 + & + & e^i _ 14(e^i(2 - _ 24 ) c_12 c_34 s_12 _ 24 - e^i(2 + _ 13 ) _ 13 s_34 ) _ 14 s_23 + & + & c_23 c_34 e^2i(+ _ 13 ) s_12 ^ 2 _ 13 ^ 2 s_23]}| . to see the order of the terms we consider the case where majorana cp phases vanish and dirac phases have the value @xmath68 . in this limit the element becomes negligible when & & c_23 c_34s_23(1-c_12 ^ 2)+\{(c_12c_34s_12_13)2_23 + & + & _ 24s_34(s_23 ^ 2+c_12 ^ 2c_23 ^ 2)+s_34(_24+c_12c_23s_12_14 ) } + & + & ^2\{s_12_13s_23s_34(s_12_14 + 2c_12c_23_24)+_14s_23(c_12c_34s_12 ^ 2s_23_13 ^ 2)}=0 . being an element of @xmath147 block , @xmath148 shows the same behaviour that of @xmath138 in normal hierarchy . in panel ( a ) of fig . 10 we plotted @xmath149 for @xmath150 which coincides with the 3 generation case and we can see that cancellation is not possible in hierarchical region . however , when all the parameters are varied in their allowed range in panel ( b ) it get contribution from the sterile part and cancellation is always possible . it can also be seen from panel ( c ) of fig . 10 that for @xmath151 there is no cancellation in the region when @xmath47 is small and the figure is quite similar to that of 3 generation case . however , as this active sterile mixing angle becomes larger there is always a possibility of allowed region towards the lower values of @xmath47 as is evident from panel ( d ) . this is because for the vanishing value of @xmath40 the terms with @xmath91 and @xmath106 become very small and can not cancel the leading term @xmath7 ( 10@xmath97 ) . it can also be seen that in this case ( i.e @xmath151 ) , there is no @xmath152 term in eq . ( 3.31 ) and this is why the figure is somewhat similar to the 3 generation case . however , when @xmath40 increases these two contributions become large and cancellation becomes possible . + figure 10 : plots of vanishing @xmath144 for normal hierarchy ( a ) for vanishing @xmath40 and @xmath39 . in panel ( b ) all parameters are varied in their full allowed range . panel(c , d ) are for specific values of @xmath40 when all other mixing angles are varied in their full range . [ fig10 ] for the case of inverted hierarchy where @xmath49 can have very small values , @xmath144 becomes |m_| & & |\ { -c_23 c_34 s_23(c_12 ^ 2 e^2 i + s_12 ^ 2 ) + & + & + & + & ^2 [ c_23 c_34 s_23 e^ 2 i _ 13(c_12 ^ 2 + e^2 i s_12 ^ 2 ) _ 13 ^ 2 + & + & c_12 s_12 s_23 ( e^2 i - 1)(c_34 e^i(_14 - _ 24 ) _ 14 + 2 s_34 c_23 e^i(_13 + _ 24 ) _ 13)_24]}| . to get an idea about the magnitude of the terms we take vanishing majorana phases and dirac cp phases to be of the order @xmath68 . the expression in this case for vanishing @xmath148 becomes & & -c_23c_34s_23+(s_34_24(c_23 ^ 2-))-^2(-s_34_13_14-c_23c_34_13 ^ 2)=0 in panel ( a ) of fig . 11 , where @xmath149 for 3 generation is plotted , we can see that unlike @xmath138 there is no cancellation in small @xmath49 region but when plotted for the full range it gets contribution from the sterile part and there is cancellation for the full range of @xmath49 ( panel ( b ) ) . clearly the cancellation of the terms do not become possible for small values of @xmath40 in strict hierarchical region . this case is similar to the three generation case in ih ( cyan / light region , panel ( c ) ) . this is because for @xmath151 the contribution of @xmath103 comes from the @xmath106 term . if we put the cp violating phase @xmath44 as zero then cancellation is not possible for whole range of @xmath49 ( blue / dark region panel ( c ) ) . however , as the value of @xmath129 increases all the terms in the above equation becomes of the same order and cancellation for very small values of @xmath49 is possible ( panel ( d ) ) . + figure 11 : plots of vanishing @xmath144 for inverted hierarchy ( a ) for vanishing @xmath40 and @xmath39 ( 3 generation ) . in panel ( b ) all parameters are varied in their full allowed range ( 3 + 1 ) . panel ( c ) and ( d ) are for specific values of @xmath40 and @xmath44 when all other mixing angles are varied in their full range . [ fig11 ] this element is related to @xmath124 by the @xmath114 symmetry . as discussed earlier , in the limit when @xmath39 and @xmath40 are not very large , the two mixing angles @xmath40 and @xmath39 will behave in the same way in the textures related by @xmath114 symmetry . the ( 3,3 ) element of the neutrino mass matrix in the presence of one sterile neutrino is given as m _ & = & e^2i(_14 + ) c_14 ^ 2 c_24 ^ 2 m_4 s_34 ^ 2 + & + & e^2i(_13 + ) m_3 \{e^i(_14 - _ 13 ) c_24 s_13 s_14 s_34 + c_13(c_23 c_34 - e^i _ 24 s_23 s_24 s_34)}^2 + & + & m_1[-s_12(-c_34 s_23 - e^i _ 24 c_23 s_24 s_34 ) + & + & c_12\{-e^i_14 c_13 c_24 s_14 s_34 - e^i _ 13 s_13(c_23 c_34 - e^i _ 24 s_23 s_24 s_34)}]^2 + & + & e^2 i m_2 [ c_12(-c_34 s_23 - e^i _ 24 c_23 s_24 s_34 ) + & + & s_12\{-e^i _ 14 c_13 c_24 s_14 s_34 - e^i _ 13 s_13(c_23 c_34 - e^i _ 24 s_23 s_24 s_34)}]^2 . it reduces to the 3 generation case for @xmath153 . using the approximation for normal hierarchy in eqs . ( [ xnh ] , [ chi1 ] , [ chi2 ] ) this becomes |m_| & & & & s_12c_12c_342_23_13-c_12c_23s_34e^2i(s_12_14e^i_14 + c_12c_23_24 e^2i_24)+s_34_24(-s_23 ^ 2e^2i(+ _ 13)+ i_24 + & -&e^2i(+ _ 14)-i_24)}+^2\ { s_12 ^ 2s_23_13e^i(2 + _ 13)(c_23c_34_13e^i_13+s_34_14e^i_14 ) + & + & c_12s_12s_23_24e^2i(2c_23s_34_13e^i(_13+_24)+c_34_14e^i(_14-_24 ) ) + & -&s_23s_34_13_14e^i(2+_13+_14)}}| . to get an idea of the order of the terms we consider the vanishing majorana phases and the dirac phases having the value equal to @xmath68 . this element vanishes when & & c_23c_34s_23(1-c_12 ^ 2)+\{s_12c_12c_342_23_13 + c_12c_23s_34(s_12_14 + & + & c_12c_23_24)-s_34_24(s_23 ^ 2-)}+^2\ { s_12 ^ 2s_23_13(c_23c_34_13+s_34_14 ) + & + & c_12s_12s_23_24(2c_23s_34_13+c_34_14)+s_23s_34_13_14}=0 . + figure 12 : plots of vanishing @xmath125 for normal hierarchy with lowest mass @xmath47 . panel ( a ) correspond to three generation case . in panel ( b ) all the mixing angles are varied in their full allowed range of parameters ( 3 + 1 ) . panel ( c ) and ( d ) are for some specific values of @xmath40 . [ fig12 ] for vanishing @xmath40 , which is the case for 3 generation , @xmath154 is disallowed for small @xmath47 as can be seen from panel ( a ) of fig . this is the generic behaviour of a element belonging to the @xmath135 block in normal hierarchy which we mentioned previously . this is because for @xmath40 equal to zero the leading order term is large ( @xmath7 ( 10@xmath97 ) ) . here the term with @xmath106 is quite small ( 10@xmath155 - 10@xmath156 ) and hence will not have very significant role to play . thus , only terms with coefficient @xmath91 can cancel the leading order term . however , for vanishing @xmath40 this term is small @xmath7 ( 10@xmath155 ) , and can not cancel the leading order term . in panel ( b ) when all the parameters are varied in their @xmath26 range we can see that cancellation is possible over the whole range of @xmath47 ( 3 + 1 case ) . now , when @xmath40 starts increasing from its lowest value there exist a region for intermediate values where both the terms become approximately of the same order and hence there can be cancellations ( panel ( c ) ) . towards very large values of @xmath40 the term with coefficient @xmath91 becomes larger than the leading order term due to which this element can not vanish . for the cancellation very large values of @xmath47 is required as can be seen from panel ( d ) of fig 12 . + figure 13 : plots of vanishing @xmath125 for inverted hierarchy with lowest mass @xmath49 . panel ( a ) correspond to three generation case . in panel ( b ) all the mixing angles are varied in their full allowed range of parameters ( 3 + 1 ) . panel ( c ) and ( d ) are for some specific values of @xmath40 and @xmath44 . [ fig13 ] for the case of inverted hierarchy where @xmath49 approaches small values we get the expression m _ & & c_34 ^ 2 s_23 ^ 2(c_12 ^ 2 e^2 i + s_12 ^ 2 ) + e^2 i ( _ 14 + ) s_34 ^ 2 + & + & 2 + & + & ^2[(c_12 ^ 2 + e^ 2 i s_12 ^ 2)\{c_23 c_34 _ 13 e^ i _ _ 13 e^ i _ 13 + 2 _ 14 s_34 e^ i _ 14 ) + e^ 2 i _ 14 _ 14 ^ 2 s_34 ^ 2 } + & + & ( c_12 ^ 2 e^ 2 i + s_12 ^ 2)c_23 ^ 2 e^ 2 i _ 24 _ 24 ^ 2 s_34 ^ 2 + & + & 2 s_12(e^2 i - 1 ) e^ i _ 24(c_34 _ 13 2_23 e^ i _ 13 + c_12 c_23 _ 14 s_34 ) s_34 _ 24 ] . for vanishing majorana cp phases and dirac phases having the value equal to @xmath68 this expression becomes m _ & & -c_23c_34s_23+s_34_24(c_23 ^ 2-)+^2s_23_13(c_23c_34_13+s_34_14 ) in panel ( a ) of fig . 13 we reproduced the 3 generation behaviour by plotting @xmath157 for @xmath151 and in panel ( b ) all the parameters are varied randomly ( 3 + 1 ) . in both the cases we can see that cancellations are possible for the whole range of @xmath49 . for @xmath151 all the terms are of same order and cancellations are always possible . but if we put @xmath133 then one term with coefficient @xmath91 and another term with coefficient @xmath106 drops out from the equation and then small values of @xmath129 can not cancel the leading order term any more . this can be seen from panel ( c ) where cancellation is not possible for lower @xmath49 region . however when @xmath129 increases to a value of about 0.02 this element can vanish ( panel ( d ) the cyan region ) . we see that when @xmath40 increase towards its upper bound the @xmath91 term becomes large @xmath158 . hence , the other terms are not able to cancel this term and we do not get small @xmath49 region allowed ( panel ( d ) , blue region ) . the elements @xmath2 , @xmath3 , @xmath4 and @xmath5 are present in the fourth row and fourth column in the neutrino mass matrix . they are the new elements that arises in 3 + 1 scenario due to the addition of one light sterile neutrino . the expressions for @xmath2 and @xmath3 are given by m_es & = & e^i(2 + _ 14 ) c_14 c_24 c_34 m_4 s_14 + & + & e^i(2 + _ 13 ) c_14 m_3 s_13\{-e^i(_14 - _ 13 ) c_24 c_34 s_13 s_14 + c_13(-e^ i _ 14 c_34 s_23 s_24 - c_23 s_34 ) } + & + & c_12 c_13 c_14 m_1[-s_12(-e^i _ 24 c_23 c_34 s_24 + s_23 s_34 ) + & + & c_12\{-e^i _ 14 c_13 c_24 c_34 s_14 - e^i _ 13 s_13(-e^i _ 24 c_34 s_23 s_24 - c_23 s_34 ) } ] + & + & e^ 2 i c_13 c_14 m_2 s_12[c_12(-e^ i _ 24 c_23 c_34 s_24+s_23s_34 ) + & + & s_12 \{- e^i _ 14 c_13 c_24 c_34 s_14 - e^i _ 13 s_13(-e^i _ 24 c_34 s_23 s_24 - c_23 s_34 ) } ] . + + + figure 14 : correlation plots for vanishing @xmath159 for both normal and inverted hierarchy . in these plots all the mixing angles are varied in their 3 @xmath61 allowed range , dirac cp phases are varied from 0 to @xmath102 and majorana phases from 0 to @xmath68 . [ fig14 ] @xmath160 \\ \nonumber & + & e^{2 i \alpha } m_2 \{c_{12 } c_{23 } c_{24 } + s_{12}(-e^{i \delta_{13 } } c_{24 } s_{13 } s_{23 } - e^{i(\delta_{14 } - \delta_{24 } } c_{13 } s_{14 } s_{24})\ } \\ \nonumber & & [ c_{12}(-e^{i \delta_{24 } } c_{23 } c_{34 } s_{24 } + s_{23 } s_{34 } ) \\ \nonumber & + & s_{12}\{-e^{i \delta_{14 } } c_{13 } c_{24 } c_{34 } s_{14 } - e^{i \delta_{13 } } s_{13}(-e^ { i \delta_{24 } } c_{34 } s_{23 } s_{24 } - c_{23 } s_{34})\ } ] . \end{aligned}\ ] ] though the equations seem very complex , one can easily understand the properties of these elements by just looking at the @xmath50 terms . the @xmath50 term in @xmath2 is proportional to @xmath161 . so in general it is quite large ( @xmath162 ) . for this element to become negligible very small values of @xmath77 is required . but as this angle is bounded by the sbl experiments , complete cancellations never occurs for both normal and inverted hierarchy ( panel ( a ) , ( b ) of fig . similar predictions are obtained for @xmath3 element which can not vanish since @xmath103 has to be negligible which is not allowed by the data . this can be seen from panel ( c ) , ( d ) of fig . 14 . for the element @xmath4 the scenario is quite different . m_s & = & c_14 ^ 2 c_24 ^ 2 c_34 e^ 2 i(_14 + ) m_4 s_34 + & + & e^2 i ( + _ 13 ) m_3\{-c_24 c_34 e^i(_14 - _ 13 ) s_13 s_14 + c_13(-c_23 s_34 - c_34 e^ i _ 24 s_23 s_24 ) } + & & \{-c_24 e^i(_14 - _ 13 ) s_13 s_14 s_34 + c_13(c_23 c_34 - e^i _ 24 s_23 s_34s_24 ) } + & + & m_1[-s_12(-c_23 c_34 e^i _ 24 s_24 + s_23 s_34 ) + & + & c_12\{-c_13 c_24 c_34 e^ i _ 14 s_14 - e^ i _ 13 s_13(-c_23 s_34 - c_34 e^i _ 24 s_23 s_34 ) } ] + & & [ -s_12(-c_34 s_23 - c_23 e^i _ 24 s_34s_24 ) + & + & c_12\{-c_13 c_24 e^ i _ 14 s_14 s_34 - e^i _ 13 s_13(c_23 c_34 - e^ i _ 24 s_23 s_34s_24 ) } ] + & + & e^ 2 i m_2[c_12(-c_23 c_34 e^i _ 24 s_34 + s_23 s_34 ) + & + & s_12\{-c_13 c_24 c_34 e^ i _ 14 s_14 - e^ i _ 13 s_13(-c_23 s_34 - c_34 e^ i _ 24 s_23 s_24 ) } ] + & & [ c_12(-c_34 s_23 - c_23 e^ i _ 24 s_34s_24 ) + & + & s_12\{-c_13 c_24 e^ i _ 14 s_14 s_34 - e^ i _ 13 s_13(c_23 c_34 - e^i _ 24 s_23 s_34s_14 ) } ] . in this case the @xmath50 term is proportional to @xmath40 and there is no lower bound on it from the sbl experiments i.e. it can approach smaller values . as a result the term with @xmath50 can be very small . thus this matrix element can possibly vanish in both hierarchies for whole range of the lowest mass ( panel ( e ) , ( f ) ) . + the ( 4,4 ) element of the neutrino mass matrix is given as m_ss & = & c_14 ^ 2 c_24 ^ 2 c_34 ^ 2 e^2 i ( + _ 14 ) m_4 + & + & e^2 i(+ _ 13 ) m_3\{-c_24 c_34 e^i(_14 - _ 13 ) s_13 s_14 + c_13(-c_23 s_34 - c_34 e^ i _ 24 s_23 s_24)}^2 + & + & m_1[-s_12(-c_23 c_34 e^ i _ 24 s_24 + s_23 s_34 ) + & + & c_12\{-c_13 c_24 c_34 e^ i _ 14 s_14 - e^ i _ 13 s_13(-c_23 s_34 - c_34 e^ i _ 24 s_23 s_24)}]^2 + & + & e^ 2 i m_2[c_12(-c_23 c_34 e^ i _ 24 s_24 + s_23 s_34 ) + & + & s_12\{-c_13 c_24 c_34 e^ i _ 14 s_14 - e^i _ 13 s_13(-c_23 s_34 - c_34 e^i _ 24 s_23 s_34)}]^2 the @xmath50 term for @xmath5 is proportional to @xmath163 . one can see that this term is of order one as a result this element can never vanish as is evident from panel ( g , h ) . in this paper we analyze systematically the one - zero textures of the @xmath12 mass matrix in presence of a sterile neutrino . assuming neutrinos to be majorana particles , this is a symmetric matrix with 10 independent entries . we use the information on the active sterile mixing angles from the short baseline experiments . we analyze if the current constraints on oscillation parameters allow each of these entries to assume a vanishing value . we also study the implications and correlations among the parameters when each matrix element is zero . we expand the mass matrix element in terms of a parameter @xmath91 with suitable coefficients @xmath164 and @xmath152 corresponding to the mixing angles @xmath35 , @xmath38 and @xmath39 . this is motivated by the observation that these angles are of same order with @xmath165 . these expressions facilitate the analytic understanding of the numerical results presented in the different plots . we study the vanishing condition as a function of the lowest mass @xmath47 ( nh ) or @xmath49 ( ih ) by varying the lightest mass in the range 0.0001 - 0.5 ev . we find that @xmath166 is possible for nh only for higher values of the smallest mass @xmath47 while for ih it is possible even for lower values . this is in sharp contrast with the 3 generation case where complete cancellation can never take place for ih . the current and upcoming @xmath83 experiments like gerda , cuore , majorana , exo , supernemo , kamland - zen , sno+ @xcite can lower the present sensitivity by one order of magnitude ( @xmath60.012 - 0.06 ev ) and hence can probe the ih region for the three neutrino scheme @xcite . however for 3 + 1 scenario , @xmath69 can be in the range of the expected sensitivity of the future @xmath83 experiments , even for nh . thus if the existence of sterile neutrinos is confirmed by future experiments @xcite then it may be difficult to probe the hierarchy from @xmath83 alone . @xmath94 can vanish over the whole range of the smallest mass for both 3 and 3 + 1 neutrino scenarios . however for larger values of the mixing angle @xmath103 , cancellation is not achieved for smaller @xmath47 for nh . for ih the cancellation condition depend on the majorana phase @xmath44 and the mixing angle @xmath39 . we obtain the correlations between these two parameters required for making this element vanishingly small . cancellation is achieved for the element @xmath113 for the full range of the lowest mass in the 3 + 1 scenario . the element @xmath87 is related to the element @xmath113 by @xmath114 symmetry . however unlike three generation case @xmath37 in these textures are not related simply by @xmath167 . the mixing angles @xmath39 and @xmath40 are also different in these two textures in general . however for small values of @xmath39 we get @xmath168 in these textures . consequently the role played by @xmath39 for @xmath87 is played by @xmath40 in @xmath169 in this limit . thus in this case cancellation is not achieved for larger values of @xmath129 in the hierarchical regime for nh . for ih we obtain correlations between @xmath44 and @xmath170 for fulfilling the condition for cancellations . the elements @xmath138 and @xmath171 are related by @xmath114 symmetry . for these cases , cancellation is not possible in the hierarchical zone for ih , in the 3 generation case . however the extra contribution coming from the sterile part helps in achieving cancellation in this region . for ih one can obtain correlations between the majorana phase @xmath44 and the mixing angle @xmath39(@xmath40 ) for @xmath172(@xmath173 ) . for @xmath148 element cancellation was possible for three generation case only for higher values of the lightest mass . however if one includes the sterile neutrino then this element can vanish over the whole range of the lightest neutrino mass considered . with the current constraints on sterile parameters it is not possible to obtain @xmath174 while @xmath2 and @xmath3 can only vanish in the qd regime of the active neutrinos . however , the element @xmath4 can be vanishingly small in the whole mass range . this is because the angle @xmath40 can take very small values and hence cancellation is possible even for smaller values of the lowest mass . the above results can be useful for building models for light sterile neutrinos and shed light on the underlying new physics if future experiments and analyses reconfirm the explanation of the present anomalies in terms of sterile neutrinos . the work of c. s. k and s. g. is supported by the national research foundation of korea ( nrf ) grant funded by korea government of the ministry of education , science and technology ( mest ) ( grant no . 2011 - 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ph ] ] . a. esmaili and a. y. .smirnov , arxiv:1307.6824 [ hep - ph ] .[/INST] in this paper we study the phenomenological implications of the one zero textures of low energy neutrino mass matrices in presence of a sterile neutrino . we consider the 3 + 1 scheme and use the results from global fit for short baseline neutrino oscillation data which provides the bounds on the three additional mixing angles . we find that the mass matrix elements @xmath0 ( @xmath1 ) involving only the active states can assume vanishing values in the allowed parameter space for all the mass spectrum . among the mass matrix elements connecting the active and sterile states , @xmath2 and @xmath3 can become small only for the quasi - degenerate neutrinos . the element @xmath4 on the other hand can vanish even for lower values of masses since the 3 - 4 mixing angle only has an upper bound from current data . the mass matrix element ( @xmath5 ) involving only the sterile state stays @xmath6 @xmath7(1 ) ev in the whole parameter region . we study the possible correlations between the sterile mixing angles and the majorana phases to give a zero element in the mass matrix . </s>

anyone else know Psy, the Gangnam Style artist, publicly held anti-American views, also encouraging the killing of soldiers? #educateyoself — Sayruhhhh(@sweetieswan) December 6, 2012 @scooterbraun Have you seen those anti-American lyrics from PSY back in 2003? I believe he sang about killing Americans.#something2ponder — Ryan Patrick (@Amabonovella) December 5, 2012 Here’s a fun fact: In 2002, Psy performed at an anti-American concert in Korea and sang about killing our soldiers and how awful we are. — Jacob Martens(@Jacob_martens) December 6, 2012 Psy the anti-American protestor: Certainly not the same guy you saw on Ellen lexne.ws/f61 – @korealawtoday — LXBN (@LXBN) December 6, 2012 TIL Psy has a very anti-American past he is trying to hide tinyurl.com/asrywrx — Today I Learned (@TodayILearnd) December 5, 2012 He has the most-watched YouTube video ever (more than 900 million views), and is set to perform for the Obamas at the annual Christmas in Washington concert later this month. Eight years ago, however, the “Gangnam Style” K-pop singer advocated the murder and torture of US military personnel and their family members. HAPS, an English-language Korean magazine, says PSY’s anti-American views have long been known in Korea, but only recently surfaced in the US. The lyrics of the anti-US song performed live by PSY and several other popular Korean singers in 2004 (shortly after the US invaded Iraq) were first translated into English two months ago on CNN’s iReport: 싸이 rap : 이라크 포로를 고문해 댄 씨발양년놈들과 고문 하라고 시킨 개 씨발 양년놈들에 딸래미 애미 며느리 애비 코쟁이 모두 죽여 아주 천천히 죽여 고통스럽게 죽여 PSY Rap: Kill those fucking Yankees who have been torturing Iraqi captives Kill those fucking Yankees who ordered them to torture Kill their daughters, mothers, daughters-in-law and fathers Kill them all slowly and painfully PSY’s anti-American views weren’t discussed when the K-Pop star appeared on Ellen. Exit question: Will anyone in the mainstream media ask PSY if he still supports killing US soldiers and their family members? Hat tip: Jon. Update: Surprise! Despite PSY’s anti-American views, President Obama still plans to attend his Christmas in Washington performance. Correction: Twitchy originally stated that PSY was set to perform at the White House. The Obamas will attend PSY’s Christmas in Washington performance, but the concert venue is the National Building Museum. This post has been updated to reflect that information. Update: In light of the overwhelming reaction to this story, PSY has issued a statement of apology this afternoon, which reads: As a proud South Korean who was educated in the United States and lived there for a very significant part of my life, I understand the sacrifices American servicemen and women have made to protect freedom and democracy in my country and around the world. The song – from eight years ago – was part of a deeply emotional reaction to the war in Iraq and the killing of two innocent Korean civilians that was part of the overall antiwar sentiment shared by others around the world at that time. While I’m grateful for the freedom to express one’s self I’ve learned there are limits to what language is appropriate and I’m deeply sorry for how these lyrics could be interpreted. I will forever be sorry for any pain I have caused anyone by those words. I have been honored to perform in front of American soldiers in recent months – including an appearance on the Jay Leno show specifically for them – and I hope they and all Americans can accept my apology. While it’s important we express our opinions, I deeply regret the inflammatory and inappropriate language I used to do so. In my music I try to give people a release, a reason to smile. I have learned that though music, our universal language we can all come together as a culture of humanity and I hope that you will accept my apology. The chances of PSY being uninvited from the Christmas in Washington event seemed slim before and are likely nonexistent now. Perhaps the best we can hope for is that the president not say, “No apology necessary.” But will Americans find it in their hearts to forgive for the sake of “a culture of humanity”? Follow @twitchyteam ||||| He has the most-watched YouTube video of all-time, an international phenomenon of a mega-hit in “Gangnam Style,” has made appearances on nearly every American morning talk show under the sun from Today to Ellen, and is scheduled to appear at a D.C. charity concert later this month with President Obama in attendance. It’s safe to say that Korean pop star PSY is now the “most-liked” entertainer on the planet. It has recently been unearthed in the states, however, that eight years ago, long before achieving this massive stardom, the mega-star rapped about “slowly and painfully” killing American military members and their families. Some context: since becoming a democracy in the late 80s, South Korea has developed a rich, sometimes over-the-top, tradition of protest. Swarms of Koreans hit the streets to protest everything from free trade agreements to North Korea to Muslim extremism to American troops stationed on their peninsula. During a 2002 protest concert against the presence of 37,000 American troops in Korea, PSY took the stage in gold face-paint and, with the crowd egging him on, lifted a miniature “American tank” and smashed it on the ground to massive applause. UPDATE: The performance was inspired by the recent death of two Korean school girls who were run over by an American tank in South Korea. The soldiers driving the tank were acquitted by a US military court. And then in 2004, a Korean missionary was captured in Iraq by Islamists who demanded that South Korea not send troops to aid America in the war in Iraq. Seoul refused to negotiate and the missionary was beheaded. The result: massive protests throughout Korea against both Muslim extremism and the U.S. military for indirectly bringing this fate upon a Korean missionary. As part of the protests, PSY and several other popular Korean musicians put on a live performance of a Korean rock band’s song “Dear American.” When PSY’s turn came, he rapped: Kill those fucking Yankees who have been torturing Iraqi captives Kill those fucking Yankees who ordered them to torture Kill their daughters, mothers, daughters-in-law and fathers Kill them all slowly and painfully As this particularly incendiary verse made its way to American news outlets, the outrage has grown. Conservative Twitter aggregator Twitchy sums up some of the anti-PSY anger, pondering why his anti-American military past was not discussed during his appearance on Ellen. Think of all the musicians who’ve said unseemly things in their art: Ice-T rapped the perspective of killing a police officer years ago in “Cop Killer,” but he is now a star actor who portrays a police officer on NBC’s Law and Order: SVU. At the time, Ice-T said he was simply rapping from the perspective of another man — telling a story — and not calling for the actual murder of police officers. On the other hand, Chris Brown and Eminem have rapped about violence against women… and have followed through on it in real life. But as others have noted, PSY’s handling of his newfound global fame has been remarkably gracious. He hasn’t thrown up the middle finger and rejected his American popularity because of the Iraq War he rightfully found so deplorable (albeit with highly vitriolic rhetoric). The question becomes: Would he have said the same thing today now that he has precious international stardom to preserve? UPDATE: PSY’s publicist has sent an apology from the musician. View here. UPDATE 2: Partial video has surfaced of one of the aforementioned anti-American military performances. Watch here. [h/t HAPS] — — >> Follow Andrew Kirell (@AndrewKirell) on Twitter Have a tip we should know? [email protected] ||||| BUSAN, South Korea -- The talented 34-year-old rapper Park Jae-sang, known better to the world as PSY, has been a controversial staple of the Korean music scene since his first full-length album, PSY from the PSYcho World!, debuted back in 2001. At that time, the traditionally conservative Korean mainstream didn’t know what to make of the blunt lyrics (one track was called “I Love Sex”) or how to react to his unconventional dance moves and eccentric appearance. When he first hit the scene, the naturally-gifted, then-24-year-old PSY, who had just returned home to Korea after withdrawing from both Boston University and the prestigious Berklee College of Music, was quickly nicknamed “The Bizarre Singer.” He wore the title as a badge of honor. And while the world has come to adore the man who is now the most-loved entertainer on the planet, articles published last month on CNN iReport the Korean language Chosun Ilbo and on other Korean sites about PSY’s outspoken role in anti-US military protests back in 2002, and then again in 2004, will either stir indignation with audiences or garner him even more respect. But first, the story must be put in context of the times. The Tragic Death of Two Korean Schoolgirls and America's Response The summer of 2002 in Korea was a time when PSY was cultivating a following while battling censors over his outlandish new style that in this day and age seems tame. It was also a period of heart-rending tragedy that saw an American military vehicle kill 13-year-old middle school girls Shim Mi-son and Shin Hyo-sun, who were walking along the roadside just outside of Seoul on the morning of June 13. In line with the Status of Forces Agreement (SOFA), that sets jurisdiction terms for US forces stationed abroad, the incident was defined “a military operation” and thus handled internally by the American military courts. A subsequent US court martial found the girls’ deaths to be accidental and acquitted service members Sergeant Mark Walker, and the vehicle’s commander, Sergeant Fernando Nino, of negligent homicide, while citing no criminal intent. The American government then paid civil damages to the families involved. “You have to look at this in context... many South Korean artists were part of this America bashing. It was part of a movement...” The Korean public’s reaction to the girls’ deaths was at first muted, as the country was then center-stage as co-host of the World Cup, but soon thereafter thousands of protestors took to the streets demanding, with arguable validity, but no legal precedence, that the soldiers be re-tried in a Korean court. Washington refused and the demonstrations went on for months, as tens of thousands gathered across the country to vent their anger at American policy that made them sole arbiter of justice for US military-related crimes on South Korean soil. The anger was palpable. While reporting on events for the the San Francisco Chronicle, I cited a Gallup poll that showed 75 percent of Koreans in their 20s said they disliked Americans. Sixty-seven percent in their 30s, along with half of those in their 40s, told Gallup they either "did not like" or "hated" the United States. Few living on the peninsula at that time were immune to the movement. Businesses around the country banned Americans (and by association, Westerners) from entering, US flags were laid on the ground at university campuses allowing students to walk on them en route to class, and graphic banners of Shim Mi-son and Shin Hyo-sun were erected at rallies, as the American military came under increasingly heated scrutiny for what was ubiquitously viewed as an unfair and unjustified handling of their deaths. PSY’s Political Performances For some Americans, the story of PSY’s participation in anti-US military protests will elicit condemnation. But should it? First, it must be recognized that thousands of Americans have protested—at times violently—against US military-related issues. After that, one must then acknowledge Korean history within the context of a country that has been under the rule of either outside powers or oppressive dictators for much of its history. A liberal democracy since only 1987, a now free Korean public worships at the altar of protest. Be it storming the office of a politician ensnared in a corruption scandal, burning North Korean flags, opposing a free trade agreement or, as the New York Times once wrote, protesting against protests themselves. Though the following events have been widely discussed in Korea, recent murmurings on the English corner of the Internet have rekindled PSY’s roles in anti-US military protest rallies in the past. The first following the 2002 acquittal of the American soldiers; and the second, PSY’s highly-provocative anti-American military performance during a 2004 protest concert in Seoul, where the entertainer's vitriol was directed towards American military personnel, military brass and their families for the June 22 beheading of a Korean Christian missionary by Islamic extremists in Iraq. First, this from the Korea Times on December 5, 2002, courtesy of the blog Flight of the Kiwi. "Following the acquittals of two U.S. soldiers from negligent homicides charges late last month, a growing number of local celebrities have offered their heart-felt sympathy with the victims in public, while expressing their strong resentment over what they see as an unfair ruling by the American military court. These public figures have composed protest songs against America to pitch in their voice, join public rallies, or have gone as far as calling for revision of the Status of Forces Agreement (SOFA), which governs the status of 37,000 American troops stationed here, through official statements. Even though these pop stars have managed to put in their own two cents' worth, pop vocalist PSY, who has upheld the cause since August through many concerts, is among the most outspoken of them all." PSY’s being "outspoken" was caught on tape and was, until recently, posted on YouTube. It has since been pulled by entertainment company CJ E&M for "copyright claims." A search for videos on Naver.com, the Korean version of Google, features several links to the video, but the videos themselves have been removed as well. During the performance featured on the video, PSY took the stage with several other musicians protesting the Status of Forces Agreement with Washington. With a gold-painted face and the crowd cheering him on, PSY lifted a miniature mock-up of an American tank and threw it to the ground, before smashing it into pieces with a mic stand, all while following along in anti-US military chants. Following the months of vocal protests, including hunger strikes outside the US embassy, the American military eventually amended SOFA, allowing Korean courts to take US servicemen in custody prior to trial. In the past, American soldiers were only tried in Korean court for off-duty crimes, such as earlier this year, when a Korean judge sentenced Pvt. Joseph J. Finley to three years in prison for raping a South Korean woman after following her home. In the end, the power of protest worked—the U.S amended the SOFA agreement. The Beheading of Kim Sun-il Nearly two years after the 2002 protests, on May 22, 2004, the Islamist group Jama'at al-Tawhid wal-Jihad kidnapped Korean missionary Kim Sun-il and held him hostage, demanding that the South Korean government cancel plans to send 3,000 troops to support the US war in Iraq. S eoul refused to negotiate and the Islamist group, led by Abu Musab al-Zarqawi, beheaded Kim, a man whose only crime was proselytizing in extremist-held territory. Kim even studied Arabic in a top Korean university, just so he could spread the Christian word throughout the Middle East. A subsequent video of the heinous act was aired on Al Jazeera with a masked executioner issuing the following statement: “Korean citizens, you were warned, your hands were the ones who killed him. Enough lies, enough cheatings. Your soldiers are here not for the sake of Iraqis, but for cursed America." He then brutally decapitated Kim Sun-il with a large knife. Massive protests erupted across South Korea with thousands rallying against Muslim extremists, as well as Seoul's plans to send troops to Iraq. And while most of the peninsula's fury was directed towards terrorists in Iraq as well as Korean government policy, some anti-US military protesters seized the moment to put forth their cause. Once again, PSY was involved. This time he admonished not only the terrorists and then president Roh Mu-hyun, but he also allegedly unleashed a vitriolic condemnation of American military personnel and military brass. According to a story on October 30, 2012 on the Korean-language version of the Chosun Ilbo and also reported on K-Pop music site AllKpop.com, PSY, along with several popular performers, took part in a live performance of Korean rock band N.EX.T's song "Dear American". 싸이 rap : 이라크 포로를 고문해 댄 씨발양년놈들과 고문 하라고 시킨 개 씨발 양년놈들에 딸래미 애미 며느리 애비 코쟁이 모두 죽여 아주 천천히 죽여 고통스럽게 죽여 PSY Rap: Kill those f****** Yankees who have been torturing Iraqi captives Kill those f****** Yankees who ordered them to torture Kill their daughters, mothers, daughters-in-law and fathers Kill them all slowly and painfully _____ Though reports of PSY performing this have long been known on Korean language sites, it only recently surfaced in English as all eyes and ears of the world have turned in his direction. Before it showed up on the Chosun Ilbo and AllKpop.com at the end of October, the translation was first posted October 6 on CNN’s iReport, an open source news feature that allows users to submit stories for CNN consideration. It was, however, never picked up by CNN staff, even though it received nearly 30,032 views, 361 “recommends” and 152 “shares” at the time of this writing. The person who posted the translation, who the Chosun Ilbo noted is Japanese (and unsurprisingly not a PSY fan), also uploaded the text of his CNN post on YouTube. Initial Reaction Western netizen response has as yet been sparse—aside of the CNN iReport and the YouTube video, there has until now, simply not been enough English language background to be found on the web. Comments posted thus far have ranged from defending PSY: SourKushBalls: “This was taken out of context and mistranslated. PSY is not attacking/dissing American soldiers.” To those offering heavy condemnation (though referencing the earlier issue and not the issue being posted): MIZZKIE: “Just because two innocent girls got accidentally killed (bless their poor souls), it doesn't mean you can spew out your hatred against others in a song sung by a person with fame and influence.” To those viewing him as a man of the times: MoReuGettDa: “You have to look at this in context. All of the South Korean media, all of the South Korean candidates for president, many South Korean artists were part of this America bashing. It was part of a movement...” While in a free society we are all entitled to our opinion of PSY’s words and actions 10 years ago, a comment on Facebook seemed quite fitting. In it, the commenter likened PSY's lyrics to famed American rapper Ice-T, who once released the song “Cop Killer” and yet now stars, ironically, as a cop on the TV show Law and Order. Should PSY Address the Issue? PSY's political prose aside, suffice it to say that while the entertainment world has given us wonderful artistry and life-changing talent, it has also given us some serious cause for pause. Have other performers around the world, at some point, spewed harsh words in the name of protest? Yes. Have entertainers taken advantage of the moment, ignoring even principles that they themselves hold dear just to make a buck? Most definitely. Should we really even care? That’s up to you. Many Americans, familiar with the US protest culture and generously blessed with acute short-term memory, will likely give PSY a pass. And why not? Americans gave Ice-T a pass for rapping about killing cops. Eminem and Chris Brown were given a pass for rapping about and actually beating on women. And, unlike the latter two, who continue to bank their fame on anti-social behavior, PSY has been nothing but gracious in the handling of his global popularity. Would patriotism or whatever it was that motivated him at that time, override his marketing sense and allow him utter those same words today? Who can say? And before passing judgment, Americans might do well to read some of the disturbingly racist comments directed towards PSY following the American Music Awards. Comments made with no political agenda, but simply hateful rhetoric directed at an international star performing a song that nearly every American loves. Whether Americans will look for PSY to explain his words and actions from the past remains to be seen. But some of his fellow countrymen have already demanded that the issue be addressed. In a mid-October article in the right-leaning Korean publication, Dailian, professor Kang Kyu-hyeong of Myongji University in Seoul, was clear in his opinion about PSY's actions ten years ago saying, "it's not just anti-American, it's anti-human." PSY: No Stranger to Controversy PSY has been controversial in Korea since the very beginning of his career. His first album, PSY from the PSYcho World!, got him fined for what government censors called “inappropriate content”, which was followed with a ban of his music and videos from young listeners. While the first album contained only one “explicit” song, PSY upped the ante on his second release, Sa 2, with half the songs receiving “explicit” warnings. Obviously, he was well-learned in the school of Madonna—get banned, sell more records. Following the second album’s release, Korean civil groups quickly rallied with complaints to the government standards board. He was fined again, and, to this day, Sa 2 remains off-limits for those under 19 years of age. With his third album, 3 PSY, came the aptly-named cut “Champion”. Though well received by Korean World Cup fans, PSY found an unlikely new group raising a fuss this time—expat English teachers. Upon the September 2002 release of “Champion” (and even now with newly-minted PSY fans), the English speaking community took offense with the song’s repeated use of the word “ni-ga”, which was interpreted as the N-word. Those who knew better laughed at this assumption—"ni-ga" is simply the Korean word for “you” or “you are,” as in, “You are the champion.” After learning what PSY was actually saying, and knowing that he spoke English well after having studied in America, many found his little dig at convention all the more appealing. In 2007, PSY got into trouble with the government again, this time for delaying and eventually dodging his “special circumstance” assignment at a software company in place of Korea’s mandatory military service. It led prosecutors to accuse PSY of "neglecting" his civil duty, since he opted to instead hold concerts and appear on local television shows rather than punch in for his required work. The doghouse was all his own, and he turned it into an estate. And here we are today, when PSY is the country’s darling. Even his former detractors have scurried onto the bandwagon hoping to hitch a ride on his rising star and the overwhelming positive attention (and money) it brings to Korea. As Oh Jeong-suk from Seoul ska band Kingston Rudieska recently told Haps, “For 10 years, PSY always stuck to his style and didn't imitate other singers. That is the reason he is successful now: because he trusted his own style.” Simply put: PSY is more than simply Gangnam Style. Statements and opinions expressed in this article do not necessarily reflect the views of the publisher. Interview with Korean Rock Legend, Yoon Do-hyun Read more from Bobby McGill < More International Air Routes to Open < Read More > Exclusive: PSY`s Once Passionate Protesting Past [Article Moved] >

– There's no doubt Korean rapper PSY is beloved across America, but the "Gangnam Style" star doesn't necessarily feel the same way about America—or at least, he didn't a few years ago. During a 2002 concert protesting the presence of US troops in Korea, PSY smashed a toy "American tank" on the ground as the crowd cheered, Mediaite reports. Two years later, during protests against the US war in Iraq after it indirectly led to the beheading of a Korean missionary in that country, PSY performed part of a vitriolic anti-America song by a Korean rock band. Some of the "Dear American" lyrics he rapped: "Kill those fucking Yankees who have been torturing Iraqi captives / Kill those fucking Yankees who ordered them to torture / Kill their daughters, mothers, daughters-in-law and fathers / Kill them all slowly and painfully." Not surprisingly, as news of PSY's past has emerged, not all Americans have taken it well. Twitchy rounds up some of the Twitter reactions, like this tweet: "Psy the anti-American protestor: Certainly not the same guy you saw on Ellen." But, Mediaite notes, musicians are often forgiven for talking about things like killing cops (Ice-T) or beating women (Eminem, Chris Brown) in their music. And it's important to put his protesting in context, as this magazine does.

<s>[INST]anyone else know Psy, the Gangnam Style artist, publicly held anti-American views, also encouraging the killing of soldiers? #educateyoself — Sayruhhhh(@sweetieswan) December 6, 2012 @scooterbraun Have you seen those anti-American lyrics from PSY back in 2003? I believe he sang about killing Americans.#something2ponder — Ryan Patrick (@Amabonovella) December 5, 2012 Here’s a fun fact: In 2002, Psy performed at an anti-American concert in Korea and sang about killing our soldiers and how awful we are. — Jacob Martens(@Jacob_martens) December 6, 2012 Psy the anti-American protestor: Certainly not the same guy you saw on Ellen lexne.ws/f61 – @korealawtoday — LXBN (@LXBN) December 6, 2012 TIL Psy has a very anti-American past he is trying to hide tinyurl.com/asrywrx — Today I Learned (@TodayILearnd) December 5, 2012 He has the most-watched YouTube video ever (more than 900 million views), and is set to perform for the Obamas at the annual Christmas in Washington concert later this month. Eight years ago, however, the “Gangnam Style” K-pop singer advocated the murder and torture of US military personnel and their family members. HAPS, an English-language Korean magazine, says PSY’s anti-American views have long been known in Korea, but only recently surfaced in the US. The lyrics of the anti-US song performed live by PSY and several other popular Korean singers in 2004 (shortly after the US invaded Iraq) were first translated into English two months ago on CNN’s iReport: 싸이 rap : 이라크 포로를 고문해 댄 씨발양년놈들과 고문 하라고 시킨 개 씨발 양년놈들에 딸래미 애미 며느리 애비 코쟁이 모두 죽여 아주 천천히 죽여 고통스럽게 죽여 PSY Rap: Kill those fucking Yankees who have been torturing Iraqi captives Kill those fucking Yankees who ordered them to torture Kill their daughters, mothers, daughters-in-law and fathers Kill them all slowly and painfully PSY’s anti-American views weren’t discussed when the K-Pop star appeared on Ellen. Exit question: Will anyone in the mainstream media ask PSY if he still supports killing US soldiers and their family members? Hat tip: Jon. Update: Surprise! Despite PSY’s anti-American views, President Obama still plans to attend his Christmas in Washington performance. Correction: Twitchy originally stated that PSY was set to perform at the White House. The Obamas will attend PSY’s Christmas in Washington performance, but the concert venue is the National Building Museum. This post has been updated to reflect that information. Update: In light of the overwhelming reaction to this story, PSY has issued a statement of apology this afternoon, which reads: As a proud South Korean who was educated in the United States and lived there for a very significant part of my life, I understand the sacrifices American servicemen and women have made to protect freedom and democracy in my country and around the world. The song – from eight years ago – was part of a deeply emotional reaction to the war in Iraq and the killing of two innocent Korean civilians that was part of the overall antiwar sentiment shared by others around the world at that time. While I’m grateful for the freedom to express one’s self I’ve learned there are limits to what language is appropriate and I’m deeply sorry for how these lyrics could be interpreted. I will forever be sorry for any pain I have caused anyone by those words. I have been honored to perform in front of American soldiers in recent months – including an appearance on the Jay Leno show specifically for them – and I hope they and all Americans can accept my apology. While it’s important we express our opinions, I deeply regret the inflammatory and inappropriate language I used to do so. In my music I try to give people a release, a reason to smile. I have learned that though music, our universal language we can all come together as a culture of humanity and I hope that you will accept my apology. The chances of PSY being uninvited from the Christmas in Washington event seemed slim before and are likely nonexistent now. Perhaps the best we can hope for is that the president not say, “No apology necessary.” But will Americans find it in their hearts to forgive for the sake of “a culture of humanity”? Follow @twitchyteam ||||| He has the most-watched YouTube video of all-time, an international phenomenon of a mega-hit in “Gangnam Style,” has made appearances on nearly every American morning talk show under the sun from Today to Ellen, and is scheduled to appear at a D.C. charity concert later this month with President Obama in attendance. It’s safe to say that Korean pop star PSY is now the “most-liked” entertainer on the planet. It has recently been unearthed in the states, however, that eight years ago, long before achieving this massive stardom, the mega-star rapped about “slowly and painfully” killing American military members and their families. Some context: since becoming a democracy in the late 80s, South Korea has developed a rich, sometimes over-the-top, tradition of protest. Swarms of Koreans hit the streets to protest everything from free trade agreements to North Korea to Muslim extremism to American troops stationed on their peninsula. During a 2002 protest concert against the presence of 37,000 American troops in Korea, PSY took the stage in gold face-paint and, with the crowd egging him on, lifted a miniature “American tank” and smashed it on the ground to massive applause. UPDATE: The performance was inspired by the recent death of two Korean school girls who were run over by an American tank in South Korea. The soldiers driving the tank were acquitted by a US military court. And then in 2004, a Korean missionary was captured in Iraq by Islamists who demanded that South Korea not send troops to aid America in the war in Iraq. Seoul refused to negotiate and the missionary was beheaded. The result: massive protests throughout Korea against both Muslim extremism and the U.S. military for indirectly bringing this fate upon a Korean missionary. As part of the protests, PSY and several other popular Korean musicians put on a live performance of a Korean rock band’s song “Dear American.” When PSY’s turn came, he rapped: Kill those fucking Yankees who have been torturing Iraqi captives Kill those fucking Yankees who ordered them to torture Kill their daughters, mothers, daughters-in-law and fathers Kill them all slowly and painfully As this particularly incendiary verse made its way to American news outlets, the outrage has grown. Conservative Twitter aggregator Twitchy sums up some of the anti-PSY anger, pondering why his anti-American military past was not discussed during his appearance on Ellen. Think of all the musicians who’ve said unseemly things in their art: Ice-T rapped the perspective of killing a police officer years ago in “Cop Killer,” but he is now a star actor who portrays a police officer on NBC’s Law and Order: SVU. At the time, Ice-T said he was simply rapping from the perspective of another man — telling a story — and not calling for the actual murder of police officers. On the other hand, Chris Brown and Eminem have rapped about violence against women… and have followed through on it in real life. But as others have noted, PSY’s handling of his newfound global fame has been remarkably gracious. He hasn’t thrown up the middle finger and rejected his American popularity because of the Iraq War he rightfully found so deplorable (albeit with highly vitriolic rhetoric). The question becomes: Would he have said the same thing today now that he has precious international stardom to preserve? UPDATE: PSY’s publicist has sent an apology from the musician. View here. UPDATE 2: Partial video has surfaced of one of the aforementioned anti-American military performances. Watch here. [h/t HAPS] — — >> Follow Andrew Kirell (@AndrewKirell) on Twitter Have a tip we should know? [email protected] ||||| BUSAN, South Korea -- The talented 34-year-old rapper Park Jae-sang, known better to the world as PSY, has been a controversial staple of the Korean music scene since his first full-length album, PSY from the PSYcho World!, debuted back in 2001. At that time, the traditionally conservative Korean mainstream didn’t know what to make of the blunt lyrics (one track was called “I Love Sex”) or how to react to his unconventional dance moves and eccentric appearance. When he first hit the scene, the naturally-gifted, then-24-year-old PSY, who had just returned home to Korea after withdrawing from both Boston University and the prestigious Berklee College of Music, was quickly nicknamed “The Bizarre Singer.” He wore the title as a badge of honor. And while the world has come to adore the man who is now the most-loved entertainer on the planet, articles published last month on CNN iReport the Korean language Chosun Ilbo and on other Korean sites about PSY’s outspoken role in anti-US military protests back in 2002, and then again in 2004, will either stir indignation with audiences or garner him even more respect. But first, the story must be put in context of the times. The Tragic Death of Two Korean Schoolgirls and America's Response The summer of 2002 in Korea was a time when PSY was cultivating a following while battling censors over his outlandish new style that in this day and age seems tame. It was also a period of heart-rending tragedy that saw an American military vehicle kill 13-year-old middle school girls Shim Mi-son and Shin Hyo-sun, who were walking along the roadside just outside of Seoul on the morning of June 13. In line with the Status of Forces Agreement (SOFA), that sets jurisdiction terms for US forces stationed abroad, the incident was defined “a military operation” and thus handled internally by the American military courts. A subsequent US court martial found the girls’ deaths to be accidental and acquitted service members Sergeant Mark Walker, and the vehicle’s commander, Sergeant Fernando Nino, of negligent homicide, while citing no criminal intent. The American government then paid civil damages to the families involved. “You have to look at this in context... many South Korean artists were part of this America bashing. It was part of a movement...” The Korean public’s reaction to the girls’ deaths was at first muted, as the country was then center-stage as co-host of the World Cup, but soon thereafter thousands of protestors took to the streets demanding, with arguable validity, but no legal precedence, that the soldiers be re-tried in a Korean court. Washington refused and the demonstrations went on for months, as tens of thousands gathered across the country to vent their anger at American policy that made them sole arbiter of justice for US military-related crimes on South Korean soil. The anger was palpable. While reporting on events for the the San Francisco Chronicle, I cited a Gallup poll that showed 75 percent of Koreans in their 20s said they disliked Americans. Sixty-seven percent in their 30s, along with half of those in their 40s, told Gallup they either "did not like" or "hated" the United States. Few living on the peninsula at that time were immune to the movement. Businesses around the country banned Americans (and by association, Westerners) from entering, US flags were laid on the ground at university campuses allowing students to walk on them en route to class, and graphic banners of Shim Mi-son and Shin Hyo-sun were erected at rallies, as the American military came under increasingly heated scrutiny for what was ubiquitously viewed as an unfair and unjustified handling of their deaths. PSY’s Political Performances For some Americans, the story of PSY’s participation in anti-US military protests will elicit condemnation. But should it? First, it must be recognized that thousands of Americans have protested—at times violently—against US military-related issues. After that, one must then acknowledge Korean history within the context of a country that has been under the rule of either outside powers or oppressive dictators for much of its history. A liberal democracy since only 1987, a now free Korean public worships at the altar of protest. Be it storming the office of a politician ensnared in a corruption scandal, burning North Korean flags, opposing a free trade agreement or, as the New York Times once wrote, protesting against protests themselves. Though the following events have been widely discussed in Korea, recent murmurings on the English corner of the Internet have rekindled PSY’s roles in anti-US military protest rallies in the past. The first following the 2002 acquittal of the American soldiers; and the second, PSY’s highly-provocative anti-American military performance during a 2004 protest concert in Seoul, where the entertainer's vitriol was directed towards American military personnel, military brass and their families for the June 22 beheading of a Korean Christian missionary by Islamic extremists in Iraq. First, this from the Korea Times on December 5, 2002, courtesy of the blog Flight of the Kiwi. "Following the acquittals of two U.S. soldiers from negligent homicides charges late last month, a growing number of local celebrities have offered their heart-felt sympathy with the victims in public, while expressing their strong resentment over what they see as an unfair ruling by the American military court. These public figures have composed protest songs against America to pitch in their voice, join public rallies, or have gone as far as calling for revision of the Status of Forces Agreement (SOFA), which governs the status of 37,000 American troops stationed here, through official statements. Even though these pop stars have managed to put in their own two cents' worth, pop vocalist PSY, who has upheld the cause since August through many concerts, is among the most outspoken of them all." PSY’s being "outspoken" was caught on tape and was, until recently, posted on YouTube. It has since been pulled by entertainment company CJ E&M for "copyright claims." A search for videos on Naver.com, the Korean version of Google, features several links to the video, but the videos themselves have been removed as well. During the performance featured on the video, PSY took the stage with several other musicians protesting the Status of Forces Agreement with Washington. With a gold-painted face and the crowd cheering him on, PSY lifted a miniature mock-up of an American tank and threw it to the ground, before smashing it into pieces with a mic stand, all while following along in anti-US military chants. Following the months of vocal protests, including hunger strikes outside the US embassy, the American military eventually amended SOFA, allowing Korean courts to take US servicemen in custody prior to trial. In the past, American soldiers were only tried in Korean court for off-duty crimes, such as earlier this year, when a Korean judge sentenced Pvt. Joseph J. Finley to three years in prison for raping a South Korean woman after following her home. In the end, the power of protest worked—the U.S amended the SOFA agreement. The Beheading of Kim Sun-il Nearly two years after the 2002 protests, on May 22, 2004, the Islamist group Jama'at al-Tawhid wal-Jihad kidnapped Korean missionary Kim Sun-il and held him hostage, demanding that the South Korean government cancel plans to send 3,000 troops to support the US war in Iraq. S eoul refused to negotiate and the Islamist group, led by Abu Musab al-Zarqawi, beheaded Kim, a man whose only crime was proselytizing in extremist-held territory. Kim even studied Arabic in a top Korean university, just so he could spread the Christian word throughout the Middle East. A subsequent video of the heinous act was aired on Al Jazeera with a masked executioner issuing the following statement: “Korean citizens, you were warned, your hands were the ones who killed him. Enough lies, enough cheatings. Your soldiers are here not for the sake of Iraqis, but for cursed America." He then brutally decapitated Kim Sun-il with a large knife. Massive protests erupted across South Korea with thousands rallying against Muslim extremists, as well as Seoul's plans to send troops to Iraq. And while most of the peninsula's fury was directed towards terrorists in Iraq as well as Korean government policy, some anti-US military protesters seized the moment to put forth their cause. Once again, PSY was involved. This time he admonished not only the terrorists and then president Roh Mu-hyun, but he also allegedly unleashed a vitriolic condemnation of American military personnel and military brass. According to a story on October 30, 2012 on the Korean-language version of the Chosun Ilbo and also reported on K-Pop music site AllKpop.com, PSY, along with several popular performers, took part in a live performance of Korean rock band N.EX.T's song "Dear American". 싸이 rap : 이라크 포로를 고문해 댄 씨발양년놈들과 고문 하라고 시킨 개 씨발 양년놈들에 딸래미 애미 며느리 애비 코쟁이 모두 죽여 아주 천천히 죽여 고통스럽게 죽여 PSY Rap: Kill those f****** Yankees who have been torturing Iraqi captives Kill those f****** Yankees who ordered them to torture Kill their daughters, mothers, daughters-in-law and fathers Kill them all slowly and painfully _____ Though reports of PSY performing this have long been known on Korean language sites, it only recently surfaced in English as all eyes and ears of the world have turned in his direction. Before it showed up on the Chosun Ilbo and AllKpop.com at the end of October, the translation was first posted October 6 on CNN’s iReport, an open source news feature that allows users to submit stories for CNN consideration. It was, however, never picked up by CNN staff, even though it received nearly 30,032 views, 361 “recommends” and 152 “shares” at the time of this writing. The person who posted the translation, who the Chosun Ilbo noted is Japanese (and unsurprisingly not a PSY fan), also uploaded the text of his CNN post on YouTube. Initial Reaction Western netizen response has as yet been sparse—aside of the CNN iReport and the YouTube video, there has until now, simply not been enough English language background to be found on the web. Comments posted thus far have ranged from defending PSY: SourKushBalls: “This was taken out of context and mistranslated. PSY is not attacking/dissing American soldiers.” To those offering heavy condemnation (though referencing the earlier issue and not the issue being posted): MIZZKIE: “Just because two innocent girls got accidentally killed (bless their poor souls), it doesn't mean you can spew out your hatred against others in a song sung by a person with fame and influence.” To those viewing him as a man of the times: MoReuGettDa: “You have to look at this in context. All of the South Korean media, all of the South Korean candidates for president, many South Korean artists were part of this America bashing. It was part of a movement...” While in a free society we are all entitled to our opinion of PSY’s words and actions 10 years ago, a comment on Facebook seemed quite fitting. In it, the commenter likened PSY's lyrics to famed American rapper Ice-T, who once released the song “Cop Killer” and yet now stars, ironically, as a cop on the TV show Law and Order. Should PSY Address the Issue? PSY's political prose aside, suffice it to say that while the entertainment world has given us wonderful artistry and life-changing talent, it has also given us some serious cause for pause. Have other performers around the world, at some point, spewed harsh words in the name of protest? Yes. Have entertainers taken advantage of the moment, ignoring even principles that they themselves hold dear just to make a buck? Most definitely. Should we really even care? That’s up to you. Many Americans, familiar with the US protest culture and generously blessed with acute short-term memory, will likely give PSY a pass. And why not? Americans gave Ice-T a pass for rapping about killing cops. Eminem and Chris Brown were given a pass for rapping about and actually beating on women. And, unlike the latter two, who continue to bank their fame on anti-social behavior, PSY has been nothing but gracious in the handling of his global popularity. Would patriotism or whatever it was that motivated him at that time, override his marketing sense and allow him utter those same words today? Who can say? And before passing judgment, Americans might do well to read some of the disturbingly racist comments directed towards PSY following the American Music Awards. Comments made with no political agenda, but simply hateful rhetoric directed at an international star performing a song that nearly every American loves. Whether Americans will look for PSY to explain his words and actions from the past remains to be seen. But some of his fellow countrymen have already demanded that the issue be addressed. In a mid-October article in the right-leaning Korean publication, Dailian, professor Kang Kyu-hyeong of Myongji University in Seoul, was clear in his opinion about PSY's actions ten years ago saying, "it's not just anti-American, it's anti-human." PSY: No Stranger to Controversy PSY has been controversial in Korea since the very beginning of his career. His first album, PSY from the PSYcho World!, got him fined for what government censors called “inappropriate content”, which was followed with a ban of his music and videos from young listeners. While the first album contained only one “explicit” song, PSY upped the ante on his second release, Sa 2, with half the songs receiving “explicit” warnings. Obviously, he was well-learned in the school of Madonna—get banned, sell more records. Following the second album’s release, Korean civil groups quickly rallied with complaints to the government standards board. He was fined again, and, to this day, Sa 2 remains off-limits for those under 19 years of age. With his third album, 3 PSY, came the aptly-named cut “Champion”. Though well received by Korean World Cup fans, PSY found an unlikely new group raising a fuss this time—expat English teachers. Upon the September 2002 release of “Champion” (and even now with newly-minted PSY fans), the English speaking community took offense with the song’s repeated use of the word “ni-ga”, which was interpreted as the N-word. Those who knew better laughed at this assumption—"ni-ga" is simply the Korean word for “you” or “you are,” as in, “You are the champion.” After learning what PSY was actually saying, and knowing that he spoke English well after having studied in America, many found his little dig at convention all the more appealing. In 2007, PSY got into trouble with the government again, this time for delaying and eventually dodging his “special circumstance” assignment at a software company in place of Korea’s mandatory military service. It led prosecutors to accuse PSY of "neglecting" his civil duty, since he opted to instead hold concerts and appear on local television shows rather than punch in for his required work. The doghouse was all his own, and he turned it into an estate. And here we are today, when PSY is the country’s darling. Even his former detractors have scurried onto the bandwagon hoping to hitch a ride on his rising star and the overwhelming positive attention (and money) it brings to Korea. As Oh Jeong-suk from Seoul ska band Kingston Rudieska recently told Haps, “For 10 years, PSY always stuck to his style and didn't imitate other singers. That is the reason he is successful now: because he trusted his own style.” Simply put: PSY is more than simply Gangnam Style. Statements and opinions expressed in this article do not necessarily reflect the views of the publisher. Interview with Korean Rock Legend, Yoon Do-hyun Read more from Bobby McGill < More International Air Routes to Open < Read More > Exclusive: PSY`s Once Passionate Protesting Past [Article Moved] >[/INST]– There's no doubt Korean rapper PSY is beloved across America, but the "Gangnam Style" star doesn't necessarily feel the same way about America—or at least, he didn't a few years ago. During a 2002 concert protesting the presence of US troops in Korea, PSY smashed a toy "American tank" on the ground as the crowd cheered, Mediaite reports. Two years later, during protests against the US war in Iraq after it indirectly led to the beheading of a Korean missionary in that country, PSY performed part of a vitriolic anti-America song by a Korean rock band. Some of the "Dear American" lyrics he rapped: "Kill those fucking Yankees who have been torturing Iraqi captives / Kill those fucking Yankees who ordered them to torture / Kill their daughters, mothers, daughters-in-law and fathers / Kill them all slowly and painfully." Not surprisingly, as news of PSY's past has emerged, not all Americans have taken it well. Twitchy rounds up some of the Twitter reactions, like this tweet: "Psy the anti-American protestor: Certainly not the same guy you saw on Ellen." But, Mediaite notes, musicians are often forgiven for talking about things like killing cops (Ice-T) or beating women (Eminem, Chris Brown) in their music. And it's important to put his protesting in context, as this magazine does.</s>

recall that an isometric action of a group @xmath1 on a metric space @xmath2 is _ acylindrical _ if for every @xmath3 there exist @xmath4 such that for every two points @xmath5 with @xmath6 , there are at most @xmath7 elements @xmath8 satisfying @xmath9 the notion of acylindricity goes back to sela s paper @xcite , where it was considered for groups acting on trees . in the context of general metric spaces , this concept is due to bowditch @xcite . the following definition was suggested by the second author in @xcite . [ df : acyl - gp ] a group @xmath1 is called _ acylindrically hyperbolic _ if there exists a generating set @xmath10 ( possibly infinite ) of @xmath1 such that the corresponding cayley graph @xmath11 is hyperbolic , non - elementary ( i.e. , its gromov boundary @xmath12 consists of more than @xmath13 points ) , and the action of @xmath1 on @xmath11 is acylindrical . the above notion generalizes non - elementary word hyperbolic groups . indeed , it is easy to see that a group is non - elementary word hyperbolic if and only if it satisfies the above definition for a finite set @xmath10 . for @xmath10 finite , the acylindricity condition is vacuous as proper and cobounded actions are always acylindrical . on the other hand , if we allow @xmath10 to be infinite , hyperbolicity and non - elementarity of @xmath11 are rather weak assumptions and acylindricity of the action turns out to be _ the _ condition that allows one to derive interesting results . in fact , acylindrically hyperbolic groups were implicitly studied by bestvina and fujiwara @xcite , bowditch @xcite , hamenst " adt @xcite , dahmani , guirardel , and osin @xcite , sisto @xcite , and many other authors before they were formally defined in @xcite . however the above - mentioned papers used different definitions stated in terms of hyperbolically embedded subgroups @xcite , weakly contracting elements @xcite , or various forms of ( weakly ) acylindrical actions @xcite . some nontrivial relations between these definitions were established in @xcite and @xcite , and finally the equivalence of all definitions was proved in @xcite ( see section [ prelim ] for details ) . the class of acylindrically hyperbolic groups , denoted by @xmath14 , encompasses many examples of interest : non-(virtually cyclic ) groups hyperbolic relative to proper subgroups , @xmath15 for @xmath16 , all but finitely many mapping class groups , non-(virtually cyclic ) groups acting properly on proper cat(@xmath17)-spaces and containing rank one elements , and so forth ( see @xcite ) . on the other hand , @xmath14 is restricted enough to possess a non - trivial theory . below we mention just few directions in the study of acylindrically hyperbolic groups ; for a more comprehensive survey we refer the reader to @xcite . * every acylindrically hyperbolic group contains non - degenerate hyperbolically embedded subgroups . this allows one to use methods from the paper @xcite by dahmani , guirardel , and osin to transfer a significant portion of the theory of relatively hyperbolic groups , including group theoretic dehn filling , to the class @xmath14 . despite their generality , the techniques from @xcite are capable of answering open questions and producing new results even for well - studied classes of groups such as relatively hyperbolic groups , mapping class groups , and @xmath15 . * acylindrical hyperbolicity shares many common features with analytic negative curvature " as defined in @xcite and @xcite . in particular , hamenst " adt @xcite showed that @xmath14 is a subclass of the monod shalom class @xmath18 ( see also @xcite and @xcite for various generalizations ) . this opens doors for the monod shalom measure rigidity and orbit rigidity theory @xcite . results about quasi - cocycles on acylindrically hyperbolic groups with coefficients in the left regular representation obtained in @xcite also seem likely to be useful in the study of the structure of group von neumann algebras via a further generalization of methods from @xcite . * sisto @xcite studied random walks on acylindrically hyperbolic groups using the language of weakly contracting elements . his main result covers many classical theorems about random elements of hyperbolic groups , mapping class groups , etc . * yet another direction is explored by hull @xcite , who developed a version of small cancellation theory for acylindrically hyperbolic groups and used it to construct groups with certain exotic properties . the abundance of non - trivial results and techniques applicable to acylindrically hyperbolic groups justifies the quest for new examples , which is the main goal of our paper . we concentrate on examples arising from actions on simplicial trees . in particular , we consider fundamental groups of finite graphs of groups , one - relator groups , automorphism groups of polynomial algebras , fundamental groups of compact @xmath0-manifolds , and graph products . to illustrate usefulness of our main results we derive a number of corollaries about the algebraic structure , analytic properties and measure equivalence rigidity of groups from these classes . however the main focus of this paper is on new examples rather than on applications . * acknowledgements . * the authors would like to thank henry wilton for helpful discussions of @xmath0-manifolds . we are also grateful to jack button for his valuable comments , and to stephane lamy for pointing out an error in an earlier version of the paper . finally , we would like to thank the referee for a careful reading of this article . we begin with a general theorem about groups acting on trees . recall that the action of a group @xmath1 by automorphisms on a simplicial tree @xmath19 is called _ minimal _ if @xmath19 contains no proper @xmath1-invariant subtree . as usual , by @xmath20 we denote the gromov boundary of @xmath19 , which can be identified with the set of ends of @xmath19 ; no topology on @xmath20 is assumed . [ main-1 ] let @xmath1 be a group acting minimally on a simplicial tree @xmath19 . suppose that @xmath1 does not fix any point of @xmath20 and there exist vertices @xmath21 of @xmath19 such that the pointwise stabilizer @xmath22 is finite . then @xmath1 is either virtually cyclic or acylindrically hyperbolic . a slightly different criterion , which does not make use of the boundary is formulated in corollary [ prop : wpd - crit ] ( see subsection [ sec : trees ] below ) . if @xmath1 is the fundamental group of a graph of groups @xmath23 , one can apply theorem [ main-1 ] to the action of @xmath1 on the associated bass - serre tree . in this case the minimality of the action and the absence of fixed points on @xmath20 can be recognized from the local structure of @xmath23 see section [ sec - gg ] . we mention here two particular cases and refer to theorem [ thm : reduced - crit ] for a more general result . below we say that a subgroup @xmath24 of a group @xmath1 is _ weakly malnormal _ if there exists @xmath8 such that @xmath25 . [ cor : amalg - intr ] let @xmath1 split as a free product of groups @xmath26 and @xmath27 with an amalgamated subgroup @xmath24 . suppose @xmath28 and @xmath24 is weakly malnormal in @xmath1 . then @xmath1 is either virtually cyclic or acylindrically hyperbolic . note that the virtually cyclic case can not be excluded from corollary [ cor : amalg - intr ] . indeed it is realized if @xmath24 is finite and has index @xmath13 in both factors . however these are the only exceptions : it is easy to show that under the assumptions of the corollary all other amalgams contain non - abelian free subgroups , and so they are are acylindrically hyperbolic . [ cor : hnn - intr ] let @xmath1 be an hnn - extension of a group @xmath26 with associated subgroups @xmath24 and @xmath29 . suppose that @xmath30 and @xmath24 is weakly malnormal in @xmath1 . then @xmath1 is acylindrically hyperbolic . [ rem : hnn ] the assumption of corollary [ cor : hnn - intr ] saying that @xmath24 is weakly malnormal in @xmath1 is equivalent to the existence of an element @xmath31 such that @xmath32 , because @xmath24 and @xmath29 are conjugate in @xmath1 . the weak malnormality condition is essential in both corollaries . this can be illustrated in many ways , but the most convincing examples are the following . [ ex : non - ah-1 ] 1 . there are simple groups splitting as @xmath33 , where @xmath26 , @xmath27 are finitely generated free groups and @xmath24 can be of finite or infinite index in both @xmath26 and @xmath27 @xcite . note that simple groups are never acylindrically hyperbolic ( see theorem [ thm : elem - prop - ah ] ) . the baumslag - solitar groups @xmath34 are not acylindrically hyperbolic unless @xmath35 or @xmath36 @xcite . furthermore , the assumption that @xmath30 in corollary [ cor : hnn - intr ] is also necessary , see examples [ ex : hnnb ] and [ ex : bg ] . it is worth noting that our corollaries [ cor : amalg - intr ] and [ cor : hnn - intr ] can be used to recover some results proved by schupp @xcite and sacerdote and schupp @xcite by using small cancellation theory for amalgamated products and hnn - extensions . in fact , our approach is slightly more general ; for details we refer to section [ sec - gg ] . the next result is inspired by @xcite . the proof makes use of corollary [ cor : hnn - intr ] and a technical result from @xcite . [ cor : one - rel ] let @xmath1 be a one - relator group with at least @xmath0 generators . then @xmath1 is acylindrically hyperbolic . corollary [ cor : one - rel ] is related to a conjecture of p. neumann @xcite , claiming that if @xmath1 is a one - relator group then either @xmath1 is cyclic or @xmath37 is a solvable baumslag - solitar group , or @xmath1 is sq - universal . recall that a group @xmath1 is said to be _ @xmath38-universal _ if every countable group embeds in a quotient of @xmath1 . the first non - trivial example of an @xmath38-universal group was provided by higman , neumann and neumann @xcite , who proved that the free group of rank @xmath13 is @xmath38-universal or , equivalently , every countable group embeds in a group generated by @xmath13 elements . it is straightforward to see that any @xmath38-universal group contains non - abelian free subgroups . furthermore , since the set of all finitely generated groups is uncountable and every countable group contains countably many finitely generated subgroups , every countable @xmath38-universal group has uncountably many non - isomorphic quotients . thus the property of being @xmath38-universal may be thought of as an indication of algebraic largeness " of a group . for a survey of @xmath38-universality we refer to @xcite . sacerdote and schupp @xcite established the sq - universality of one - relator groups with at least @xmath0 generators , thus confirming neumann s conjecture in this case . corollary [ cor : one - rel ] can be regarded as a strengthening of this result ( indeed , by a theorem of dahmani , guirardel and osin @xcite , every acylindrically hyperbolic group is sq - universal ) . the case of one - relator groups with two generators is more complicated , as one can see by looking at the baumslag - solitar groups . the full proof of neumann s conjecture was announced by sacerdote @xcite , but it was never published , and it seems that the conjecture is still open . in section [ sec:1-rel ] , we make a step towards the resolution of this conjecture by showing that every one - relator group with a sufficiently complicated magnus - moldavanskii hierarchy is acylindrically hyperbolic ( see proposition [ cor:1-rel-2-gen ] ) . more precisely , all non - acylindrically hyperbolic one - relator groups belong to the class of hnn - extensions of ( finitely generated free)-by - cyclic groups . unfortunately , our techniques do not apply to ascending hnn - extensions ( cf . examples [ ex : hnnb ] , [ ex : bg ] ) , therefore for groups with magnus - moldavanskii hierarchy of low complexity we only have partial results . another example having the structure described in corollary [ cor : amalg - intr ] is @xmath39 $ ] , the group of automorphisms of the polynomial algebra @xmath40 $ ] for any field @xmath41 . this group is sometimes called the _ integral 2-dimensional cremona groups _ over @xmath41 and is also isomorphic to the group of automorphisms of the free associative algebra @xmath42 @xcite ; if @xmath43 it is also isomorphic to the group of automorphisms of the free @xmath13-generated poisson algebra @xcite . the algebraic structure of these groups has received a lot of attention but is still far from being well understood , see @xcite and references therein . we prove the following . [ ga2 ] for any field @xmath41 , the group @xmath39 $ ] is acylindrically hyperbolic . for motivation and a survey of some related results we refer to section [ sec - gg ] . note that @xmath44 $ ] is solvable and hence it is not acylindrically hyperbolic . we do not know if the analogue of corollary [ ga2 ] holds true for the group @xmath45 $ ] when @xmath46 , but we would rather expect some higher rank phenomena to prevent it from being acylindrically hyperbolic . other examples of acylindrically hyperbolic groups obtained in section [ sec - gg ] by using corollaries [ cor : amalg - intr ] and [ cor : hnn - intr ] include the higman group @xmath47 and amalgamated products ( respectively , hnn - extensions ) of the form @xmath48 ( respectively , @xmath49 ) , where @xmath26 is a hyperbolic group and @xmath24 is a quasi - convex subgroup of infinite index in @xmath26 . the latter examples should be compared to simple groups mentioned in example [ ex : non - ah-1 ] . for details we refer to section [ sec : misc ] by default , all manifolds considered in this paper are assumed to be connected . our next goal is to show that most @xmath0-manifold groups are acylindrically hyperbolic . more precisely , let @xmath50 denote the class of all _ subgroups _ of fundamental groups of compact @xmath0-manifolds . note that by scott s theorem @xcite , every finitely generated group @xmath51 is itself the fundamental group of a compact @xmath0-manifold . however the groups we consider are not necessarily finitely generated . [ main-3-dim ] let @xmath51 . then exactly one of the following three conditions holds . 1 . @xmath1 is acylindrically hyperbolic . @xmath1 contains an infinite cyclic normal subgroup @xmath52 and @xmath53 is acylindrically hyperbolic . @xmath1 is virtually polycyclic . if @xmath1 is itself a fundamental group of a compact irreducible @xmath0-manifold , we can give a more geometric description of the non - acylindrically hyperbolic cases . [ cor : geom ] let @xmath54 be a compact irreducible @xmath0-manifold such that @xmath55 is not acylindrically hyperbolic . then either @xmath55 is virtually polycyclic or @xmath54 is seifert fibered . theorem [ main-3-dim ] allows to bring many results known for acylindrically hyperbolic groups to the world of @xmath0-manifold groups . we discuss some examples below . let us say that a group @xmath51 has _ type _ ( i ) , ( ii ) , or ( iii ) if the corresponding condition from theorem [ main-3-dim ] holds for @xmath1 . [ 3-dim - cor-1 ] a group @xmath51 is inner amenable iff it is of type ( ii ) or ( iii ) . recall that a group @xmath1 is _ inner amenable _ if there exists a finitely additive conjugacy invariant probability measure on @xmath56 . inner amenability is closely related to the murray von neumann property @xmath57 for operator algebras . in particular , if @xmath1 is not inner amenable , the von neumann algebra @xmath58 of @xmath1 does not have property @xmath57 @xcite . for further details and motivation we refer to @xcite and section [ sec:3m - app ] . [ 3-dim - cor-2 ] type is a measure equivalence invariant in @xmath50 . that is , if @xmath59 and @xmath1 is measure equivalent to @xmath60 , then @xmath1 and @xmath60 have the same type . this result can be seen as the first step towards measure equivalence classification of @xmath0-manifold groups . we note that a classification of fundamental groups of compact @xmath0-manifolds up to quasi - isometry was done by behrstock and neumann @xcite , while no non - trivial results about measure equivalence seem to be known . finally we mention that theorem [ main-3-dim ] is used in @xcite to show the following : _ the outer automorphism group @xmath61 is residually finite for any compact @xmath0-manifold @xmath54_. the proof is based on the approach suggested in @xcite and essentially uses acylindrical hyperbolicity . let @xmath57 be a graph without loops and multiple edges with vertex set @xmath62 . let also @xmath63 be a family of groups , called _ vertex groups _ , indexed by vertices of @xmath64 . the _ graph product _ of @xmath63 with respect to @xmath57 , denoted @xmath65 , is the quotient group of the free product @xmath66 by the relations @xmath67=1 $ ] for all @xmath68 , @xmath69 whenever @xmath70 and @xmath71 are adjacent in @xmath64 . graph products generalize free and direct products of groups . other basic examples include right angled artin and coxeter groups . the study of graph products and their subgroups has gained additional importance in view of the recent breakthrough results of agol , haglund , wise , and their co - authors , which claim that many groups can be virtually embedded into right angled artin groups ( see @xcite and references therein ) . for any subset @xmath72 , the subgroup @xmath73 of the graph product @xmath74 is said to be a _ full subgroup _ ; it is naturally isomorphic to to the graph product @xmath75 , where @xmath76 is the full subgraph of @xmath64 spanned on the vertices from @xmath77 . any conjugate of a full subgroup is called _ parabolic_. we will say that the graph @xmath78 is _ irreducible _ if its complement graph @xmath79 is connected ; this equivalent to saying that the graph product @xmath65 does not naturally split as a direct product of two proper full subgroups . graph products naturally decompose as amalgamated products in many ways ( see subsection [ sec : wpd_in_gp ] ) . in section [ sec : gp ] we study subgroups of graph products using the actions on the associated bass - serre trees together with the theory of parabolic subgroups developed in @xcite . in particular , we prove the following ( see section 6.3 ) . [ cor : gp - hyp ] let @xmath80 be the graph product of non - trivial groups with respect to some finite irreducible graph @xmath64 with at least two vertices . suppose that @xmath81 is a subgroup that is not contained in a proper parabolic subgroup of @xmath1 . if @xmath60 is not virtually cyclic then @xmath82 . the corollary below covers the particular case when @xmath83 . [ thm : gpacyl ] let @xmath74 be the graph product of non - trivial groups with respect to some finite irreducible graph @xmath64 with at least two vertices . then @xmath1 is either virtually cyclic or acylindrically hyperbolic . graph products are simplest examples of groups having relative non - positive curvature " with respect to the vertex subgroups . from this point of view , corollary [ thm : gpacyl ] can be considered as another instance of a more general phenomenon : irreducibility " of nice " non - positively curved groups ( or spaces ) often implies the existence of hyperbolic directions " in an appropriate sense ; in turn , the latter condition implies acylindrical hyperbolicity . in the context of groups acting on @xmath84 spaces , a more formal version of this claim is sometimes called the _ rank rigidity conjecture _ @xcite and is closely related to the classical work of ballman , brin , burns , and spatzier @xcite as well as more recent results of caprace and sageev @xcite . for a more detailed discussion we refer to section [ sec : subgr - class ] . theorem [ cor : gp - hyp ] is quite useful for studying properties of subgroups of graph products . for example , it is used in @xcite to prove that @xmath85 is residually finite for any virtually compact special ( in the sense of haglund and wise @xcite ) group @xmath1 . theorem [ cor : gp - hyp ] implies that every subgroup @xmath60 of a graph product @xmath1 is either acylindrically hyperbolic , or `` reducible '' , or `` elementary '' in the appropriate sense ( see theorem [ thm : subgroups ] ) . a particular application to right angled artin groups gives rise to the following algebraic alternative : [ cor : raag_in_x ] let @xmath60 be a non - cyclic subgroup of a finitely generated right angled artin group . then exactly one of the following holds : * @xmath60 is acylindrically hyperbolic ; * @xmath60 contains two non - trivial normal subgroups @xmath86 such that @xmath87 . we also mention one application of graph products to groups with hyperbolically embedded subgroups . recall that if a group @xmath1 is hyperbolic relative to a subgroup @xmath60 , then many `` nice '' properties of @xmath60 ( e.g. , solvability of algorithmic problems , finiteness of the asymptotic dimension , various analytic properties , etc . ) are inherited by @xmath1 @xcite . as shown in @xcite , many properties of acylindrically hyperbolic groups resemble those of relatively hyperbolic groups , and hyperbolically embedded subgroups ( see subsection [ sec : eqdef ] for the definition ) serve as analogues of peripheral subgroups in the relatively hyperbolic case . thus one may wonder if the structure of an acylindrically hyperbolic group is determined , to some extent , by the structure of its hyperbolically embedded subgroups . the following result provides a strong negative answer ; it is a simplified version of theorem [ thm : emb ] . any finitely generated group can be embedded into a finitely generated acylindrically hyperbolic group @xmath1 such that every proper hyperbolically embedded subgroup of @xmath1 is finitely generated and virtually free . recall that a countable group @xmath1 belongs to the monod shalom class @xmath88 if @xmath89 @xcite . an a priori different class @xmath90 was defined by thom @xcite : a countable group @xmath1 is in @xmath90 if @xmath1 is non - amenable and there exists an unbounded quasi - cocycle @xmath91 . groups from @xmath88 and @xmath90 exhibit behavior typical to non - elementary hyperbolic groups . moreover , most known examples from these classes come from the world of groups acting on hyperbolic spaces . motivated by these observations , monod @xcite and thom @xcite suggested to consider @xmath88 and @xmath90 as analytic analogues of the class of negatively curved " groups . it is worth noting that no non - trivial relation between @xmath88 and @xmath90 is known , although they are likely to coincide ( see remark 2.7 in @xcite ) monod ( * ? ? ? * problem j ) asked whether @xmath88 can be characterized by a geometric condition . in this paper we discuss the relation between @xmath88 , @xmath90 , and @xmath14 . first we recall that @xmath92 . this was originally proved by hamenstdt @xcite in slightly different terms and also follows from the results of hull - osin @xcite and bestvina fujiwara @xcite . moreover , acylindrically hyperbolic groups constitute the majority of examples from @xmath88 or @xmath90 . indeed the only examples of non - acylindrically hyperbolic groups from @xmath93 known up to now are those constructed by osin @xcite and lck and osin @xcite . these are finitely generated infinite torsion groups with positive first @xmath94-betti numbers . note that @xmath95 implies @xmath96 while torsion groups are never acylindrically hyperbolic ( see example [ ex : non - ah ] ( b ) ) . groups from @xcite and @xcite are not finitely presented . on the other hand , there is an evidence that for finitely presented groups , existence of non - trivial quasi - cocycles may be used to construct non - elementary actions on hyperbolic spaces @xcite . this motivates the following question : are the conditions @xmath97 , @xmath98 , and @xmath99 equivalent for a finitely presented group @xmath1 ? we do not really believe in a positive answer to this question in full generality . however , in section [ sec : nc ] we obtain the following as immediate applications of other results from the paper . [ cor : ganc ] the conditions @xmath97 , @xmath98 , and @xmath99 are equivalent for any group @xmath1 from the following classes : 1 . subgroups of fundamental groups of compact @xmath0-manifolds . 2 . groups commensurable up to a finite kernel with subgroups of graph products of amenable groups . in particular , this class includes virtually special groups in the sense of haglund and wise . recall that two groups @xmath100 and @xmath101 are commensurable up to a finite kernel if there are finite index subgroups @xmath102 and finite normal subgroups @xmath103 , @xmath104 , such that @xmath105 . for definitions , details , and related questions we refer to section [ sec : nc ] and @xcite . in this section we collect the main definitions and results about acylindrically hyperbolic groups relevant to our paper . for more details we refer to @xcite . given a group @xmath1 acting on a hyperbolic space @xmath106 , an element @xmath8 is called _ elliptic _ if some ( equivalently , any ) orbit of @xmath107 is bounded , and _ loxodromic _ ( or _ hyperbolic _ ) if the map @xmath108 defined by @xmath109 is a quasi - isometry for some ( equivalently , any ) @xmath110 . in papers devoted to groups acting on general hyperbolic spaces , the terms loxodromic " and hyperbolic " are used as synonyms . recent papers on relatively hyperbolic and acylindrically hyperbolic groups ( including papers by the second author ) tend to use the term loxodromic " more often . in this paper we switch to hyperbolic " since we mostly deal with actions on trees for which this term is well established . every hyperbolic element @xmath8 has exactly @xmath13 limit points @xmath111 on the gromov s boundary @xmath112 . hyperbolic elements @xmath113 are called _ independent _ if the sets @xmath114 and @xmath115 are disjoint . the next theorem classifies acylindrical group actions on hyperbolic spaces . [ class ] let @xmath1 be a group acting acylindrically on a hyperbolic space . then @xmath1 satisfies exactly one of the following three conditions . 1 . @xmath1 has bounded orbits . @xmath1 is virtually cyclic and contains a hyperbolic element . 3 . @xmath1 contains infinitely many independent hyperbolic elements . compared to the general classification of groups acting on hyperbolic spaces , theorem [ class ] rules out parabolic and quasi - parabolic actions in gromov s terminology @xcite . for details we refer to @xcite . recall that the action of a group @xmath1 on a hyperbolic space @xmath106 is called _ elementary _ if the limit set of @xmath1 in the gromov boundary @xmath112 consists of at most @xmath13 points and _ non - elementary _ otherwise . according to theorem [ class ] , an acylindrical action of @xmath1 is non - elementary if and only if the orbits are unbounded and @xmath1 is not virtually cyclic . the next theorem provides equivalent characterizations of acylindrically hyperbolic groups . in practice , ( ah@xmath116 ) is the most useful condition for proving that a certain group is acylindrically hyperbolic , while ( ah@xmath117 ) , ( ah@xmath118 ) , and ( ah@xmath119 ) are more useful for proving theorems about acylindrically hyperbolic groups . [ acyl ] for any group @xmath1 , the following conditions are equivalent . 1 . the group @xmath1 is acylindrically hyperbolic in the sense of definition [ df : acyl - gp ] . 2 . @xmath1 admits a non - elementary acylindrical action on a hyperbolic space . @xmath1 is not virtually cyclic and admits an action on a hyperbolic space such that at least one element of @xmath1 is hyperbolic and satisfies the wpd condition . 4 . @xmath1 contains a proper infinite hyperbolically embedded subgroup . note that every group has an obvious acylindrical action on a hyperbolic space , namely the trivial action on a point . thus considering elementary acylindrically hyperbolic groups does not make much sense . for this reason we include non - elementarity in the definition . the terminology used in conditions ( ah@xmath116 ) and ( ah@xmath119 ) will also be used in our paper , so we explain it below . given a group @xmath1 acting on a metric space @xmath2 , a subset @xmath120 , and @xmath121 , we define the _ pointwise @xmath122-stabilizer _ of @xmath26 in @xmath1 as the set of all @xmath8 that move every point of @xmath26 by at most @xmath122 . that is , @xmath123 thus the pointwise @xmath17-stabilizer is the same as the usual pointwise stabilizer , which will be denoted @xmath124 . note that , in general , pointwise @xmath122-stabilizers are not subgroups . [ rem : equiv_def - acyl ] in these terms , the action of @xmath1 on @xmath106 is acylindrical if and only if for every @xmath3 there exists @xmath125 such that for all @xmath126 with @xmath6 , the sizes of pointwise @xmath122-stabilizers of @xmath127 are uniformly bounded by a constant @xmath7 which only depends on @xmath122 . [ def : wpd ] an element @xmath128 of a group @xmath1 acting isometrically on a metric space @xmath106 satisfies the _ weak proper discontinuity _ condition ( or @xmath128 is a _ wpd element _ ) if for some @xmath110 ( or , equivalently , for all @xmath129 ) and every @xmath121 , exists @xmath130 such that @xmath131 this definition is essentially due to bestvina and fujiwara @xcite . the notion of a hyperbolically embedded subgroup was introduced in @xcite ; it generalizes the notion of a peripheral subgroup of a relatively hyperbolic group . more precisely , let @xmath1 be a group , @xmath132 , @xmath133 . we assume that @xmath134 and denote by @xmath135 the cayley graph of @xmath1 with respect to the generating set @xmath136 ( even though @xmath10 and @xmath60 might intersect as subsets of @xmath1 , for the purposes of constructing @xmath135 we consider them to be disjoint ) and by @xmath137 the cayley graph of @xmath60 with respect to the generating set @xmath60 . clearly @xmath137 is a complete subgraph of @xmath138 . given two elements @xmath139 , we define @xmath140 to be the length of a shortest path @xmath141 in @xmath142 that connects @xmath143 to @xmath144 and does not contain edges of @xmath137 . if no such path exists we set @xmath145 . clearly @xmath146 $ ] is an extended metric on @xmath60 . we say that @xmath60 is _ hyperbolically embedded in @xmath1 with respect to _ @xmath133 ( and write @xmath147 ) if the following conditions hold : 1 . @xmath148 and @xmath138 is hyperbolic . 2 . @xmath149 is a locally finite space , i.e. , every ball ( of finite radius ) is finite . we also say that @xmath60 is _ hyperbolically embedded in @xmath1 _ ( and write @xmath150 ) if @xmath147 for some @xmath133 . let us consider three basic examples . [ he s ] 1 . for any group @xmath1 , we have @xmath151 . indeed take @xmath152 . then the cayley graph @xmath135 has diameter @xmath153 and @xmath145 whenever @xmath154 . further , if @xmath60 is a finite subgroup of a group @xmath1 , then @xmath155 . indeed @xmath156 for @xmath157 . these cases are referred to as _ degenerate_. 2 . let @xmath158 , @xmath159 , where @xmath160 is a generator of @xmath161 . then @xmath138 is quasi - isometric to a line and hence it is hyperbolic . however @xmath162 for every @xmath163 . if @xmath60 is infinite , then @xmath164 , and moreover @xmath165 . 3 . let @xmath166 , @xmath159 , where @xmath160 is a generator of @xmath161 . in this case @xmath138 is quasi - isometric to a tree and @xmath145 unless @xmath167 . thus @xmath156 . it is known that a group @xmath1 is hyperbolic relative to a subgroup @xmath60 if and only if @xmath147 for some finite set @xmath10 @xcite . we begin with some elementary algebraic properties of acylindrically hyperbolic groups . the theorem below summarizes some results from ( * ? ? ? * section 7 ) and ( * ? ? ? * theorems 2.23 , 2.25 , 2.30 ) . recall that a subgroup @xmath132 is _ @xmath168-normal _ in @xmath1 if for every @xmath8 , we have @xmath169 . clearly every infinite normal subgroup is @xmath168-normal . recall also that a group @xmath1 is @xmath38-universal if every countable group embeds in a quotient of @xmath1 . [ thm : elem - prop - ah ] for any acylindrically hyperbolic group @xmath1 the following conditions hold . 1 . the amenable radical of @xmath1 is finite . 2 . if @xmath170 , then @xmath171 for @xmath172 or @xmath173 . every @xmath168-normal subgroup of @xmath1 is acylindrically hyperbolic . 4 . if @xmath174 for some subgroups @xmath175 of @xmath1 . then @xmath176 is acylindrically hyperbolic for at least one @xmath177 . in particular , @xmath1 is not boundedly generated . @xmath1 is @xmath38-universal . in particular , @xmath1 contains non - abelian free subgroups . @xmath1 contains uncountably many normal subgroups . it is useful to keep this theorem in mind when searching for examples of acylindrically hyperbolic groups as it allows one to show that certain groups are _ not _ acylindrically hyperbolic . [ ex : non - ah ] 1 . 2 . no amenable group is acylindrically hyperbolic . no group without non - abelian free subgroups is acylindrically hyperbolic . in particular , no torsion group or a group satisfying a non - trivial identity is acylindrically hyperbolic . 4 . the baumslag - solitar groups @xmath178 are not acylindrically hyperbolic unless @xmath35 or @xmath36 , because the cyclic subgroup @xmath179 is @xmath168-normal in @xmath180 in this case . @xmath181 is not acylindrically hyperbolic for @xmath182 , since it is boundedly generated . another argument is based on the margulis theorem , which states that for @xmath182 every normal subgroup of @xmath183 is either finite or of finite index and hence @xmath183 has only countably many normal subgroups . for a generalization , see ( * ? ? ? * example 7.5 ) . recall that two groups @xmath100 and @xmath101 are said to be _ commensurable up to finite kernels _ , @xmath184 , if there are finite index subgroups @xmath185 , @xmath104 , a group @xmath60 and epimorphisms @xmath186 such that @xmath187 is finite for @xmath104 . it is not difficult to check that @xmath188 is the smallest equivalence relation whose classes are closed under taking subgroups of finite index and quotients modulo finite normal subgroups . [ lem : com ] the class @xmath14 is closed under commensurability up to finite kernels . let @xmath1 be a group , @xmath60 a finite index subgroup of @xmath1 . suppose that @xmath189 . then , by definition [ df : acyl - gp ] , there exists a generating set @xmath10 of @xmath60 such that the cayley graph @xmath190 is hyperbolic , non - elementary ( i.e. , @xmath191 ) , and the action of @xmath60 on @xmath190 is acylindrical . let @xmath192 be a set of representatives of left cosets of @xmath60 in @xmath1 . obviously @xmath193 generates @xmath1 . since @xmath194 , the natural map @xmath195 is a quasi - isometry . in particular , @xmath196 is also hyperbolic and non - elementary . moreover , it is straightforward to verify that the action of @xmath1 on @xmath196 is acylindrical ( in fact , acylindricity of the action is preserved under equivariant quasi - isometries ) . therefore @xmath197 by definition [ df : acyl - gp ] . conversely if @xmath198 , and @xmath60 is a finite index subgroup of @xmath1 , then @xmath60 is @xmath168-normal in @xmath1 and thus @xmath189 by theorem [ thm : elem - prop - ah ] . further , let @xmath1 be a group , @xmath199 a finite normal subgroup and let @xmath200 be the natural epimorphism . then for any generating set @xmath10 of @xmath1 , @xmath201 generates @xmath202 and the natural map @xmath203 is a @xmath1-equivariant quasi - isometry . thus if @xmath204 is non - elementary hyperbolic then so is @xmath205 . also observe that the action of @xmath1 on @xmath205 factors through the canonical action of @xmath202 . hence if the former is acylindrical then so is the latter . thus if @xmath197 then @xmath206 . conversely , if @xmath192 is some generating set of @xmath202 then @xmath207 is a generating set of @xmath1 and the cayley graphs @xmath204 and @xmath208 are @xmath1-equivariantly quasi - isometric . since @xmath209 , if the action of @xmath202 on @xmath208 is acylindrical , then so is the natural action of @xmath1 on @xmath208 . this allows to argue as above to conclude that @xmath206 implies @xmath197 . the next two results will be used in section 7 of our paper . the first one was proved by dahmani , guirardel and the second author in ( * ? ? ? * theorem 2.32 ) . [ thm : prop - ah-2 ] for any acylindrically hyperbolic group @xmath1 , there exists a maximal normal finite subgroup @xmath210 and the following conditions are equivalent . 1 . @xmath211 . @xmath1 has infinite conjugacy classes ( equivalently , the von neumann algebra @xmath58 of @xmath1 is a @xmath212 factor ) . @xmath1 is not inner amenable . in particular , @xmath58 does not have property @xmath57 of murray and von neumann . the reduced @xmath213-algebra of @xmath1 is simple with unique trace . the next theorem was first proved in @xcite under a certain assumption equivalent to acylindrical hyperbolicity ( see @xcite ) ; it also follows from the main result of @xcite , where the language of hyperbolically embedded subgroups was used . for details about quasi - cocycles and bounded cohomology we refer to @xcite . [ thm : prop - ah-3 ] @xmath92 . finally we mention a theorem from @xcite . recall that the conjugacy growth function of a finitely generated group for every @xmath214 measures the number of conjugacy classes intersecting the ball of radius @xmath215 centered at @xmath153 in the word metric . for details we refer to @xcite . [ thm : prop - ah-4 ] every acylindrically hyperbolic group has exponential conjugacy growth . given an oriented edge @xmath216 of a graph @xmath78 , @xmath217 and @xmath218 will denote the initial vertex and the terminal vertex of @xmath216 respectively , and @xmath219 will denote the inverse edge to @xmath216 ( i.e. , @xmath216 equipped with the opposite orientation ) . in this paper , a tree means a simplicial tree , unless specified otherwise . let @xmath220 be a tree . the natural metric on @xmath19 , induced by identification of edges with @xmath221 $ ] , is denoted by @xmath222 . we will think of @xmath19 as a simplicial tree and a metric space simultaneously ; in particular we will talk about vertices and edges as well as points of @xmath19 . given two points @xmath223 , @xmath224 $ ] will denote the unique geodesic segment connecting @xmath160 and @xmath225 . throughout this subsection let @xmath1 denote a group acting on @xmath19 by isometries . it is well known that any element @xmath31 either fixes a point of @xmath220 ( which is either a vertex or the midpoint of an edge ) or there exists a unique minimal @xmath226-subtree of @xmath220 , which is a bi - infinite geodesic path , called the _ axis _ of @xmath107 and denoted by @xmath227 , on which @xmath107 acts by translation @xcite . in the former case @xmath107 is said to be _ elliptic _ , and in the latter case it is said to be _ hyperbolic_. for a hyperbolic element @xmath107 , we denote by @xmath228 the limit points of the axis of @xmath107 in @xmath229 . the _ translation length _ @xmath230 , of an element @xmath31 , is defined as the minimum of the distances @xmath231 , where @xmath71 runs over the set of all vertices of @xmath19 . since @xmath19 is a simplicial tree , @xmath230 is a non - negative integer . the translation length can be used to classify the elements of @xmath1 : @xmath232 if and only if @xmath107 is elliptic . and if @xmath107 is hyperbolic , then the set set of all points @xmath160 of @xmath19 such that @xmath233 is exactly the axis of @xmath107 . [ df : edge_transl ] consider an edge @xmath216 of @xmath19 with some fixed orientation . we will say that an element @xmath31 _ translates _ @xmath216 if @xmath234 and the vertices @xmath217 and @xmath235 lie outside of the geodesic segment @xmath236 $ ] . note that , in this terminology , if @xmath31 acts as a hyperbolic isometry and @xmath216 is an edge on the axis of @xmath107 then @xmath216 is translated by exactly one of the elements @xmath107 or @xmath237 ( the above definition implies that @xmath238 in the sense of ( * ? ? ? * i.4.10 ) ) . conversely , if @xmath31 translates some edge @xmath216 of @xmath19 then @xmath107 is hyperbolic and the axis of @xmath107 contains the segment @xmath239 $ ] ( see ( * ? ? ? * i.4.11 ) ) . our main goal in this section is to establish a criterion for the existence of hyperbolic wpd elements in @xmath1 . we begin with a technical result about pointwise @xmath122-stabilizers defined in section [ sec : eqdef ] . [ lem : epst ] fix any @xmath121 . let @xmath5 be any two points in @xmath19 with @xmath240 and let @xmath21 be any two vertices on the geodesic segment @xmath224 $ ] such that @xmath241 . then @xmath242 is contained in the union of at most @xmath243 left cosets of @xmath244 . let @xmath245 $ ] , @xmath246 , be the set of all translations of @xmath247 $ ] by elements of @xmath1 such that @xmath248\subset [ x , y]$ ] and @xmath249 . obviously @xmath250 ( note that edge inversions are possible ) . for each @xmath251 , choose any element @xmath252 such that @xmath248=t_i [ u , v]$ ] . let @xmath107 be an element of @xmath242 . that is , @xmath253 let @xmath254 ( respectively , @xmath255 ) be the point on @xmath224 $ ] closest to @xmath256 ( respectively , @xmath257 ) . thus @xmath258 $ ] is a concatenation of @xmath259 $ ] and @xmath260 $ ] and , similarly , @xmath261 $ ] is a concatenation of @xmath262 $ ] and @xmath263 $ ] . using ( [ eq : dtgx ] ) we obtain @xmath264 and @xmath265 since @xmath266 , ( [ eq : dtxa ] ) implies that @xmath267 and hence @xmath268=[x , y]\cap [ g x , g y]$ ] . since @xmath269 $ ] and @xmath270 , we obtain @xmath271 $ ] using again . similarly we obtain @xmath272 $ ] and @xmath273 $ ] using ( [ eq : dtgxa ] ) . since @xmath274\subseteq [ g x , g y]$ ] , we have @xmath275 thus @xmath276=[u_i , v_i]$ ] for some @xmath277 . this means that @xmath278 and hence @xmath279 [ prop : wpd - crit ] let @xmath1 be a group acting on a simplicial tree @xmath19 and let @xmath280 be a hyperbolic element . suppose that for some vertices @xmath281 , the pointwise stabilizer @xmath282 is finite ( the possibility @xmath283 is allowed ) . then @xmath128 satisfies the wpd condition . in particular , either @xmath1 is virtually cyclic or @xmath197 . without loss of generality we can assume that @xmath284 $ ] for some @xmath285 ( otherwise , exchange @xmath70 and @xmath71 ) . we will show that in this case @xmath128 satisfies definition [ def : wpd ] for @xmath286 . take any @xmath3 . evidently we can increase @xmath122 to assume that @xmath287 . let @xmath288 be such that @xmath289 and let @xmath290 and @xmath291 . then @xmath247 \subset [ u , h^m u]\subset [ x , y]$ ] and @xmath292 . applying lemma [ lem : epst ] , we obtain that @xmath293 is finite . since @xmath294 , @xmath295 is conjugate to @xmath293 in @xmath1 , and hence it is also finite . thus the definition of wpd is satisfied for @xmath286 and @xmath296 . the last claim of the corollary follows from theorem [ acyl ] together the observation that a hyperbolic isometry of a simplicial tree is hyperbolic ( loxodromic ) in the sense defined at the beginning of subsection [ sec : eqdef ] . the action of @xmath297 on itself by translations shows that corollary [ prop : wpd - crit ] does not extend to actions on @xmath297-trees . recall that the action of @xmath1 on @xmath19 is _ minimal _ if @xmath19 does not contain any proper @xmath1-invariant subtree . let @xmath298 be the natural compactification of @xmath19 . take any point @xmath299 . limit set _ @xmath300 , of @xmath1 in the boundary @xmath20 , is the intersection of the closure of @xmath301 in @xmath302 with @xmath20 . since @xmath1 acts on @xmath19 isometrically , @xmath300 does not depend on the choice of the point @xmath160 . [ axisuv ] let @xmath19 be a tree with at least @xmath0 vertices . suppose that a group @xmath1 acts minimally on @xmath19 and does not fix any point of @xmath20 . then for any two vertices @xmath21 of @xmath19 , there exists a hyperbolic element @xmath8 such that @xmath303 contains @xmath70 and @xmath71 . since @xmath304 has at least @xmath0 vertices , there exists a vertex @xmath71 of degree at least @xmath13 . let @xmath305 be the minimal subtree of @xmath19 containing the orbit @xmath306 . obviously @xmath305 is @xmath1-invariant and no vertex of @xmath305 has degree @xmath153 in @xmath19 . since the action of @xmath1 is minimal , @xmath307 . thus @xmath19 does not contain vertices of degree @xmath153 . this implies that any two vertices @xmath21 of @xmath19 are contained in a bi - infinite geodesic @xmath308 . in particular , @xmath19 is unbounded . if the action of @xmath1 is elliptic ( i.e. , orbits are bounded ) , then for any vertex @xmath71 of @xmath19 , the minimal subtree @xmath309 containing the orbit @xmath306 is bounded . obviously @xmath309 is @xmath1-invariant . however this contradicts minimality of the action since @xmath19 is unbounded . thus the action of @xmath1 can not be elliptic . since @xmath1 does not fix any point of @xmath310 , the action of @xmath1 on @xmath19 can not be parabolic or quasi - parabolic in gromov s terminology either ( see ( * ? ? ? * section 8.2 ) ) . hence the set @xmath311 , where @xmath312 is the set of all hyperbolic elements of @xmath1 , is dense in @xmath313 ( * ? ? ? * corollary 8.2.g ) ( for a detailed proof in a more general situation see @xcite ) . moreover , since the action of @xmath1 on @xmath19 is minimal , for any vertex @xmath314 , @xmath19 coincides with the convex span of the orbit @xmath306 . thus any point of @xmath19 lies on a geodesic segment connecting two vertices from @xmath306 . it follows that @xmath315 , and so the set @xmath311 is dense in @xmath316 . this implies that for any segment @xmath317 of @xmath308 , there is a hyperbolic element @xmath8 with @xmath318 , as claimed . note that the lemma does not hold for the tree @xmath319 consisting of a single edge . indeed @xmath320 acts on @xmath319 by inversion . the action is minimal and obviously @xmath320 does not fix any point of @xmath321 as the latter is empty . similar counterexamples can be constructed by using any group that surjects onto @xmath320 . however if we assume that @xmath1 acts of @xmath19 without inversions , then the condition @xmath322 in the lemma can be relaxed to @xmath323 . the next result is obtained in the course of proving part ( 3 ) of proposition 6 in @xcite . note that although the authors assume that every hyperbolic element satisfies wpd there , the proof only uses the existence of a single hyperbolic wpd element . [ bf ] let @xmath1 be a group acting on a hyperbolic space @xmath10 and containing a hyperbolic wpd element . if @xmath1 is not virtually cyclic , then it contains two hyperbolic elements @xmath324 such that @xmath325 . we are now ready to prove the main result of this subsection . [ prop : min - wpd ] let @xmath1 be a group acting minimally on a simplicial tree @xmath19 . if @xmath1 is not virtually cyclic then the following conditions are equivalent : 1 . @xmath1 contains a hyperbolic wpd element ( for the given action of @xmath1 on @xmath19 ) . 2 . @xmath1 does not fix any point of @xmath20 and there exist vertices @xmath21 of @xmath19 such that @xmath326 is finite . suppose that @xmath1 is non - elementary and contains a hyperbolic wpd element @xmath8 . let @xmath327 be the axis of @xmath107 and let @xmath328 be any vertex . let @xmath54 be the constant from the definition of the wpd condition for @xmath107 corresponding to @xmath329 . set @xmath330 , then @xmath326 is finite by the wpd condition . since the only points of @xmath20 fixed by a hyperbolic element @xmath331 are @xmath332 , lemma [ bf ] implies that @xmath1 does not fix any point of @xmath20 . conversely , suppose @xmath1 does not fix any point of @xmath20 and there exist vertices @xmath21 of @xmath19 such that @xmath326 is finite . if @xmath304 were finite then @xmath282 would have finite index in @xmath1 implying that @xmath333 , which would contradict the assumption that @xmath1 is not virtually cyclic . hence the tree @xmath304 must be infinite , so , by lemma [ axisuv ] , there exists a hyperbolic element @xmath8 such that @xmath303 passes through @xmath70 and @xmath71 . therefore , according to corollary [ prop : wpd - crit ] , @xmath107 satisfies the wpd condition . suppose that @xmath1 is not virtually cyclic . then it contains a hyperbolic wpd element ( with respect to the action on @xmath19 ) by proposition [ prop : min - wpd ] . hence @xmath1 is acylindrically hyperbolic by theorem [ acyl ] . in this subsection we assume that the reader is familiar with bass - serre theory . for a detailed exposition we refer to @xcite . let @xmath23 be a graph of groups , where @xmath78 is a connected graph and @xmath334 is a collection consisting of 1 . edge groups @xmath335 and vertex groups @xmath336 associated to edges @xmath337 and vertices @xmath338 of @xmath57 ; 2 . maps @xmath339 and @xmath340 , which for every edge @xmath216 of @xmath78 , define the embeddings of the edge group @xmath335 into the vertex groups @xmath341 and @xmath342 , respectively . let also @xmath343 denote the fundamental group of @xmath23 . as we know , this fundamental group naturally acts on the associated bass - serre tree @xmath19 . in this section we will investigate various conditions ensuring that this action satisfies the assumptions of theorem [ main-1 ] . first we will characterize the situation when @xmath343 fixes a point of @xmath20 . the proof of the following statement is essentially contained in the proof of theorem 4.1 from @xcite : [ lem : fix_end ] suppose that @xmath1 is a group acting isometrically on a simplicial tree @xmath19 . if @xmath1 fixes a point of @xmath20 then all elliptic elements in @xmath1 form a normal subgroup @xmath344 such that the quotient @xmath202 is either trivial or infinite cyclic . let @xmath345 be the point fixed by @xmath1 and let @xmath346 be an elliptic element . then @xmath160 fixes some vertex @xmath70 of @xmath19 , and hence it must fix ( pointwise ) the unique geodesic ray @xmath347 $ ] from @xmath70 to @xmath348 . if @xmath349 is another elliptic element , then @xmath225 fixes the geodesic ray @xmath350 $ ] for some vertex @xmath71 of @xmath19 . the intersection of the rays @xmath347 $ ] and @xmath350 $ ] is again a geodesic ray @xmath351 $ ] for some vertex @xmath352 . it follows that @xmath352 is fixed by both @xmath160 and @xmath225 , hence the product @xmath353 is elliptic . evidently an inverse and a conjugate of an elliptic element is again elliptic , therefore the set of elliptic elements forms a normal subgroup @xmath344 . if @xmath1 has no hyperbolic elements , then @xmath354 and the lemma is proved . so , assume that @xmath1 has at least one hyperbolic element . then there is a hyperbolic element @xmath280 which has minimal translation length @xmath355 . recall that the only fixed points of @xmath128 on @xmath20 are @xmath356 . after replacing @xmath128 with @xmath357 , if necessary , we can assume that @xmath358 . take any other hyperbolic element @xmath31 . we want to show that @xmath359 . as above , we can suppose that @xmath360 . hence the intersection of @xmath227 and @xmath361 contains an infinite geodesic ray @xmath362 $ ] for some vertex @xmath71 of @xmath19 , and positive powers of @xmath128 and @xmath107 translate this ray into itself . by the construction of @xmath128 , @xmath363 , hence there exist @xmath364 such that @xmath365 and @xmath366 , @xmath367 . set @xmath368 and observe that @xmath369 translates the ray @xmath350 $ ] into itself and @xmath370 . so , if @xmath371 then @xmath369 is a hyperbolic element with @xmath372 , contradicting the choice of @xmath128 . therefore @xmath36 , i.e. , @xmath369 fixes @xmath71 , and so it is elliptic . thus @xmath373 , which implies that @xmath374 . since @xmath375 , we see that @xmath376 is infinite cyclic , and the lemma is proved . suppose that @xmath216 is an edge between vertices @xmath70 and @xmath71 in a graph of groups @xmath23 . we will say that @xmath216 is _ good _ if the natural images of @xmath335 in @xmath377 and @xmath336 are proper subgroups . any edge that is not good will be called _ bad_. [ lem : ab ] if the graph of groups @xmath23 has at least one good edge then the elliptic elements of @xmath378 do not form a subgroup . in particular , @xmath1 does not fix any point of @xmath20 , where @xmath19 is the corresponding bass - serre tree . let @xmath216 be any edge of @xmath19 which maps onto a good edge of @xmath379 . fixing some orientation of @xmath216 and abusing the notation , we let @xmath335 , @xmath342 and @xmath341 denote the @xmath1-stabilizers of @xmath216 , @xmath217 and @xmath218 respectively . since the image of @xmath216 in @xmath78 is good , there is an element @xmath380 and an element @xmath381 . clearly @xmath254 and @xmath255 are elliptic , and to prove the statement it suffices to show that the element @xmath382 is hyperbolic . let @xmath383 , then @xmath384 but @xmath385 as @xmath386 . on the other hand , the edge @xmath387 starts at @xmath217 and is also distinct from @xmath216 ( see figure [ fig : ab ] ) . thus we see that the edge @xmath369 is translated by @xmath128 ( cf . [ df : edge_transl ] ) , which implies that @xmath128 is hyperbolic . the last claim of the lemma now follows from lemma [ lem : fix_end ] . we will say that an oriented edge @xmath216 of @xmath78 is _ reducible _ if @xmath388 and at least one of the maps @xmath389 , @xmath390 is onto . a graph of groups @xmath23 is _ reduced _ if it does not contain reducible edges . thus a reducible edge is a bad edge which is not a loop . it is easy to see that any reducible edge can be contracted without affecting the fundamental group . therefore every finite graph of groups can be contracted to a reduced graph of groups with the same fundamental group ( see @xcite for details , where reducible edges are called _ directed _ ) . recall that an hnn - extension @xmath391 of a group @xmath26 with associated subgroups @xmath24 and @xmath29 is called _ ascending _ if @xmath392 or @xmath393 . ascending hnn - extension gives a basic example of a reduced graph of groups that has a single vertex and a single bad loop at this vertex . the following proposition characterizes the case when the fundamental group of a reduced graph of groups fixes a point on the boundary of the corresponding bass - serre tree : [ prop : charact ] suppose that @xmath23 is a reduced graph of groups with at least one edge . let @xmath378 and let @xmath19 be the corresponding bass - serre tree . then the following are equivalent : * @xmath1 fixes a point of the boundary @xmath20 ; * @xmath23 has only one vertex @xmath71 and one ( unoriented ) bad edge @xmath216 with @xmath394 . in other words , @xmath1 is an ascending hnn - extension of @xmath336 . the fact that ( ii ) implies ( i ) is well - known and we leave it as an exercise for the reader . now , suppose that ( i ) holds . then @xmath23 has no good edges by lemma [ lem : ab ] . since @xmath23 has no reducible edges by the assumptions and @xmath78 is connected , one concludes that @xmath78 has only one vertex @xmath71 and all the edges of @xmath78 are loops at @xmath71 . the quotient of @xmath378 by the normal closure @xmath344 , of @xmath336 in @xmath1 , is the free group , whose rank is equal to the number of ( unoriented ) loops at @xmath71 . since @xmath71 is the only vertex of @xmath78 , every elliptic element is conjugate to an element of @xmath336 in @xmath1 . so , by lemma [ lem : fix_end ] , @xmath7 is the set of all elliptic elements , and the quotient @xmath202 is cyclic . thus @xmath78 can have at most one loop at @xmath71 , which is a bad edge ( as defined above ) , i.e. , ( ii ) holds . for a general graph of groups @xmath23 , the situation when the canonical action of @xmath378 on the corresponding bass - serre tree @xmath19 is minimal was characterized by bass in @xcite . the next lemma follows from ( * ? ? ? 7.12 ) : [ lem : min - act ] let @xmath23 be a reduced graph of groups of finite diameter . then the action of @xmath343 on the corresponding bass - serre tree is minimal . a combination of proposition [ prop : charact ] with lemma [ lem : min - act ] and theorem [ main-1 ] gives a criterion to show that the fundamental group of a finite reduced graph of groups is acylindrically hyperbolic ( see theorem [ thm : reduced - crit ] below ) . before formulating it we need to make a couple of observations . [ rem : vert - edg ] suppose that @xmath1 is a group acting on a simplicial tree @xmath19 . if the tree @xmath19 has at least two vertices , the existence of vertices @xmath395 with @xmath396 is equivalent to the existence of two edges @xmath397 of @xmath19 such that @xmath398 . ( note that we allow the possibilities @xmath283 and/or @xmath399 . ) indeed , in one direction this is evident . for the other direction , suppose that @xmath216 and @xmath369 are edges of @xmath19 with @xmath398 . without loss of generality we can assume that the segment @xmath400 $ ] contains both of these edges . then @xmath401)={{\rm pstab}}_g(\{e , f\})$ ] , i.e. , one can take @xmath402 and @xmath403 . [ rem : fin_pst ] suppose that @xmath1 is the fundamental group of a graph of groups @xmath23 and @xmath19 is the corresponding bass - serre tree . in algebraic terms , the existence of vertices @xmath21 of @xmath19 such that @xmath326 is finite means that @xmath404 for some @xmath8 and some vertices @xmath405 , @xmath406 of @xmath78 . similarly , the existence of two edges @xmath397 of @xmath19 such that @xmath398 corresponds to @xmath407 for some @xmath8 and some edges @xmath408 , @xmath409 of @xmath78 . [ thm : reduced - crit ] let @xmath1 be the fundamental group of a finite reduced graph of groups @xmath23 with at least one edge such that the condition ( ii ) from proposition [ prop : charact ] does not hold . suppose that there are edges @xmath397 of @xmath78 ( not necessarily distinct ) and an element @xmath31 such that @xmath410 . then @xmath1 is either virtually cyclic or acylindrically hyperbolic . let @xmath19 be the bass - serre tree associated to @xmath23 . by lemma [ lem : min - act ] , the action of @xmath1 on @xmath19 is minimal , and , by proposition [ prop : charact ] , @xmath1 does not fix any point of @xmath20 . since @xmath23 is reduced and has at least one edge , it is easy to see that the tree @xmath19 must be infinite ( any loop gives rise to a hyperbolic element ; if there are no loops , then all the edges must be good , hence a hyperbolic element can be produced as in the proof lemma [ lem : ab ] ) . by remarks [ rem : fin_pst ] and [ rem : vert - edg ] , the assumptions imply that @xmath19 contains two vertices @xmath21 such that @xmath282 is finite . therefore , we can apply theorem [ main-1 ] to conclude that @xmath1 is either virtually cyclic or acylindrically hyperbolic . corollary [ cor : amalg - intr ] from section [ sec : results ] is an immediate consequence of theorem [ thm : reduced - crit ] applied in the situation when @xmath23 consists of two vertices and a good edge connecting them . corollary [ cor : hnn - intr ] corresponds to the case when @xmath23 has one vertex and one ( good ) loop at this vertex . thus its claim also follows from theorem [ thm : reduced - crit ] modulo the observation that a non - ascending hnn - extension of any group contains non - abelian free subgroups ( see , for example , ( * ? ? ? * thm . 6.1 ) ) , and so it can not be virtually cyclic . it is easy to see that the condition @xmath28 is necessary in corollary [ cor : amalg - intr ] . as for the requirement @xmath30 in corollary [ cor : hnn - intr ] , the situation is more complicated and counterexamples are not so obvious . we note the following . [ prop : asc - hnn ] let @xmath1 be an ascending hnn - extension of a group @xmath26 . if @xmath1 is acylindrically hyperbolic , then so is @xmath26 . let @xmath411 be the stable letter of the hnn - extension , @xmath412 . then the subgroup @xmath413 is normal in @xmath1 and @xmath414 . consequently we have @xmath415 . thus by part ( d ) of theorem [ thm : elem - prop - ah ] @xmath26 must be acylindrically hyperbolic . proposition [ prop : asc - hnn ] allows to construct examples of ascending hnn - extensions with weakly malnormal base which are not acylindrically hyperbolic . [ ex : hnnb ] using methods from ( * ? ? ? * section 4.2 ) it is not hard to construct a proper malnormal subgroup @xmath416 of a free burnside group @xmath26 of rank @xmath13 and large odd exponent such that @xmath417 . let @xmath1 be the corresponding ascending hnn - extension of @xmath26 . then @xmath26 and @xmath27 are weakly malnormal in @xmath1 , but @xmath1 is not acylindrically hyperbolic by a combination of proposition [ prop : asc - hnn ] and example [ ex : non - ah ] ( b ) . if @xmath26 is acylindrically hyperbolic , then its ascending hnn - extensions can be acylindrically hyperbolic as well . for example , many ascending hnn - extensions of free groups are hyperbolic . nevertheless the example below shows that acylindrical hyperbolicity ( even relative hyperbolicity ) of @xmath26 together with weak malnormality is still not sufficient to derive acylindrical hyperbolicity of @xmath1 . [ ex : bg ] in the proof of ( * ? ? ? * prop . 18 ) , the second author constructed a boundedly generated finitely presented group ( denoted by @xmath1 in @xcite ) which is universal , i.e. , contains an isomorphic copy of every recursively presented group . let us denote this group by @xmath418 . let @xmath419 and let @xmath420 be a generator of the subgroup @xmath161 . then @xmath26 is acylindrically hyperbolic ( in fact , it is hyperbolic relative to @xmath418 ) . since @xmath26 is finitely presented , it is isomorphic to a subgroup @xmath421 . let @xmath1 be the corresponding ascending hnn - extension of @xmath26 with the stable letter @xmath411 . obviously @xmath422 and hence @xmath26 and @xmath27 are weakly malnormal in @xmath1 . arguing as in the proof of proposition [ prop : asc - hnn ] , we obtain @xmath423 . since @xmath418 is boundedly generated , so is @xmath1 . hence @xmath1 is not acylindrically hyperbolic by part ( d ) of theorem [ thm : elem - prop - ah ] . we begin with the proof of corollary [ cor : one - rel ] , which is inspired by @xcite and @xcite . it is proved in @xcite ( see the proof of theorem iii there ) that @xmath1 splits as @xmath424 , where @xmath425 are proper subgroups of @xmath60 , and there exists @xmath426 such that @xmath427 . thus the claim follows from corollary [ cor : amalg - intr ] and the well known fact that a one relator group with at least @xmath0 generators is never virtually cyclic . our next goal is to study one - relator groups with @xmath13 generators . as we already mentioned in example [ ex : non - ah-1 ] , the baumslag - solitar groups @xmath180 are not acylindrically hyperbolic unless @xmath35 or @xmath36 . the obstacle for acylindrical hyperbolicity of @xmath180 is the existence of an infinite cyclic @xmath168-normal subgroup . the are are many other one - relator groups with the same property . however , we will show that all of them ( as well as other potential examples of non - acylindrically hyperbolic one - relator groups ) have low complexity in a certain sense . recall that , given a group @xmath60 and an injective ( but not necessarily surjective ) endomorphism @xmath428 , the _ mapping torus of @xmath429 _ is the ( ascending ) hnn - extension @xmath430 [ cor:1-rel-2-gen ] let @xmath1 be a group with two generators and one defining relator . then at least one of the following holds : * @xmath1 is acylindrically hyperbolic ; * @xmath1 contains an infinite cyclic @xmath168-normal subgroup . more precisely , either @xmath1 is infinite cyclic or it is an hnn - extension of the form @xmath431 of a one - relator group @xmath432 with non - trivial center , so that @xmath433 in @xmath60 for some @xmath434 . in the latter case @xmath60 is ( finitely generated free)-by - cyclic and contains a finite index normal subgroup splitting as a direct product of a finitely generated free group with an infinite cyclic group . * @xmath1 is isomorphic to the mapping torus of an injective endomorphism of a finitely generated free group . moreover , the possibilities ( i ) and ( ii ) are mutually exclusive . in order to prove proposition [ cor:1-rel-2-gen ] we will need the following lemma : [ lem : inter_conj_free_gps ] if @xmath24 and @xmath29 are finitely generated subgroups of infinite index in a finitely generated free group @xmath26 then there exists an element @xmath435 such that @xmath436 . one way to prove this would be to refer , first , to a result of w. neumann ( 2.1 ) stating that there are finitely many elements @xmath437 such that if @xmath438 then @xmath439 for some @xmath440 . second , one can use the fact that the free group @xmath26 can not be covered by finitely many double cosets from @xmath441 because @xmath24 and @xmath29 are finitely generated and have infinite index in @xmath26 ( a generalization of this fact for quasiconvex subgroups of hyperbolic groups was proved in ( * ? ? ? this implies that there is some @xmath435 such that @xmath442 , and hence @xmath443 . however , let us give a direct proof of the lemma using stallings core graphs ( see @xcite for an introduction to this method ) . suppose that @xmath26 has a free generating set @xmath10 of cardinality @xmath444 . let @xmath445 and @xmath446 be the finite @xmath10-labelled directed core graphs corresponding to the subgroups @xmath24 and @xmath29 of @xmath26 respectively ( cf . thus each @xmath447 has a distinguished vertex @xmath448 such that the language of reduced closed loops at this vertex coincides with @xmath24 if @xmath172 and with @xmath29 if @xmath173 . since @xmath24 and @xmath29 have infinite index in @xmath26 , each @xmath447 possesses a vertex of degree strictly less than @xmath449 ( see ( * ? ? ? after replacing @xmath24 and @xmath29 with their conjugates we can assume that these vertices are @xmath448 , @xmath104 . thus @xmath450 has no outgoing edge labelled by @xmath451 for some @xmath452 , and @xmath453 has no incoming edge labelled by @xmath454 for some @xmath455 . now , take a freely reduced word @xmath352 over @xmath456 such that @xmath352 starts with @xmath451 and ends with @xmath454 . let @xmath141 be the simple directed path ( regarded as a simplicial graph ) labelled by @xmath352 . construct the new @xmath10-labelled directed graph @xmath457 by attaching the endpoint of @xmath141 to the graph @xmath446 at @xmath453 . let @xmath458 be the initial vertex of @xmath141 . observe that , by construction , the graph @xmath457 is folded , and so , equipped with the base vertex @xmath458 , it represents the core graph of the subgroup @xmath459 in @xmath26 , where @xmath460 is the element given by the word @xmath352 . moreover , the label of a non - trivial reduced loop at @xmath458 in @xmath457 can not be equal to the label of a reduced loop at @xmath450 in @xmath445 , because the former starts with the letter @xmath451 and @xmath450 has no outgoing edges with that label . therefore @xmath461 , as required . if @xmath1 is cyclic , ( ii ) holds , so we suppose that @xmath1 is not cyclic . thus @xmath462 , where @xmath463 is a cyclically reduced word over the alphabet @xmath464 . without loss of generality we can assume that the word @xmath463 is non - empty and the total exponent of @xmath411 in @xmath463 is @xmath17 by ( * ? ? ? * lemma 4.1 ) . then , using the standard magnus - moldavanski re - writing procedure ( see , for example , @xcite ) one shows that @xmath1 has a presentation @xmath465 where @xmath214 and @xmath466 is a cyclically reduced word in the alphabet @xmath467 involving both @xmath468 and @xmath469 . let @xmath60 be the one - relator group given by the presentation @xmath470 . if @xmath471 , then @xmath472 . if @xmath473 , @xmath1 is infinite cyclic . if @xmath60 is non - trivial but finite , @xmath1 is non - elementary hyperbolic and , hence , it is acylindrically hyperbolic . finally , if @xmath60 is infinite , @xmath1 is also acylindrically hyperbolic as @xmath60 is a non - degenerate and hyperbolically embedded subgroup in @xmath1 ( see example [ he s ] and theorem [ acyl ] ) . suppose , now , that @xmath474 . by construction , both @xmath468 and @xmath469 occur in @xmath466 . consequently , using the magnus s freiheitssatz , the elements @xmath475 and @xmath476 freely generated free subgroups of rank @xmath477 in @xmath60 . the presentation now shows that @xmath1 is the hnn - extension of @xmath60 with the associated magnus subgroups @xmath478 and @xmath479 . again we consider two possibilities . first , let us consider the case @xmath480 . then @xmath481 and @xmath482 are infinite cyclic groups . if @xmath483 then @xmath197 by corollary [ cor : hnn - intr ] and remark [ rem : hnn ] . so , assume that @xmath484 in @xmath60 for some @xmath434 . then @xmath485 is central in @xmath60 and @xmath486 , which easily implies that @xmath26 is @xmath168-normal in @xmath1 . it also follows that @xmath487\not\cong \mathbb z\oplus \mathbb z$ ] . therefore @xmath60 can be represented as a stem product of cyclic groups by a theorem of pietrowski ( * ? ? ? moreover , in @xcite murasugi showed that @xmath60 is ( finitely generated free)-by - cyclic in this case ( see the first paragraph of the proof of theorem 1 in @xcite ) . thus @xmath60 contains a finitely generated normal free subgroup @xmath488 and an element @xmath489 of infinite order so that @xmath490 ; in other words , @xmath491 . if @xmath492 is trivial or infinite cyclic then @xmath60 is virtually abelian , and thus ( ii ) holds . so , assume that @xmath492 is non - cyclic . then it has trivial center , and since the center of @xmath60 is non - trivial , there must exist @xmath493 and @xmath494 such that the element @xmath495 is central in @xmath60 . observe that the subgroup @xmath496 is normal in @xmath60 and has index @xmath497 . clearly @xmath498 hence ( ii ) holds . thus we can further assume that @xmath499 . consider the subgroups @xmath500 and @xmath501 in @xmath1 . then @xmath502 as @xmath503 and @xmath504 in @xmath1 . if @xmath393 then @xmath505 , i.e. , @xmath506 in @xmath60 , which implies that @xmath507 and hence @xmath1 is isomorphic to the mapping torus of some injective endomorphism of the free group @xmath26 . similarly , ( iii ) holds if @xmath508 . it remains to deal with the case when @xmath509 are proper subgroups of @xmath26 and @xmath499 . by a result of collins @xcite the intersection @xmath510 , of the magnus subgroups of @xmath60 is a free subgroup of rank at most @xmath477 . thus @xmath24 and @xmath29 are proper subgroups of the free group @xmath26 and their rank does not exceed the rank of @xmath26 . since the rank of @xmath26 is @xmath511 , the schreier index formula ( cf . * i.3.9 ) ) implies that the rank of any proper finite index subgroup of @xmath26 is strictly greater than @xmath477 . hence both @xmath24 and @xmath29 must have infinite index in @xmath26 . consequently , we can apply lemma [ lem : inter_conj_free_gps ] to find an element @xmath435 such that @xmath512 in @xmath26 . set @xmath513 . we will now check that @xmath514 , which would yield that @xmath197 by corollary [ cor : hnn - intr ] and remark [ rem : hnn ] , finishing the proof . indeed , suppose that @xmath515 , i.e. , there exist @xmath516 and @xmath517 such that @xmath518 in @xmath1 . by britton s lemma ( see ( * ? ? ? * iv.2 ) ) , @xmath519 , hence @xmath520 . therefore @xmath521 , but @xmath522 and so @xmath523 implying that @xmath524 . the above contradiction shows that @xmath514 , as claimed . finally we observe that conditions ( i ) and ( ii ) are indeed mutually exclusive , because the first claim in ( ii ) implies that @xmath1 is not acylindrically hyperbolic by theorem [ thm : elem - prop - ah ] . let @xmath41 be a field . we denote by @xmath525 $ ] the group of @xmath41-automorphisms of the ( formal , commutative ) polynomial algebra @xmath526 $ ] , i.e. , those automorphisms of the ring @xmath526 $ ] that fix @xmath41 . this group is sometimes called the integral cremona group of dimension @xmath215 over @xmath41 . note that every @xmath41-automorphism @xmath348 of @xmath526 $ ] is uniquely determined by the images @xmath527 . thus elements of @xmath525 $ ] can be represented by polynomial maps @xmath528 where @xmath529 $ ] for @xmath530 . obviously multiplication in @xmath525 $ ] corresponds to the composition of such maps . it is easy to see that @xmath44 $ ] is generated by the affine maps @xmath531 , where @xmath532 and @xmath533 . therefore , @xmath44 \cong k \rtimes k^\ast$ ] , where @xmath534 acts on the additive group @xmath41 by multiplication . in particular , @xmath44 $ ] is metabelian and hence it is not acylindrically hyperbolic . for @xmath480 , the situation is completely different . we recall a well - known decomposition theorem for @xmath39 $ ] . let @xmath26 be the group of all affine maps @xmath535 where @xmath536 and @xmath537 . let also @xmath27 be the so - called triangular group consisting of all maps of the form @xmath538 where @xmath539 , @xmath533 , and @xmath540 $ ] . it is easy to see that the intersection @xmath541 consists of all maps of the form ( [ triang ] ) , where @xmath107 is a linear polynomial . it is known that @xmath542=a\ast _ cb.\ ] ] the fact that @xmath39 $ ] is generated by @xmath26 and @xmath27 was proved by jung @xcite for @xmath43 and van der kulk @xcite in the general case . the above amalgamated product decomposition can be derived from their work quite easily . alternative proofs were later suggested by many people including dicks @xcite , nagata @xcite , and wright @xcite . for @xmath543 the lemma below can be extracted from @xcite . it is quite possible that similar ( rather sophisticated ) arguments work for any field . we provide an elementary hands on " proof . [ acac ] there exists @xmath544 $ ] such that @xmath545 . our choice of @xmath348 will depend on the characteristic of @xmath41 . we first consider the case when @xmath546 . let @xmath348 be the map @xmath547 where @xmath548 . it is obvious that @xmath544 $ ] . let @xmath549 . then @xmath550 has the form @xmath551 and @xmath552 for some @xmath553 , @xmath554 computing the compositions in ( [ ag = ga ] ) , we obtain @xmath555 and @xmath556 equating the coefficients at @xmath225 in ( [ ag2 ] ) , we obtain @xmath557 . note that if @xmath558 , then ( [ ag2 ] ) yields @xmath559 , which implies that @xmath560 is not an automorphism . thus @xmath561 . now using ( [ ag1 ] ) , we obtain @xmath562 and then @xmath563 and @xmath564 . the later equality in turn gives @xmath565 as @xmath561 and @xmath546 . using these we can rewrite ( [ ag2 ] ) as @xmath566 further replacing @xmath567 with the right side of ( [ ag1 ] ) and denoting @xmath568 by @xmath411 , we obtain @xmath569 now equating the coefficients at @xmath570 in ( [ ag3 ] ) we obtain @xmath571 . substituting this to ( [ ag3 ] ) and expanding @xmath141 yields @xmath572 thus we have @xmath573 and @xmath574 , which in turn implies @xmath575 . as @xmath576 , we obtain @xmath577 . finally substituting @xmath571 and @xmath565 in ( [ ag1 ] ) , we obtain @xmath578 . thus @xmath550 is the identity . now assume that @xmath579 . then we let @xmath348 be the map @xmath580 where @xmath581 . arguing as above we obtain @xmath582 . this case is completely analogous to the previous one and we leave it to the reader . clearly @xmath583 and @xmath584 . hence @xmath585 = a*_c b$ ] contains non - abelian free subgroups ( cf . * thm . 6.1 ) ) and therefore it is not virtually cyclic . thus the claim follows from corollary [ cor : amalg - intr ] and lemma [ acac ] . [ cor : am - hyp ] let @xmath586 ( @xmath587 ) , where @xmath26 is a hyperbolic group , @xmath24 is a quasi - convex subgroup of infinite index in @xmath26 , and @xmath27 is arbitrary ( respectively , @xmath588 ) . then @xmath1 is either virtually cyclic or acylindrically hyperbolic . in the case when @xmath589 , if @xmath590 then @xmath591 is hyperbolic , and hence @xmath197 unless it is virtually cyclic . so , we can further assume that @xmath592 . recall that a quasi - convex subgroup of a hyperbolic group has finite width see ( * ? ? ? * main thm . ) . this means that there is @xmath214 such that for any collection of elements @xmath593 , with @xmath594 whenever @xmath595 , there exist @xmath596 , @xmath597 , such that @xmath598 . since @xmath599 , a collection of elements @xmath600 with these properties exists , therefore @xmath24 is weakly malnormal in @xmath26 ( and , hence , in @xmath1 ) . thus to reach the required conclusion it remains to apply corollary [ cor : amalg - intr ] in the case of the amalgamated product or corollary [ cor : hnn - intr ] in the case of the hnn - extension . it is not hard to show that in corollary [ cor : am - hyp ] @xmath1 will be virtually cyclic only if @xmath26 is virtually cyclic and @xmath590 . let us mention one particular case , which may be compared with simple groups discussed in example [ ex : non - ah-1].(a ) , showing that neither the assumption that @xmath24 is finitely generated nor the assumption that @xmath24 has infinite index in @xmath26 can be dropped . [ cor : am - free ] let @xmath586 , where @xmath26 is a free group and @xmath601 is a finitely generated subgroup of infinite index . then @xmath1 is either infinite cyclic or acylindrically hyperbolic . obviously , under the assumptions of the corollary , @xmath1 is cyclic if and only if so is @xmath26 and @xmath590 . it is worth mentioning that non - simplicity of groups from corollary [ cor : am - free ] with @xmath27 free was proved in @xcite using the small cancellation theory . in this particular case the assumptions of corollary [ cor : amalg - intr ] can be easily verified using the following theorem of m. hall : _ every finitely generated subgroup of a free group @xmath492 is a free factor of a finite index subgroup of @xmath492 . _ it seems plausible that corollary [ cor : am - hyp ] generalizes to amalgamated products and hnn - extensions of relatively hyperbolic and even acylindrically hyperbolic groups ( for a suitable definition of quasi - convex subgroups ) . we leave such generalizations to the reader . schupp s arguments from @xcite combined with corollary [ cor : amalg - intr ] also yield the following : the higman group @xmath602 is acylindrically hyperbolic . we begin by reviewing some results about @xmath0-manifolds and their fundamental groups used in this paper . for basic definitions we refer to @xcite . our main reference for properties of fundamental groups of @xmath0-manifold groups is @xcite . details about seifert fibered manifolds can be found in @xcite . let @xmath54 be a closed , orientable , irreducible @xmath0-manifold . the jaco - shalen - johannson decomposition theorem provides a canonical finite collection of disjoint incompressible tori @xmath603 in @xmath54 such that all connected components of @xmath604 are either a seifert fibred or atoroidal . a minimal such collection is unique up to isotopy . by the seifert - van kampen theorem , this decomposition of @xmath54 induces a decomposition of @xmath605 into a graph of groups . we will call it the _ jsj decomposition _ of @xmath605 . recall that the action of a group @xmath1 on a tree @xmath19 is _ @xmath41-acylindrical in the sense of sela _ , if the diameter of the fixed point set of every @xmath606 is at most @xmath41 . for example , the action of a free product @xmath607 on the associated bass - serre tree is @xmath153-acylindrical . the following result was proved by wilton and zalesskii in @xcite . [ wz ] let @xmath54 be a closed , orientable , irreducible @xmath0-manifold . then either @xmath54 has a finite - sheeted covering space that is a torus bundle over a circle or the action of @xmath55 on the bass - serre tree associated to the jsj decomposition of @xmath55 is @xmath608-acylindrical . we now briefly discuss the pieces of the jsj decomposition . by the perelman s proof of the thurston s geometrization conjecture @xcite@xcite , atoroidal pieces admit a finite volume hyperbolic structure ( in the case of haken manifolds this was originally proved by thurston see ( * ? ? ? * thm . 1.42 ) ) . hence the fundamental group of each atoroidal piece is hyperbolic relative to peripheral subgroups isomorphic to @xmath609 @xcite . as for a seifert fibered piece @xmath106 , we will just use the fact that if the fundamental group @xmath610 is infinite then it fits into the short exact sequence @xmath611 where @xmath52 is infinite cyclic and @xmath60 has a finite index subgroup which is a surface group ( here by a surface group we mean any group isomorphic to the fundamental group of a compact surface ) see ( * ? ? ? 1.6 ) . we say that an action of a group @xmath1 on a tree is @xmath19 _ acylindrical in the sense of sela _ if it is @xmath41-acylindrical for some @xmath612 . we begin with a lemma that relates the notion to acylindricity in the sense of sela to the one defined in the introduction . [ lem : sa ] if the action of a group @xmath1 on a tree @xmath19 is acylindrical in the sense of sela , then it is acylindrical ( as defined in the introduction ) . suppose that the action is @xmath41-acylindrical for some @xmath612 . fix any @xmath3 and consider any two points @xmath5 on @xmath19 such that @xmath613 . then the segment @xmath224 $ ] contains a subsegment @xmath247 $ ] , where @xmath21 are vertices of @xmath19 , such that @xmath241 and @xmath614 . by our assumption , @xmath615 and hence @xmath616 by lemma [ lem : epst ] . thus the action of @xmath1 on @xmath19 is acylindrical by remark [ rem : equiv_def - acyl ] . recall that every acylindrically hyperbolic group @xmath1 contains a unique maximal finite normal subgroup @xmath617 , called the _ finite radical _ of @xmath1 ( see theorem [ thm : prop - ah-2 ] ) . [ lem : at ] let @xmath1 be the a group acting acylindrically in the sense of sela and without inversions on a tree @xmath19 . then either @xmath1 is acylindrically hyperbolic with trivial finite radical , or it is infinite cyclic or infinite dihedral , or @xmath1 fixes a vertex of @xmath19 . by lemma [ lem : sa ] the action of @xmath1 on @xmath19 is acylindrical ( as defined in the introduction ) . so , in view of theorems [ class ] and [ acyl ] , @xmath1 is either acylindrically hyperbolic , or virtually cyclic containing a hyperbolic element , or has bounded orbits . in the latter case @xmath1 fixes a vertex @xmath160 of @xmath19 ( see ( * ? ? ? * i.4.7 ) ) . now assume that @xmath1 is acylindrically hyperbolic or virtually cyclic and contains a hyperbolic element @xmath128 . recall that every virtually cyclic group @xmath618 has a finite normal subgroup @xmath619 such that @xmath620 is either infinite cyclic or infinite dihedral . thus to prove the lemma it suffices to show that @xmath1 has no non - trivial finite normal subgroups . suppose @xmath621 is a finite normal subgroup of @xmath1 . after passing from @xmath128 to some non - trivial power , we can assume that @xmath128 belongs to the centralizer @xmath622 . since @xmath621 is finite , it fixes a vertex @xmath71 of @xmath304 . assume that the action of @xmath1 on @xmath19 is @xmath41-acylindrical in the sense of sela . since @xmath128 is hyperbolic , there exists @xmath623 such that @xmath624 for @xmath625 . obviously for every @xmath626 , we have @xmath627 ; hence @xmath621 fixes @xmath70 as well . now the @xmath41-acylindricity of the action in the sense of sela implies that @xmath628 . the next lemma is proved in @xcite . [ lem:613 ] suppose that @xmath60 is a proper infinite hyperbolically embedded subgroup of a group @xmath1 . let @xmath621 be a subgroup of @xmath1 such that @xmath629 is infinite and @xmath630 . then @xmath621 contains proper infinite hyperbolically embedded subgroups . finally , we will need the following result , which is a ( probably well - known ) consequence of the projective plane theorem proved in @xcite . by @xmath631 we denote the free group of rank @xmath215 . [ epstein ] @xmath632 . assume that @xmath633 . then @xmath634 for some @xmath0-manifold @xmath54 . by ( * theorem 9.5 ) , if @xmath635 embeds in the fundamental group of some @xmath0-manifold @xmath7 , then either @xmath636 or @xmath637 is a non - trivial free product . applying this result to @xmath54 we obtain that @xmath638 is a non - trivial free product . however , a non - trivial free product must have trivial center . a contradiction . now we are ready to prove the main result of this section , which is slightly stronger than theorem [ main-3-dim ] from section [ sec : results ] ( see parts ( i@xmath639 ) and ( ii@xmath639 ) ) . [ main-3d ] let @xmath54 be a compact @xmath0-manifold and let @xmath1 be a subgroup of @xmath55 . then exactly one of the following three conditions holds . 1 . @xmath1 is acylindrically hyperbolic with trivial finite radical . 2 . @xmath1 contains an infinite cyclic normal subgroup @xmath52 and @xmath53 is acylindrically hyperbolic . in fact , @xmath53 is virtually a subgroup of a surface group in this case . @xmath1 is virtually polycyclic . note that the three conditions ( i@xmath639 ) , ( ii@xmath639 ) and ( iii ) are mutually exclusive by theorem [ thm : elem - prop - ah ] ( c ) and example [ ex : non - ah ] ( a ) . thus we only need to show that at least one of them holds . if the boundary @xmath640 is non - empty , we take the double @xmath641 . since @xmath54 is a retract of @xmath7 , @xmath55 embeds in @xmath637 ( cf . * lemma 1.6 ) ) . thus without loss of generality we can assume that @xmath54 is also closed . further if @xmath54 is non - orientable , we pass to its orientable double cover @xmath642 and consider the index @xmath13 subgroup @xmath643 such that @xmath644 . note that if one of the conditions ( i@xmath639 ) , ( ii@xmath639 ) or ( iii ) holds for @xmath645 , then the same condition holds for @xmath1 . indeed , for ( iii ) this is obvious . further assume that @xmath645 satisfies ( ii@xmath639 ) . thus @xmath645 contains a finite index subgroup @xmath646 such that there is an infinite cyclic subgroup @xmath647 and @xmath648 is isomorphic to a subgroup of the fundamental group of a compact surface . after replacing @xmath7 with a finite index subgroup if necessary we can suppose that @xmath344 and @xmath52 is central in @xmath7 . since @xmath648 can not be cyclic ( as ( iii ) does not hold for @xmath645 ) , the group @xmath648 is either a non - abelian free group or a closed hyperbolic surface group . in particular , @xmath648 has trivial center , which means that @xmath52 is the center of @xmath7 . therefore @xmath52 is characteristic in @xmath7 and so @xmath649 . the group @xmath648 is acylindrically hyperbolic and has finite index in the quotient @xmath53 . by lemma [ lem : com ] @xmath53 is also acylindrically hyperbolic and hence ( ii@xmath639 ) holds for @xmath1 . finally assume that ( i@xmath639 ) holds for @xmath645 . again , by lemma [ lem : com ] , @xmath1 is acylindrically hyperbolic . if @xmath1 has non - trivial finite radical , then @xmath650 as @xmath651 . therefore , by theorem [ thm : elem - prop - ah].(e ) , @xmath1 contains @xmath638 , which contradicts lemma [ epstein ] . hence @xmath1 satisfies ( i@xmath639 ) . thus we can ( and will ) assume that @xmath1 is a subgroup of @xmath55 for an orientable closed @xmath0-manifold @xmath54 . by the kneser - milnor theorem , @xmath54 decomposes as a connected sum @xmath652 of prime @xmath0-manifolds . consequently , @xmath653 . suppose , first , that @xmath1 is not conjugate to a subgroup of @xmath654 for any @xmath177 . then by kurosh theorem @xmath1 is a free product of two non - trivial groups and whence ( i@xmath639 ) or ( iii ) holds in this case by lemma [ lem : at ] , because the action of this free product on the associated bass - serre tree is @xmath153-acylindrical in the sense of sela and has no global fixed points . now , assume that @xmath1 is conjugate to a subgroup of some @xmath654 . since @xmath54 is closed and orientable , so is @xmath655 . recall that every orientable prime manifold , other than @xmath656 , is irreducible ( cf . * lemma 3.13 ) ) . since @xmath657 is cyclic , it suffices to consider the case when @xmath1 is isomorphic to a subgroup of a closed orientable irreducible @xmath0-manifold . from now on , we assume that @xmath658 for a closed orientable irreducible @xmath0-manifold @xmath54 . recall that if the fundamental group of such a manifold @xmath54 is infinite , then it is torsion - free ( see , for example , ( * ? ? ? * ( c.2 ) ) ) . thus we can also assume that @xmath55 is torsion - free . in particular , in ( i@xmath639 ) it will suffice to prove acylindrical hyperbolicity ; triviality of the finite radical will follow from the absence of torsion . by lemma [ wz ] either @xmath54 has a finite - sheeted covering space that is a torus bundle over a circle or the action of @xmath55 on the bass - serre tree @xmath19 associated to the jsj decomposition of @xmath55 is acylindrical in the sense of sela . in the former case ( iii ) holds . in the latter case , by lemma [ lem : at ] , @xmath1 either satisfies one of the conditions ( i@xmath639 ) , ( iii ) , or fixes a vertex of @xmath19 . thus it remains to consider the case when @xmath1 is a subgroup of the fundamental group of a seifert fibered piece or an atoroidal piece of the jsj decomposition . suppose , first , that @xmath1 is a subgroup of the fundamental group of a seifert fibered space @xmath106 . if @xmath659 is finite , we are done . if @xmath659 is infinite , then it contains an infinite normal cyclic subgroup @xmath52 such that the quotient @xmath660 contains a surface subgroup of finite index ( see ( * ? ? ? 1.6 ) ) . in particular , @xmath60 is either virtually @xmath661 for @xmath662 or is a non - elementary hyperbolic group . if @xmath60 is virtually @xmath661 for @xmath662 , so is @xmath663 , where @xmath664 . if @xmath60 is non - elementary hyperbolic , we fix any finite generating set @xmath10 of @xmath60 and note that the natural action of @xmath663 on the cayley graph @xmath190 is acylindrical since this is true for the action of @xmath60 . by theorem [ class ] , the action of @xmath663 on @xmath190 is elliptic ( in which case @xmath663 is finite as the action is proper ) , or @xmath663 is virtually cyclic , or @xmath663 is acylindrically hyperbolic . summarizing , we conclude that , in any case , @xmath663 is either virtually @xmath661 for @xmath662 or acylindrically hyperbolic . thus if @xmath665 , @xmath1 satisfies ( ii@xmath639 ) or ( iii ) . otherwise , @xmath666 , @xmath667 , and again ( i@xmath639 ) or ( iii ) holds . now assume that @xmath1 fixes a vertex of @xmath19 corresponding to an atoroidal piece . as we explained above , in this case @xmath1 is a subgroup of a group @xmath668 hyperbolic relative to free abelian subgroups of rank @xmath13 . let @xmath669 be the collection of peripheral subgroups of @xmath668 , @xmath10 a finite generating set of @xmath668 , @xmath670 . then every @xmath671 is hyperbolically embedded in @xmath668 ( see ( * ? ? ? * prop . 4.28 and remark 4.26 ) ) . if @xmath672 , fix any @xmath606 . since @xmath1 is torsion - free , by ( * 4.20 ) the element @xmath107 is either conjugate to an element of @xmath671 for some @xmath177 , or acts hyperbolically on @xmath673 ( note that the term hyperbolic element " is used in a slightly different sense in @xcite ) . again , we consider two cases . if @xmath107 is conjugate to an element of @xmath671 for some @xmath177 , then passing from @xmath1 to its conjugate if necessary , we can assume that @xmath674 is infinite . if @xmath675 , then we have ( iii ) . otherwise @xmath1 contains a proper infinite hyperbolically embedded subgroup by lemma [ lem:613 ] , and hence @xmath1 is acylindrically hyperbolic by theorem [ acyl ] . finally assume that @xmath107 is hyperbolic with respect to the action on @xmath673 . in particular , the action of @xmath1 is not elliptic . by ( 5.2 ) , the action of @xmath668 ( and , hence , of @xmath1 ) on the cayley graph @xmath673 is acylindrical . applying now theorem [ class ] we conclude that @xmath1 is either virtually cyclic or acylindrically hyperbolic . this completes the proof of the theorem . let @xmath54 be a compact irreducible @xmath0-manifold and @xmath676 . suppose that @xmath1 is neither virtually polycyclic nor acylindrically hyperbolic . then , by theorem [ main-3-dim ] , @xmath1 contains an infinite cyclic normal subgroup @xmath52 . hence , since @xmath54 is irreducible , we can use ( * ? ? ? 1.39 ) claiming that @xmath54 is a seifert fibered manifold . suppose that @xmath78 is a _ finite _ simplicial graph with vertex set @xmath677 , and @xmath678 is a family of _ non - trivial _ groups ( called _ vertex groups _ ) . the _ graph product _ @xmath679 , of this collection of groups with respect to @xmath78 , is the group obtained from the free product of the @xmath336 , @xmath680 , by adding the relations @xmath681=1 \text { for all } g_v\in g_v,\ , g_u\in g_u \text { whenever $ \{v , u\}$ is an edge of } { \gamma}.\ ] ] graph product of groups is a natural group - theoretic construction generalizing free products ( when @xmath78 has no edges ) and direct products ( when @xmath78 is a complete graph ) of groups @xmath336 , @xmath680 . graph products were first introduced and studied by e. green in her ph.d . thesis @xcite . further properties of graph products have been investigated in the works of hermiller and meier @xcite , hsu and wise @xcite , januszkiewicz and wiatkowski @xcite , and antoln and minasyan @xcite . recall that the _ link _ @xmath682 , of a vertex @xmath683 , is the set of all vertices of @xmath78 that are adjacent to @xmath71 ( excluding @xmath71 itself ) ; in other words , @xmath684 . for a non - empty subset @xmath685 , we define @xmath686 . note that @xmath687 . for any subset @xmath688 the subgroup @xmath689 , generated by @xmath690 , is called _ full _ ; according to a standard convention , @xmath691 . by the normal form theorem for graph products ( see @xcite or @xcite ) , @xmath692 is the graph product of the family @xmath693 with respect to the full subgraph @xmath694 of @xmath78 , spanned on the vertices from @xmath26 . it is easy to see that there is a canonical retraction @xmath695 , defined ( on the generators of @xmath1 ) by @xmath696 for each @xmath697 with @xmath698 , and @xmath699 for each @xmath700 with @xmath701 . any conjugate of a full subgroup in @xmath1 is called _ parabolic_. parabolic subgroups of graph products were studied and used by antoln and the first author in @xcite . in this subsection we summarize some of the known properties of parabolic subgroups of graph products . for a subset @xmath702 , @xmath703 and @xmath704 will denote the centralizer and the normalizer of @xmath10 in @xmath1 respectively . all of the claims in the lemma below were proved in section 3 of @xcite . [ lem : parab_props ] * * if @xmath705 and @xmath706 are such that @xmath707 then @xmath708 . * if @xmath709 is a parabolic subgroup of @xmath1 and @xmath710 for some @xmath31 , then @xmath711 . * if @xmath712 , where @xmath713 and @xmath714 , then @xmath715 is a parabolic subgroup of @xmath1 . * the intersection of two parabolic subgroups of @xmath1 is also a parabolic subgroup of @xmath1 . suppose that @xmath712 is a parabolic subgroup of @xmath1 , for some @xmath713 and @xmath714 . we define the _ parabolic dimension _ @xmath716 of @xmath709 to be the number of elements in @xmath106 . part ( i ) of lemma [ lem : parab_props ] shows that the parabolic dimension is well - defined as @xmath106 is completely determined by @xmath709 . [ lem : pdim ] let @xmath709 and @xmath717 be parabolic subgroups of @xmath1 . * if @xmath718 then @xmath719 with equality if and only if @xmath720 . * if @xmath721 then @xmath722 . first note that , according to lemma [ lem : parab_props].(iv ) , @xmath723 is also a parabolic subgroup of @xmath1 . therefore @xmath724 is defined and part ( b ) is an immediate consequence of part ( a ) . to prove part ( a ) , suppose that @xmath722 and @xmath725 , @xmath726 for some @xmath705 , @xmath706 . lemma [ lem : parab_props].(i ) implies that @xmath708 , hence @xmath727 . now , if @xmath728 then @xmath729 and thus @xmath730 , where @xmath731 . by lemma [ lem : parab_props].(ii ) , the inclusion of @xmath709 in @xmath732 yields that @xmath733 , as required . by part ( iv ) of lemma [ lem : parab_props ] the intersection of finitely many parabolic subgroups is again a parabolic subgroup . in fact a more general statement holds : [ lem : inter_parab_fam ] intersection of any family of parabolic subgroups of @xmath1 is equal to the intersection of a finite subfamily . in particular , this intersection is itself a parabolic subgroup of @xmath1 . consider a family @xmath734 of parabolic subgroups of @xmath1 . for any finite subset @xmath735 of @xmath317 , the intersection @xmath736 is a parabolic subgroup of @xmath1 , thus its parabolic dimension is defined . since this dimension is a non - negative integer , and non - negative integers are well - ordered , the function , which assigns to each finite subset @xmath737 the value @xmath738 , reaches its minimum on some finite subset @xmath739 . consider any @xmath740 and set @xmath741 . then @xmath742 by the choice of @xmath743 , hence lemma [ lem : pdim].(b ) implies that @xmath744 . since the latter is true for all @xmath740 we can conclude that @xmath745 . in ( * ? ? ? 3.10 ) it was proved that any subset @xmath702 is contained in a unique minimal parabolic subgroup @xmath746 , which is called _ the parabolic closure _ of @xmath10 . the next lemma lists two important properties of parabolic closures , which were also established in ( * ? ? ? * sec . 3 ) . [ lem : parab_clos ] let @xmath702 be an arbitrary subset and let @xmath747 be its parabolic closure in the graph product @xmath1 . * the normalizer @xmath704 is contained in the normalizer @xmath748 . * there exists a finite subset @xmath749 such that @xmath750 . [ lem : par_clos_in_spec ] consider any subset @xmath751 and the corresponding full subgroup @xmath692 of @xmath1 . as we know , @xmath692 is equal to the graph product @xmath752 , where @xmath753 is the full subgraph of @xmath78 spanned by @xmath26 , and @xmath693 . then for an arbitrary subset @xmath754 , the parabolic closure @xmath755 of @xmath10 in @xmath756 coincides with the parabolic closure @xmath746 of @xmath10 in @xmath679 . indeed , suppose that @xmath757 for some @xmath758 and @xmath714 . since @xmath754 and @xmath692 is a parabolic subgroup of @xmath1 , we have @xmath759 , implying that @xmath760 by lemma [ lem : parab_props].(i ) . let @xmath761 be the canonical retraction . the inclusions @xmath762 , yield that @xmath763 , where @xmath764 . hence @xmath765 is a parabolic subgroup of @xmath692 containing @xmath10 . consequently @xmath766 . on the other hand , @xmath767 because any parabolic subgroup of @xmath756 is also a parabolic subgroup of @xmath679 . therefore @xmath768 . [ df : join ] let @xmath769 be a parabolic subgroup of @xmath1 , where @xmath713 and @xmath714 . we shall say that @xmath621 is a _ join subgroup _ of @xmath1 if there are non - empty disjoint subsets @xmath770 such that @xmath771 and @xmath772 . if , in addition , both @xmath692 and @xmath773 are infinite then we will say that @xmath621 is a _ principal join subgroup _ of @xmath1 . in other words , a join subgroup is a parabolic subgroup which naturally splits as a direct product of smaller parabolic subgroups , and in a principal join subgroup these smaller parabolic subgroups must be infinite . using the terminology from @xcite , the _ essential support _ @xmath774 of a subset @xmath702 is defined as the smallest subset @xmath106 of @xmath775 such that @xmath10 is contained in a conjugate of @xmath776 in @xmath1 . equivalently , @xmath777 if @xmath778 for some @xmath714 . a subset @xmath304 of @xmath677 is said to be _ irreducible _ if @xmath304 can not be represented as a union of disjoint non - empty subsets @xmath779 such that @xmath772 . thus @xmath304 is irreducible if and only if @xmath780 is an irreducible graph ( as defined in subsection [ subsec : gp ] ) , which is also equivalent to @xmath781 not being a join subgroup of @xmath1 . the above definitions together with lemma [ lem : parab_props].(i ) immediately imply the following fact : [ rem : cont_in_join ] suppose that @xmath10 is a subset of the graph product @xmath1 . then @xmath10 is contained in a join subgroup of @xmath1 if and only if there are non - empty disjoint subsets @xmath770 such that @xmath772 and @xmath782 . similarly , @xmath10 is contained in a principal join subgroup of @xmath1 if and only if there exist non - empty disjoint subsets @xmath783 such that @xmath772 , @xmath782 and @xmath784 , @xmath785 . [ lem : h_in_join ] let @xmath60 and @xmath7 be non - trivial subgroups of @xmath1 such that @xmath60 normalizes @xmath7 and @xmath60 is not contained in the parabolic closure @xmath786 . then @xmath60 is contained in a join subgroup of @xmath1 . moreover , if @xmath787 and @xmath788 then @xmath60 is contained in a principal join subgroup of @xmath1 . by definition , @xmath789 for some non - empty subset @xmath790 and an element @xmath714 . by lemma [ lem : parab_clos].(i ) , since @xmath709 is the parabolic closure of @xmath7 , @xmath791 in @xmath1 . and , according to lemma [ lem : parab_props].(iii ) , @xmath792 . since @xmath60 is contained in @xmath748 but not in @xmath709 , it follows that @xmath793 . hence @xmath748 is a join subgroup of @xmath1 containing @xmath60 and the first claim is proved . now , if @xmath7 is infinite then @xmath692 is infinite . and if @xmath788 then @xmath794 , and so @xmath795 . recalling that @xmath692 commutes with @xmath773 ( by definition of @xmath27 ) , we see that @xmath796 , hence @xmath797 . thus @xmath748 is a principal join subgroup of @xmath1 containing @xmath60 , and the second claim of the lemma also holds . as before , we fix a finite simplicial graph @xmath78 with the vertex set @xmath775 and consider the graph product @xmath679 , of a family of non - trivial groups @xmath798 , with respect to @xmath78 . the definition of graph product immediately implies that for any @xmath799 the group @xmath1 naturally splits as the free amalgamated product : @xmath800 , where @xmath801 , @xmath802 and @xmath803 ( cf . * lemma 3.20 ) ) . it follows that @xmath1 acts ( simplicially by isometries and without edge inversions ) on the bass - serre tree @xmath19 associated to this splitting , and full vertex and edge stabilizers for this action are parabolic subgroups of @xmath1 ( conjugates of @xmath692 , @xmath773 and @xmath804 ) . [ lem : h_has_hyp_elt ] consider a subgroup @xmath132 and a vertex @xmath805 . suppose that @xmath806 in @xmath78 . let @xmath807 , @xmath808 and @xmath809 . as we know , @xmath1 splits as an amalgamated product @xmath810 and acts on the corresponding simplicial bass - serre tree @xmath19 . then there exists an element @xmath811 which acts as a hyperbolic isometry of @xmath19 . arguing by contradiction , suppose that @xmath60 contains no hyperbolic elements ; then every element of @xmath60 is elliptic . by lemma [ lem : parab_clos].(ii ) , there is a finite subset @xmath812 such that @xmath813 . the subgroup @xmath814 is finitely generated and every element of @xmath815 fixes a vertex of @xmath220 , therefore @xmath815 fixes some vertex of @xmath220 ( see ( * ? ? ? * i.6.5 , cor . 3 ) ) . but full @xmath1-stabilizers of vertices of @xmath220 are conjugates of @xmath692 and @xmath773 in @xmath1 , which are parabolic subgroups of @xmath1 . therefore there is @xmath714 such that @xmath816 where @xmath817 is either @xmath26 or @xmath27 . it follows that @xmath818 one can now apply lemma [ lem : parab_props].(i ) to conclude that @xmath819 , and so @xmath820 by the definition of @xmath26 . therefore @xmath821 and @xmath822 . recall that @xmath823 , thus @xmath824 , which contradicts our assumptions . suppose that a group @xmath1 acts on a tree @xmath19 and let @xmath825 be the metric on @xmath19 . for any two points @xmath826 of @xmath19 , @xmath224 $ ] will denote the geodesic segment between @xmath160 and @xmath225 in @xmath19 . if @xmath827 is a subset of @xmath19 , we will write @xmath828 and @xmath829 to denote the setwise and pointwise stabilizers of @xmath830 in @xmath1 respectively . evidently @xmath831 . [ lem : axis_pst ] consider an element @xmath280 that acts on the tree @xmath19 as a hyperbolic isometry , and let @xmath832 be the axis of @xmath128 . assume that @xmath833)$ ] for some geodesic subsegment @xmath224 $ ] of @xmath834 with @xmath835 . then there exists @xmath836 such that for any points @xmath837 with @xmath838 one has @xmath839)={{\rm pstab}}_g({\mathcal{l}})$ ] . recall that @xmath128 acts on @xmath834 by translation with positive translation length @xmath355 . let @xmath840 , and consider any subsegment @xmath841 $ ] of @xmath834 with @xmath842 . then for some integer @xmath843 , @xmath844 $ ] will be contained in @xmath841 $ ] . consequently one has @xmath845)\subseteq { { \rm pstab}}_g(h^m [ x , y])=h^m { { \rm pstab}}_g([x , y ] ) h^{-m } = h^m { { \rm pstab}}_g({\mathcal{l}})h^{-m}.\ ] ] clearly @xmath846 normalizes @xmath847 , thus @xmath839)\subseteq { { \rm pstab}}_g({\mathcal{l}})$ ] . on the other hand , since @xmath841 $ ] is a subsegment of @xmath834 one sees that @xmath848)$ ] . therefore @xmath839)={{\rm pstab}}_g({\mathcal{l}})$ ] , as claimed . for the remainder of this section we assume that @xmath679 , @xmath132 is a subgroup and @xmath805 is such that @xmath806 in @xmath78 . as before , set @xmath807 , @xmath808 and @xmath809 . let @xmath19 be the bass - serre tree associated to the natural splitting @xmath810 . [ lem : pst - parab ] if @xmath834 is the axis of some hyperbolic element @xmath280 then @xmath847 is a parabolic subgroup of @xmath1 , which is contained in a conjugate of @xmath804 . moreover , there exist vertices @xmath5 on @xmath834 such that @xmath833)$ ] . by definition , @xmath849 , where @xmath850 is the set of all edges of @xmath834 . since each @xmath851 is a conjugate of @xmath804 in @xmath1 , @xmath852 is a parabolic subgroup of @xmath1 by lemma [ lem : inter_parab_fam ] . in fact lemma [ lem : inter_parab_fam ] implies that @xmath853 for some finite collection @xmath854 of edges of @xmath834 . since any finite collection of edges of @xmath834 is contained in a finite subsegment we can find vertices @xmath835 such that @xmath855)$ ] . with the above assumptions on @xmath60 , lemma [ lem : h_has_hyp_elt ] tells us that @xmath60 contains at least one element that acts as a hyperbolic isometry on @xmath19 . the main technical statement of this section is the following proposition : [ prop : pst(axis)-normal ] let @xmath811 be a hyperbolic element such that @xmath856 is minimal , where @xmath834 is the axis of @xmath128 . then the parabolic subgroup @xmath847 is normalized by @xmath60 in @xmath1 . we will first show that for any element @xmath857 , which also acts as a hyperbolic isometry on @xmath19 , @xmath858 , where @xmath859 is the axis of @xmath107 . let @xmath860 and @xmath861 be the constants obtained by applying lemma [ lem : axis_pst ] to @xmath128 and @xmath107 respectively ( this can be done in view of lemma [ lem : pst - parab ] ) . choose a natural number @xmath214 so that @xmath862 and @xmath863 . we need to consider two separate cases . _ the intersection of @xmath834 with @xmath859 contains at least one edge @xmath216 . after replacing @xmath128 and @xmath107 with their inverses , if necessary , we can suppose that both @xmath128 and @xmath107 translate @xmath216 ( cf . [ df : edge_transl ] ) . set @xmath864 and note that the element @xmath865 translates @xmath408 . therefore @xmath369 is hyperbolic and @xmath866 $ ] lies on the axis @xmath867 of @xmath369 . by construction , the edge @xmath216 is contained in the segment @xmath866 $ ] ( see figure [ fig:1 ] ) . observe that @xmath408 is an edge of @xmath834 ( as @xmath834 is @xmath868-invariant and @xmath869 ) , hence the intersection of @xmath867 and @xmath834 contains the segment @xmath870 $ ] , whose length is equal to @xmath871 , which is greater than @xmath872 . therefore lemma [ lem : axis_pst ] implies that @xmath873)={{\rm pstab}}_g({\mathcal{l}}).\ ] ] similarly , as @xmath874 , we have @xmath875 \subseteq { \mathcal{n}}\cap { \mathcal{m}}$ ] , and so @xmath876)={{\rm pstab}}_g({\mathcal{m}}).\ ] ] however , since @xmath834 was chosen so that @xmath856 is minimal , we know that @xmath877 combining with lemma [ lem : pdim].(a ) we get that @xmath878 , and hence yields that @xmath858 . _ case 2 . _ the intersection of @xmath834 with @xmath859 is empty or consists of a single vertex . let @xmath879 and @xmath880 be vertices with the property @xmath881 ; thus ( in the terminology of @xcite ) @xmath882 $ ] is the _ spanning geodesic _ between @xmath834 and @xmath859 . in @xcite it is shown that the element @xmath883 is hyperbolic and the segment @xmath884 $ ] lies on the axis @xmath885 of @xmath369 . by construction , both @xmath141 and @xmath886 belong to this segment ( see figure [ fig:2 ] ) . again , we observe that @xmath887 \subseteq { \mathcal{l}}\cap { \mathcal{n}}$ ] and @xmath888 . therefore lemma [ lem : axis_pst ] tells us that @xmath889)={{\rm pstab}}_g({\mathcal{l}})$ ] . similarly , @xmath890)={{\rm pstab}}_g({\mathcal{m}})$ ] . as before , using minimality of @xmath856 , one can conclude that @xmath891 . let @xmath892 denote the set of axis of the elements of @xmath60 that act as hyperbolic isometries of @xmath19 . we have shown above that @xmath893 note that @xmath60 naturally acts on the set @xmath892 , and so it acts by conjugation on the collection of its subgroups @xmath894 ( if @xmath895 and @xmath859 is the axis of a hyperbolic @xmath857 then @xmath896 , where @xmath897 is the axis of the hyperbolic element @xmath898 ) . it follows that the intersection @xmath899 is normalized by @xmath60 ; but , according to , this intersection is equal to @xmath847 . thus the proposition is proved . [ thm : join ] suppose that @xmath1 , @xmath60 and @xmath19 are as above . let @xmath811 be a hyperbolic element with minimal @xmath856 , where @xmath834 is the axis of @xmath128 . if @xmath847 is non - trivial then @xmath60 is contained in a join subgroup of @xmath1 . and if @xmath900 then @xmath60 is contained in a principal join subgroup of @xmath1 . if we set @xmath901 , then @xmath7 is parabolic by lemma [ lem : pst - parab ] , thus @xmath902 . clearly the infinite cyclic subgroup @xmath868 of @xmath60 trivially intersects @xmath901 , hence @xmath903 . both claims of the theorem now follow from lemma [ lem : h_in_join ] , as @xmath7 is normalized by @xmath60 by proposition [ prop : pst(axis)-normal ] . [ cor : cyc - centr ] let @xmath60 be a subgroup of a graph product @xmath679 such that @xmath904 and @xmath60 is not contained in a join subgroup of @xmath1 . then there is a non - trivial element @xmath811 such that the centralizer @xmath905 is infinite cyclic . take any @xmath805 and define @xmath906 , and the bass - serre tree @xmath19 as above . since @xmath904 and @xmath60 is not contained in a join subgroup of @xmath1 , we see that @xmath806 in @xmath78 . according to lemma [ lem : h_has_hyp_elt ] and theorem [ thm : join ] , there is an element @xmath811 , that acts as a hyperbolic isometry on @xmath19 , such that @xmath847 is trivial , where @xmath834 is the axis of @xmath128 . since @xmath128 has a unique axis ( cf . @xcite ) , it follows that @xmath907 . since @xmath908 , @xmath909 is isomorphic to a subgroup of the infinite dihedral group ( which corresponds to the group of all simplicial isometries of the line @xmath834 ) . hence @xmath905 must be infinite cyclic because it contains the non - trivial central element @xmath128 . again , let @xmath78 be a finite graph with the vertex set @xmath775 and let @xmath1 be the graph product of a family of non - trivial groups @xmath910 with respect to @xmath78 . the following result can be regarded as an improvement of claim ( ii ) in lemma [ lem : parab_clos ] . [ thm : one_elt ] suppose that @xmath60 is a subgroup of @xmath1 such that @xmath911 is irreducible . then there exists an element @xmath811 such that @xmath912 . theorem [ thm : one_elt ] will be derived from the following auxiliary lemma , which is essentially a corollary of theorem [ thm : join ] . [ lem : irred ] assume that @xmath81 , @xmath913 , @xmath775 is irreducible in @xmath78 and @xmath914 . then there exists a non - trivial element @xmath811 such that @xmath905 is infinite cyclic and @xmath915 . starting with @xmath78 we construct a new graph @xmath916 as follows . let @xmath917 . take a @xmath41-element set @xmath918 and let the set of vertices @xmath919 of @xmath916 be defined by @xmath920 . the set of edges @xmath921 of @xmath916 ( which we identify with a subset of @xmath922 ) is defined by @xmath923 where @xmath618 is the set of edges of @xmath78 . thus @xmath78 is a full subgraph of @xmath916 and @xmath924 , @xmath925 . basically , @xmath916 is obtained from @xmath78 by adding a new vertex @xmath926 for each vertex @xmath927 of @xmath78 and connecting @xmath926 by an edge with every @xmath448 except for @xmath928 . for each @xmath929 let @xmath930 be an infinite cyclic group generated by @xmath931 , and set @xmath932 we now have a new graph product @xmath933 of the family @xmath934 with respect to the finite graph @xmath916 , and @xmath935 is a full subgroup of @xmath934 . first , note that , by lemma [ lem : par_clos_in_spec ] , the parabolic closure @xmath936 of @xmath60 in @xmath937 is still equal to @xmath935 . second , let us check that @xmath60 is not contained in a join subgroup of @xmath937 . suppose , on the contrary , that @xmath938 for some @xmath939 and @xmath940 , where @xmath941 such that @xmath942 are disjoint , non - empty and @xmath943 . then @xmath944 and so @xmath945 by lemma [ lem : parab_props].(i ) . note that @xmath775 is an irreducible subset of @xmath916 ( because it is irreducible in @xmath78 and @xmath78 is a full subgraph of @xmath916 ) . therefore either @xmath946 or @xmath947 . without loss of generality assume that @xmath947 , so that @xmath948 . hence @xmath949 and , as @xmath950 , there must exist @xmath929 with @xmath951 . however , @xmath952 and @xmath953 by construction , which contradicts @xmath943 . thus @xmath60 is not contained in a join subgroup of @xmath937 and all of the assumptions of corollary [ cor : cyc - centr ] are satisfied . therefore there exists @xmath954 such that @xmath955 is infinite cyclic . let us prove that @xmath915 . indeed , otherwise @xmath956 for some proper subset @xmath957 and @xmath714 . then @xmath958 for some @xmath929 , hence @xmath926 is adjacent to every vertex from @xmath106 in @xmath916 . consequently , @xmath959 . since @xmath931 lies in the kernel of the canonical retraction of @xmath937 onto @xmath935 , we have @xmath960 in @xmath937 . this implies that the infinite cyclic group @xmath955 contains the subgroup @xmath961 , which is naturally isomorphic to @xmath962 . as the latter is impossible , we conclude that @xmath915 , as claimed . we are now ready to prove theorem [ thm : one_elt ] . after replacing @xmath60 with its conjugate , we can assume that @xmath963 for some @xmath713 . as we know , @xmath776 is itself the graph product of the family @xmath964 with respect to the full subgraph @xmath965 of @xmath78 , spanned by the vertices from @xmath106 . moreover , @xmath966 since every parabolic subgroup of @xmath776 is also a parabolic subgroup of @xmath1 . if @xmath967 then the statement obviously holds , so we can assume that @xmath968 . since @xmath106 is irreducible , by lemma [ lem : irred ] there is @xmath811 such that the parabolic closure of @xmath969 in @xmath970 is @xmath776 . it remains to apply lemma [ lem : par_clos_in_spec ] to conclude that @xmath971 , as claimed . let us now give an example showing that in theorem [ thm : one_elt ] it is indeed necessary to assume that @xmath911 is irreducible . let @xmath492 be a group with an element @xmath972 of prime order @xmath973 . let @xmath974 be the direct product of @xmath975 copies of @xmath492 . then @xmath1 is naturally isomorphic to the graph product of @xmath975 copies of @xmath492 with respect to the complete graph @xmath78 on @xmath975 vertices . set @xmath976 , @xmath977 and @xmath978 . clearly @xmath913 and so @xmath979 . by construction , for any element @xmath811 there are @xmath980 such that @xmath981 in @xmath1 . it is easy to see that if @xmath982 then @xmath983 and so @xmath984 . on the other hand , if @xmath985 then @xmath986 for some @xmath987 , hence @xmath988 in @xmath1 and @xmath128 belongs to a proper parabolic subgroup of @xmath1 . thus @xmath989 for all @xmath811 . the following is a consequence of theorem [ thm : join ] and corollary [ prop : wpd - crit ] . [ cor : wpd_in_gp ] suppose that @xmath60 is a subgroup of @xmath679 and @xmath805 is such that @xmath806 in @xmath78 . let @xmath807 , @xmath808 and @xmath809 . let @xmath220 be the bass - serre tree corresponding to the natural splitting @xmath810 . assume that @xmath60 is not contained in a principal join subgroup of @xmath1 . then there exists @xmath811 which is a wpd element ( for the action of @xmath1 on @xmath19 ) and induces a hyperbolic isometry of @xmath19 . thus , if @xmath60 is not virtually cyclic then @xmath189 . by lemma [ lem : h_has_hyp_elt ] , at least one element of @xmath60 induces a hyperbolic isometry of @xmath19 . hence we can apply theorem [ thm : join ] to find a hyperbolic element @xmath811 such that @xmath990 , where @xmath834 denotes the axis of @xmath128 in @xmath19 . lemma [ lem : pst - parab ] claims that @xmath991)={{\rm pstab}}_g(\{u , v\})$ ] for some vertices @xmath992 . therefore corollary [ prop : wpd - crit ] applies , telling us that @xmath128 is a wpd element for the action of @xmath1 on @xmath19 . clearly the latter yields that @xmath811 is also a wpd element for the action of @xmath60 on @xmath19 . the last claim of the corollary now follows from theorem [ acyl ] . if @xmath78 is irreducible , @xmath993 and @xmath994 ( equivalently , @xmath913 ) then any vertex @xmath799 will satisfy the assumptions of corollary [ cor : wpd_in_gp ] . thus we get the following : [ cor : wpd_in_gp - simplified ] let @xmath78 be a finite irreducible graph with at least two vertices and let @xmath995 be the graph product of a family of non - trivial groups @xmath996 with respect to @xmath78 . then there is a simplicial tree @xmath19 on which @xmath1 acts coboundedly and by simplicial isometries such that the following holds . if @xmath81 is subgroup with @xmath913 then @xmath60 contains a hyperbolic wpd element for the action of @xmath1 on @xmath19 . thus either @xmath60 is virtually cyclic or @xmath82 . this theorem is an immediate consequence of corollary [ cor : wpd_in_gp - simplified ] . in the case of right angled artin groups theorem [ cor : gp - hyp ] would follow from theorem 5.2 of @xcite , because if a subgroup of a cat(@xmath17 ) group contains a rank one element , then it is either virtually cyclic or acylindrically hyperbolic ( see ( * ? ? ? 3.13 , thm . 5.6 ) ) . unfortunately the proof of this theorem , given in @xcite , is invalid : the third paragraph of this proof claims that if @xmath997 are elements of a right angled artin group @xmath1 and @xmath998 is cyclically reduced then in the product @xmath999 cancellations can only occur between the letters from @xmath998 and the letters from @xmath128 , which is not always the case ( one can easily construct counterexamples ) . nevertheless , the statement is still true : one can use corollary [ cor : cyc - centr ] above to fix the argument from @xcite . corollary [ thm : gpacyl ] is a direct consequence of theorem [ cor : gp - hyp ] . as we already mentioned in section [ sec : results ] , it can be considered as another instance of a more general phenomenon : irreducibility " of nice " non - positively curved groups ( or spaces ) often implies the existence of hyperbolic directions " in an appropriate sense . for groups acting on @xmath84 spaces , the standard formalization of the latter condition is the existence of a _ rank one element _ , i.e. , an axial hyperbolic isometry none of whose axes bounds a flat half - plane . the notion of a rank one element originates in the celebrated rank rigidity theorem for hadamard manifolds proved by ballmann , brin , burns , eberlein , and spatzier ( for more information and detailed references we refer to @xcite ) : _ let @xmath1 be a discrete group acting properly and cocompactly on an irreducible hadamard manifold @xmath54 , which is not a higher rank symmetric space ; then @xmath1 contains a rank one isometry . _ we recall that a hadamard manifold is a simply connected complete riemannian manifold of non - positive curvature , and such a manifold is said to be irreducible if it does not admit a nontrivial decomposition as a metric product of two manifolds . motivated by this theorem , ballman and buyalo @xcite suggested the following : let @xmath10 be a locally compact geodesically complete @xmath84 space and let @xmath1 be an infinite discrete group acting properly and cocompactly on @xmath10 . if @xmath10 is irreducible and is not a higher rank symmetric space or a euclidean building of dimension at least @xmath13 , then @xmath1 contains a rank one isometry . caprace and sageev @xcite confirmed this conjecture for @xmath84 cube complexes . more precisely , they showed that _ if an infinite discrete group @xmath1 acts properly and cocompactly on a locally compact geodesically complete @xmath84 cube complex @xmath10 , then @xmath10 is a product of two geodesically complete unbounded convex subcomplexes or @xmath1 contains a rank one isometry . _ ( neither higher rank symmetric spaces nor euclidean buildings of dimension at least @xmath13 occur in these settings . ) any rank one element @xmath107 in a group @xmath1 , acting properly on proper @xmath84 space , is contained in a virtually cyclic subgroup @xmath1000 which is hyperbolically embedded in @xmath1 @xcite . such subgroups can be thought of as a formalization of hyperbolic directions " in the context of abstract groups ( for details and the relation to _ generalized loxodromic elements _ see ( * ? ? ? * section 6 ) ) . recall that the existence of a virtually cyclic subgroup @xmath1001 implies that @xmath1 is either virtually cyclic ( if @xmath1002 ) or acylindrically hyperbolic . thus the caprace sageev result @xcite , being applied to a right angled artin ( respectively , coxeter ) group acting on the universal cover of its salvetti ( respectively , davis ) complex , yields corollary [ thm : gpacyl ] . note , however , that theorem [ cor : gp - hyp ] generalizes this in two directions : it deals with arbitrary subgroups ( which corresponds to non - cocompact actions in the settings of the caprace - sageev theorem ) and more general graph products which may not act properly on any @xmath84 spaces . in fact , theorem [ thm : join ] , under the assumptions of theorem [ cor : gp - hyp ] , produces an action of the subgroup @xmath60 of a graph product @xmath1 on a simplicial tree @xmath19 so that the pointwise stabilizer of a finite segment of the axis of some hyperbolic element @xmath811 is finite . since a tree can not contain half - flats , the latter condition can be thought of as an additional requirement one should include in the definition of a rank one isometry for discrete non - proper actions on @xmath84 spaces . [ def : n ] let @xmath885 denote the class of all groups @xmath1 with the following property : @xmath1 contains two infinite normal subgroups @xmath1003 such that @xmath1004 . [ lem : sn ] the intersection @xmath1005 is empty . suppose that @xmath1006 . thus @xmath1 contains two infinite normal subgroups @xmath1007 such that @xmath1008 is finite . let @xmath1009 , and observe that @xmath1010 . by theorem [ thm : elem - prop - ah].(c ) , we know that @xmath7 is acylindrically hyperbolic . therefore , by lemma [ lem : com ] , @xmath1011 . however this contradicts theorem [ thm : elem - prop - ah].(b ) because @xmath1012 for @xmath104 . recall that the relation @xmath188 , between two groups , denotes commensurability up to finite kernels ( see the paragraph above lemma [ lem : com ] ) . using theorem [ cor : gp - hyp ] we obtain the following classification of subgroups of graph products . [ thm : subgroups ] let @xmath60 be a subgroup of a graph product @xmath679 of non - trivial groups with respect to some finite graph @xmath78 . then at least one of the following holds : * there is a short exact sequence @xmath1013 , where @xmath621 is finite and @xmath106 is isomorphic to a subgroup of a vertex group . in particular , @xmath1014 ; * @xmath60 is virtually cyclic ; * @xmath1015 ; * @xmath189 . moreover , the possibilities ( b),(c ) , and ( d ) are mutually exclusive . the argument will proceed by induction on @xmath1016 . if @xmath1017 then ( a ) holds trivially , so we can assume that @xmath1018 and the statement has already been established for subgroups of graph products with at most @xmath477 vertices . without loss of generality we can assume that @xmath60 is not contained in a proper parabolic subgroup of @xmath1 , i.e. , @xmath979 . let us first prove that at least one of ( a)(d ) holds . suppose that @xmath60 is not virtually cyclic and @xmath1019 . then , by theorem [ cor : gp - hyp ] , there exists a decomposition @xmath1020 , such that @xmath1021 and @xmath772 . thus @xmath1 naturally splits as the direct product @xmath1022 . let @xmath1023 and @xmath1024 . clearly @xmath1025 for @xmath104 and @xmath87 . if both @xmath1026 and @xmath1027 are infinite , we have ( c ) . otherwise @xmath1028 for some @xmath1029 , and then @xmath60 splits as @xmath1030 where @xmath1031 a subgroup of @xmath692 or @xmath773 . by induction , @xmath1031 satisfies one of ( a)(d ) . if @xmath1031 satisfies ( a ) then evidently the same is true for @xmath60 , because the kernel of the epimorphism @xmath1032 is finite . by the same reason , @xmath1033 , hence @xmath1034 is not virtually cyclic and @xmath1035 ( by lemma [ lem : com ] ) . so , it remains to consider the case when @xmath1034 satisfies ( c ) , i.e. , there are infinite normal subgroups @xmath1036 such that @xmath1037 . then @xmath1038 are infinite normal subgroups of @xmath60 and @xmath1039 which shows that @xmath60 satisfies ( c ) . it remains to note that ( c ) and ( d ) are mutually exclusive by lemma [ lem : sn ] , and the fact that ( b ) is incompatible with ( c ) and ( d ) is obvious . corollary [ cor : raag_in_x ] from section [ sec : results ] is special case of theorem [ thm : subgroups ] , because any right angled artin group is a graph product of infinite cyclic groups ( we also need to use the well - known fact that right angled artin groups are torsion - free ) . the goal of this section is to use theorem [ main-3d ] to obtain some new results about @xmath0-manifold groups . we begin by proving corollaries [ 3-dim - cor-1 ] and [ 3-dim - cor-2 ] . if @xmath1 is of type ( iii ) , it is inner amenable since every amenable group is inner amenable . further assume that @xmath1 is of type ( ii ) . since @xmath52 is amenable , there exists a finitely additive @xmath52-invariant probability measure @xmath1040 $ ] . given a subset @xmath1041 , we let @xmath1042 . we define a probability measure on @xmath1043 by the rule @xmath1044 for every @xmath1045 . it is easy to see that @xmath1046 is finitely additive and invariant under conjugation by elements of @xmath1 ( indeed conjugation by an element of @xmath1 preserves the collection @xmath1047 for every @xmath1041 ) . thus every group of type ( ii ) is inner amenable . finally suppose that @xmath1 is of type ( i ) , then @xmath1 has trivial finite radical ( see theorem [ main-3d].(i@xmath639 ) ) and hence @xmath1 is not inner amenable by theorem [ thm : prop - ah-2 ] . using corollary [ cor : geom ] , we obtain the following . let @xmath54 be a compact irreducible @xmath0-manifold . suppose that @xmath55 is inner amenable . then either @xmath54 is seifert fibered or @xmath605 is amenable . recall that a countable group belongs to the class @xmath1048 if its quotient modulo the amenable radical belongs to @xmath88 @xcite . [ cor : ganc-3 m ] for any @xmath51 , the following holds . 1 . @xmath1049 iff @xmath96 iff @xmath1 is of type ( i ) . 2 . @xmath1050 iff @xmath1 is non - amenable iff @xmath1 is of type ( i ) or ( ii ) . recall that every @xmath1051 is infinite and the amenable radical of any group @xmath1051 is finite @xcite . thus @xmath1052 whenever @xmath24 is of type ( ii ) or ( iii ) . on the other hand , @xmath1053 whenever @xmath1 is of type ( i ) by theorem [ thm : prop - ah-3 ] . this proves ( a ) ; ( b ) obviously follows from ( a ) . it is proved in ( * ? ? ? 7.6 and 7.9 ) that being in @xmath88 and @xmath1048 is a measure equivalence invariant . on the other hand , it is well known that being amenable is also a measure equivalence invariant ( see , for example , @xcite ) . thus the claim follows from corollary [ cor : ganc-3 m ] . we mention one more application . for the definition and details about conjugacy growth we refer to @xcite . recall that , in general , any non - decreasing function @xmath1054 bounded from above by an exponential function can be realized up to a standard equivalence as the conjugacy growth function of a finitely generated group @xcite . for @xmath0-manifolds groups , the situation is more rigid . let @xmath54 be a compact @xmath0-manifold . then @xmath55 has either exponential or polynomially bounded conjugacy growth . moreover , the conjugacy growth function of @xmath55 is polynomially bounded if and only if @xmath55 is virtually nilpotent . by theorem [ thm : prop - ah-4 ] , the conjugacy growth of @xmath55 is exponential if @xmath55 has type ( i ) or ( ii ) . on the other hand , it is proved in @xcite that if @xmath55 is of type ( iii ) , its conjugacy growth is either exponential or polynomially bounded and the latter possibility happens iff @xmath55 is virtually nilpotent . it is worth noting that , in some cases , one can obtain results similar to the above corollaries using relative hyperbolicity . for example , it is not hard to prove that if @xmath54 is a closed oriented @xmath0-manifold with a hyperbolic piece in the jsj decomposition , then @xmath55 is hyperbolic relative to proper subgroups . however this approach does not always work ( for example for graph manifolds ) . let @xmath1055 be the class of all groups @xmath1 containing a subnormal subgroup @xmath7 and a finite subgroup @xmath1056 such that @xmath1057 splits as a direct product two infinite groups . let also @xmath1058 be the class defined in definition [ def : n ] . @xmath1059 . if @xmath1 contains two infinite normal subgroups @xmath1003 such that @xmath1004 , then @xmath1060 is a normal subgroup of @xmath1 and @xmath1061 decomposes as a direct product of two infinite groups ( isomorphic to @xmath1062 and @xmath1063 ) . the next observation is an easy consequence of known results . [ cdn ] 1 . 2 . @xmath1065 . let @xmath1066 be a group containing a subnormal subgroup @xmath7 and a finite subgroup @xmath1056 such that @xmath1057 splits as a direct product two infinite groups . suppose first that @xmath1067 . the class @xmath18 is closed under taking infinite subnormal subgroups by ( * ? ? ? hence @xmath1068 . further we have @xmath1069 by ( * ? ? ? * lemma 7.3 ) . however this contradicts ( * ? ? ? 7.10.(iii ) ) , which states that no group from @xmath18 decomposes as a direct product of two infinite groups . therefore @xmath1064 . suppose now that @xmath1070 . by ( * ? ? ? * thm 3.4 ) , every infinite normal subgroup of a group from @xmath1071 itself belongs to @xmath1071 . hence we obtain @xmath1072 as above . further by ( * ? ? ? * lemma 2.8 ) , @xmath7 either belongs to @xmath18 or has non - vanishing first @xmath94-betti number . we have already shown that @xmath1068 is impossible . if @xmath1073 , then we have @xmath1074 , say by ( * ? ? ? * thm . 7.34 ) . however the latter inequality is impossible since @xmath1057 decomposes as a direct product of two infinite groups ( see ( * ? ? ? 6.54.(5 ) ) ) . claim ( a ) follows from corollary [ cor : ganc-3m].(a ) , so it remains to prove claim ( b ) . let @xmath1 be a graph product of amenable groups , let @xmath81 , and let @xmath1075 . if @xmath60 is amenable , then so is @xmath621 and hence @xmath621 does not belong to either of the classes @xmath14 , @xmath88 , @xmath1071 . thus we can assume that @xmath60 is non - amenable . then , according to theorem [ thm : subgroups ] , either @xmath1076 or @xmath82 . assume , first , that @xmath1076 . the class @xmath885 is obviously closed under taking subgroups of finite index , quotients modulo finite normal subgroups , and extensions with finite kernels . thus @xmath1015 implies that @xmath621 contains a finite index normal subgroup @xmath1077 . obviously this implies that @xmath1078 . hence @xmath1079 by lemma [ cdn ] . we also have @xmath1080 by lemmas [ lem : com ] and [ lem : sn ] . finally , if @xmath82 , then @xmath1081 by lemma [ lem : com ] , hence @xmath1082 as @xmath92 by theorem [ thm : prop - ah-3 ] . as demonstrated by theorems [ thm : elem - prop - ah][thm : prop - ah-4 ] , global properties of acylindrically hyperbolic groups resemble those of relatively hyperbolic groups . one can then ask if the same is true for _ local _ properties ( i.e. , properties that pass to finitely generated subgroups ) . if a group @xmath1 is hyperbolic relative to a subgroup @xmath60 then many local properties of @xmath60 are inherited by @xmath1 ( e.g. , if @xmath60 is finitely generated and has solvable word problem then the same is true for @xmath1 see @xcite , if @xmath60 has finite asymptotic dimension then so does @xmath1 see @xcite , etc . ) . however , the same can not be said if @xmath60 is hyperbolically embedded in @xmath1 . indeed , if a property @xmath709 is local , one can simply take some finitely generated group @xmath26 which does not possess this property and set @xmath1083 . then @xmath60 will be hyperbolically embedded into @xmath1 but @xmath1 will not satisfy @xmath709 even if @xmath60 does satisfy it . of course in this example both @xmath60 and @xmath26 are hyperbolically embedded into @xmath1 ( and @xmath1 is hyperbolic relative to @xmath1084 ) , and so , naturally , to ensure `` niceness '' of @xmath1 one should require that both @xmath60 and @xmath26 are `` nice '' . this leads to the following question : let @xmath1 be a finitely generated acylindrically hyperbolic group . suppose that every proper hyperbolically embedded subgroup @xmath1085 satisfies some local property @xmath709 . does @xmath1 also have this property ? our investigation of graph products allows to produce simple examples showing that the answer to the above question is almost always negative . namely , we have the following statement : [ thm : emb ] any finitely generated group @xmath621 can be embedded into a finitely generated group @xmath1 so that all of the following hold : 1 . @xmath197 ; 2 . every proper hyperbolically embedded subgroup @xmath1085 is finitely generated and virtually free ; 3 . @xmath621 is a retract of @xmath1 ; 4 . if @xmath621 is torsion - free then so is @xmath1 ; 5 . if @xmath621 is finitely presented then so is @xmath1 . let @xmath78 be the simplicial path of length @xmath0 with ( consecutive ) vertices @xmath1086 , where @xmath254 and @xmath1087 have valency @xmath153 and @xmath1088 have valency @xmath13 . let @xmath1089 and let @xmath1090 , @xmath1091 and @xmath1092 be infinite cyclic groups generated by elements @xmath1093 and @xmath1094 respectively . let @xmath679 be the graph product of these groups with respect to @xmath78 ( see figure [ fig:4 ] ) . clearly @xmath78 is irreducible and @xmath1 is not virtually cyclic , hence @xmath197 by theorem [ cor : gp - hyp ] . the properties ( c)-(e ) of @xmath1 follow from general properties of graph products , so it remains only to verify property ( b ) . by the definition , @xmath1 splits as the amalgamated free product @xmath1095 , where @xmath1096 , @xmath1097 and @xmath1098 . then @xmath1 acts on the bass - serre tree @xmath19 corresponding to this splitting with vertex stabilizers being conjugates of @xmath1099 or @xmath1100 . note that @xmath1101 is central in @xmath1099 and @xmath1102 is central in @xmath1100 . consider any @xmath1085 . then @xmath60 is _ almost malnormal _ in @xmath1 , i.e. , @xmath1103 for any @xmath1104 ( see ( * ? ? ? suppose that the intersection @xmath1105 is infinite for some @xmath31 . since @xmath1106 is the image of @xmath60 under an inner automorphism , it is also almost malnormal in @xmath1 . since @xmath1107 is central in @xmath1099 , @xmath1108 is infinite , hence @xmath1109 by almost malnormality of @xmath1110 . but then for any @xmath1111 , the infinite order element @xmath1107 belongs to @xmath1112 , implying that @xmath1113 . thus @xmath1114 . now , since @xmath1115 commutes with @xmath1116 , we can similarly get that @xmath1117 , and since @xmath1094 commutes with @xmath1115 we conclude that @xmath1118 . thus all the generators of @xmath1 are contained in @xmath1110 , therefore @xmath1119 , yielding that @xmath83 . similarly , one can show that @xmath83 if @xmath60 has infinite intersection with some conjugate of @xmath1100 ( using the fact that @xmath1115 is central in @xmath1100 ) . thus if @xmath1085 is a proper subgroup , then @xmath60 has finite intersection with every vertex stabilizer for the action of @xmath1 on @xmath19 . observe that @xmath1 is finitely generated because @xmath621 is , hence we can apply ( * ? ? ? 4.32 ) claiming that @xmath60 is finitely generated as well . by ( * i.4.12 ) @xmath60 either fixes a vertex of @xmath19 or contains an element that acts on @xmath19 as a hyperbolic isometry . in the former case @xmath60 will have to be finite ( because it acts with finite vertex stabilizers ) , and in the latter case by ( * ? ? ? * i.4.13 ) there is a unique minimal @xmath60-invariant subtree @xmath1120 of @xmath19 on which @xmath60 acts cocompactly . now we can apply ( * ? ? ? * iv.1.9 ) to conclude that @xmath60 is virtually free , as desired . for example , if @xmath621 is a finitely presented torsion - free group with unsolvable word problem , then , by theorem [ thm : emb ] , @xmath621 can be embedded into a finitely presented torsion - free acylindrically hyperbolic group @xmath1 such that every hyperbolically embedded subgroup in @xmath1 is free of finite rank . yet another application is related to maximal elliptic subgroups ( a subgroup is _ elliptic _ if all of its orbits are bounded ) . recall that for every group @xmath1 acting acylindrically on a hyperbolic space , every elliptic subgroup of @xmath1 is contained in a maximal elliptic subgroup of @xmath1 , and maximal elliptic subgroups exhibit malnormality - type properties similar to hyperbolically embedded subgroups ( see ( * ? ? ? * corollary 1.6 ) ) . it is easy to show that if @xmath156 and @xmath60 is infinite , then @xmath60 is maximal elliptic with respect to the action of @xmath1 on the cayley graph @xmath138 . thus it is natural to ask whether maximal elliptic subgroups are hyperbolically embedded . the following corollary provides the negative answer . in what follows we say that a subgroup @xmath132 is _ absolutely elliptic _ if it is elliptic with respect to any acylindrical action of @xmath1 on a hyperbolic space . there exists a group @xmath198 and an absolutely elliptic subgroup @xmath1121 such that @xmath621 is not contained in any proper hyperbolically embedded subgroup of @xmath1 . in particular , for any non - elliptic acylindrical action of @xmath1 on a hyperbolic space , the maximal elliptic subgroup of @xmath1 containing @xmath621 is not hyperbolically embedded . let @xmath1122 and let @xmath1 be the group provided by theorem [ thm : emb ] . note that @xmath621 is absolutely elliptic by theorem [ class ] ( it is not acylindrically hyperbolic by theorem [ thm : elem - prop - ah ] ) . on the other hand , it can not be a subgroup of any proper hyperbolically embedded subgroup of @xmath1 by part ( b ) of theorem [ thm : emb ] . we showed that every one - relator group with at least @xmath0 generators and most " one - relator group with least @xmath13 generators are acylindrically hyperbolic . however the case of @xmath13-generator groups is far from being clear . the next two questions are motivated by our results about the integral @xmath13-dimensional cremona group @xmath585 $ ] . wright @xcite proved that the @xmath13-dimensional cremona group @xmath1123 ( i.e. , the group of birational transformations of the complex projective plane ) is isomorphic to the fundamental group of a finite developable complex of groups . let @xmath1124 denote its development . thus @xmath1123 acts on @xmath1124 cocompactly . the positive answer to the following question could lead to a new way of proving that @xmath1123 is acylindrically hyperbolic and hence not simple . note that acylindrical hyperbolicity of @xmath1123 was proved in @xcite and non - simplicity of @xmath1123 was a long - standing conjecture in algebraic geometry resolved in @xcite . the last problem is inspired by corollary [ ga2 ] . note that for @xmath182 no nontrivial decomposition of @xmath45 $ ] in an amalgamated product is known , so our strategy of the proof of corollary [ ga2 ] does not work . in fact , we rather expect the answer to be negative . collins , intersections of magnus subgroups of one - relator groups . _ groups : topological , combinatorial and arithmetic aspects _ , 255 - 296 , _ london math . lecture note ser . _ , 311 , _ cambridge univ . press , cambridge _ , 2004 . w. lck , @xmath1127-invariants : theory and applications to geometry and k - theory . ergebnisse der mathematik und ihrer grenzgebiete . 3 . folge . a series of modern surveys in mathematics , vol . springer - verlag , berlin _ , 2002 . serre , trees . translated from the french original by j. stillwell . corrected 2nd printing of the 1980 english translation . springer monographs in mathematics . _ springer - verlag , berlin _ , 2003 .

we provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees . in particular , we consider amalgamated products and hnn - extensions , one - relator groups , automorphism groups of polynomial algebras , @xmath0-manifold groups and graph products . acylindrical hyperbolicity is then used to obtain some results about the algebraic structure , analytic properties and measure equivalence rigidity of groups from these classes .

<s>[INST]recall that an isometric action of a group @xmath1 on a metric space @xmath2 is _ acylindrical _ if for every @xmath3 there exist @xmath4 such that for every two points @xmath5 with @xmath6 , there are at most @xmath7 elements @xmath8 satisfying @xmath9 the notion of acylindricity goes back to sela s paper @xcite , where it was considered for groups acting on trees . in the context of general metric spaces , this concept is due to bowditch @xcite . the following definition was suggested by the second author in @xcite . [ df : acyl - gp ] a group @xmath1 is called _ acylindrically hyperbolic _ if there exists a generating set @xmath10 ( possibly infinite ) of @xmath1 such that the corresponding cayley graph @xmath11 is hyperbolic , non - elementary ( i.e. , its gromov boundary @xmath12 consists of more than @xmath13 points ) , and the action of @xmath1 on @xmath11 is acylindrical . the above notion generalizes non - elementary word hyperbolic groups . indeed , it is easy to see that a group is non - elementary word hyperbolic if and only if it satisfies the above definition for a finite set @xmath10 . for @xmath10 finite , the acylindricity condition is vacuous as proper and cobounded actions are always acylindrical . on the other hand , if we allow @xmath10 to be infinite , hyperbolicity and non - elementarity of @xmath11 are rather weak assumptions and acylindricity of the action turns out to be _ the _ condition that allows one to derive interesting results . in fact , acylindrically hyperbolic groups were implicitly studied by bestvina and fujiwara @xcite , bowditch @xcite , hamenst " adt @xcite , dahmani , guirardel , and osin @xcite , sisto @xcite , and many other authors before they were formally defined in @xcite . however the above - mentioned papers used different definitions stated in terms of hyperbolically embedded subgroups @xcite , weakly contracting elements @xcite , or various forms of ( weakly ) acylindrical actions @xcite . some nontrivial relations between these definitions were established in @xcite and @xcite , and finally the equivalence of all definitions was proved in @xcite ( see section [ prelim ] for details ) . the class of acylindrically hyperbolic groups , denoted by @xmath14 , encompasses many examples of interest : non-(virtually cyclic ) groups hyperbolic relative to proper subgroups , @xmath15 for @xmath16 , all but finitely many mapping class groups , non-(virtually cyclic ) groups acting properly on proper cat(@xmath17)-spaces and containing rank one elements , and so forth ( see @xcite ) . on the other hand , @xmath14 is restricted enough to possess a non - trivial theory . below we mention just few directions in the study of acylindrically hyperbolic groups ; for a more comprehensive survey we refer the reader to @xcite . * every acylindrically hyperbolic group contains non - degenerate hyperbolically embedded subgroups . this allows one to use methods from the paper @xcite by dahmani , guirardel , and osin to transfer a significant portion of the theory of relatively hyperbolic groups , including group theoretic dehn filling , to the class @xmath14 . despite their generality , the techniques from @xcite are capable of answering open questions and producing new results even for well - studied classes of groups such as relatively hyperbolic groups , mapping class groups , and @xmath15 . * acylindrical hyperbolicity shares many common features with analytic negative curvature " as defined in @xcite and @xcite . in particular , hamenst " adt @xcite showed that @xmath14 is a subclass of the monod shalom class @xmath18 ( see also @xcite and @xcite for various generalizations ) . this opens doors for the monod shalom measure rigidity and orbit rigidity theory @xcite . results about quasi - cocycles on acylindrically hyperbolic groups with coefficients in the left regular representation obtained in @xcite also seem likely to be useful in the study of the structure of group von neumann algebras via a further generalization of methods from @xcite . * sisto @xcite studied random walks on acylindrically hyperbolic groups using the language of weakly contracting elements . his main result covers many classical theorems about random elements of hyperbolic groups , mapping class groups , etc . * yet another direction is explored by hull @xcite , who developed a version of small cancellation theory for acylindrically hyperbolic groups and used it to construct groups with certain exotic properties . the abundance of non - trivial results and techniques applicable to acylindrically hyperbolic groups justifies the quest for new examples , which is the main goal of our paper . we concentrate on examples arising from actions on simplicial trees . in particular , we consider fundamental groups of finite graphs of groups , one - relator groups , automorphism groups of polynomial algebras , fundamental groups of compact @xmath0-manifolds , and graph products . to illustrate usefulness of our main results we derive a number of corollaries about the algebraic structure , analytic properties and measure equivalence rigidity of groups from these classes . however the main focus of this paper is on new examples rather than on applications . * acknowledgements . * the authors would like to thank henry wilton for helpful discussions of @xmath0-manifolds . we are also grateful to jack button for his valuable comments , and to stephane lamy for pointing out an error in an earlier version of the paper . finally , we would like to thank the referee for a careful reading of this article . we begin with a general theorem about groups acting on trees . recall that the action of a group @xmath1 by automorphisms on a simplicial tree @xmath19 is called _ minimal _ if @xmath19 contains no proper @xmath1-invariant subtree . as usual , by @xmath20 we denote the gromov boundary of @xmath19 , which can be identified with the set of ends of @xmath19 ; no topology on @xmath20 is assumed . [ main-1 ] let @xmath1 be a group acting minimally on a simplicial tree @xmath19 . suppose that @xmath1 does not fix any point of @xmath20 and there exist vertices @xmath21 of @xmath19 such that the pointwise stabilizer @xmath22 is finite . then @xmath1 is either virtually cyclic or acylindrically hyperbolic . a slightly different criterion , which does not make use of the boundary is formulated in corollary [ prop : wpd - crit ] ( see subsection [ sec : trees ] below ) . if @xmath1 is the fundamental group of a graph of groups @xmath23 , one can apply theorem [ main-1 ] to the action of @xmath1 on the associated bass - serre tree . in this case the minimality of the action and the absence of fixed points on @xmath20 can be recognized from the local structure of @xmath23 see section [ sec - gg ] . we mention here two particular cases and refer to theorem [ thm : reduced - crit ] for a more general result . below we say that a subgroup @xmath24 of a group @xmath1 is _ weakly malnormal _ if there exists @xmath8 such that @xmath25 . [ cor : amalg - intr ] let @xmath1 split as a free product of groups @xmath26 and @xmath27 with an amalgamated subgroup @xmath24 . suppose @xmath28 and @xmath24 is weakly malnormal in @xmath1 . then @xmath1 is either virtually cyclic or acylindrically hyperbolic . note that the virtually cyclic case can not be excluded from corollary [ cor : amalg - intr ] . indeed it is realized if @xmath24 is finite and has index @xmath13 in both factors . however these are the only exceptions : it is easy to show that under the assumptions of the corollary all other amalgams contain non - abelian free subgroups , and so they are are acylindrically hyperbolic . [ cor : hnn - intr ] let @xmath1 be an hnn - extension of a group @xmath26 with associated subgroups @xmath24 and @xmath29 . suppose that @xmath30 and @xmath24 is weakly malnormal in @xmath1 . then @xmath1 is acylindrically hyperbolic . [ rem : hnn ] the assumption of corollary [ cor : hnn - intr ] saying that @xmath24 is weakly malnormal in @xmath1 is equivalent to the existence of an element @xmath31 such that @xmath32 , because @xmath24 and @xmath29 are conjugate in @xmath1 . the weak malnormality condition is essential in both corollaries . this can be illustrated in many ways , but the most convincing examples are the following . [ ex : non - ah-1 ] 1 . there are simple groups splitting as @xmath33 , where @xmath26 , @xmath27 are finitely generated free groups and @xmath24 can be of finite or infinite index in both @xmath26 and @xmath27 @xcite . note that simple groups are never acylindrically hyperbolic ( see theorem [ thm : elem - prop - ah ] ) . the baumslag - solitar groups @xmath34 are not acylindrically hyperbolic unless @xmath35 or @xmath36 @xcite . furthermore , the assumption that @xmath30 in corollary [ cor : hnn - intr ] is also necessary , see examples [ ex : hnnb ] and [ ex : bg ] . it is worth noting that our corollaries [ cor : amalg - intr ] and [ cor : hnn - intr ] can be used to recover some results proved by schupp @xcite and sacerdote and schupp @xcite by using small cancellation theory for amalgamated products and hnn - extensions . in fact , our approach is slightly more general ; for details we refer to section [ sec - gg ] . the next result is inspired by @xcite . the proof makes use of corollary [ cor : hnn - intr ] and a technical result from @xcite . [ cor : one - rel ] let @xmath1 be a one - relator group with at least @xmath0 generators . then @xmath1 is acylindrically hyperbolic . corollary [ cor : one - rel ] is related to a conjecture of p. neumann @xcite , claiming that if @xmath1 is a one - relator group then either @xmath1 is cyclic or @xmath37 is a solvable baumslag - solitar group , or @xmath1 is sq - universal . recall that a group @xmath1 is said to be _ @xmath38-universal _ if every countable group embeds in a quotient of @xmath1 . the first non - trivial example of an @xmath38-universal group was provided by higman , neumann and neumann @xcite , who proved that the free group of rank @xmath13 is @xmath38-universal or , equivalently , every countable group embeds in a group generated by @xmath13 elements . it is straightforward to see that any @xmath38-universal group contains non - abelian free subgroups . furthermore , since the set of all finitely generated groups is uncountable and every countable group contains countably many finitely generated subgroups , every countable @xmath38-universal group has uncountably many non - isomorphic quotients . thus the property of being @xmath38-universal may be thought of as an indication of algebraic largeness " of a group . for a survey of @xmath38-universality we refer to @xcite . sacerdote and schupp @xcite established the sq - universality of one - relator groups with at least @xmath0 generators , thus confirming neumann s conjecture in this case . corollary [ cor : one - rel ] can be regarded as a strengthening of this result ( indeed , by a theorem of dahmani , guirardel and osin @xcite , every acylindrically hyperbolic group is sq - universal ) . the case of one - relator groups with two generators is more complicated , as one can see by looking at the baumslag - solitar groups . the full proof of neumann s conjecture was announced by sacerdote @xcite , but it was never published , and it seems that the conjecture is still open . in section [ sec:1-rel ] , we make a step towards the resolution of this conjecture by showing that every one - relator group with a sufficiently complicated magnus - moldavanskii hierarchy is acylindrically hyperbolic ( see proposition [ cor:1-rel-2-gen ] ) . more precisely , all non - acylindrically hyperbolic one - relator groups belong to the class of hnn - extensions of ( finitely generated free)-by - cyclic groups . unfortunately , our techniques do not apply to ascending hnn - extensions ( cf . examples [ ex : hnnb ] , [ ex : bg ] ) , therefore for groups with magnus - moldavanskii hierarchy of low complexity we only have partial results . another example having the structure described in corollary [ cor : amalg - intr ] is @xmath39 $ ] , the group of automorphisms of the polynomial algebra @xmath40 $ ] for any field @xmath41 . this group is sometimes called the _ integral 2-dimensional cremona groups _ over @xmath41 and is also isomorphic to the group of automorphisms of the free associative algebra @xmath42 @xcite ; if @xmath43 it is also isomorphic to the group of automorphisms of the free @xmath13-generated poisson algebra @xcite . the algebraic structure of these groups has received a lot of attention but is still far from being well understood , see @xcite and references therein . we prove the following . [ ga2 ] for any field @xmath41 , the group @xmath39 $ ] is acylindrically hyperbolic . for motivation and a survey of some related results we refer to section [ sec - gg ] . note that @xmath44 $ ] is solvable and hence it is not acylindrically hyperbolic . we do not know if the analogue of corollary [ ga2 ] holds true for the group @xmath45 $ ] when @xmath46 , but we would rather expect some higher rank phenomena to prevent it from being acylindrically hyperbolic . other examples of acylindrically hyperbolic groups obtained in section [ sec - gg ] by using corollaries [ cor : amalg - intr ] and [ cor : hnn - intr ] include the higman group @xmath47 and amalgamated products ( respectively , hnn - extensions ) of the form @xmath48 ( respectively , @xmath49 ) , where @xmath26 is a hyperbolic group and @xmath24 is a quasi - convex subgroup of infinite index in @xmath26 . the latter examples should be compared to simple groups mentioned in example [ ex : non - ah-1 ] . for details we refer to section [ sec : misc ] by default , all manifolds considered in this paper are assumed to be connected . our next goal is to show that most @xmath0-manifold groups are acylindrically hyperbolic . more precisely , let @xmath50 denote the class of all _ subgroups _ of fundamental groups of compact @xmath0-manifolds . note that by scott s theorem @xcite , every finitely generated group @xmath51 is itself the fundamental group of a compact @xmath0-manifold . however the groups we consider are not necessarily finitely generated . [ main-3-dim ] let @xmath51 . then exactly one of the following three conditions holds . 1 . @xmath1 is acylindrically hyperbolic . @xmath1 contains an infinite cyclic normal subgroup @xmath52 and @xmath53 is acylindrically hyperbolic . @xmath1 is virtually polycyclic . if @xmath1 is itself a fundamental group of a compact irreducible @xmath0-manifold , we can give a more geometric description of the non - acylindrically hyperbolic cases . [ cor : geom ] let @xmath54 be a compact irreducible @xmath0-manifold such that @xmath55 is not acylindrically hyperbolic . then either @xmath55 is virtually polycyclic or @xmath54 is seifert fibered . theorem [ main-3-dim ] allows to bring many results known for acylindrically hyperbolic groups to the world of @xmath0-manifold groups . we discuss some examples below . let us say that a group @xmath51 has _ type _ ( i ) , ( ii ) , or ( iii ) if the corresponding condition from theorem [ main-3-dim ] holds for @xmath1 . [ 3-dim - cor-1 ] a group @xmath51 is inner amenable iff it is of type ( ii ) or ( iii ) . recall that a group @xmath1 is _ inner amenable _ if there exists a finitely additive conjugacy invariant probability measure on @xmath56 . inner amenability is closely related to the murray von neumann property @xmath57 for operator algebras . in particular , if @xmath1 is not inner amenable , the von neumann algebra @xmath58 of @xmath1 does not have property @xmath57 @xcite . for further details and motivation we refer to @xcite and section [ sec:3m - app ] . [ 3-dim - cor-2 ] type is a measure equivalence invariant in @xmath50 . that is , if @xmath59 and @xmath1 is measure equivalent to @xmath60 , then @xmath1 and @xmath60 have the same type . this result can be seen as the first step towards measure equivalence classification of @xmath0-manifold groups . we note that a classification of fundamental groups of compact @xmath0-manifolds up to quasi - isometry was done by behrstock and neumann @xcite , while no non - trivial results about measure equivalence seem to be known . finally we mention that theorem [ main-3-dim ] is used in @xcite to show the following : _ the outer automorphism group @xmath61 is residually finite for any compact @xmath0-manifold @xmath54_. the proof is based on the approach suggested in @xcite and essentially uses acylindrical hyperbolicity . let @xmath57 be a graph without loops and multiple edges with vertex set @xmath62 . let also @xmath63 be a family of groups , called _ vertex groups _ , indexed by vertices of @xmath64 . the _ graph product _ of @xmath63 with respect to @xmath57 , denoted @xmath65 , is the quotient group of the free product @xmath66 by the relations @xmath67=1 $ ] for all @xmath68 , @xmath69 whenever @xmath70 and @xmath71 are adjacent in @xmath64 . graph products generalize free and direct products of groups . other basic examples include right angled artin and coxeter groups . the study of graph products and their subgroups has gained additional importance in view of the recent breakthrough results of agol , haglund , wise , and their co - authors , which claim that many groups can be virtually embedded into right angled artin groups ( see @xcite and references therein ) . for any subset @xmath72 , the subgroup @xmath73 of the graph product @xmath74 is said to be a _ full subgroup _ ; it is naturally isomorphic to to the graph product @xmath75 , where @xmath76 is the full subgraph of @xmath64 spanned on the vertices from @xmath77 . any conjugate of a full subgroup is called _ parabolic_. we will say that the graph @xmath78 is _ irreducible _ if its complement graph @xmath79 is connected ; this equivalent to saying that the graph product @xmath65 does not naturally split as a direct product of two proper full subgroups . graph products naturally decompose as amalgamated products in many ways ( see subsection [ sec : wpd_in_gp ] ) . in section [ sec : gp ] we study subgroups of graph products using the actions on the associated bass - serre trees together with the theory of parabolic subgroups developed in @xcite . in particular , we prove the following ( see section 6.3 ) . [ cor : gp - hyp ] let @xmath80 be the graph product of non - trivial groups with respect to some finite irreducible graph @xmath64 with at least two vertices . suppose that @xmath81 is a subgroup that is not contained in a proper parabolic subgroup of @xmath1 . if @xmath60 is not virtually cyclic then @xmath82 . the corollary below covers the particular case when @xmath83 . [ thm : gpacyl ] let @xmath74 be the graph product of non - trivial groups with respect to some finite irreducible graph @xmath64 with at least two vertices . then @xmath1 is either virtually cyclic or acylindrically hyperbolic . graph products are simplest examples of groups having relative non - positive curvature " with respect to the vertex subgroups . from this point of view , corollary [ thm : gpacyl ] can be considered as another instance of a more general phenomenon : irreducibility " of nice " non - positively curved groups ( or spaces ) often implies the existence of hyperbolic directions " in an appropriate sense ; in turn , the latter condition implies acylindrical hyperbolicity . in the context of groups acting on @xmath84 spaces , a more formal version of this claim is sometimes called the _ rank rigidity conjecture _ @xcite and is closely related to the classical work of ballman , brin , burns , and spatzier @xcite as well as more recent results of caprace and sageev @xcite . for a more detailed discussion we refer to section [ sec : subgr - class ] . theorem [ cor : gp - hyp ] is quite useful for studying properties of subgroups of graph products . for example , it is used in @xcite to prove that @xmath85 is residually finite for any virtually compact special ( in the sense of haglund and wise @xcite ) group @xmath1 . theorem [ cor : gp - hyp ] implies that every subgroup @xmath60 of a graph product @xmath1 is either acylindrically hyperbolic , or `` reducible '' , or `` elementary '' in the appropriate sense ( see theorem [ thm : subgroups ] ) . a particular application to right angled artin groups gives rise to the following algebraic alternative : [ cor : raag_in_x ] let @xmath60 be a non - cyclic subgroup of a finitely generated right angled artin group . then exactly one of the following holds : * @xmath60 is acylindrically hyperbolic ; * @xmath60 contains two non - trivial normal subgroups @xmath86 such that @xmath87 . we also mention one application of graph products to groups with hyperbolically embedded subgroups . recall that if a group @xmath1 is hyperbolic relative to a subgroup @xmath60 , then many `` nice '' properties of @xmath60 ( e.g. , solvability of algorithmic problems , finiteness of the asymptotic dimension , various analytic properties , etc . ) are inherited by @xmath1 @xcite . as shown in @xcite , many properties of acylindrically hyperbolic groups resemble those of relatively hyperbolic groups , and hyperbolically embedded subgroups ( see subsection [ sec : eqdef ] for the definition ) serve as analogues of peripheral subgroups in the relatively hyperbolic case . thus one may wonder if the structure of an acylindrically hyperbolic group is determined , to some extent , by the structure of its hyperbolically embedded subgroups . the following result provides a strong negative answer ; it is a simplified version of theorem [ thm : emb ] . any finitely generated group can be embedded into a finitely generated acylindrically hyperbolic group @xmath1 such that every proper hyperbolically embedded subgroup of @xmath1 is finitely generated and virtually free . recall that a countable group @xmath1 belongs to the monod shalom class @xmath88 if @xmath89 @xcite . an a priori different class @xmath90 was defined by thom @xcite : a countable group @xmath1 is in @xmath90 if @xmath1 is non - amenable and there exists an unbounded quasi - cocycle @xmath91 . groups from @xmath88 and @xmath90 exhibit behavior typical to non - elementary hyperbolic groups . moreover , most known examples from these classes come from the world of groups acting on hyperbolic spaces . motivated by these observations , monod @xcite and thom @xcite suggested to consider @xmath88 and @xmath90 as analytic analogues of the class of negatively curved " groups . it is worth noting that no non - trivial relation between @xmath88 and @xmath90 is known , although they are likely to coincide ( see remark 2.7 in @xcite ) monod ( * ? ? ? * problem j ) asked whether @xmath88 can be characterized by a geometric condition . in this paper we discuss the relation between @xmath88 , @xmath90 , and @xmath14 . first we recall that @xmath92 . this was originally proved by hamenstdt @xcite in slightly different terms and also follows from the results of hull - osin @xcite and bestvina fujiwara @xcite . moreover , acylindrically hyperbolic groups constitute the majority of examples from @xmath88 or @xmath90 . indeed the only examples of non - acylindrically hyperbolic groups from @xmath93 known up to now are those constructed by osin @xcite and lck and osin @xcite . these are finitely generated infinite torsion groups with positive first @xmath94-betti numbers . note that @xmath95 implies @xmath96 while torsion groups are never acylindrically hyperbolic ( see example [ ex : non - ah ] ( b ) ) . groups from @xcite and @xcite are not finitely presented . on the other hand , there is an evidence that for finitely presented groups , existence of non - trivial quasi - cocycles may be used to construct non - elementary actions on hyperbolic spaces @xcite . this motivates the following question : are the conditions @xmath97 , @xmath98 , and @xmath99 equivalent for a finitely presented group @xmath1 ? we do not really believe in a positive answer to this question in full generality . however , in section [ sec : nc ] we obtain the following as immediate applications of other results from the paper . [ cor : ganc ] the conditions @xmath97 , @xmath98 , and @xmath99 are equivalent for any group @xmath1 from the following classes : 1 . subgroups of fundamental groups of compact @xmath0-manifolds . 2 . groups commensurable up to a finite kernel with subgroups of graph products of amenable groups . in particular , this class includes virtually special groups in the sense of haglund and wise . recall that two groups @xmath100 and @xmath101 are commensurable up to a finite kernel if there are finite index subgroups @xmath102 and finite normal subgroups @xmath103 , @xmath104 , such that @xmath105 . for definitions , details , and related questions we refer to section [ sec : nc ] and @xcite . in this section we collect the main definitions and results about acylindrically hyperbolic groups relevant to our paper . for more details we refer to @xcite . given a group @xmath1 acting on a hyperbolic space @xmath106 , an element @xmath8 is called _ elliptic _ if some ( equivalently , any ) orbit of @xmath107 is bounded , and _ loxodromic _ ( or _ hyperbolic _ ) if the map @xmath108 defined by @xmath109 is a quasi - isometry for some ( equivalently , any ) @xmath110 . in papers devoted to groups acting on general hyperbolic spaces , the terms loxodromic " and hyperbolic " are used as synonyms . recent papers on relatively hyperbolic and acylindrically hyperbolic groups ( including papers by the second author ) tend to use the term loxodromic " more often . in this paper we switch to hyperbolic " since we mostly deal with actions on trees for which this term is well established . every hyperbolic element @xmath8 has exactly @xmath13 limit points @xmath111 on the gromov s boundary @xmath112 . hyperbolic elements @xmath113 are called _ independent _ if the sets @xmath114 and @xmath115 are disjoint . the next theorem classifies acylindrical group actions on hyperbolic spaces . [ class ] let @xmath1 be a group acting acylindrically on a hyperbolic space . then @xmath1 satisfies exactly one of the following three conditions . 1 . @xmath1 has bounded orbits . @xmath1 is virtually cyclic and contains a hyperbolic element . 3 . @xmath1 contains infinitely many independent hyperbolic elements . compared to the general classification of groups acting on hyperbolic spaces , theorem [ class ] rules out parabolic and quasi - parabolic actions in gromov s terminology @xcite . for details we refer to @xcite . recall that the action of a group @xmath1 on a hyperbolic space @xmath106 is called _ elementary _ if the limit set of @xmath1 in the gromov boundary @xmath112 consists of at most @xmath13 points and _ non - elementary _ otherwise . according to theorem [ class ] , an acylindrical action of @xmath1 is non - elementary if and only if the orbits are unbounded and @xmath1 is not virtually cyclic . the next theorem provides equivalent characterizations of acylindrically hyperbolic groups . in practice , ( ah@xmath116 ) is the most useful condition for proving that a certain group is acylindrically hyperbolic , while ( ah@xmath117 ) , ( ah@xmath118 ) , and ( ah@xmath119 ) are more useful for proving theorems about acylindrically hyperbolic groups . [ acyl ] for any group @xmath1 , the following conditions are equivalent . 1 . the group @xmath1 is acylindrically hyperbolic in the sense of definition [ df : acyl - gp ] . 2 . @xmath1 admits a non - elementary acylindrical action on a hyperbolic space . @xmath1 is not virtually cyclic and admits an action on a hyperbolic space such that at least one element of @xmath1 is hyperbolic and satisfies the wpd condition . 4 . @xmath1 contains a proper infinite hyperbolically embedded subgroup . note that every group has an obvious acylindrical action on a hyperbolic space , namely the trivial action on a point . thus considering elementary acylindrically hyperbolic groups does not make much sense . for this reason we include non - elementarity in the definition . the terminology used in conditions ( ah@xmath116 ) and ( ah@xmath119 ) will also be used in our paper , so we explain it below . given a group @xmath1 acting on a metric space @xmath2 , a subset @xmath120 , and @xmath121 , we define the _ pointwise @xmath122-stabilizer _ of @xmath26 in @xmath1 as the set of all @xmath8 that move every point of @xmath26 by at most @xmath122 . that is , @xmath123 thus the pointwise @xmath17-stabilizer is the same as the usual pointwise stabilizer , which will be denoted @xmath124 . note that , in general , pointwise @xmath122-stabilizers are not subgroups . [ rem : equiv_def - acyl ] in these terms , the action of @xmath1 on @xmath106 is acylindrical if and only if for every @xmath3 there exists @xmath125 such that for all @xmath126 with @xmath6 , the sizes of pointwise @xmath122-stabilizers of @xmath127 are uniformly bounded by a constant @xmath7 which only depends on @xmath122 . [ def : wpd ] an element @xmath128 of a group @xmath1 acting isometrically on a metric space @xmath106 satisfies the _ weak proper discontinuity _ condition ( or @xmath128 is a _ wpd element _ ) if for some @xmath110 ( or , equivalently , for all @xmath129 ) and every @xmath121 , exists @xmath130 such that @xmath131 this definition is essentially due to bestvina and fujiwara @xcite . the notion of a hyperbolically embedded subgroup was introduced in @xcite ; it generalizes the notion of a peripheral subgroup of a relatively hyperbolic group . more precisely , let @xmath1 be a group , @xmath132 , @xmath133 . we assume that @xmath134 and denote by @xmath135 the cayley graph of @xmath1 with respect to the generating set @xmath136 ( even though @xmath10 and @xmath60 might intersect as subsets of @xmath1 , for the purposes of constructing @xmath135 we consider them to be disjoint ) and by @xmath137 the cayley graph of @xmath60 with respect to the generating set @xmath60 . clearly @xmath137 is a complete subgraph of @xmath138 . given two elements @xmath139 , we define @xmath140 to be the length of a shortest path @xmath141 in @xmath142 that connects @xmath143 to @xmath144 and does not contain edges of @xmath137 . if no such path exists we set @xmath145 . clearly @xmath146 $ ] is an extended metric on @xmath60 . we say that @xmath60 is _ hyperbolically embedded in @xmath1 with respect to _ @xmath133 ( and write @xmath147 ) if the following conditions hold : 1 . @xmath148 and @xmath138 is hyperbolic . 2 . @xmath149 is a locally finite space , i.e. , every ball ( of finite radius ) is finite . we also say that @xmath60 is _ hyperbolically embedded in @xmath1 _ ( and write @xmath150 ) if @xmath147 for some @xmath133 . let us consider three basic examples . [ he s ] 1 . for any group @xmath1 , we have @xmath151 . indeed take @xmath152 . then the cayley graph @xmath135 has diameter @xmath153 and @xmath145 whenever @xmath154 . further , if @xmath60 is a finite subgroup of a group @xmath1 , then @xmath155 . indeed @xmath156 for @xmath157 . these cases are referred to as _ degenerate_. 2 . let @xmath158 , @xmath159 , where @xmath160 is a generator of @xmath161 . then @xmath138 is quasi - isometric to a line and hence it is hyperbolic . however @xmath162 for every @xmath163 . if @xmath60 is infinite , then @xmath164 , and moreover @xmath165 . 3 . let @xmath166 , @xmath159 , where @xmath160 is a generator of @xmath161 . in this case @xmath138 is quasi - isometric to a tree and @xmath145 unless @xmath167 . thus @xmath156 . it is known that a group @xmath1 is hyperbolic relative to a subgroup @xmath60 if and only if @xmath147 for some finite set @xmath10 @xcite . we begin with some elementary algebraic properties of acylindrically hyperbolic groups . the theorem below summarizes some results from ( * ? ? ? * section 7 ) and ( * ? ? ? * theorems 2.23 , 2.25 , 2.30 ) . recall that a subgroup @xmath132 is _ @xmath168-normal _ in @xmath1 if for every @xmath8 , we have @xmath169 . clearly every infinite normal subgroup is @xmath168-normal . recall also that a group @xmath1 is @xmath38-universal if every countable group embeds in a quotient of @xmath1 . [ thm : elem - prop - ah ] for any acylindrically hyperbolic group @xmath1 the following conditions hold . 1 . the amenable radical of @xmath1 is finite . 2 . if @xmath170 , then @xmath171 for @xmath172 or @xmath173 . every @xmath168-normal subgroup of @xmath1 is acylindrically hyperbolic . 4 . if @xmath174 for some subgroups @xmath175 of @xmath1 . then @xmath176 is acylindrically hyperbolic for at least one @xmath177 . in particular , @xmath1 is not boundedly generated . @xmath1 is @xmath38-universal . in particular , @xmath1 contains non - abelian free subgroups . @xmath1 contains uncountably many normal subgroups . it is useful to keep this theorem in mind when searching for examples of acylindrically hyperbolic groups as it allows one to show that certain groups are _ not _ acylindrically hyperbolic . [ ex : non - ah ] 1 . 2 . no amenable group is acylindrically hyperbolic . no group without non - abelian free subgroups is acylindrically hyperbolic . in particular , no torsion group or a group satisfying a non - trivial identity is acylindrically hyperbolic . 4 . the baumslag - solitar groups @xmath178 are not acylindrically hyperbolic unless @xmath35 or @xmath36 , because the cyclic subgroup @xmath179 is @xmath168-normal in @xmath180 in this case . @xmath181 is not acylindrically hyperbolic for @xmath182 , since it is boundedly generated . another argument is based on the margulis theorem , which states that for @xmath182 every normal subgroup of @xmath183 is either finite or of finite index and hence @xmath183 has only countably many normal subgroups . for a generalization , see ( * ? ? ? * example 7.5 ) . recall that two groups @xmath100 and @xmath101 are said to be _ commensurable up to finite kernels _ , @xmath184 , if there are finite index subgroups @xmath185 , @xmath104 , a group @xmath60 and epimorphisms @xmath186 such that @xmath187 is finite for @xmath104 . it is not difficult to check that @xmath188 is the smallest equivalence relation whose classes are closed under taking subgroups of finite index and quotients modulo finite normal subgroups . [ lem : com ] the class @xmath14 is closed under commensurability up to finite kernels . let @xmath1 be a group , @xmath60 a finite index subgroup of @xmath1 . suppose that @xmath189 . then , by definition [ df : acyl - gp ] , there exists a generating set @xmath10 of @xmath60 such that the cayley graph @xmath190 is hyperbolic , non - elementary ( i.e. , @xmath191 ) , and the action of @xmath60 on @xmath190 is acylindrical . let @xmath192 be a set of representatives of left cosets of @xmath60 in @xmath1 . obviously @xmath193 generates @xmath1 . since @xmath194 , the natural map @xmath195 is a quasi - isometry . in particular , @xmath196 is also hyperbolic and non - elementary . moreover , it is straightforward to verify that the action of @xmath1 on @xmath196 is acylindrical ( in fact , acylindricity of the action is preserved under equivariant quasi - isometries ) . therefore @xmath197 by definition [ df : acyl - gp ] . conversely if @xmath198 , and @xmath60 is a finite index subgroup of @xmath1 , then @xmath60 is @xmath168-normal in @xmath1 and thus @xmath189 by theorem [ thm : elem - prop - ah ] . further , let @xmath1 be a group , @xmath199 a finite normal subgroup and let @xmath200 be the natural epimorphism . then for any generating set @xmath10 of @xmath1 , @xmath201 generates @xmath202 and the natural map @xmath203 is a @xmath1-equivariant quasi - isometry . thus if @xmath204 is non - elementary hyperbolic then so is @xmath205 . also observe that the action of @xmath1 on @xmath205 factors through the canonical action of @xmath202 . hence if the former is acylindrical then so is the latter . thus if @xmath197 then @xmath206 . conversely , if @xmath192 is some generating set of @xmath202 then @xmath207 is a generating set of @xmath1 and the cayley graphs @xmath204 and @xmath208 are @xmath1-equivariantly quasi - isometric . since @xmath209 , if the action of @xmath202 on @xmath208 is acylindrical , then so is the natural action of @xmath1 on @xmath208 . this allows to argue as above to conclude that @xmath206 implies @xmath197 . the next two results will be used in section 7 of our paper . the first one was proved by dahmani , guirardel and the second author in ( * ? ? ? * theorem 2.32 ) . [ thm : prop - ah-2 ] for any acylindrically hyperbolic group @xmath1 , there exists a maximal normal finite subgroup @xmath210 and the following conditions are equivalent . 1 . @xmath211 . @xmath1 has infinite conjugacy classes ( equivalently , the von neumann algebra @xmath58 of @xmath1 is a @xmath212 factor ) . @xmath1 is not inner amenable . in particular , @xmath58 does not have property @xmath57 of murray and von neumann . the reduced @xmath213-algebra of @xmath1 is simple with unique trace . the next theorem was first proved in @xcite under a certain assumption equivalent to acylindrical hyperbolicity ( see @xcite ) ; it also follows from the main result of @xcite , where the language of hyperbolically embedded subgroups was used . for details about quasi - cocycles and bounded cohomology we refer to @xcite . [ thm : prop - ah-3 ] @xmath92 . finally we mention a theorem from @xcite . recall that the conjugacy growth function of a finitely generated group for every @xmath214 measures the number of conjugacy classes intersecting the ball of radius @xmath215 centered at @xmath153 in the word metric . for details we refer to @xcite . [ thm : prop - ah-4 ] every acylindrically hyperbolic group has exponential conjugacy growth . given an oriented edge @xmath216 of a graph @xmath78 , @xmath217 and @xmath218 will denote the initial vertex and the terminal vertex of @xmath216 respectively , and @xmath219 will denote the inverse edge to @xmath216 ( i.e. , @xmath216 equipped with the opposite orientation ) . in this paper , a tree means a simplicial tree , unless specified otherwise . let @xmath220 be a tree . the natural metric on @xmath19 , induced by identification of edges with @xmath221 $ ] , is denoted by @xmath222 . we will think of @xmath19 as a simplicial tree and a metric space simultaneously ; in particular we will talk about vertices and edges as well as points of @xmath19 . given two points @xmath223 , @xmath224 $ ] will denote the unique geodesic segment connecting @xmath160 and @xmath225 . throughout this subsection let @xmath1 denote a group acting on @xmath19 by isometries . it is well known that any element @xmath31 either fixes a point of @xmath220 ( which is either a vertex or the midpoint of an edge ) or there exists a unique minimal @xmath226-subtree of @xmath220 , which is a bi - infinite geodesic path , called the _ axis _ of @xmath107 and denoted by @xmath227 , on which @xmath107 acts by translation @xcite . in the former case @xmath107 is said to be _ elliptic _ , and in the latter case it is said to be _ hyperbolic_. for a hyperbolic element @xmath107 , we denote by @xmath228 the limit points of the axis of @xmath107 in @xmath229 . the _ translation length _ @xmath230 , of an element @xmath31 , is defined as the minimum of the distances @xmath231 , where @xmath71 runs over the set of all vertices of @xmath19 . since @xmath19 is a simplicial tree , @xmath230 is a non - negative integer . the translation length can be used to classify the elements of @xmath1 : @xmath232 if and only if @xmath107 is elliptic . and if @xmath107 is hyperbolic , then the set set of all points @xmath160 of @xmath19 such that @xmath233 is exactly the axis of @xmath107 . [ df : edge_transl ] consider an edge @xmath216 of @xmath19 with some fixed orientation . we will say that an element @xmath31 _ translates _ @xmath216 if @xmath234 and the vertices @xmath217 and @xmath235 lie outside of the geodesic segment @xmath236 $ ] . note that , in this terminology , if @xmath31 acts as a hyperbolic isometry and @xmath216 is an edge on the axis of @xmath107 then @xmath216 is translated by exactly one of the elements @xmath107 or @xmath237 ( the above definition implies that @xmath238 in the sense of ( * ? ? ? * i.4.10 ) ) . conversely , if @xmath31 translates some edge @xmath216 of @xmath19 then @xmath107 is hyperbolic and the axis of @xmath107 contains the segment @xmath239 $ ] ( see ( * ? ? ? * i.4.11 ) ) . our main goal in this section is to establish a criterion for the existence of hyperbolic wpd elements in @xmath1 . we begin with a technical result about pointwise @xmath122-stabilizers defined in section [ sec : eqdef ] . [ lem : epst ] fix any @xmath121 . let @xmath5 be any two points in @xmath19 with @xmath240 and let @xmath21 be any two vertices on the geodesic segment @xmath224 $ ] such that @xmath241 . then @xmath242 is contained in the union of at most @xmath243 left cosets of @xmath244 . let @xmath245 $ ] , @xmath246 , be the set of all translations of @xmath247 $ ] by elements of @xmath1 such that @xmath248\subset [ x , y]$ ] and @xmath249 . obviously @xmath250 ( note that edge inversions are possible ) . for each @xmath251 , choose any element @xmath252 such that @xmath248=t_i [ u , v]$ ] . let @xmath107 be an element of @xmath242 . that is , @xmath253 let @xmath254 ( respectively , @xmath255 ) be the point on @xmath224 $ ] closest to @xmath256 ( respectively , @xmath257 ) . thus @xmath258 $ ] is a concatenation of @xmath259 $ ] and @xmath260 $ ] and , similarly , @xmath261 $ ] is a concatenation of @xmath262 $ ] and @xmath263 $ ] . using ( [ eq : dtgx ] ) we obtain @xmath264 and @xmath265 since @xmath266 , ( [ eq : dtxa ] ) implies that @xmath267 and hence @xmath268=[x , y]\cap [ g x , g y]$ ] . since @xmath269 $ ] and @xmath270 , we obtain @xmath271 $ ] using again . similarly we obtain @xmath272 $ ] and @xmath273 $ ] using ( [ eq : dtgxa ] ) . since @xmath274\subseteq [ g x , g y]$ ] , we have @xmath275 thus @xmath276=[u_i , v_i]$ ] for some @xmath277 . this means that @xmath278 and hence @xmath279 [ prop : wpd - crit ] let @xmath1 be a group acting on a simplicial tree @xmath19 and let @xmath280 be a hyperbolic element . suppose that for some vertices @xmath281 , the pointwise stabilizer @xmath282 is finite ( the possibility @xmath283 is allowed ) . then @xmath128 satisfies the wpd condition . in particular , either @xmath1 is virtually cyclic or @xmath197 . without loss of generality we can assume that @xmath284 $ ] for some @xmath285 ( otherwise , exchange @xmath70 and @xmath71 ) . we will show that in this case @xmath128 satisfies definition [ def : wpd ] for @xmath286 . take any @xmath3 . evidently we can increase @xmath122 to assume that @xmath287 . let @xmath288 be such that @xmath289 and let @xmath290 and @xmath291 . then @xmath247 \subset [ u , h^m u]\subset [ x , y]$ ] and @xmath292 . applying lemma [ lem : epst ] , we obtain that @xmath293 is finite . since @xmath294 , @xmath295 is conjugate to @xmath293 in @xmath1 , and hence it is also finite . thus the definition of wpd is satisfied for @xmath286 and @xmath296 . the last claim of the corollary follows from theorem [ acyl ] together the observation that a hyperbolic isometry of a simplicial tree is hyperbolic ( loxodromic ) in the sense defined at the beginning of subsection [ sec : eqdef ] . the action of @xmath297 on itself by translations shows that corollary [ prop : wpd - crit ] does not extend to actions on @xmath297-trees . recall that the action of @xmath1 on @xmath19 is _ minimal _ if @xmath19 does not contain any proper @xmath1-invariant subtree . let @xmath298 be the natural compactification of @xmath19 . take any point @xmath299 . limit set _ @xmath300 , of @xmath1 in the boundary @xmath20 , is the intersection of the closure of @xmath301 in @xmath302 with @xmath20 . since @xmath1 acts on @xmath19 isometrically , @xmath300 does not depend on the choice of the point @xmath160 . [ axisuv ] let @xmath19 be a tree with at least @xmath0 vertices . suppose that a group @xmath1 acts minimally on @xmath19 and does not fix any point of @xmath20 . then for any two vertices @xmath21 of @xmath19 , there exists a hyperbolic element @xmath8 such that @xmath303 contains @xmath70 and @xmath71 . since @xmath304 has at least @xmath0 vertices , there exists a vertex @xmath71 of degree at least @xmath13 . let @xmath305 be the minimal subtree of @xmath19 containing the orbit @xmath306 . obviously @xmath305 is @xmath1-invariant and no vertex of @xmath305 has degree @xmath153 in @xmath19 . since the action of @xmath1 is minimal , @xmath307 . thus @xmath19 does not contain vertices of degree @xmath153 . this implies that any two vertices @xmath21 of @xmath19 are contained in a bi - infinite geodesic @xmath308 . in particular , @xmath19 is unbounded . if the action of @xmath1 is elliptic ( i.e. , orbits are bounded ) , then for any vertex @xmath71 of @xmath19 , the minimal subtree @xmath309 containing the orbit @xmath306 is bounded . obviously @xmath309 is @xmath1-invariant . however this contradicts minimality of the action since @xmath19 is unbounded . thus the action of @xmath1 can not be elliptic . since @xmath1 does not fix any point of @xmath310 , the action of @xmath1 on @xmath19 can not be parabolic or quasi - parabolic in gromov s terminology either ( see ( * ? ? ? * section 8.2 ) ) . hence the set @xmath311 , where @xmath312 is the set of all hyperbolic elements of @xmath1 , is dense in @xmath313 ( * ? ? ? * corollary 8.2.g ) ( for a detailed proof in a more general situation see @xcite ) . moreover , since the action of @xmath1 on @xmath19 is minimal , for any vertex @xmath314 , @xmath19 coincides with the convex span of the orbit @xmath306 . thus any point of @xmath19 lies on a geodesic segment connecting two vertices from @xmath306 . it follows that @xmath315 , and so the set @xmath311 is dense in @xmath316 . this implies that for any segment @xmath317 of @xmath308 , there is a hyperbolic element @xmath8 with @xmath318 , as claimed . note that the lemma does not hold for the tree @xmath319 consisting of a single edge . indeed @xmath320 acts on @xmath319 by inversion . the action is minimal and obviously @xmath320 does not fix any point of @xmath321 as the latter is empty . similar counterexamples can be constructed by using any group that surjects onto @xmath320 . however if we assume that @xmath1 acts of @xmath19 without inversions , then the condition @xmath322 in the lemma can be relaxed to @xmath323 . the next result is obtained in the course of proving part ( 3 ) of proposition 6 in @xcite . note that although the authors assume that every hyperbolic element satisfies wpd there , the proof only uses the existence of a single hyperbolic wpd element . [ bf ] let @xmath1 be a group acting on a hyperbolic space @xmath10 and containing a hyperbolic wpd element . if @xmath1 is not virtually cyclic , then it contains two hyperbolic elements @xmath324 such that @xmath325 . we are now ready to prove the main result of this subsection . [ prop : min - wpd ] let @xmath1 be a group acting minimally on a simplicial tree @xmath19 . if @xmath1 is not virtually cyclic then the following conditions are equivalent : 1 . @xmath1 contains a hyperbolic wpd element ( for the given action of @xmath1 on @xmath19 ) . 2 . @xmath1 does not fix any point of @xmath20 and there exist vertices @xmath21 of @xmath19 such that @xmath326 is finite . suppose that @xmath1 is non - elementary and contains a hyperbolic wpd element @xmath8 . let @xmath327 be the axis of @xmath107 and let @xmath328 be any vertex . let @xmath54 be the constant from the definition of the wpd condition for @xmath107 corresponding to @xmath329 . set @xmath330 , then @xmath326 is finite by the wpd condition . since the only points of @xmath20 fixed by a hyperbolic element @xmath331 are @xmath332 , lemma [ bf ] implies that @xmath1 does not fix any point of @xmath20 . conversely , suppose @xmath1 does not fix any point of @xmath20 and there exist vertices @xmath21 of @xmath19 such that @xmath326 is finite . if @xmath304 were finite then @xmath282 would have finite index in @xmath1 implying that @xmath333 , which would contradict the assumption that @xmath1 is not virtually cyclic . hence the tree @xmath304 must be infinite , so , by lemma [ axisuv ] , there exists a hyperbolic element @xmath8 such that @xmath303 passes through @xmath70 and @xmath71 . therefore , according to corollary [ prop : wpd - crit ] , @xmath107 satisfies the wpd condition . suppose that @xmath1 is not virtually cyclic . then it contains a hyperbolic wpd element ( with respect to the action on @xmath19 ) by proposition [ prop : min - wpd ] . hence @xmath1 is acylindrically hyperbolic by theorem [ acyl ] . in this subsection we assume that the reader is familiar with bass - serre theory . for a detailed exposition we refer to @xcite . let @xmath23 be a graph of groups , where @xmath78 is a connected graph and @xmath334 is a collection consisting of 1 . edge groups @xmath335 and vertex groups @xmath336 associated to edges @xmath337 and vertices @xmath338 of @xmath57 ; 2 . maps @xmath339 and @xmath340 , which for every edge @xmath216 of @xmath78 , define the embeddings of the edge group @xmath335 into the vertex groups @xmath341 and @xmath342 , respectively . let also @xmath343 denote the fundamental group of @xmath23 . as we know , this fundamental group naturally acts on the associated bass - serre tree @xmath19 . in this section we will investigate various conditions ensuring that this action satisfies the assumptions of theorem [ main-1 ] . first we will characterize the situation when @xmath343 fixes a point of @xmath20 . the proof of the following statement is essentially contained in the proof of theorem 4.1 from @xcite : [ lem : fix_end ] suppose that @xmath1 is a group acting isometrically on a simplicial tree @xmath19 . if @xmath1 fixes a point of @xmath20 then all elliptic elements in @xmath1 form a normal subgroup @xmath344 such that the quotient @xmath202 is either trivial or infinite cyclic . let @xmath345 be the point fixed by @xmath1 and let @xmath346 be an elliptic element . then @xmath160 fixes some vertex @xmath70 of @xmath19 , and hence it must fix ( pointwise ) the unique geodesic ray @xmath347 $ ] from @xmath70 to @xmath348 . if @xmath349 is another elliptic element , then @xmath225 fixes the geodesic ray @xmath350 $ ] for some vertex @xmath71 of @xmath19 . the intersection of the rays @xmath347 $ ] and @xmath350 $ ] is again a geodesic ray @xmath351 $ ] for some vertex @xmath352 . it follows that @xmath352 is fixed by both @xmath160 and @xmath225 , hence the product @xmath353 is elliptic . evidently an inverse and a conjugate of an elliptic element is again elliptic , therefore the set of elliptic elements forms a normal subgroup @xmath344 . if @xmath1 has no hyperbolic elements , then @xmath354 and the lemma is proved . so , assume that @xmath1 has at least one hyperbolic element . then there is a hyperbolic element @xmath280 which has minimal translation length @xmath355 . recall that the only fixed points of @xmath128 on @xmath20 are @xmath356 . after replacing @xmath128 with @xmath357 , if necessary , we can assume that @xmath358 . take any other hyperbolic element @xmath31 . we want to show that @xmath359 . as above , we can suppose that @xmath360 . hence the intersection of @xmath227 and @xmath361 contains an infinite geodesic ray @xmath362 $ ] for some vertex @xmath71 of @xmath19 , and positive powers of @xmath128 and @xmath107 translate this ray into itself . by the construction of @xmath128 , @xmath363 , hence there exist @xmath364 such that @xmath365 and @xmath366 , @xmath367 . set @xmath368 and observe that @xmath369 translates the ray @xmath350 $ ] into itself and @xmath370 . so , if @xmath371 then @xmath369 is a hyperbolic element with @xmath372 , contradicting the choice of @xmath128 . therefore @xmath36 , i.e. , @xmath369 fixes @xmath71 , and so it is elliptic . thus @xmath373 , which implies that @xmath374 . since @xmath375 , we see that @xmath376 is infinite cyclic , and the lemma is proved . suppose that @xmath216 is an edge between vertices @xmath70 and @xmath71 in a graph of groups @xmath23 . we will say that @xmath216 is _ good _ if the natural images of @xmath335 in @xmath377 and @xmath336 are proper subgroups . any edge that is not good will be called _ bad_. [ lem : ab ] if the graph of groups @xmath23 has at least one good edge then the elliptic elements of @xmath378 do not form a subgroup . in particular , @xmath1 does not fix any point of @xmath20 , where @xmath19 is the corresponding bass - serre tree . let @xmath216 be any edge of @xmath19 which maps onto a good edge of @xmath379 . fixing some orientation of @xmath216 and abusing the notation , we let @xmath335 , @xmath342 and @xmath341 denote the @xmath1-stabilizers of @xmath216 , @xmath217 and @xmath218 respectively . since the image of @xmath216 in @xmath78 is good , there is an element @xmath380 and an element @xmath381 . clearly @xmath254 and @xmath255 are elliptic , and to prove the statement it suffices to show that the element @xmath382 is hyperbolic . let @xmath383 , then @xmath384 but @xmath385 as @xmath386 . on the other hand , the edge @xmath387 starts at @xmath217 and is also distinct from @xmath216 ( see figure [ fig : ab ] ) . thus we see that the edge @xmath369 is translated by @xmath128 ( cf . [ df : edge_transl ] ) , which implies that @xmath128 is hyperbolic . the last claim of the lemma now follows from lemma [ lem : fix_end ] . we will say that an oriented edge @xmath216 of @xmath78 is _ reducible _ if @xmath388 and at least one of the maps @xmath389 , @xmath390 is onto . a graph of groups @xmath23 is _ reduced _ if it does not contain reducible edges . thus a reducible edge is a bad edge which is not a loop . it is easy to see that any reducible edge can be contracted without affecting the fundamental group . therefore every finite graph of groups can be contracted to a reduced graph of groups with the same fundamental group ( see @xcite for details , where reducible edges are called _ directed _ ) . recall that an hnn - extension @xmath391 of a group @xmath26 with associated subgroups @xmath24 and @xmath29 is called _ ascending _ if @xmath392 or @xmath393 . ascending hnn - extension gives a basic example of a reduced graph of groups that has a single vertex and a single bad loop at this vertex . the following proposition characterizes the case when the fundamental group of a reduced graph of groups fixes a point on the boundary of the corresponding bass - serre tree : [ prop : charact ] suppose that @xmath23 is a reduced graph of groups with at least one edge . let @xmath378 and let @xmath19 be the corresponding bass - serre tree . then the following are equivalent : * @xmath1 fixes a point of the boundary @xmath20 ; * @xmath23 has only one vertex @xmath71 and one ( unoriented ) bad edge @xmath216 with @xmath394 . in other words , @xmath1 is an ascending hnn - extension of @xmath336 . the fact that ( ii ) implies ( i ) is well - known and we leave it as an exercise for the reader . now , suppose that ( i ) holds . then @xmath23 has no good edges by lemma [ lem : ab ] . since @xmath23 has no reducible edges by the assumptions and @xmath78 is connected , one concludes that @xmath78 has only one vertex @xmath71 and all the edges of @xmath78 are loops at @xmath71 . the quotient of @xmath378 by the normal closure @xmath344 , of @xmath336 in @xmath1 , is the free group , whose rank is equal to the number of ( unoriented ) loops at @xmath71 . since @xmath71 is the only vertex of @xmath78 , every elliptic element is conjugate to an element of @xmath336 in @xmath1 . so , by lemma [ lem : fix_end ] , @xmath7 is the set of all elliptic elements , and the quotient @xmath202 is cyclic . thus @xmath78 can have at most one loop at @xmath71 , which is a bad edge ( as defined above ) , i.e. , ( ii ) holds . for a general graph of groups @xmath23 , the situation when the canonical action of @xmath378 on the corresponding bass - serre tree @xmath19 is minimal was characterized by bass in @xcite . the next lemma follows from ( * ? ? ? 7.12 ) : [ lem : min - act ] let @xmath23 be a reduced graph of groups of finite diameter . then the action of @xmath343 on the corresponding bass - serre tree is minimal . a combination of proposition [ prop : charact ] with lemma [ lem : min - act ] and theorem [ main-1 ] gives a criterion to show that the fundamental group of a finite reduced graph of groups is acylindrically hyperbolic ( see theorem [ thm : reduced - crit ] below ) . before formulating it we need to make a couple of observations . [ rem : vert - edg ] suppose that @xmath1 is a group acting on a simplicial tree @xmath19 . if the tree @xmath19 has at least two vertices , the existence of vertices @xmath395 with @xmath396 is equivalent to the existence of two edges @xmath397 of @xmath19 such that @xmath398 . ( note that we allow the possibilities @xmath283 and/or @xmath399 . ) indeed , in one direction this is evident . for the other direction , suppose that @xmath216 and @xmath369 are edges of @xmath19 with @xmath398 . without loss of generality we can assume that the segment @xmath400 $ ] contains both of these edges . then @xmath401)={{\rm pstab}}_g(\{e , f\})$ ] , i.e. , one can take @xmath402 and @xmath403 . [ rem : fin_pst ] suppose that @xmath1 is the fundamental group of a graph of groups @xmath23 and @xmath19 is the corresponding bass - serre tree . in algebraic terms , the existence of vertices @xmath21 of @xmath19 such that @xmath326 is finite means that @xmath404 for some @xmath8 and some vertices @xmath405 , @xmath406 of @xmath78 . similarly , the existence of two edges @xmath397 of @xmath19 such that @xmath398 corresponds to @xmath407 for some @xmath8 and some edges @xmath408 , @xmath409 of @xmath78 . [ thm : reduced - crit ] let @xmath1 be the fundamental group of a finite reduced graph of groups @xmath23 with at least one edge such that the condition ( ii ) from proposition [ prop : charact ] does not hold . suppose that there are edges @xmath397 of @xmath78 ( not necessarily distinct ) and an element @xmath31 such that @xmath410 . then @xmath1 is either virtually cyclic or acylindrically hyperbolic . let @xmath19 be the bass - serre tree associated to @xmath23 . by lemma [ lem : min - act ] , the action of @xmath1 on @xmath19 is minimal , and , by proposition [ prop : charact ] , @xmath1 does not fix any point of @xmath20 . since @xmath23 is reduced and has at least one edge , it is easy to see that the tree @xmath19 must be infinite ( any loop gives rise to a hyperbolic element ; if there are no loops , then all the edges must be good , hence a hyperbolic element can be produced as in the proof lemma [ lem : ab ] ) . by remarks [ rem : fin_pst ] and [ rem : vert - edg ] , the assumptions imply that @xmath19 contains two vertices @xmath21 such that @xmath282 is finite . therefore , we can apply theorem [ main-1 ] to conclude that @xmath1 is either virtually cyclic or acylindrically hyperbolic . corollary [ cor : amalg - intr ] from section [ sec : results ] is an immediate consequence of theorem [ thm : reduced - crit ] applied in the situation when @xmath23 consists of two vertices and a good edge connecting them . corollary [ cor : hnn - intr ] corresponds to the case when @xmath23 has one vertex and one ( good ) loop at this vertex . thus its claim also follows from theorem [ thm : reduced - crit ] modulo the observation that a non - ascending hnn - extension of any group contains non - abelian free subgroups ( see , for example , ( * ? ? ? * thm . 6.1 ) ) , and so it can not be virtually cyclic . it is easy to see that the condition @xmath28 is necessary in corollary [ cor : amalg - intr ] . as for the requirement @xmath30 in corollary [ cor : hnn - intr ] , the situation is more complicated and counterexamples are not so obvious . we note the following . [ prop : asc - hnn ] let @xmath1 be an ascending hnn - extension of a group @xmath26 . if @xmath1 is acylindrically hyperbolic , then so is @xmath26 . let @xmath411 be the stable letter of the hnn - extension , @xmath412 . then the subgroup @xmath413 is normal in @xmath1 and @xmath414 . consequently we have @xmath415 . thus by part ( d ) of theorem [ thm : elem - prop - ah ] @xmath26 must be acylindrically hyperbolic . proposition [ prop : asc - hnn ] allows to construct examples of ascending hnn - extensions with weakly malnormal base which are not acylindrically hyperbolic . [ ex : hnnb ] using methods from ( * ? ? ? * section 4.2 ) it is not hard to construct a proper malnormal subgroup @xmath416 of a free burnside group @xmath26 of rank @xmath13 and large odd exponent such that @xmath417 . let @xmath1 be the corresponding ascending hnn - extension of @xmath26 . then @xmath26 and @xmath27 are weakly malnormal in @xmath1 , but @xmath1 is not acylindrically hyperbolic by a combination of proposition [ prop : asc - hnn ] and example [ ex : non - ah ] ( b ) . if @xmath26 is acylindrically hyperbolic , then its ascending hnn - extensions can be acylindrically hyperbolic as well . for example , many ascending hnn - extensions of free groups are hyperbolic . nevertheless the example below shows that acylindrical hyperbolicity ( even relative hyperbolicity ) of @xmath26 together with weak malnormality is still not sufficient to derive acylindrical hyperbolicity of @xmath1 . [ ex : bg ] in the proof of ( * ? ? ? * prop . 18 ) , the second author constructed a boundedly generated finitely presented group ( denoted by @xmath1 in @xcite ) which is universal , i.e. , contains an isomorphic copy of every recursively presented group . let us denote this group by @xmath418 . let @xmath419 and let @xmath420 be a generator of the subgroup @xmath161 . then @xmath26 is acylindrically hyperbolic ( in fact , it is hyperbolic relative to @xmath418 ) . since @xmath26 is finitely presented , it is isomorphic to a subgroup @xmath421 . let @xmath1 be the corresponding ascending hnn - extension of @xmath26 with the stable letter @xmath411 . obviously @xmath422 and hence @xmath26 and @xmath27 are weakly malnormal in @xmath1 . arguing as in the proof of proposition [ prop : asc - hnn ] , we obtain @xmath423 . since @xmath418 is boundedly generated , so is @xmath1 . hence @xmath1 is not acylindrically hyperbolic by part ( d ) of theorem [ thm : elem - prop - ah ] . we begin with the proof of corollary [ cor : one - rel ] , which is inspired by @xcite and @xcite . it is proved in @xcite ( see the proof of theorem iii there ) that @xmath1 splits as @xmath424 , where @xmath425 are proper subgroups of @xmath60 , and there exists @xmath426 such that @xmath427 . thus the claim follows from corollary [ cor : amalg - intr ] and the well known fact that a one relator group with at least @xmath0 generators is never virtually cyclic . our next goal is to study one - relator groups with @xmath13 generators . as we already mentioned in example [ ex : non - ah-1 ] , the baumslag - solitar groups @xmath180 are not acylindrically hyperbolic unless @xmath35 or @xmath36 . the obstacle for acylindrical hyperbolicity of @xmath180 is the existence of an infinite cyclic @xmath168-normal subgroup . the are are many other one - relator groups with the same property . however , we will show that all of them ( as well as other potential examples of non - acylindrically hyperbolic one - relator groups ) have low complexity in a certain sense . recall that , given a group @xmath60 and an injective ( but not necessarily surjective ) endomorphism @xmath428 , the _ mapping torus of @xmath429 _ is the ( ascending ) hnn - extension @xmath430 [ cor:1-rel-2-gen ] let @xmath1 be a group with two generators and one defining relator . then at least one of the following holds : * @xmath1 is acylindrically hyperbolic ; * @xmath1 contains an infinite cyclic @xmath168-normal subgroup . more precisely , either @xmath1 is infinite cyclic or it is an hnn - extension of the form @xmath431 of a one - relator group @xmath432 with non - trivial center , so that @xmath433 in @xmath60 for some @xmath434 . in the latter case @xmath60 is ( finitely generated free)-by - cyclic and contains a finite index normal subgroup splitting as a direct product of a finitely generated free group with an infinite cyclic group . * @xmath1 is isomorphic to the mapping torus of an injective endomorphism of a finitely generated free group . moreover , the possibilities ( i ) and ( ii ) are mutually exclusive . in order to prove proposition [ cor:1-rel-2-gen ] we will need the following lemma : [ lem : inter_conj_free_gps ] if @xmath24 and @xmath29 are finitely generated subgroups of infinite index in a finitely generated free group @xmath26 then there exists an element @xmath435 such that @xmath436 . one way to prove this would be to refer , first , to a result of w. neumann ( 2.1 ) stating that there are finitely many elements @xmath437 such that if @xmath438 then @xmath439 for some @xmath440 . second , one can use the fact that the free group @xmath26 can not be covered by finitely many double cosets from @xmath441 because @xmath24 and @xmath29 are finitely generated and have infinite index in @xmath26 ( a generalization of this fact for quasiconvex subgroups of hyperbolic groups was proved in ( * ? ? ? this implies that there is some @xmath435 such that @xmath442 , and hence @xmath443 . however , let us give a direct proof of the lemma using stallings core graphs ( see @xcite for an introduction to this method ) . suppose that @xmath26 has a free generating set @xmath10 of cardinality @xmath444 . let @xmath445 and @xmath446 be the finite @xmath10-labelled directed core graphs corresponding to the subgroups @xmath24 and @xmath29 of @xmath26 respectively ( cf . thus each @xmath447 has a distinguished vertex @xmath448 such that the language of reduced closed loops at this vertex coincides with @xmath24 if @xmath172 and with @xmath29 if @xmath173 . since @xmath24 and @xmath29 have infinite index in @xmath26 , each @xmath447 possesses a vertex of degree strictly less than @xmath449 ( see ( * ? ? ? after replacing @xmath24 and @xmath29 with their conjugates we can assume that these vertices are @xmath448 , @xmath104 . thus @xmath450 has no outgoing edge labelled by @xmath451 for some @xmath452 , and @xmath453 has no incoming edge labelled by @xmath454 for some @xmath455 . now , take a freely reduced word @xmath352 over @xmath456 such that @xmath352 starts with @xmath451 and ends with @xmath454 . let @xmath141 be the simple directed path ( regarded as a simplicial graph ) labelled by @xmath352 . construct the new @xmath10-labelled directed graph @xmath457 by attaching the endpoint of @xmath141 to the graph @xmath446 at @xmath453 . let @xmath458 be the initial vertex of @xmath141 . observe that , by construction , the graph @xmath457 is folded , and so , equipped with the base vertex @xmath458 , it represents the core graph of the subgroup @xmath459 in @xmath26 , where @xmath460 is the element given by the word @xmath352 . moreover , the label of a non - trivial reduced loop at @xmath458 in @xmath457 can not be equal to the label of a reduced loop at @xmath450 in @xmath445 , because the former starts with the letter @xmath451 and @xmath450 has no outgoing edges with that label . therefore @xmath461 , as required . if @xmath1 is cyclic , ( ii ) holds , so we suppose that @xmath1 is not cyclic . thus @xmath462 , where @xmath463 is a cyclically reduced word over the alphabet @xmath464 . without loss of generality we can assume that the word @xmath463 is non - empty and the total exponent of @xmath411 in @xmath463 is @xmath17 by ( * ? ? ? * lemma 4.1 ) . then , using the standard magnus - moldavanski re - writing procedure ( see , for example , @xcite ) one shows that @xmath1 has a presentation @xmath465 where @xmath214 and @xmath466 is a cyclically reduced word in the alphabet @xmath467 involving both @xmath468 and @xmath469 . let @xmath60 be the one - relator group given by the presentation @xmath470 . if @xmath471 , then @xmath472 . if @xmath473 , @xmath1 is infinite cyclic . if @xmath60 is non - trivial but finite , @xmath1 is non - elementary hyperbolic and , hence , it is acylindrically hyperbolic . finally , if @xmath60 is infinite , @xmath1 is also acylindrically hyperbolic as @xmath60 is a non - degenerate and hyperbolically embedded subgroup in @xmath1 ( see example [ he s ] and theorem [ acyl ] ) . suppose , now , that @xmath474 . by construction , both @xmath468 and @xmath469 occur in @xmath466 . consequently , using the magnus s freiheitssatz , the elements @xmath475 and @xmath476 freely generated free subgroups of rank @xmath477 in @xmath60 . the presentation now shows that @xmath1 is the hnn - extension of @xmath60 with the associated magnus subgroups @xmath478 and @xmath479 . again we consider two possibilities . first , let us consider the case @xmath480 . then @xmath481 and @xmath482 are infinite cyclic groups . if @xmath483 then @xmath197 by corollary [ cor : hnn - intr ] and remark [ rem : hnn ] . so , assume that @xmath484 in @xmath60 for some @xmath434 . then @xmath485 is central in @xmath60 and @xmath486 , which easily implies that @xmath26 is @xmath168-normal in @xmath1 . it also follows that @xmath487\not\cong \mathbb z\oplus \mathbb z$ ] . therefore @xmath60 can be represented as a stem product of cyclic groups by a theorem of pietrowski ( * ? ? ? moreover , in @xcite murasugi showed that @xmath60 is ( finitely generated free)-by - cyclic in this case ( see the first paragraph of the proof of theorem 1 in @xcite ) . thus @xmath60 contains a finitely generated normal free subgroup @xmath488 and an element @xmath489 of infinite order so that @xmath490 ; in other words , @xmath491 . if @xmath492 is trivial or infinite cyclic then @xmath60 is virtually abelian , and thus ( ii ) holds . so , assume that @xmath492 is non - cyclic . then it has trivial center , and since the center of @xmath60 is non - trivial , there must exist @xmath493 and @xmath494 such that the element @xmath495 is central in @xmath60 . observe that the subgroup @xmath496 is normal in @xmath60 and has index @xmath497 . clearly @xmath498 hence ( ii ) holds . thus we can further assume that @xmath499 . consider the subgroups @xmath500 and @xmath501 in @xmath1 . then @xmath502 as @xmath503 and @xmath504 in @xmath1 . if @xmath393 then @xmath505 , i.e. , @xmath506 in @xmath60 , which implies that @xmath507 and hence @xmath1 is isomorphic to the mapping torus of some injective endomorphism of the free group @xmath26 . similarly , ( iii ) holds if @xmath508 . it remains to deal with the case when @xmath509 are proper subgroups of @xmath26 and @xmath499 . by a result of collins @xcite the intersection @xmath510 , of the magnus subgroups of @xmath60 is a free subgroup of rank at most @xmath477 . thus @xmath24 and @xmath29 are proper subgroups of the free group @xmath26 and their rank does not exceed the rank of @xmath26 . since the rank of @xmath26 is @xmath511 , the schreier index formula ( cf . * i.3.9 ) ) implies that the rank of any proper finite index subgroup of @xmath26 is strictly greater than @xmath477 . hence both @xmath24 and @xmath29 must have infinite index in @xmath26 . consequently , we can apply lemma [ lem : inter_conj_free_gps ] to find an element @xmath435 such that @xmath512 in @xmath26 . set @xmath513 . we will now check that @xmath514 , which would yield that @xmath197 by corollary [ cor : hnn - intr ] and remark [ rem : hnn ] , finishing the proof . indeed , suppose that @xmath515 , i.e. , there exist @xmath516 and @xmath517 such that @xmath518 in @xmath1 . by britton s lemma ( see ( * ? ? ? * iv.2 ) ) , @xmath519 , hence @xmath520 . therefore @xmath521 , but @xmath522 and so @xmath523 implying that @xmath524 . the above contradiction shows that @xmath514 , as claimed . finally we observe that conditions ( i ) and ( ii ) are indeed mutually exclusive , because the first claim in ( ii ) implies that @xmath1 is not acylindrically hyperbolic by theorem [ thm : elem - prop - ah ] . let @xmath41 be a field . we denote by @xmath525 $ ] the group of @xmath41-automorphisms of the ( formal , commutative ) polynomial algebra @xmath526 $ ] , i.e. , those automorphisms of the ring @xmath526 $ ] that fix @xmath41 . this group is sometimes called the integral cremona group of dimension @xmath215 over @xmath41 . note that every @xmath41-automorphism @xmath348 of @xmath526 $ ] is uniquely determined by the images @xmath527 . thus elements of @xmath525 $ ] can be represented by polynomial maps @xmath528 where @xmath529 $ ] for @xmath530 . obviously multiplication in @xmath525 $ ] corresponds to the composition of such maps . it is easy to see that @xmath44 $ ] is generated by the affine maps @xmath531 , where @xmath532 and @xmath533 . therefore , @xmath44 \cong k \rtimes k^\ast$ ] , where @xmath534 acts on the additive group @xmath41 by multiplication . in particular , @xmath44 $ ] is metabelian and hence it is not acylindrically hyperbolic . for @xmath480 , the situation is completely different . we recall a well - known decomposition theorem for @xmath39 $ ] . let @xmath26 be the group of all affine maps @xmath535 where @xmath536 and @xmath537 . let also @xmath27 be the so - called triangular group consisting of all maps of the form @xmath538 where @xmath539 , @xmath533 , and @xmath540 $ ] . it is easy to see that the intersection @xmath541 consists of all maps of the form ( [ triang ] ) , where @xmath107 is a linear polynomial . it is known that @xmath542=a\ast _ cb.\ ] ] the fact that @xmath39 $ ] is generated by @xmath26 and @xmath27 was proved by jung @xcite for @xmath43 and van der kulk @xcite in the general case . the above amalgamated product decomposition can be derived from their work quite easily . alternative proofs were later suggested by many people including dicks @xcite , nagata @xcite , and wright @xcite . for @xmath543 the lemma below can be extracted from @xcite . it is quite possible that similar ( rather sophisticated ) arguments work for any field . we provide an elementary hands on " proof . [ acac ] there exists @xmath544 $ ] such that @xmath545 . our choice of @xmath348 will depend on the characteristic of @xmath41 . we first consider the case when @xmath546 . let @xmath348 be the map @xmath547 where @xmath548 . it is obvious that @xmath544 $ ] . let @xmath549 . then @xmath550 has the form @xmath551 and @xmath552 for some @xmath553 , @xmath554 computing the compositions in ( [ ag = ga ] ) , we obtain @xmath555 and @xmath556 equating the coefficients at @xmath225 in ( [ ag2 ] ) , we obtain @xmath557 . note that if @xmath558 , then ( [ ag2 ] ) yields @xmath559 , which implies that @xmath560 is not an automorphism . thus @xmath561 . now using ( [ ag1 ] ) , we obtain @xmath562 and then @xmath563 and @xmath564 . the later equality in turn gives @xmath565 as @xmath561 and @xmath546 . using these we can rewrite ( [ ag2 ] ) as @xmath566 further replacing @xmath567 with the right side of ( [ ag1 ] ) and denoting @xmath568 by @xmath411 , we obtain @xmath569 now equating the coefficients at @xmath570 in ( [ ag3 ] ) we obtain @xmath571 . substituting this to ( [ ag3 ] ) and expanding @xmath141 yields @xmath572 thus we have @xmath573 and @xmath574 , which in turn implies @xmath575 . as @xmath576 , we obtain @xmath577 . finally substituting @xmath571 and @xmath565 in ( [ ag1 ] ) , we obtain @xmath578 . thus @xmath550 is the identity . now assume that @xmath579 . then we let @xmath348 be the map @xmath580 where @xmath581 . arguing as above we obtain @xmath582 . this case is completely analogous to the previous one and we leave it to the reader . clearly @xmath583 and @xmath584 . hence @xmath585 = a*_c b$ ] contains non - abelian free subgroups ( cf . * thm . 6.1 ) ) and therefore it is not virtually cyclic . thus the claim follows from corollary [ cor : amalg - intr ] and lemma [ acac ] . [ cor : am - hyp ] let @xmath586 ( @xmath587 ) , where @xmath26 is a hyperbolic group , @xmath24 is a quasi - convex subgroup of infinite index in @xmath26 , and @xmath27 is arbitrary ( respectively , @xmath588 ) . then @xmath1 is either virtually cyclic or acylindrically hyperbolic . in the case when @xmath589 , if @xmath590 then @xmath591 is hyperbolic , and hence @xmath197 unless it is virtually cyclic . so , we can further assume that @xmath592 . recall that a quasi - convex subgroup of a hyperbolic group has finite width see ( * ? ? ? * main thm . ) . this means that there is @xmath214 such that for any collection of elements @xmath593 , with @xmath594 whenever @xmath595 , there exist @xmath596 , @xmath597 , such that @xmath598 . since @xmath599 , a collection of elements @xmath600 with these properties exists , therefore @xmath24 is weakly malnormal in @xmath26 ( and , hence , in @xmath1 ) . thus to reach the required conclusion it remains to apply corollary [ cor : amalg - intr ] in the case of the amalgamated product or corollary [ cor : hnn - intr ] in the case of the hnn - extension . it is not hard to show that in corollary [ cor : am - hyp ] @xmath1 will be virtually cyclic only if @xmath26 is virtually cyclic and @xmath590 . let us mention one particular case , which may be compared with simple groups discussed in example [ ex : non - ah-1].(a ) , showing that neither the assumption that @xmath24 is finitely generated nor the assumption that @xmath24 has infinite index in @xmath26 can be dropped . [ cor : am - free ] let @xmath586 , where @xmath26 is a free group and @xmath601 is a finitely generated subgroup of infinite index . then @xmath1 is either infinite cyclic or acylindrically hyperbolic . obviously , under the assumptions of the corollary , @xmath1 is cyclic if and only if so is @xmath26 and @xmath590 . it is worth mentioning that non - simplicity of groups from corollary [ cor : am - free ] with @xmath27 free was proved in @xcite using the small cancellation theory . in this particular case the assumptions of corollary [ cor : amalg - intr ] can be easily verified using the following theorem of m. hall : _ every finitely generated subgroup of a free group @xmath492 is a free factor of a finite index subgroup of @xmath492 . _ it seems plausible that corollary [ cor : am - hyp ] generalizes to amalgamated products and hnn - extensions of relatively hyperbolic and even acylindrically hyperbolic groups ( for a suitable definition of quasi - convex subgroups ) . we leave such generalizations to the reader . schupp s arguments from @xcite combined with corollary [ cor : amalg - intr ] also yield the following : the higman group @xmath602 is acylindrically hyperbolic . we begin by reviewing some results about @xmath0-manifolds and their fundamental groups used in this paper . for basic definitions we refer to @xcite . our main reference for properties of fundamental groups of @xmath0-manifold groups is @xcite . details about seifert fibered manifolds can be found in @xcite . let @xmath54 be a closed , orientable , irreducible @xmath0-manifold . the jaco - shalen - johannson decomposition theorem provides a canonical finite collection of disjoint incompressible tori @xmath603 in @xmath54 such that all connected components of @xmath604 are either a seifert fibred or atoroidal . a minimal such collection is unique up to isotopy . by the seifert - van kampen theorem , this decomposition of @xmath54 induces a decomposition of @xmath605 into a graph of groups . we will call it the _ jsj decomposition _ of @xmath605 . recall that the action of a group @xmath1 on a tree @xmath19 is _ @xmath41-acylindrical in the sense of sela _ , if the diameter of the fixed point set of every @xmath606 is at most @xmath41 . for example , the action of a free product @xmath607 on the associated bass - serre tree is @xmath153-acylindrical . the following result was proved by wilton and zalesskii in @xcite . [ wz ] let @xmath54 be a closed , orientable , irreducible @xmath0-manifold . then either @xmath54 has a finite - sheeted covering space that is a torus bundle over a circle or the action of @xmath55 on the bass - serre tree associated to the jsj decomposition of @xmath55 is @xmath608-acylindrical . we now briefly discuss the pieces of the jsj decomposition . by the perelman s proof of the thurston s geometrization conjecture @xcite@xcite , atoroidal pieces admit a finite volume hyperbolic structure ( in the case of haken manifolds this was originally proved by thurston see ( * ? ? ? * thm . 1.42 ) ) . hence the fundamental group of each atoroidal piece is hyperbolic relative to peripheral subgroups isomorphic to @xmath609 @xcite . as for a seifert fibered piece @xmath106 , we will just use the fact that if the fundamental group @xmath610 is infinite then it fits into the short exact sequence @xmath611 where @xmath52 is infinite cyclic and @xmath60 has a finite index subgroup which is a surface group ( here by a surface group we mean any group isomorphic to the fundamental group of a compact surface ) see ( * ? ? ? 1.6 ) . we say that an action of a group @xmath1 on a tree is @xmath19 _ acylindrical in the sense of sela _ if it is @xmath41-acylindrical for some @xmath612 . we begin with a lemma that relates the notion to acylindricity in the sense of sela to the one defined in the introduction . [ lem : sa ] if the action of a group @xmath1 on a tree @xmath19 is acylindrical in the sense of sela , then it is acylindrical ( as defined in the introduction ) . suppose that the action is @xmath41-acylindrical for some @xmath612 . fix any @xmath3 and consider any two points @xmath5 on @xmath19 such that @xmath613 . then the segment @xmath224 $ ] contains a subsegment @xmath247 $ ] , where @xmath21 are vertices of @xmath19 , such that @xmath241 and @xmath614 . by our assumption , @xmath615 and hence @xmath616 by lemma [ lem : epst ] . thus the action of @xmath1 on @xmath19 is acylindrical by remark [ rem : equiv_def - acyl ] . recall that every acylindrically hyperbolic group @xmath1 contains a unique maximal finite normal subgroup @xmath617 , called the _ finite radical _ of @xmath1 ( see theorem [ thm : prop - ah-2 ] ) . [ lem : at ] let @xmath1 be the a group acting acylindrically in the sense of sela and without inversions on a tree @xmath19 . then either @xmath1 is acylindrically hyperbolic with trivial finite radical , or it is infinite cyclic or infinite dihedral , or @xmath1 fixes a vertex of @xmath19 . by lemma [ lem : sa ] the action of @xmath1 on @xmath19 is acylindrical ( as defined in the introduction ) . so , in view of theorems [ class ] and [ acyl ] , @xmath1 is either acylindrically hyperbolic , or virtually cyclic containing a hyperbolic element , or has bounded orbits . in the latter case @xmath1 fixes a vertex @xmath160 of @xmath19 ( see ( * ? ? ? * i.4.7 ) ) . now assume that @xmath1 is acylindrically hyperbolic or virtually cyclic and contains a hyperbolic element @xmath128 . recall that every virtually cyclic group @xmath618 has a finite normal subgroup @xmath619 such that @xmath620 is either infinite cyclic or infinite dihedral . thus to prove the lemma it suffices to show that @xmath1 has no non - trivial finite normal subgroups . suppose @xmath621 is a finite normal subgroup of @xmath1 . after passing from @xmath128 to some non - trivial power , we can assume that @xmath128 belongs to the centralizer @xmath622 . since @xmath621 is finite , it fixes a vertex @xmath71 of @xmath304 . assume that the action of @xmath1 on @xmath19 is @xmath41-acylindrical in the sense of sela . since @xmath128 is hyperbolic , there exists @xmath623 such that @xmath624 for @xmath625 . obviously for every @xmath626 , we have @xmath627 ; hence @xmath621 fixes @xmath70 as well . now the @xmath41-acylindricity of the action in the sense of sela implies that @xmath628 . the next lemma is proved in @xcite . [ lem:613 ] suppose that @xmath60 is a proper infinite hyperbolically embedded subgroup of a group @xmath1 . let @xmath621 be a subgroup of @xmath1 such that @xmath629 is infinite and @xmath630 . then @xmath621 contains proper infinite hyperbolically embedded subgroups . finally , we will need the following result , which is a ( probably well - known ) consequence of the projective plane theorem proved in @xcite . by @xmath631 we denote the free group of rank @xmath215 . [ epstein ] @xmath632 . assume that @xmath633 . then @xmath634 for some @xmath0-manifold @xmath54 . by ( * theorem 9.5 ) , if @xmath635 embeds in the fundamental group of some @xmath0-manifold @xmath7 , then either @xmath636 or @xmath637 is a non - trivial free product . applying this result to @xmath54 we obtain that @xmath638 is a non - trivial free product . however , a non - trivial free product must have trivial center . a contradiction . now we are ready to prove the main result of this section , which is slightly stronger than theorem [ main-3-dim ] from section [ sec : results ] ( see parts ( i@xmath639 ) and ( ii@xmath639 ) ) . [ main-3d ] let @xmath54 be a compact @xmath0-manifold and let @xmath1 be a subgroup of @xmath55 . then exactly one of the following three conditions holds . 1 . @xmath1 is acylindrically hyperbolic with trivial finite radical . 2 . @xmath1 contains an infinite cyclic normal subgroup @xmath52 and @xmath53 is acylindrically hyperbolic . in fact , @xmath53 is virtually a subgroup of a surface group in this case . @xmath1 is virtually polycyclic . note that the three conditions ( i@xmath639 ) , ( ii@xmath639 ) and ( iii ) are mutually exclusive by theorem [ thm : elem - prop - ah ] ( c ) and example [ ex : non - ah ] ( a ) . thus we only need to show that at least one of them holds . if the boundary @xmath640 is non - empty , we take the double @xmath641 . since @xmath54 is a retract of @xmath7 , @xmath55 embeds in @xmath637 ( cf . * lemma 1.6 ) ) . thus without loss of generality we can assume that @xmath54 is also closed . further if @xmath54 is non - orientable , we pass to its orientable double cover @xmath642 and consider the index @xmath13 subgroup @xmath643 such that @xmath644 . note that if one of the conditions ( i@xmath639 ) , ( ii@xmath639 ) or ( iii ) holds for @xmath645 , then the same condition holds for @xmath1 . indeed , for ( iii ) this is obvious . further assume that @xmath645 satisfies ( ii@xmath639 ) . thus @xmath645 contains a finite index subgroup @xmath646 such that there is an infinite cyclic subgroup @xmath647 and @xmath648 is isomorphic to a subgroup of the fundamental group of a compact surface . after replacing @xmath7 with a finite index subgroup if necessary we can suppose that @xmath344 and @xmath52 is central in @xmath7 . since @xmath648 can not be cyclic ( as ( iii ) does not hold for @xmath645 ) , the group @xmath648 is either a non - abelian free group or a closed hyperbolic surface group . in particular , @xmath648 has trivial center , which means that @xmath52 is the center of @xmath7 . therefore @xmath52 is characteristic in @xmath7 and so @xmath649 . the group @xmath648 is acylindrically hyperbolic and has finite index in the quotient @xmath53 . by lemma [ lem : com ] @xmath53 is also acylindrically hyperbolic and hence ( ii@xmath639 ) holds for @xmath1 . finally assume that ( i@xmath639 ) holds for @xmath645 . again , by lemma [ lem : com ] , @xmath1 is acylindrically hyperbolic . if @xmath1 has non - trivial finite radical , then @xmath650 as @xmath651 . therefore , by theorem [ thm : elem - prop - ah].(e ) , @xmath1 contains @xmath638 , which contradicts lemma [ epstein ] . hence @xmath1 satisfies ( i@xmath639 ) . thus we can ( and will ) assume that @xmath1 is a subgroup of @xmath55 for an orientable closed @xmath0-manifold @xmath54 . by the kneser - milnor theorem , @xmath54 decomposes as a connected sum @xmath652 of prime @xmath0-manifolds . consequently , @xmath653 . suppose , first , that @xmath1 is not conjugate to a subgroup of @xmath654 for any @xmath177 . then by kurosh theorem @xmath1 is a free product of two non - trivial groups and whence ( i@xmath639 ) or ( iii ) holds in this case by lemma [ lem : at ] , because the action of this free product on the associated bass - serre tree is @xmath153-acylindrical in the sense of sela and has no global fixed points . now , assume that @xmath1 is conjugate to a subgroup of some @xmath654 . since @xmath54 is closed and orientable , so is @xmath655 . recall that every orientable prime manifold , other than @xmath656 , is irreducible ( cf . * lemma 3.13 ) ) . since @xmath657 is cyclic , it suffices to consider the case when @xmath1 is isomorphic to a subgroup of a closed orientable irreducible @xmath0-manifold . from now on , we assume that @xmath658 for a closed orientable irreducible @xmath0-manifold @xmath54 . recall that if the fundamental group of such a manifold @xmath54 is infinite , then it is torsion - free ( see , for example , ( * ? ? ? * ( c.2 ) ) ) . thus we can also assume that @xmath55 is torsion - free . in particular , in ( i@xmath639 ) it will suffice to prove acylindrical hyperbolicity ; triviality of the finite radical will follow from the absence of torsion . by lemma [ wz ] either @xmath54 has a finite - sheeted covering space that is a torus bundle over a circle or the action of @xmath55 on the bass - serre tree @xmath19 associated to the jsj decomposition of @xmath55 is acylindrical in the sense of sela . in the former case ( iii ) holds . in the latter case , by lemma [ lem : at ] , @xmath1 either satisfies one of the conditions ( i@xmath639 ) , ( iii ) , or fixes a vertex of @xmath19 . thus it remains to consider the case when @xmath1 is a subgroup of the fundamental group of a seifert fibered piece or an atoroidal piece of the jsj decomposition . suppose , first , that @xmath1 is a subgroup of the fundamental group of a seifert fibered space @xmath106 . if @xmath659 is finite , we are done . if @xmath659 is infinite , then it contains an infinite normal cyclic subgroup @xmath52 such that the quotient @xmath660 contains a surface subgroup of finite index ( see ( * ? ? ? 1.6 ) ) . in particular , @xmath60 is either virtually @xmath661 for @xmath662 or is a non - elementary hyperbolic group . if @xmath60 is virtually @xmath661 for @xmath662 , so is @xmath663 , where @xmath664 . if @xmath60 is non - elementary hyperbolic , we fix any finite generating set @xmath10 of @xmath60 and note that the natural action of @xmath663 on the cayley graph @xmath190 is acylindrical since this is true for the action of @xmath60 . by theorem [ class ] , the action of @xmath663 on @xmath190 is elliptic ( in which case @xmath663 is finite as the action is proper ) , or @xmath663 is virtually cyclic , or @xmath663 is acylindrically hyperbolic . summarizing , we conclude that , in any case , @xmath663 is either virtually @xmath661 for @xmath662 or acylindrically hyperbolic . thus if @xmath665 , @xmath1 satisfies ( ii@xmath639 ) or ( iii ) . otherwise , @xmath666 , @xmath667 , and again ( i@xmath639 ) or ( iii ) holds . now assume that @xmath1 fixes a vertex of @xmath19 corresponding to an atoroidal piece . as we explained above , in this case @xmath1 is a subgroup of a group @xmath668 hyperbolic relative to free abelian subgroups of rank @xmath13 . let @xmath669 be the collection of peripheral subgroups of @xmath668 , @xmath10 a finite generating set of @xmath668 , @xmath670 . then every @xmath671 is hyperbolically embedded in @xmath668 ( see ( * ? ? ? * prop . 4.28 and remark 4.26 ) ) . if @xmath672 , fix any @xmath606 . since @xmath1 is torsion - free , by ( * 4.20 ) the element @xmath107 is either conjugate to an element of @xmath671 for some @xmath177 , or acts hyperbolically on @xmath673 ( note that the term hyperbolic element " is used in a slightly different sense in @xcite ) . again , we consider two cases . if @xmath107 is conjugate to an element of @xmath671 for some @xmath177 , then passing from @xmath1 to its conjugate if necessary , we can assume that @xmath674 is infinite . if @xmath675 , then we have ( iii ) . otherwise @xmath1 contains a proper infinite hyperbolically embedded subgroup by lemma [ lem:613 ] , and hence @xmath1 is acylindrically hyperbolic by theorem [ acyl ] . finally assume that @xmath107 is hyperbolic with respect to the action on @xmath673 . in particular , the action of @xmath1 is not elliptic . by ( 5.2 ) , the action of @xmath668 ( and , hence , of @xmath1 ) on the cayley graph @xmath673 is acylindrical . applying now theorem [ class ] we conclude that @xmath1 is either virtually cyclic or acylindrically hyperbolic . this completes the proof of the theorem . let @xmath54 be a compact irreducible @xmath0-manifold and @xmath676 . suppose that @xmath1 is neither virtually polycyclic nor acylindrically hyperbolic . then , by theorem [ main-3-dim ] , @xmath1 contains an infinite cyclic normal subgroup @xmath52 . hence , since @xmath54 is irreducible , we can use ( * ? ? ? 1.39 ) claiming that @xmath54 is a seifert fibered manifold . suppose that @xmath78 is a _ finite _ simplicial graph with vertex set @xmath677 , and @xmath678 is a family of _ non - trivial _ groups ( called _ vertex groups _ ) . the _ graph product _ @xmath679 , of this collection of groups with respect to @xmath78 , is the group obtained from the free product of the @xmath336 , @xmath680 , by adding the relations @xmath681=1 \text { for all } g_v\in g_v,\ , g_u\in g_u \text { whenever $ \{v , u\}$ is an edge of } { \gamma}.\ ] ] graph product of groups is a natural group - theoretic construction generalizing free products ( when @xmath78 has no edges ) and direct products ( when @xmath78 is a complete graph ) of groups @xmath336 , @xmath680 . graph products were first introduced and studied by e. green in her ph.d . thesis @xcite . further properties of graph products have been investigated in the works of hermiller and meier @xcite , hsu and wise @xcite , januszkiewicz and wiatkowski @xcite , and antoln and minasyan @xcite . recall that the _ link _ @xmath682 , of a vertex @xmath683 , is the set of all vertices of @xmath78 that are adjacent to @xmath71 ( excluding @xmath71 itself ) ; in other words , @xmath684 . for a non - empty subset @xmath685 , we define @xmath686 . note that @xmath687 . for any subset @xmath688 the subgroup @xmath689 , generated by @xmath690 , is called _ full _ ; according to a standard convention , @xmath691 . by the normal form theorem for graph products ( see @xcite or @xcite ) , @xmath692 is the graph product of the family @xmath693 with respect to the full subgraph @xmath694 of @xmath78 , spanned on the vertices from @xmath26 . it is easy to see that there is a canonical retraction @xmath695 , defined ( on the generators of @xmath1 ) by @xmath696 for each @xmath697 with @xmath698 , and @xmath699 for each @xmath700 with @xmath701 . any conjugate of a full subgroup in @xmath1 is called _ parabolic_. parabolic subgroups of graph products were studied and used by antoln and the first author in @xcite . in this subsection we summarize some of the known properties of parabolic subgroups of graph products . for a subset @xmath702 , @xmath703 and @xmath704 will denote the centralizer and the normalizer of @xmath10 in @xmath1 respectively . all of the claims in the lemma below were proved in section 3 of @xcite . [ lem : parab_props ] * * if @xmath705 and @xmath706 are such that @xmath707 then @xmath708 . * if @xmath709 is a parabolic subgroup of @xmath1 and @xmath710 for some @xmath31 , then @xmath711 . * if @xmath712 , where @xmath713 and @xmath714 , then @xmath715 is a parabolic subgroup of @xmath1 . * the intersection of two parabolic subgroups of @xmath1 is also a parabolic subgroup of @xmath1 . suppose that @xmath712 is a parabolic subgroup of @xmath1 , for some @xmath713 and @xmath714 . we define the _ parabolic dimension _ @xmath716 of @xmath709 to be the number of elements in @xmath106 . part ( i ) of lemma [ lem : parab_props ] shows that the parabolic dimension is well - defined as @xmath106 is completely determined by @xmath709 . [ lem : pdim ] let @xmath709 and @xmath717 be parabolic subgroups of @xmath1 . * if @xmath718 then @xmath719 with equality if and only if @xmath720 . * if @xmath721 then @xmath722 . first note that , according to lemma [ lem : parab_props].(iv ) , @xmath723 is also a parabolic subgroup of @xmath1 . therefore @xmath724 is defined and part ( b ) is an immediate consequence of part ( a ) . to prove part ( a ) , suppose that @xmath722 and @xmath725 , @xmath726 for some @xmath705 , @xmath706 . lemma [ lem : parab_props].(i ) implies that @xmath708 , hence @xmath727 . now , if @xmath728 then @xmath729 and thus @xmath730 , where @xmath731 . by lemma [ lem : parab_props].(ii ) , the inclusion of @xmath709 in @xmath732 yields that @xmath733 , as required . by part ( iv ) of lemma [ lem : parab_props ] the intersection of finitely many parabolic subgroups is again a parabolic subgroup . in fact a more general statement holds : [ lem : inter_parab_fam ] intersection of any family of parabolic subgroups of @xmath1 is equal to the intersection of a finite subfamily . in particular , this intersection is itself a parabolic subgroup of @xmath1 . consider a family @xmath734 of parabolic subgroups of @xmath1 . for any finite subset @xmath735 of @xmath317 , the intersection @xmath736 is a parabolic subgroup of @xmath1 , thus its parabolic dimension is defined . since this dimension is a non - negative integer , and non - negative integers are well - ordered , the function , which assigns to each finite subset @xmath737 the value @xmath738 , reaches its minimum on some finite subset @xmath739 . consider any @xmath740 and set @xmath741 . then @xmath742 by the choice of @xmath743 , hence lemma [ lem : pdim].(b ) implies that @xmath744 . since the latter is true for all @xmath740 we can conclude that @xmath745 . in ( * ? ? ? 3.10 ) it was proved that any subset @xmath702 is contained in a unique minimal parabolic subgroup @xmath746 , which is called _ the parabolic closure _ of @xmath10 . the next lemma lists two important properties of parabolic closures , which were also established in ( * ? ? ? * sec . 3 ) . [ lem : parab_clos ] let @xmath702 be an arbitrary subset and let @xmath747 be its parabolic closure in the graph product @xmath1 . * the normalizer @xmath704 is contained in the normalizer @xmath748 . * there exists a finite subset @xmath749 such that @xmath750 . [ lem : par_clos_in_spec ] consider any subset @xmath751 and the corresponding full subgroup @xmath692 of @xmath1 . as we know , @xmath692 is equal to the graph product @xmath752 , where @xmath753 is the full subgraph of @xmath78 spanned by @xmath26 , and @xmath693 . then for an arbitrary subset @xmath754 , the parabolic closure @xmath755 of @xmath10 in @xmath756 coincides with the parabolic closure @xmath746 of @xmath10 in @xmath679 . indeed , suppose that @xmath757 for some @xmath758 and @xmath714 . since @xmath754 and @xmath692 is a parabolic subgroup of @xmath1 , we have @xmath759 , implying that @xmath760 by lemma [ lem : parab_props].(i ) . let @xmath761 be the canonical retraction . the inclusions @xmath762 , yield that @xmath763 , where @xmath764 . hence @xmath765 is a parabolic subgroup of @xmath692 containing @xmath10 . consequently @xmath766 . on the other hand , @xmath767 because any parabolic subgroup of @xmath756 is also a parabolic subgroup of @xmath679 . therefore @xmath768 . [ df : join ] let @xmath769 be a parabolic subgroup of @xmath1 , where @xmath713 and @xmath714 . we shall say that @xmath621 is a _ join subgroup _ of @xmath1 if there are non - empty disjoint subsets @xmath770 such that @xmath771 and @xmath772 . if , in addition , both @xmath692 and @xmath773 are infinite then we will say that @xmath621 is a _ principal join subgroup _ of @xmath1 . in other words , a join subgroup is a parabolic subgroup which naturally splits as a direct product of smaller parabolic subgroups , and in a principal join subgroup these smaller parabolic subgroups must be infinite . using the terminology from @xcite , the _ essential support _ @xmath774 of a subset @xmath702 is defined as the smallest subset @xmath106 of @xmath775 such that @xmath10 is contained in a conjugate of @xmath776 in @xmath1 . equivalently , @xmath777 if @xmath778 for some @xmath714 . a subset @xmath304 of @xmath677 is said to be _ irreducible _ if @xmath304 can not be represented as a union of disjoint non - empty subsets @xmath779 such that @xmath772 . thus @xmath304 is irreducible if and only if @xmath780 is an irreducible graph ( as defined in subsection [ subsec : gp ] ) , which is also equivalent to @xmath781 not being a join subgroup of @xmath1 . the above definitions together with lemma [ lem : parab_props].(i ) immediately imply the following fact : [ rem : cont_in_join ] suppose that @xmath10 is a subset of the graph product @xmath1 . then @xmath10 is contained in a join subgroup of @xmath1 if and only if there are non - empty disjoint subsets @xmath770 such that @xmath772 and @xmath782 . similarly , @xmath10 is contained in a principal join subgroup of @xmath1 if and only if there exist non - empty disjoint subsets @xmath783 such that @xmath772 , @xmath782 and @xmath784 , @xmath785 . [ lem : h_in_join ] let @xmath60 and @xmath7 be non - trivial subgroups of @xmath1 such that @xmath60 normalizes @xmath7 and @xmath60 is not contained in the parabolic closure @xmath786 . then @xmath60 is contained in a join subgroup of @xmath1 . moreover , if @xmath787 and @xmath788 then @xmath60 is contained in a principal join subgroup of @xmath1 . by definition , @xmath789 for some non - empty subset @xmath790 and an element @xmath714 . by lemma [ lem : parab_clos].(i ) , since @xmath709 is the parabolic closure of @xmath7 , @xmath791 in @xmath1 . and , according to lemma [ lem : parab_props].(iii ) , @xmath792 . since @xmath60 is contained in @xmath748 but not in @xmath709 , it follows that @xmath793 . hence @xmath748 is a join subgroup of @xmath1 containing @xmath60 and the first claim is proved . now , if @xmath7 is infinite then @xmath692 is infinite . and if @xmath788 then @xmath794 , and so @xmath795 . recalling that @xmath692 commutes with @xmath773 ( by definition of @xmath27 ) , we see that @xmath796 , hence @xmath797 . thus @xmath748 is a principal join subgroup of @xmath1 containing @xmath60 , and the second claim of the lemma also holds . as before , we fix a finite simplicial graph @xmath78 with the vertex set @xmath775 and consider the graph product @xmath679 , of a family of non - trivial groups @xmath798 , with respect to @xmath78 . the definition of graph product immediately implies that for any @xmath799 the group @xmath1 naturally splits as the free amalgamated product : @xmath800 , where @xmath801 , @xmath802 and @xmath803 ( cf . * lemma 3.20 ) ) . it follows that @xmath1 acts ( simplicially by isometries and without edge inversions ) on the bass - serre tree @xmath19 associated to this splitting , and full vertex and edge stabilizers for this action are parabolic subgroups of @xmath1 ( conjugates of @xmath692 , @xmath773 and @xmath804 ) . [ lem : h_has_hyp_elt ] consider a subgroup @xmath132 and a vertex @xmath805 . suppose that @xmath806 in @xmath78 . let @xmath807 , @xmath808 and @xmath809 . as we know , @xmath1 splits as an amalgamated product @xmath810 and acts on the corresponding simplicial bass - serre tree @xmath19 . then there exists an element @xmath811 which acts as a hyperbolic isometry of @xmath19 . arguing by contradiction , suppose that @xmath60 contains no hyperbolic elements ; then every element of @xmath60 is elliptic . by lemma [ lem : parab_clos].(ii ) , there is a finite subset @xmath812 such that @xmath813 . the subgroup @xmath814 is finitely generated and every element of @xmath815 fixes a vertex of @xmath220 , therefore @xmath815 fixes some vertex of @xmath220 ( see ( * ? ? ? * i.6.5 , cor . 3 ) ) . but full @xmath1-stabilizers of vertices of @xmath220 are conjugates of @xmath692 and @xmath773 in @xmath1 , which are parabolic subgroups of @xmath1 . therefore there is @xmath714 such that @xmath816 where @xmath817 is either @xmath26 or @xmath27 . it follows that @xmath818 one can now apply lemma [ lem : parab_props].(i ) to conclude that @xmath819 , and so @xmath820 by the definition of @xmath26 . therefore @xmath821 and @xmath822 . recall that @xmath823 , thus @xmath824 , which contradicts our assumptions . suppose that a group @xmath1 acts on a tree @xmath19 and let @xmath825 be the metric on @xmath19 . for any two points @xmath826 of @xmath19 , @xmath224 $ ] will denote the geodesic segment between @xmath160 and @xmath225 in @xmath19 . if @xmath827 is a subset of @xmath19 , we will write @xmath828 and @xmath829 to denote the setwise and pointwise stabilizers of @xmath830 in @xmath1 respectively . evidently @xmath831 . [ lem : axis_pst ] consider an element @xmath280 that acts on the tree @xmath19 as a hyperbolic isometry , and let @xmath832 be the axis of @xmath128 . assume that @xmath833)$ ] for some geodesic subsegment @xmath224 $ ] of @xmath834 with @xmath835 . then there exists @xmath836 such that for any points @xmath837 with @xmath838 one has @xmath839)={{\rm pstab}}_g({\mathcal{l}})$ ] . recall that @xmath128 acts on @xmath834 by translation with positive translation length @xmath355 . let @xmath840 , and consider any subsegment @xmath841 $ ] of @xmath834 with @xmath842 . then for some integer @xmath843 , @xmath844 $ ] will be contained in @xmath841 $ ] . consequently one has @xmath845)\subseteq { { \rm pstab}}_g(h^m [ x , y])=h^m { { \rm pstab}}_g([x , y ] ) h^{-m } = h^m { { \rm pstab}}_g({\mathcal{l}})h^{-m}.\ ] ] clearly @xmath846 normalizes @xmath847 , thus @xmath839)\subseteq { { \rm pstab}}_g({\mathcal{l}})$ ] . on the other hand , since @xmath841 $ ] is a subsegment of @xmath834 one sees that @xmath848)$ ] . therefore @xmath839)={{\rm pstab}}_g({\mathcal{l}})$ ] , as claimed . for the remainder of this section we assume that @xmath679 , @xmath132 is a subgroup and @xmath805 is such that @xmath806 in @xmath78 . as before , set @xmath807 , @xmath808 and @xmath809 . let @xmath19 be the bass - serre tree associated to the natural splitting @xmath810 . [ lem : pst - parab ] if @xmath834 is the axis of some hyperbolic element @xmath280 then @xmath847 is a parabolic subgroup of @xmath1 , which is contained in a conjugate of @xmath804 . moreover , there exist vertices @xmath5 on @xmath834 such that @xmath833)$ ] . by definition , @xmath849 , where @xmath850 is the set of all edges of @xmath834 . since each @xmath851 is a conjugate of @xmath804 in @xmath1 , @xmath852 is a parabolic subgroup of @xmath1 by lemma [ lem : inter_parab_fam ] . in fact lemma [ lem : inter_parab_fam ] implies that @xmath853 for some finite collection @xmath854 of edges of @xmath834 . since any finite collection of edges of @xmath834 is contained in a finite subsegment we can find vertices @xmath835 such that @xmath855)$ ] . with the above assumptions on @xmath60 , lemma [ lem : h_has_hyp_elt ] tells us that @xmath60 contains at least one element that acts as a hyperbolic isometry on @xmath19 . the main technical statement of this section is the following proposition : [ prop : pst(axis)-normal ] let @xmath811 be a hyperbolic element such that @xmath856 is minimal , where @xmath834 is the axis of @xmath128 . then the parabolic subgroup @xmath847 is normalized by @xmath60 in @xmath1 . we will first show that for any element @xmath857 , which also acts as a hyperbolic isometry on @xmath19 , @xmath858 , where @xmath859 is the axis of @xmath107 . let @xmath860 and @xmath861 be the constants obtained by applying lemma [ lem : axis_pst ] to @xmath128 and @xmath107 respectively ( this can be done in view of lemma [ lem : pst - parab ] ) . choose a natural number @xmath214 so that @xmath862 and @xmath863 . we need to consider two separate cases . _ the intersection of @xmath834 with @xmath859 contains at least one edge @xmath216 . after replacing @xmath128 and @xmath107 with their inverses , if necessary , we can suppose that both @xmath128 and @xmath107 translate @xmath216 ( cf . [ df : edge_transl ] ) . set @xmath864 and note that the element @xmath865 translates @xmath408 . therefore @xmath369 is hyperbolic and @xmath866 $ ] lies on the axis @xmath867 of @xmath369 . by construction , the edge @xmath216 is contained in the segment @xmath866 $ ] ( see figure [ fig:1 ] ) . observe that @xmath408 is an edge of @xmath834 ( as @xmath834 is @xmath868-invariant and @xmath869 ) , hence the intersection of @xmath867 and @xmath834 contains the segment @xmath870 $ ] , whose length is equal to @xmath871 , which is greater than @xmath872 . therefore lemma [ lem : axis_pst ] implies that @xmath873)={{\rm pstab}}_g({\mathcal{l}}).\ ] ] similarly , as @xmath874 , we have @xmath875 \subseteq { \mathcal{n}}\cap { \mathcal{m}}$ ] , and so @xmath876)={{\rm pstab}}_g({\mathcal{m}}).\ ] ] however , since @xmath834 was chosen so that @xmath856 is minimal , we know that @xmath877 combining with lemma [ lem : pdim].(a ) we get that @xmath878 , and hence yields that @xmath858 . _ case 2 . _ the intersection of @xmath834 with @xmath859 is empty or consists of a single vertex . let @xmath879 and @xmath880 be vertices with the property @xmath881 ; thus ( in the terminology of @xcite ) @xmath882 $ ] is the _ spanning geodesic _ between @xmath834 and @xmath859 . in @xcite it is shown that the element @xmath883 is hyperbolic and the segment @xmath884 $ ] lies on the axis @xmath885 of @xmath369 . by construction , both @xmath141 and @xmath886 belong to this segment ( see figure [ fig:2 ] ) . again , we observe that @xmath887 \subseteq { \mathcal{l}}\cap { \mathcal{n}}$ ] and @xmath888 . therefore lemma [ lem : axis_pst ] tells us that @xmath889)={{\rm pstab}}_g({\mathcal{l}})$ ] . similarly , @xmath890)={{\rm pstab}}_g({\mathcal{m}})$ ] . as before , using minimality of @xmath856 , one can conclude that @xmath891 . let @xmath892 denote the set of axis of the elements of @xmath60 that act as hyperbolic isometries of @xmath19 . we have shown above that @xmath893 note that @xmath60 naturally acts on the set @xmath892 , and so it acts by conjugation on the collection of its subgroups @xmath894 ( if @xmath895 and @xmath859 is the axis of a hyperbolic @xmath857 then @xmath896 , where @xmath897 is the axis of the hyperbolic element @xmath898 ) . it follows that the intersection @xmath899 is normalized by @xmath60 ; but , according to , this intersection is equal to @xmath847 . thus the proposition is proved . [ thm : join ] suppose that @xmath1 , @xmath60 and @xmath19 are as above . let @xmath811 be a hyperbolic element with minimal @xmath856 , where @xmath834 is the axis of @xmath128 . if @xmath847 is non - trivial then @xmath60 is contained in a join subgroup of @xmath1 . and if @xmath900 then @xmath60 is contained in a principal join subgroup of @xmath1 . if we set @xmath901 , then @xmath7 is parabolic by lemma [ lem : pst - parab ] , thus @xmath902 . clearly the infinite cyclic subgroup @xmath868 of @xmath60 trivially intersects @xmath901 , hence @xmath903 . both claims of the theorem now follow from lemma [ lem : h_in_join ] , as @xmath7 is normalized by @xmath60 by proposition [ prop : pst(axis)-normal ] . [ cor : cyc - centr ] let @xmath60 be a subgroup of a graph product @xmath679 such that @xmath904 and @xmath60 is not contained in a join subgroup of @xmath1 . then there is a non - trivial element @xmath811 such that the centralizer @xmath905 is infinite cyclic . take any @xmath805 and define @xmath906 , and the bass - serre tree @xmath19 as above . since @xmath904 and @xmath60 is not contained in a join subgroup of @xmath1 , we see that @xmath806 in @xmath78 . according to lemma [ lem : h_has_hyp_elt ] and theorem [ thm : join ] , there is an element @xmath811 , that acts as a hyperbolic isometry on @xmath19 , such that @xmath847 is trivial , where @xmath834 is the axis of @xmath128 . since @xmath128 has a unique axis ( cf . @xcite ) , it follows that @xmath907 . since @xmath908 , @xmath909 is isomorphic to a subgroup of the infinite dihedral group ( which corresponds to the group of all simplicial isometries of the line @xmath834 ) . hence @xmath905 must be infinite cyclic because it contains the non - trivial central element @xmath128 . again , let @xmath78 be a finite graph with the vertex set @xmath775 and let @xmath1 be the graph product of a family of non - trivial groups @xmath910 with respect to @xmath78 . the following result can be regarded as an improvement of claim ( ii ) in lemma [ lem : parab_clos ] . [ thm : one_elt ] suppose that @xmath60 is a subgroup of @xmath1 such that @xmath911 is irreducible . then there exists an element @xmath811 such that @xmath912 . theorem [ thm : one_elt ] will be derived from the following auxiliary lemma , which is essentially a corollary of theorem [ thm : join ] . [ lem : irred ] assume that @xmath81 , @xmath913 , @xmath775 is irreducible in @xmath78 and @xmath914 . then there exists a non - trivial element @xmath811 such that @xmath905 is infinite cyclic and @xmath915 . starting with @xmath78 we construct a new graph @xmath916 as follows . let @xmath917 . take a @xmath41-element set @xmath918 and let the set of vertices @xmath919 of @xmath916 be defined by @xmath920 . the set of edges @xmath921 of @xmath916 ( which we identify with a subset of @xmath922 ) is defined by @xmath923 where @xmath618 is the set of edges of @xmath78 . thus @xmath78 is a full subgraph of @xmath916 and @xmath924 , @xmath925 . basically , @xmath916 is obtained from @xmath78 by adding a new vertex @xmath926 for each vertex @xmath927 of @xmath78 and connecting @xmath926 by an edge with every @xmath448 except for @xmath928 . for each @xmath929 let @xmath930 be an infinite cyclic group generated by @xmath931 , and set @xmath932 we now have a new graph product @xmath933 of the family @xmath934 with respect to the finite graph @xmath916 , and @xmath935 is a full subgroup of @xmath934 . first , note that , by lemma [ lem : par_clos_in_spec ] , the parabolic closure @xmath936 of @xmath60 in @xmath937 is still equal to @xmath935 . second , let us check that @xmath60 is not contained in a join subgroup of @xmath937 . suppose , on the contrary , that @xmath938 for some @xmath939 and @xmath940 , where @xmath941 such that @xmath942 are disjoint , non - empty and @xmath943 . then @xmath944 and so @xmath945 by lemma [ lem : parab_props].(i ) . note that @xmath775 is an irreducible subset of @xmath916 ( because it is irreducible in @xmath78 and @xmath78 is a full subgraph of @xmath916 ) . therefore either @xmath946 or @xmath947 . without loss of generality assume that @xmath947 , so that @xmath948 . hence @xmath949 and , as @xmath950 , there must exist @xmath929 with @xmath951 . however , @xmath952 and @xmath953 by construction , which contradicts @xmath943 . thus @xmath60 is not contained in a join subgroup of @xmath937 and all of the assumptions of corollary [ cor : cyc - centr ] are satisfied . therefore there exists @xmath954 such that @xmath955 is infinite cyclic . let us prove that @xmath915 . indeed , otherwise @xmath956 for some proper subset @xmath957 and @xmath714 . then @xmath958 for some @xmath929 , hence @xmath926 is adjacent to every vertex from @xmath106 in @xmath916 . consequently , @xmath959 . since @xmath931 lies in the kernel of the canonical retraction of @xmath937 onto @xmath935 , we have @xmath960 in @xmath937 . this implies that the infinite cyclic group @xmath955 contains the subgroup @xmath961 , which is naturally isomorphic to @xmath962 . as the latter is impossible , we conclude that @xmath915 , as claimed . we are now ready to prove theorem [ thm : one_elt ] . after replacing @xmath60 with its conjugate , we can assume that @xmath963 for some @xmath713 . as we know , @xmath776 is itself the graph product of the family @xmath964 with respect to the full subgraph @xmath965 of @xmath78 , spanned by the vertices from @xmath106 . moreover , @xmath966 since every parabolic subgroup of @xmath776 is also a parabolic subgroup of @xmath1 . if @xmath967 then the statement obviously holds , so we can assume that @xmath968 . since @xmath106 is irreducible , by lemma [ lem : irred ] there is @xmath811 such that the parabolic closure of @xmath969 in @xmath970 is @xmath776 . it remains to apply lemma [ lem : par_clos_in_spec ] to conclude that @xmath971 , as claimed . let us now give an example showing that in theorem [ thm : one_elt ] it is indeed necessary to assume that @xmath911 is irreducible . let @xmath492 be a group with an element @xmath972 of prime order @xmath973 . let @xmath974 be the direct product of @xmath975 copies of @xmath492 . then @xmath1 is naturally isomorphic to the graph product of @xmath975 copies of @xmath492 with respect to the complete graph @xmath78 on @xmath975 vertices . set @xmath976 , @xmath977 and @xmath978 . clearly @xmath913 and so @xmath979 . by construction , for any element @xmath811 there are @xmath980 such that @xmath981 in @xmath1 . it is easy to see that if @xmath982 then @xmath983 and so @xmath984 . on the other hand , if @xmath985 then @xmath986 for some @xmath987 , hence @xmath988 in @xmath1 and @xmath128 belongs to a proper parabolic subgroup of @xmath1 . thus @xmath989 for all @xmath811 . the following is a consequence of theorem [ thm : join ] and corollary [ prop : wpd - crit ] . [ cor : wpd_in_gp ] suppose that @xmath60 is a subgroup of @xmath679 and @xmath805 is such that @xmath806 in @xmath78 . let @xmath807 , @xmath808 and @xmath809 . let @xmath220 be the bass - serre tree corresponding to the natural splitting @xmath810 . assume that @xmath60 is not contained in a principal join subgroup of @xmath1 . then there exists @xmath811 which is a wpd element ( for the action of @xmath1 on @xmath19 ) and induces a hyperbolic isometry of @xmath19 . thus , if @xmath60 is not virtually cyclic then @xmath189 . by lemma [ lem : h_has_hyp_elt ] , at least one element of @xmath60 induces a hyperbolic isometry of @xmath19 . hence we can apply theorem [ thm : join ] to find a hyperbolic element @xmath811 such that @xmath990 , where @xmath834 denotes the axis of @xmath128 in @xmath19 . lemma [ lem : pst - parab ] claims that @xmath991)={{\rm pstab}}_g(\{u , v\})$ ] for some vertices @xmath992 . therefore corollary [ prop : wpd - crit ] applies , telling us that @xmath128 is a wpd element for the action of @xmath1 on @xmath19 . clearly the latter yields that @xmath811 is also a wpd element for the action of @xmath60 on @xmath19 . the last claim of the corollary now follows from theorem [ acyl ] . if @xmath78 is irreducible , @xmath993 and @xmath994 ( equivalently , @xmath913 ) then any vertex @xmath799 will satisfy the assumptions of corollary [ cor : wpd_in_gp ] . thus we get the following : [ cor : wpd_in_gp - simplified ] let @xmath78 be a finite irreducible graph with at least two vertices and let @xmath995 be the graph product of a family of non - trivial groups @xmath996 with respect to @xmath78 . then there is a simplicial tree @xmath19 on which @xmath1 acts coboundedly and by simplicial isometries such that the following holds . if @xmath81 is subgroup with @xmath913 then @xmath60 contains a hyperbolic wpd element for the action of @xmath1 on @xmath19 . thus either @xmath60 is virtually cyclic or @xmath82 . this theorem is an immediate consequence of corollary [ cor : wpd_in_gp - simplified ] . in the case of right angled artin groups theorem [ cor : gp - hyp ] would follow from theorem 5.2 of @xcite , because if a subgroup of a cat(@xmath17 ) group contains a rank one element , then it is either virtually cyclic or acylindrically hyperbolic ( see ( * ? ? ? 3.13 , thm . 5.6 ) ) . unfortunately the proof of this theorem , given in @xcite , is invalid : the third paragraph of this proof claims that if @xmath997 are elements of a right angled artin group @xmath1 and @xmath998 is cyclically reduced then in the product @xmath999 cancellations can only occur between the letters from @xmath998 and the letters from @xmath128 , which is not always the case ( one can easily construct counterexamples ) . nevertheless , the statement is still true : one can use corollary [ cor : cyc - centr ] above to fix the argument from @xcite . corollary [ thm : gpacyl ] is a direct consequence of theorem [ cor : gp - hyp ] . as we already mentioned in section [ sec : results ] , it can be considered as another instance of a more general phenomenon : irreducibility " of nice " non - positively curved groups ( or spaces ) often implies the existence of hyperbolic directions " in an appropriate sense . for groups acting on @xmath84 spaces , the standard formalization of the latter condition is the existence of a _ rank one element _ , i.e. , an axial hyperbolic isometry none of whose axes bounds a flat half - plane . the notion of a rank one element originates in the celebrated rank rigidity theorem for hadamard manifolds proved by ballmann , brin , burns , eberlein , and spatzier ( for more information and detailed references we refer to @xcite ) : _ let @xmath1 be a discrete group acting properly and cocompactly on an irreducible hadamard manifold @xmath54 , which is not a higher rank symmetric space ; then @xmath1 contains a rank one isometry . _ we recall that a hadamard manifold is a simply connected complete riemannian manifold of non - positive curvature , and such a manifold is said to be irreducible if it does not admit a nontrivial decomposition as a metric product of two manifolds . motivated by this theorem , ballman and buyalo @xcite suggested the following : let @xmath10 be a locally compact geodesically complete @xmath84 space and let @xmath1 be an infinite discrete group acting properly and cocompactly on @xmath10 . if @xmath10 is irreducible and is not a higher rank symmetric space or a euclidean building of dimension at least @xmath13 , then @xmath1 contains a rank one isometry . caprace and sageev @xcite confirmed this conjecture for @xmath84 cube complexes . more precisely , they showed that _ if an infinite discrete group @xmath1 acts properly and cocompactly on a locally compact geodesically complete @xmath84 cube complex @xmath10 , then @xmath10 is a product of two geodesically complete unbounded convex subcomplexes or @xmath1 contains a rank one isometry . _ ( neither higher rank symmetric spaces nor euclidean buildings of dimension at least @xmath13 occur in these settings . ) any rank one element @xmath107 in a group @xmath1 , acting properly on proper @xmath84 space , is contained in a virtually cyclic subgroup @xmath1000 which is hyperbolically embedded in @xmath1 @xcite . such subgroups can be thought of as a formalization of hyperbolic directions " in the context of abstract groups ( for details and the relation to _ generalized loxodromic elements _ see ( * ? ? ? * section 6 ) ) . recall that the existence of a virtually cyclic subgroup @xmath1001 implies that @xmath1 is either virtually cyclic ( if @xmath1002 ) or acylindrically hyperbolic . thus the caprace sageev result @xcite , being applied to a right angled artin ( respectively , coxeter ) group acting on the universal cover of its salvetti ( respectively , davis ) complex , yields corollary [ thm : gpacyl ] . note , however , that theorem [ cor : gp - hyp ] generalizes this in two directions : it deals with arbitrary subgroups ( which corresponds to non - cocompact actions in the settings of the caprace - sageev theorem ) and more general graph products which may not act properly on any @xmath84 spaces . in fact , theorem [ thm : join ] , under the assumptions of theorem [ cor : gp - hyp ] , produces an action of the subgroup @xmath60 of a graph product @xmath1 on a simplicial tree @xmath19 so that the pointwise stabilizer of a finite segment of the axis of some hyperbolic element @xmath811 is finite . since a tree can not contain half - flats , the latter condition can be thought of as an additional requirement one should include in the definition of a rank one isometry for discrete non - proper actions on @xmath84 spaces . [ def : n ] let @xmath885 denote the class of all groups @xmath1 with the following property : @xmath1 contains two infinite normal subgroups @xmath1003 such that @xmath1004 . [ lem : sn ] the intersection @xmath1005 is empty . suppose that @xmath1006 . thus @xmath1 contains two infinite normal subgroups @xmath1007 such that @xmath1008 is finite . let @xmath1009 , and observe that @xmath1010 . by theorem [ thm : elem - prop - ah].(c ) , we know that @xmath7 is acylindrically hyperbolic . therefore , by lemma [ lem : com ] , @xmath1011 . however this contradicts theorem [ thm : elem - prop - ah].(b ) because @xmath1012 for @xmath104 . recall that the relation @xmath188 , between two groups , denotes commensurability up to finite kernels ( see the paragraph above lemma [ lem : com ] ) . using theorem [ cor : gp - hyp ] we obtain the following classification of subgroups of graph products . [ thm : subgroups ] let @xmath60 be a subgroup of a graph product @xmath679 of non - trivial groups with respect to some finite graph @xmath78 . then at least one of the following holds : * there is a short exact sequence @xmath1013 , where @xmath621 is finite and @xmath106 is isomorphic to a subgroup of a vertex group . in particular , @xmath1014 ; * @xmath60 is virtually cyclic ; * @xmath1015 ; * @xmath189 . moreover , the possibilities ( b),(c ) , and ( d ) are mutually exclusive . the argument will proceed by induction on @xmath1016 . if @xmath1017 then ( a ) holds trivially , so we can assume that @xmath1018 and the statement has already been established for subgroups of graph products with at most @xmath477 vertices . without loss of generality we can assume that @xmath60 is not contained in a proper parabolic subgroup of @xmath1 , i.e. , @xmath979 . let us first prove that at least one of ( a)(d ) holds . suppose that @xmath60 is not virtually cyclic and @xmath1019 . then , by theorem [ cor : gp - hyp ] , there exists a decomposition @xmath1020 , such that @xmath1021 and @xmath772 . thus @xmath1 naturally splits as the direct product @xmath1022 . let @xmath1023 and @xmath1024 . clearly @xmath1025 for @xmath104 and @xmath87 . if both @xmath1026 and @xmath1027 are infinite , we have ( c ) . otherwise @xmath1028 for some @xmath1029 , and then @xmath60 splits as @xmath1030 where @xmath1031 a subgroup of @xmath692 or @xmath773 . by induction , @xmath1031 satisfies one of ( a)(d ) . if @xmath1031 satisfies ( a ) then evidently the same is true for @xmath60 , because the kernel of the epimorphism @xmath1032 is finite . by the same reason , @xmath1033 , hence @xmath1034 is not virtually cyclic and @xmath1035 ( by lemma [ lem : com ] ) . so , it remains to consider the case when @xmath1034 satisfies ( c ) , i.e. , there are infinite normal subgroups @xmath1036 such that @xmath1037 . then @xmath1038 are infinite normal subgroups of @xmath60 and @xmath1039 which shows that @xmath60 satisfies ( c ) . it remains to note that ( c ) and ( d ) are mutually exclusive by lemma [ lem : sn ] , and the fact that ( b ) is incompatible with ( c ) and ( d ) is obvious . corollary [ cor : raag_in_x ] from section [ sec : results ] is special case of theorem [ thm : subgroups ] , because any right angled artin group is a graph product of infinite cyclic groups ( we also need to use the well - known fact that right angled artin groups are torsion - free ) . the goal of this section is to use theorem [ main-3d ] to obtain some new results about @xmath0-manifold groups . we begin by proving corollaries [ 3-dim - cor-1 ] and [ 3-dim - cor-2 ] . if @xmath1 is of type ( iii ) , it is inner amenable since every amenable group is inner amenable . further assume that @xmath1 is of type ( ii ) . since @xmath52 is amenable , there exists a finitely additive @xmath52-invariant probability measure @xmath1040 $ ] . given a subset @xmath1041 , we let @xmath1042 . we define a probability measure on @xmath1043 by the rule @xmath1044 for every @xmath1045 . it is easy to see that @xmath1046 is finitely additive and invariant under conjugation by elements of @xmath1 ( indeed conjugation by an element of @xmath1 preserves the collection @xmath1047 for every @xmath1041 ) . thus every group of type ( ii ) is inner amenable . finally suppose that @xmath1 is of type ( i ) , then @xmath1 has trivial finite radical ( see theorem [ main-3d].(i@xmath639 ) ) and hence @xmath1 is not inner amenable by theorem [ thm : prop - ah-2 ] . using corollary [ cor : geom ] , we obtain the following . let @xmath54 be a compact irreducible @xmath0-manifold . suppose that @xmath55 is inner amenable . then either @xmath54 is seifert fibered or @xmath605 is amenable . recall that a countable group belongs to the class @xmath1048 if its quotient modulo the amenable radical belongs to @xmath88 @xcite . [ cor : ganc-3 m ] for any @xmath51 , the following holds . 1 . @xmath1049 iff @xmath96 iff @xmath1 is of type ( i ) . 2 . @xmath1050 iff @xmath1 is non - amenable iff @xmath1 is of type ( i ) or ( ii ) . recall that every @xmath1051 is infinite and the amenable radical of any group @xmath1051 is finite @xcite . thus @xmath1052 whenever @xmath24 is of type ( ii ) or ( iii ) . on the other hand , @xmath1053 whenever @xmath1 is of type ( i ) by theorem [ thm : prop - ah-3 ] . this proves ( a ) ; ( b ) obviously follows from ( a ) . it is proved in ( * ? ? ? 7.6 and 7.9 ) that being in @xmath88 and @xmath1048 is a measure equivalence invariant . on the other hand , it is well known that being amenable is also a measure equivalence invariant ( see , for example , @xcite ) . thus the claim follows from corollary [ cor : ganc-3 m ] . we mention one more application . for the definition and details about conjugacy growth we refer to @xcite . recall that , in general , any non - decreasing function @xmath1054 bounded from above by an exponential function can be realized up to a standard equivalence as the conjugacy growth function of a finitely generated group @xcite . for @xmath0-manifolds groups , the situation is more rigid . let @xmath54 be a compact @xmath0-manifold . then @xmath55 has either exponential or polynomially bounded conjugacy growth . moreover , the conjugacy growth function of @xmath55 is polynomially bounded if and only if @xmath55 is virtually nilpotent . by theorem [ thm : prop - ah-4 ] , the conjugacy growth of @xmath55 is exponential if @xmath55 has type ( i ) or ( ii ) . on the other hand , it is proved in @xcite that if @xmath55 is of type ( iii ) , its conjugacy growth is either exponential or polynomially bounded and the latter possibility happens iff @xmath55 is virtually nilpotent . it is worth noting that , in some cases , one can obtain results similar to the above corollaries using relative hyperbolicity . for example , it is not hard to prove that if @xmath54 is a closed oriented @xmath0-manifold with a hyperbolic piece in the jsj decomposition , then @xmath55 is hyperbolic relative to proper subgroups . however this approach does not always work ( for example for graph manifolds ) . let @xmath1055 be the class of all groups @xmath1 containing a subnormal subgroup @xmath7 and a finite subgroup @xmath1056 such that @xmath1057 splits as a direct product two infinite groups . let also @xmath1058 be the class defined in definition [ def : n ] . @xmath1059 . if @xmath1 contains two infinite normal subgroups @xmath1003 such that @xmath1004 , then @xmath1060 is a normal subgroup of @xmath1 and @xmath1061 decomposes as a direct product of two infinite groups ( isomorphic to @xmath1062 and @xmath1063 ) . the next observation is an easy consequence of known results . [ cdn ] 1 . 2 . @xmath1065 . let @xmath1066 be a group containing a subnormal subgroup @xmath7 and a finite subgroup @xmath1056 such that @xmath1057 splits as a direct product two infinite groups . suppose first that @xmath1067 . the class @xmath18 is closed under taking infinite subnormal subgroups by ( * ? ? ? hence @xmath1068 . further we have @xmath1069 by ( * ? ? ? * lemma 7.3 ) . however this contradicts ( * ? ? ? 7.10.(iii ) ) , which states that no group from @xmath18 decomposes as a direct product of two infinite groups . therefore @xmath1064 . suppose now that @xmath1070 . by ( * ? ? ? * thm 3.4 ) , every infinite normal subgroup of a group from @xmath1071 itself belongs to @xmath1071 . hence we obtain @xmath1072 as above . further by ( * ? ? ? * lemma 2.8 ) , @xmath7 either belongs to @xmath18 or has non - vanishing first @xmath94-betti number . we have already shown that @xmath1068 is impossible . if @xmath1073 , then we have @xmath1074 , say by ( * ? ? ? * thm . 7.34 ) . however the latter inequality is impossible since @xmath1057 decomposes as a direct product of two infinite groups ( see ( * ? ? ? 6.54.(5 ) ) ) . claim ( a ) follows from corollary [ cor : ganc-3m].(a ) , so it remains to prove claim ( b ) . let @xmath1 be a graph product of amenable groups , let @xmath81 , and let @xmath1075 . if @xmath60 is amenable , then so is @xmath621 and hence @xmath621 does not belong to either of the classes @xmath14 , @xmath88 , @xmath1071 . thus we can assume that @xmath60 is non - amenable . then , according to theorem [ thm : subgroups ] , either @xmath1076 or @xmath82 . assume , first , that @xmath1076 . the class @xmath885 is obviously closed under taking subgroups of finite index , quotients modulo finite normal subgroups , and extensions with finite kernels . thus @xmath1015 implies that @xmath621 contains a finite index normal subgroup @xmath1077 . obviously this implies that @xmath1078 . hence @xmath1079 by lemma [ cdn ] . we also have @xmath1080 by lemmas [ lem : com ] and [ lem : sn ] . finally , if @xmath82 , then @xmath1081 by lemma [ lem : com ] , hence @xmath1082 as @xmath92 by theorem [ thm : prop - ah-3 ] . as demonstrated by theorems [ thm : elem - prop - ah][thm : prop - ah-4 ] , global properties of acylindrically hyperbolic groups resemble those of relatively hyperbolic groups . one can then ask if the same is true for _ local _ properties ( i.e. , properties that pass to finitely generated subgroups ) . if a group @xmath1 is hyperbolic relative to a subgroup @xmath60 then many local properties of @xmath60 are inherited by @xmath1 ( e.g. , if @xmath60 is finitely generated and has solvable word problem then the same is true for @xmath1 see @xcite , if @xmath60 has finite asymptotic dimension then so does @xmath1 see @xcite , etc . ) . however , the same can not be said if @xmath60 is hyperbolically embedded in @xmath1 . indeed , if a property @xmath709 is local , one can simply take some finitely generated group @xmath26 which does not possess this property and set @xmath1083 . then @xmath60 will be hyperbolically embedded into @xmath1 but @xmath1 will not satisfy @xmath709 even if @xmath60 does satisfy it . of course in this example both @xmath60 and @xmath26 are hyperbolically embedded into @xmath1 ( and @xmath1 is hyperbolic relative to @xmath1084 ) , and so , naturally , to ensure `` niceness '' of @xmath1 one should require that both @xmath60 and @xmath26 are `` nice '' . this leads to the following question : let @xmath1 be a finitely generated acylindrically hyperbolic group . suppose that every proper hyperbolically embedded subgroup @xmath1085 satisfies some local property @xmath709 . does @xmath1 also have this property ? our investigation of graph products allows to produce simple examples showing that the answer to the above question is almost always negative . namely , we have the following statement : [ thm : emb ] any finitely generated group @xmath621 can be embedded into a finitely generated group @xmath1 so that all of the following hold : 1 . @xmath197 ; 2 . every proper hyperbolically embedded subgroup @xmath1085 is finitely generated and virtually free ; 3 . @xmath621 is a retract of @xmath1 ; 4 . if @xmath621 is torsion - free then so is @xmath1 ; 5 . if @xmath621 is finitely presented then so is @xmath1 . let @xmath78 be the simplicial path of length @xmath0 with ( consecutive ) vertices @xmath1086 , where @xmath254 and @xmath1087 have valency @xmath153 and @xmath1088 have valency @xmath13 . let @xmath1089 and let @xmath1090 , @xmath1091 and @xmath1092 be infinite cyclic groups generated by elements @xmath1093 and @xmath1094 respectively . let @xmath679 be the graph product of these groups with respect to @xmath78 ( see figure [ fig:4 ] ) . clearly @xmath78 is irreducible and @xmath1 is not virtually cyclic , hence @xmath197 by theorem [ cor : gp - hyp ] . the properties ( c)-(e ) of @xmath1 follow from general properties of graph products , so it remains only to verify property ( b ) . by the definition , @xmath1 splits as the amalgamated free product @xmath1095 , where @xmath1096 , @xmath1097 and @xmath1098 . then @xmath1 acts on the bass - serre tree @xmath19 corresponding to this splitting with vertex stabilizers being conjugates of @xmath1099 or @xmath1100 . note that @xmath1101 is central in @xmath1099 and @xmath1102 is central in @xmath1100 . consider any @xmath1085 . then @xmath60 is _ almost malnormal _ in @xmath1 , i.e. , @xmath1103 for any @xmath1104 ( see ( * ? ? ? suppose that the intersection @xmath1105 is infinite for some @xmath31 . since @xmath1106 is the image of @xmath60 under an inner automorphism , it is also almost malnormal in @xmath1 . since @xmath1107 is central in @xmath1099 , @xmath1108 is infinite , hence @xmath1109 by almost malnormality of @xmath1110 . but then for any @xmath1111 , the infinite order element @xmath1107 belongs to @xmath1112 , implying that @xmath1113 . thus @xmath1114 . now , since @xmath1115 commutes with @xmath1116 , we can similarly get that @xmath1117 , and since @xmath1094 commutes with @xmath1115 we conclude that @xmath1118 . thus all the generators of @xmath1 are contained in @xmath1110 , therefore @xmath1119 , yielding that @xmath83 . similarly , one can show that @xmath83 if @xmath60 has infinite intersection with some conjugate of @xmath1100 ( using the fact that @xmath1115 is central in @xmath1100 ) . thus if @xmath1085 is a proper subgroup , then @xmath60 has finite intersection with every vertex stabilizer for the action of @xmath1 on @xmath19 . observe that @xmath1 is finitely generated because @xmath621 is , hence we can apply ( * ? ? ? 4.32 ) claiming that @xmath60 is finitely generated as well . by ( * i.4.12 ) @xmath60 either fixes a vertex of @xmath19 or contains an element that acts on @xmath19 as a hyperbolic isometry . in the former case @xmath60 will have to be finite ( because it acts with finite vertex stabilizers ) , and in the latter case by ( * ? ? ? * i.4.13 ) there is a unique minimal @xmath60-invariant subtree @xmath1120 of @xmath19 on which @xmath60 acts cocompactly . now we can apply ( * ? ? ? * iv.1.9 ) to conclude that @xmath60 is virtually free , as desired . for example , if @xmath621 is a finitely presented torsion - free group with unsolvable word problem , then , by theorem [ thm : emb ] , @xmath621 can be embedded into a finitely presented torsion - free acylindrically hyperbolic group @xmath1 such that every hyperbolically embedded subgroup in @xmath1 is free of finite rank . yet another application is related to maximal elliptic subgroups ( a subgroup is _ elliptic _ if all of its orbits are bounded ) . recall that for every group @xmath1 acting acylindrically on a hyperbolic space , every elliptic subgroup of @xmath1 is contained in a maximal elliptic subgroup of @xmath1 , and maximal elliptic subgroups exhibit malnormality - type properties similar to hyperbolically embedded subgroups ( see ( * ? ? ? * corollary 1.6 ) ) . it is easy to show that if @xmath156 and @xmath60 is infinite , then @xmath60 is maximal elliptic with respect to the action of @xmath1 on the cayley graph @xmath138 . thus it is natural to ask whether maximal elliptic subgroups are hyperbolically embedded . the following corollary provides the negative answer . in what follows we say that a subgroup @xmath132 is _ absolutely elliptic _ if it is elliptic with respect to any acylindrical action of @xmath1 on a hyperbolic space . there exists a group @xmath198 and an absolutely elliptic subgroup @xmath1121 such that @xmath621 is not contained in any proper hyperbolically embedded subgroup of @xmath1 . in particular , for any non - elliptic acylindrical action of @xmath1 on a hyperbolic space , the maximal elliptic subgroup of @xmath1 containing @xmath621 is not hyperbolically embedded . let @xmath1122 and let @xmath1 be the group provided by theorem [ thm : emb ] . note that @xmath621 is absolutely elliptic by theorem [ class ] ( it is not acylindrically hyperbolic by theorem [ thm : elem - prop - ah ] ) . on the other hand , it can not be a subgroup of any proper hyperbolically embedded subgroup of @xmath1 by part ( b ) of theorem [ thm : emb ] . we showed that every one - relator group with at least @xmath0 generators and most " one - relator group with least @xmath13 generators are acylindrically hyperbolic . however the case of @xmath13-generator groups is far from being clear . the next two questions are motivated by our results about the integral @xmath13-dimensional cremona group @xmath585 $ ] . wright @xcite proved that the @xmath13-dimensional cremona group @xmath1123 ( i.e. , the group of birational transformations of the complex projective plane ) is isomorphic to the fundamental group of a finite developable complex of groups . let @xmath1124 denote its development . thus @xmath1123 acts on @xmath1124 cocompactly . the positive answer to the following question could lead to a new way of proving that @xmath1123 is acylindrically hyperbolic and hence not simple . note that acylindrical hyperbolicity of @xmath1123 was proved in @xcite and non - simplicity of @xmath1123 was a long - standing conjecture in algebraic geometry resolved in @xcite . the last problem is inspired by corollary [ ga2 ] . note that for @xmath182 no nontrivial decomposition of @xmath45 $ ] in an amalgamated product is known , so our strategy of the proof of corollary [ ga2 ] does not work . in fact , we rather expect the answer to be negative . collins , intersections of magnus subgroups of one - relator groups . _ groups : topological , combinatorial and arithmetic aspects _ , 255 - 296 , _ london math . lecture note ser . _ , 311 , _ cambridge univ . press , cambridge _ , 2004 . w. lck , @xmath1127-invariants : theory and applications to geometry and k - theory . ergebnisse der mathematik und ihrer grenzgebiete . 3 . folge . a series of modern surveys in mathematics , vol . springer - verlag , berlin _ , 2002 . serre , trees . translated from the french original by j. stillwell . corrected 2nd printing of the 1980 english translation . springer monographs in mathematics . _ springer - verlag , berlin _ , 2003 .[/INST] we provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees . in particular , we consider amalgamated products and hnn - extensions , one - relator groups , automorphism groups of polynomial algebras , @xmath0-manifold groups and graph products . acylindrical hyperbolicity is then used to obtain some results about the algebraic structure , analytic properties and measure equivalence rigidity of groups from these classes . </s>

the mixed phase of type - ii superconductors with random pinning is generally regarded to be an archetypal test system for the study of the effects of quenched disorder on the structure and melting of solids . in this phase , magnetic flux penetrates the sample as quantized vortex lines which form a special physical system known as `` vortex matter '' . the fascinating equilibrium and dynamical properties of vortex matter in the mixed phase of high - temperature superconductors ( htscs ) have prompted considerable experimental and theoretical attention for more than a decade ( see ref . for an early review ) . the mixed phase of htscs is strongly affected by the presence of pinning centers , either intrinsic or artificially generated . understanding the effects of pinning in these systems is basic for practical applications because pinning strongly influences the value of the critical current @xcite . the vortex lines in a pure type - ii superconductor form a triangular lattice ( the abrikosov lattice ) at low temperatures . because of enhanced thermal fluctuations in highly anisotropic , layered htscs , the abrikosov lattice in very pure samples , in a magnetic field perpendicular to the layers ( the field will be assumed to be in this direction throughout our discussion ) , undergoes a first - order melting transition@xcite into a resistive vortex liquid ( vl ) as the temperature @xmath0 increases . random pinning destroys the long - range translational order of the abrikosov lattice and leads to the occurrence of a variety of glassy phases at low @xmath0 . it is now generally accepted that in systems with random point pinning , a topologically ordered low - temperature phase with quasi - long - range translational order ( denoted as the `` bragg glass '' ( brg ) phase ) occurs at low fields if the pinning disorder is sufficiently weak . this has been established theoretically @xcite as well as experimentally ( see e.g. ref . ) . the possibility of an amorphous vortex glass ( vg ) phase , with nonlinear voltage - current characteristics and vanishing resistance in the zero - current limit , in systems with strong pinning ( or at high magnetic fields where the effects of pinning disorder are enhanced ) was suggested by fisher@xcite ( see also ref . ) . however , in spite of extensive investigations , the existence of a true vg phase ( i.e. , an amorphous glassy phase thermodynamically distinct from the high - temperature vl ) in systems with uncorrelated point pinning remains very controversial : different calculations @xcite lead to different conclusions and the experimental situation@xcite is similarly contradictory . a variety of `` glassy '' behavior has been reported in different experiments ( see ref . and references therein ) near the first - order melting transition of the brg phase of both conventional superconductors and htscs with point pinning . it has been suggested@xcite that these observations may be understood if it is assumed that the melting of the brg phase occurs in two steps : the brg first transforms into a `` multidomain '' glassy phase that melts into the usual vl at a slightly higher @xmath0 . columnar pinning defects can be produced for example as damage tracks arising from heavy - ion bombardment . the technological importance of these extended defects oriented parallel to the direction of the external magnetic field has been long recognized@xcite : they are highly effective in increasing the critical current by localizing vortex lines along their length . heavy - ion irradiation produces a random array of parallel columnar defects each of which can trap one or more vortices at low temperatures . the effects of such random arrays of extended defects , oriented perpendicular to the superconducting layers , on the properties of the mixed phase of htscs have been extensively studied experimentally@xcite . the same question has also been examined theoretically@xcite and numerically@xcite . when the columnar pinning is strong , and their concentration exceeds that of the vortex lines , a so - called `` strong '' bose glass ( bog ) phase with nearly all the vortex lines localized at the pinning centers occurs@xcite at low @xmath0 . this phase is strongly disordered with very short - range translational and bond - orientational correlations . the behavior in this regime is fairly well - understood in terms of a mapping@xcite of the thermodynamics of the system to the quantum mechanical properties of a two - dimensional system of interacting bosons in a random potential . much less is known about the behavior in the dilute pin limit where the concentration of pins is much smaller than that of vortex lines . in such systems , one expects@xcite a `` weak '' bog phase at low temperatures , with a small fraction of vortex lines localized strongly at the pinning centers and the remaining ones localized relatively weakly in the interstitial region between pinning centers . as the temperature is increased , this phase should@xcite melt into an interstitial liquid ( il ) . in the il phase , some of the vortices remain trapped at the pinning centers , while the other , interstitial ones , form a liquid . the pinned vortices are expected@xcite to delocalize , thereby forming the usual vl , at a crossover occuring at a higher temperature . the melting transition of the `` weak '' bog phase into the il is predicted@xcite to be first - order for small pin concentrations , whereas the `` strong '' bog to vl transition occurring for large pin concentrations is known@xcite to be a continuous one . a first - order melting transition of the `` weak '' bog phase has been observed@xcite in recent experiments on samples of @xmath1 ( bscco ) with a small concentration of columnar pins . the bog phase in these systems is found@xcite to have a polycrystalline structure with ordered vortex crystallites of different orientations embedded in the interstitial region between vortices pinned at the columnar defects . if the pin concentration is sufficiently small , the melting of this bog phase upon increasing the temperature occurs into an il phase with a fraction of vortex lines remaining pinned at the defects . these pinned vortices delocalize at a higher temperature@xcite . the temperature at which the first - order bog to il transition occurs is@xcite very close to the melting temperature of the same system without the columnar pins , if the pin concentration is small . as the pin concentration is increased , the melting temperature increases and the transition eventually becomes continuous . the difference between the melting temperature and the temperature at which the pinned vortices in the il phase delocalizes decreases and eventually goes to zero as the pin concentration increases . another interesting feature , found experimentally for both point@xcite and columnar@xcite pinning , is that the melting of the low @xmath0 `` solid '' phase is `` inhomogeneous '' in that it occurs locally over a range of temperatures : the local transition temperature , which can be measured from the local magnetization , is different in different regions of the sample . this inhomogeneity of the local melting temperature is believed@xcite to be closely related to the local arrangement of the specific pinning centers ( the so - called `` pinning landscape '' ) in each sample studied . the polycrystalline nature of the bog phase for small pin concentrations has also been observed in simulations@xcite . recent numerical work@xcite indicates that a brg phase , with topological order , may also exist in such systems provided that the pin concentration is sufficiently small . in these simulations , the brg phase is found to melt into the il phase via a first - order transition as the temperature is increased . as the pin concentration is increased beyond a critical value , the brg phase disappears@xcite and a low - temperature bog phase with a continuous bog to il transition upon increasing the temperature is found@xcite . in this paper , we approach these problems through a different numerical method . we consider a layered , strongly anisotropic superconductor ( such as bscco ) with a dilute random array of columnar defects oriented perpendicular to the layers , and with a magnetic field applied parallel to the columnar pins . we describe the equilibrium properties of this system in terms of vortex density variables , using a free energy functional of the ramakrishnan - yussouff@xcite ( ry ) form . we numericall minimize a spatially discretized version of this free energy functional and obtain the vortex density configuration at each local minimum . analysis of these density configurations , both in terms of a variety of correlation functions and by direct visualization of the arrangement of the vortices ( vortex positions are identified with those of local peaks of the vortex density ) , allows us to identify the nature of the phases corresponding to different local minima of the free energy . comparison of the values of the free energy at the minima as the temperature varies yields the transition temperatures . a similar procedure has been successfully employed for the case of a regular array@xcite of columnar pinning centers . we find in our study that that a bragg glass phase exists at low temperatures for samples with a small concentration of columnar pins . we will present evidence for this phase from our analysis of the vortex density and associated correlation functions . upon warming , this phase melts into what we show to be an insterstitial liquid ( il ) phase , but the melting is shown@xcite to occur in two steps : the brg and il phases are separated , over a narrow temperature range , by an intermediate phase which exhibits a multi - domain polycrystalline structure . we show that this intermediate phase should be identified as a bose glass ( bog ) . the temperature of the upper ( bog to il ) transition is approximately independent of the columnar pin concentration @xmath2 , at the low @xmath2 values studied . both the brg to bog and the bog to il transitions are found to be first - order . we also find that a local melting temperature can be suitably defined using a criterion based on the degree of localization of the vortices , and that its behavior ( in particular , its spatial variation ) is quite consistent with what is seen in experiments@xcite . the value of the local melting temperature is strongly correlated with the presence of topological defects ( dislocations ) in the vortex solid which , in turn , is correlated with the local arrangement of the pinning centers . we also show that the transition to the il phase corresponds to a percolation of regions containing liquid - like ( delocalized ) vortices across the sample . after this introduction , we discuss our definitions , model and numerical methods in the next section . then in section [ results ] we present our results . we discuss first the free energy minima and their study through the use of tools such as correlation functions , local peak - density plots , and voronoi construction for the lattice formed by local density peaks . these tools allow the identification of the phases at each free energy minimum , as we shall show . then we derive the phase diagram and show that indeed the brg and il phases are separated by a thin sliver of bog . finally , our results for the nature of the local melting are displayed and discussed . a brief conclusions section recapitulates the main points of the paper and discusses them in the context of existing results . the general procedures that we use are quite similar to those employed in previous work on a regular array of columnar pins@xcite . we will therefore give here only a brief summary , emphasizing the details that are different in the random case considered here . the system we study is a layered superconductor in the extreme anisotropic limit , that is , with vanishing josephson coupling between layers , which are then coupled via the electromagnetic interaction only . this limit is appropriate for the bi- and tl- based htsc compounds in a large region of the magnetic field ( @xmath3)@xmath0 plane . in this work , we will use material parameter values appropriate to bscco . with these assumptions , one can write the energy of a system of `` pancake '' vortices residing in the layers as a sum of anisotropic two - body interactions . for straight columnar pins normal to the layers , the pinning potential is the same in every layer . it is then possible to write the free energy as a functional of the _ time averaged _ areal vortex density @xmath4 : @xmath5-f_0=f_{ry}[\rho]+f_p[\rho ] . \label{fe}\ ] ] where @xmath6 is the free energy corresponding to a uniform vortex liquid of density @xmath7 ( @xmath8 is the magnetic induction and @xmath9 the superconducting flux quantum ) . the first term in the right - hand side of eq . ( [ fe ] ) is the free energy functional in the absence of pinning . as explained above we use for this free energy the ry@xcite functional , which is known@xcite to give a quantitatively accurate description of the vortex - lattice melting transition in the absence of pinning . it is of the form : @xmath10 & = & \int d^2r\left[\rho({\bf r } ) \ { \ln(\rho({\bf r}))-\ln ( \rho_0)\ } - \delta\rho({\bf r})\right ] \nonumber \\ & -&\frac{1}{2}\int d^2r \int d^2r^\prime \,\tilde{c}(|{\bf r } - { \bf r}^\prime | ) \delta\rho({\bf r } ) \delta\rho({\bf r}^\prime ) . \label{ryfe}\end{aligned}\ ] ] here @xmath11 is the inverse temperature , @xmath12 , and @xmath13 is the usual direct pair correlation function@xcite which may be written as a sum over layers : @xmath14 , with @xmath15 ( where @xmath16 is the layer separation and @xmath17 the in - layer distance ) being the corresponding direct pair correlation function of a layered liquid of pancake vortices . the direct correlation function , which is needed as input in our free energy , can be accurately calculated in a number of ways . we will use here the results of the hypernetted chain calculation of ref . . in general , the results in the limit considered depend on the values of the in - plane london penetration length @xmath18 , the interlayer spacing @xmath19 and a dimensionless coupling parameter @xmath20 given by : @xmath21 for bscco we will take @xmath22 , and we will assume a standard two - fluid temperature dependence for @xmath18 with @xmath23 and @xmath24k ( at zero field ) . the second term in the right - hand side of eq . ( [ fe ] ) represents the pinning and is of the form : @xmath25 = \int d^2r v_p({\bf r } ) \delta\rho({\bf r } ) . \label{pin}\ ] ] where @xmath26 is the pinning potential which can be written as @xmath27 with the sum extending over the planar positions of the random pinning centers . we take the potential @xmath28 corresponding to a single pinning center to be of the usual truncated parabolic form:@xcite @xmath29\theta(r_0-r ) \label{single}\ ] ] where @xmath30 is the range . the basic length in the problem , which we will use as our unit of length unless otherwise indicated , is @xmath31 , defined by the relation @xmath32 . we choose @xmath30 to be @xmath33 and take the dimensionless constant @xmath34 , for which value , as previously shown,@xcite each pinning center traps approximately one vortex in bscco , in the temperature range of interest . this range is determined by the following considerations . we will keep the field fixed at @xmath35 t , and vary the temperature . the melting temperature of the unpinned lattice is then @xmath36k@xcite , and we , therefore , consider the neighborhood of this temperature . then one has , to a very good approximation @xmath37 ( with the temperature in kelvin ) , while @xmath38 . to carry out our numerical calculations , we discretize the density variables on a computational triangular grid of lattice spacing @xmath39 , containing @xmath40 sites . we take the spacing @xmath39 to be @xmath41 in our calculations , where @xmath42 is the equilibrium lattice constant of the vortex lattice in the temperature range considered at the indicated field . this value , as pointed out in ref . , is slightly higher than that of a triangular vortex lattice of density @xmath43 , which is @xmath44 . we define at each site @xmath45 on this computational lattice a variable @xmath46 , with @xmath47 , where @xmath48 is the area of each computational unit cell . results reported here are for @xmath49 , which , for the chosen value of @xmath39 , corresponds to including @xmath50 4096 vortices in the calculation . preliminary and confirmatory results at @xmath51 ( 1024 vortices ) were also obtained . a number of pinning sites ( @xmath52 ) are put , at random , on some of the computational lattice sites . the results presented here , which correspond to the dilute limit , will be primarily for a pin concentration @xmath2 of @xmath53 , that is , a number of pins @xmath54 at @xmath49 ( or @xmath55 at @xmath51 ) . some preliminary results for @xmath56 ( @xmath57 at @xmath49 , or @xmath58 at @xmath51 ) will also be discussed briefly . with random pins , the results depend on the particular random pin configuration and averaging over different such configurations is required . the dependence is however not strong : as we shall see , averaging over five to ten configurations is enough to make statistical errors sufficiently small for our purposes . to perform our studies , we numerically minimize the discretized free energy with respect to the @xmath40 discretized density variables @xmath59 . to do so , the interaction term in the right side of eq . ( [ ryfe ] ) must be repeatedly evaluated , and since this term is of a convolution form , this is most efficiently done in momentum space , through the use of efficient fast fourier transform ( fft ) routines . this avoids having to evaluate this term as a double sum which would be computationally much more cumbersome than performing the direct and inverse fft s . in performing the minimization , one must keep in mind that the variables @xmath59 must be nonnegative . this precludes the use of many efficient minimization algorithms . we use a procedure@xcite that ensures that this constraint is satisfied . numerical minimization is performed starting with an appropriate initial condition for the density variables . as explained in sec . [ results ] below , different local minima may be found , at the same field and temperature , depending on the initial conditions . these minima correspond to different phases . the minimization procedure yields not only the value of the free energy at each minimum but also the detailed vortex density configuration at the minimum found , i.e. the values of the set @xmath59 at the minimum . it is then straightforward to analyze the actual density configuration in several ways . it is also possible to evaluate any desired density correlations . the nature of the phase corresponding to each local minimum of the free energy can be inferred from such analysis . the ( mean - field ) phase diagram is then obtained from a comparison of the free energies of the different minima as the temperature @xmath0 is varied . the results of carrying out this program are discussed below . as explained above , minima of the free energy are found by starting the minimization process with appropriate initial conditions . we use three different kinds of initial conditions . the first kind is a uniform density ( @xmath60 for all @xmath61 ) , corresponding to a completely disordered liquid state . this is typically used to obtain , as we shall see , liquid - like states at temperatures near the equilibrium melting temperature of the pure vortex lattice , which is@xcite @xmath62k for the value of @xmath8 considered here . the second kind corresponds to a crystalline initial state , with values of @xmath59 as obtained in ref . for the pure vortex lattice . in our system with a spatially varying random pinning potential , the pinning energy of such a crystalline density configuration depends on the choice of the computational lattice sites at which the periodic local peaks of the density are located . we take , among all possible choices equivalent by symmetry operations in the computational lattice , the one for which the pinning energy is lowest for the specific pinning configuration under consideration . these initial conditions are used to obtain ordered states at lower temperatures . finally , states originally obtained by either of these two procedures can be slowly warmed up , or cooled down : in this case the initial conditions are simply the final state obtained at the previous temperature . as one warms up or cools down a state , its nature in general changes : liquid configurations may become unstable upon cooling and ordered configurations upon warming . whichever initial conditions one uses , a local minimum of the free energy is eventually found . at a given temperature , in general several local minima with different density configurations , characterized by the values of the set of @xmath59 variables , are obtained . the minimum with the lowest free energy represents , at a given @xmath0 , the true equilibrium state . it is obviously necessary to develop systematic procedures to identify the structure of each of these diverse minima . since we have access to the full set of density variables at the computational lattice sites , we have at our disposal a variety of methods to achieve that goal . the first is to calculate the density correlations , e.g. the structure factor @xmath63 : @xmath64 where @xmath65 is the discrete fourier transform of the set @xmath59 . equivalently , one can consider the fourier transform of @xmath63 , which is the two - point spatial correlation function @xmath66 of the time - averaged local density . we will present here results for @xmath63 , considered as a function of the vector @xmath67 , and for the angularly averaged spatial density correlation function , @xmath68 . it is also very useful to consider the spatial structure formed by the _ vortices _ at low temperatures . for this purpose we have extracted from @xmath59 the local peak densities . we say that the density locally peaks at site @xmath61 if the value of @xmath46 at @xmath69 is higher than that at any other computational lattice site within a distance @xmath70 from @xmath61 , where , as defined above , @xmath71 is the equilibrium spacing of the unpinned vortex lattice . as expected , we find that at low - temperature solid - like minima where the vortices are strongly localized , the number of local density peaks matches the number of vortices @xmath72 . the positions of these peaks determine what we will call the `` vortex lattice '' . much useful information about the spatial structure of this vortex lattice may be obtained by plotting directly the local density values at the vortex lattice points . an excellent , and complementary , alternative to help elucidate the degree of vortex lattice order is to carry out a voronoi construction : we recall that in the voronoi construction one determines cells around each lattice point by a wigner - seitz procedure . in a perfect crystal , all the resulting wigner - seitz cells are identical , while in the general case the cells can have different sizes and shapes . the number of sides of the wigner - seitz cell surrounding a lattice point is identified with the number of `` nearest neighbors '' of that lattice point , and the difference between this number and the average ( six in our case ) marks the position of defects ( disclinations ) . we will make use of such plots below . since we will be concerned not only about translational , but also with orientational order , we will also examine the bond - orientational correlation function @xmath73 in the vortex lattice defined as : [ angular ] @xmath74 where the angular brackets denote overall average over the vortex lattice and the field @xmath75 is given by : @xmath76\ ] ] with @xmath77 being the angle that the bond connecting a vortex at @xmath78 to its @xmath45-th neighbor makes with a fixed axis , and @xmath79 is the number of neighbors of the vortex at @xmath78 . it is also possible , and as we shall see , useful , to define what we will call a `` translational correlation function '' in the vortex lattice in a way that is quite analogous to the definition of @xmath73 . this function , which we denote as @xmath80 , is defined by an equation identical to the right - hand side of eq . ( [ ang1 ] ) , but with the field @xmath81 being defined as @xmath82 where @xmath83 is a reciprocal lattice vector of the triangular vortex lattice in the absence of pinning . we will consider here only the case where @xmath83 is a shortest nonzero reciprocal lattice vector and average over the results obtained for the six equivalent @xmath84 s . ( color online ) the static structure factor @xmath63 ( see eq . ( [ sofk ] ) ) for three local minima obtained at @xmath85k for the same pin configuration . the ( red ) circles are for a state identified , from the overall evidence ( see text ) , as a bragg glass ( brg ) , the ( blue ) triangles are for a bose glass ( bog ) state , and the ( green ) crosses are for an insterstitial liquid ( il ) . the vertical lines are guides to the eye . ] our identification of the different phases is based on analysis of all this information . we show some of the results in the next few figures . these all correspond to samples with 64 pins and 4096 vortices . first , in fig . [ fig1 ] , we show the structure factor , as defined in eq . ( [ sofk ] ) . the three sets of results shown there are for local free energy minima at the same temperature , @xmath85k , obtained with different initial conditions of the three kinds described above , and the same pin configuration . other pin configurations yield very similar results ( a different example is shown in fig . 1c of ref . ) . the green symbols correspond to the free energy minimum obtained by starting with uniform initial conditions . clearly , the structure factor is completely featureless and liquid - like in this case the absolute value of @xmath86 never exceeds five . the red circles are for a local minimum obtained with initial conditions corresponding to the best crystalline state , as explained above , for this pin configuration . the structure factor now exhibits typical ordered behavior , highlighted by six sharp bragg - like peaks which are emphasized by the added vertical lines in the figure . finally , the blue triangles correspond to a minimum obtained by first `` quenching '' with uniform initial conditions to a relatively low temperature ( 16.8k ) where the liquid - like state is found not to be stable , and then slowly warming , at 0.2k temperature intervals , back up to 18.4k . as one can see , the @xmath63 for this minimum has an intermediate structure , with several relatively well - defined peaks , more than six in number , whose heights are considerably lower than those of the peaks found for the ordered minimum . ( color online ) . the angularly averaged density correlation function @xmath68 plotted at the same temperature as in fig . [ fig1 ] as a function of dimensionless distance . the results are this time averaged over five different pin configurations . the results for the bog and il minima are shown in the top panel . the ( blue ) dotted line plot with higher peaks corresponds to bog minima and the ( green ) light grey plot with fewer and lower peaks to il minima . the bottom panel displays the results for the brg minima . the vertical and horizontal scales are the same in the two panels and the color scheme is the same as that in fig . [ fig1].,title="fig : " ] ( color online ) . the angularly averaged density correlation function @xmath68 plotted at the same temperature as in fig . [ fig1 ] as a function of dimensionless distance . the results are this time averaged over five different pin configurations . the results for the bog and il minima are shown in the top panel . the ( blue ) dotted line plot with higher peaks corresponds to bog minima and the ( green ) light grey plot with fewer and lower peaks to il minima . the bottom panel displays the results for the brg minima . the vertical and horizontal scales are the same in the two panels and the color scheme is the same as that in fig . [ fig1].,title="fig : " ] in fig . [ fig2 ] , results for the angularly averaged density correlation function @xmath68 are displayed . these results are for minima obtained at the same temperature , and using the same initial condition procedures , as those for the data shown in fig . [ fig1 ] however , the results shown here are averages over five different pin configurations . the nearly flat ( green ) curve in the top panel corresponds to minima obtained from quenches with uniform initial conditions , the ( red ) curve with the well - defined peaks shown in the bottom panel corresponds to minima obtained with crystalline initial conditions , and the ( blue ) curve with the intermediate peaks shown in the top panel is for minima obtained by quenching with uniform initial conditions to a low temperature and subsequent slow warming ( very similar results can alternatively be obtained by slowly cooling a high - temperature liquid - like minimum to a temperature where it is unstable ) . one can see then that the results for @xmath68 are fully consistent with those found in fig . [ fig1 ] : the minimum obtained from uniform initial conditions is fully disordered , while that obtained from crystalline initial conditions exhibits a large degree of crystalline order . for the the third kind of minima , we find some degree of intermediate range order . ( color online ) . local peak densities at three different local minima of the free energy . the positions of the local density peaks and the values of the density at these peaks are displayed according to the following scheme : ( cyan ) solid circles : peaks with @xmath87 , ( red ) circles : @xmath88 , ( blue ) squares : @xmath89 , ( green ) plus signs : @xmath90 , and ( purple ) triangles : @xmath91 . blank areas , found mainly in the bottom panel , correspond to regions where no local peaks are found . the temperature is 18.2k in all panels , which all correspond to the same pin configuration as that for the results in fig.[fig1 ] . pin locations are indicated by ( black ) asterisks . from top to bottom , the results displayed correspond respectively to ordered ( identified as brg ) , intermediate ( bog ) and disordered ( il ) minima . , title="fig : " ] ( color online ) . local peak densities at three different local minima of the free energy . the positions of the local density peaks and the values of the density at these peaks are displayed according to the following scheme : ( cyan ) solid circles : peaks with @xmath87 , ( red ) circles : @xmath88 , ( blue ) squares : @xmath89 , ( green ) plus signs : @xmath90 , and ( purple ) triangles : @xmath91 . blank areas , found mainly in the bottom panel , correspond to regions where no local peaks are found . the temperature is 18.2k in all panels , which all correspond to the same pin configuration as that for the results in fig.[fig1 ] . pin locations are indicated by ( black ) asterisks . from top to bottom , the results displayed correspond respectively to ordered ( identified as brg ) , intermediate ( bog ) and disordered ( il ) minima . , title="fig : " ] ( color online ) . local peak densities at three different local minima of the free energy . the positions of the local density peaks and the values of the density at these peaks are displayed according to the following scheme : ( cyan ) solid circles : peaks with @xmath87 , ( red ) circles : @xmath88 , ( blue ) squares : @xmath89 , ( green ) plus signs : @xmath90 , and ( purple ) triangles : @xmath91 . blank areas , found mainly in the bottom panel , correspond to regions where no local peaks are found . the temperature is 18.2k in all panels , which all correspond to the same pin configuration as that for the results in fig.[fig1 ] . pin locations are indicated by ( black ) asterisks . from top to bottom , the results displayed correspond respectively to ordered ( identified as brg ) , intermediate ( bog ) and disordered ( il ) minima . , title="fig : " ] we next examine the structure of the minima in terms of the `` vortex lattice '' found by the procedure explained above . sample results are shown in fig . [ fig3 ] , all for the same pin configuration , at the temperature @xmath92k . results for three minima , obtained from the same procedures and initial conditions as the three minima in the previous two figures , are shown . the positions of the local density peaks and the values of the density at these peaks are displayed through a symbol and color coding scheme described in the caption of the figure . blank regions denote areas where no local peak was found using the algorithm described above : such areas are mostly found only in the most disordered case ( uniform initial conditions ) . we see that the results are quite consistent with those obtained from the previous correlation functions : quenching with the appropriate crystalline initial conditions leads to a fairly well - ordered ( but not perfectly ordered ) lattice , while from uniform initial conditions , one obtains a rather disordered , liquid - like structure where the density is nearly uniform and close to @xmath43 , except near the pinning centers at each of which one vortex is trapped . an intermediate result , on the whole more solid than liquid - like , but definitely disordered , is obtained through the slow warming or cooling scheme . ( color online ) . voronoi plots for the three cases for which density plots are shown in fig . [ fig3 ] , except that the temperature is now @xmath93k . the ( black ) dots denote lattice sites with six neighbors , the ( red ) triangles denote five - fold coordinated sites , and the ( green ) solid circles , seven - fold coordinated sites . rarely occurring four - fold and eight - fold coordinated sites are indicated by ( blue ) squares and ( purple ) inverted triangles , respectively . sites surrounded by black circles denote locations of pinning centers . see text for explanations.,title="fig : " ] ( color online ) . voronoi plots for the three cases for which density plots are shown in fig . [ fig3 ] , except that the temperature is now @xmath93k . the ( black ) dots denote lattice sites with six neighbors , the ( red ) triangles denote five - fold coordinated sites , and the ( green ) solid circles , seven - fold coordinated sites . rarely occurring four - fold and eight - fold coordinated sites are indicated by ( blue ) squares and ( purple ) inverted triangles , respectively . sites surrounded by black circles denote locations of pinning centers . see text for explanations.,title="fig : " ] ( color online ) . voronoi plots for the three cases for which density plots are shown in fig . [ fig3 ] , except that the temperature is now @xmath93k . the ( black ) dots denote lattice sites with six neighbors , the ( red ) triangles denote five - fold coordinated sites , and the ( green ) solid circles , seven - fold coordinated sites . rarely occurring four - fold and eight - fold coordinated sites are indicated by ( blue ) squares and ( purple ) inverted triangles , respectively . sites surrounded by black circles denote locations of pinning centers . see text for explanations.,title="fig : " ] to better gauge the degree of disorder present in each case , we construct , in fig . [ fig4 ] , the corresponding voronoi plots . to display the behavior in a more obvious way , the temperature in these plots is lower by @xmath94k than that of the plots in fig . as mentioned above , sites with number of nearest neighbors ( @xmath79 ) different from six represent the locations of disclinations . in the solid - like minima ( top two panels of fig . [ fig4 ] ) , nearly all the sites with @xmath95 have @xmath96 or @xmath97 ( the disclinations have unit `` charge '' ) . also , six- and seven - coordinates sites , indicated respectively by ( red ) triangles and ( green ) solid circles in the plots , always occur in nearest - neighbor pairs . such pairs correspond to dislocations . in the first panel , which displays the results for the most ordered state obtained from crystalline initial configurations , we see that the number of dislocations , while nonzero , is quite small and that they form fairly isolated small clusters , each of which has zero net burgers vector . these defect clusters occur near the pinning centers and they represent the local disruption of crystalline order due to the pinning . in the second panel , which shows the results for the minimum with intermediate order , the dislocations are organized to form well - defined grain boundaries that separate crystallites with different orientations . as a result of this polycrystalline structure , both translational and bond - orientational correlations are short - range . performing the same construction for other pin configurations ( results for a different pin configuration are shown in fig.1b of ref . ) , one finds that the crystallite arrangement depends on the pin configuration , as one would expect . the grain boundaries tend to lie away from pinning centers , which makes sense physically . finally , in the last panel , which shows the results for the minimum obtained from uniform initial conditions , the high degree of disorder is evident . the voronoi construction shown in this panel is not very meaningful because our method of obtaining the vortex positions is not reliable for liquid - like minima . the identification of the position of a vortex with that of a local peak of the density field is justified only when the peak is sharp . this is the case in the solid - like minima , but not so in the liquid - like minima with low peak densities . we have shown here the results for the liquid - like minimum only for the purpose of illustrating the difference between the structure of this minimum and those of the more ordered ones . for this minimum , we find a very large number of defects , and it is difficult to determine whether disclinations of opposite `` charge '' always pair up to form dislocations . inspection of the defect distribution suggests the presence of free disclinations , but not conclusively . the total number of local peaks of the density field in liquid - like minima turns out to be substantially smaller than the expected number of vortices . this problem is not present at the solid - like minima where nearly all the vortices are strongly localized . ( color online ) . bond - orientational correlation function @xmath73 as defined in eq . ( [ angular ] ) , and `` translational '' correlation function , @xmath80 , see eq . ( [ bo ] ) . these are results averaged over five pin configurations , at @xmath98k . the ( purple ) triangles and ( red ) circles denote @xmath73 for ordered ( brg ) and polycrystalline ( bog ) minima ( liquid - like minima are not stable at this lower @xmath0 ) respectively . the black squares are @xmath80 for the brg minima . the dashed line is an exponential fit to @xmath73 for the bog minima . the dotted line is a similar exponential fit to @xmath80 for the brg minima at small distances , showing that the decay is slower than exponential for large values of @xmath17 . the solid lines connecting symbols are guides to the eye . ] next , we show in fig . [ fig5 ] examples of the bond - orientational and `` translational '' correlation functions , @xmath73 and @xmath80 as defined in eqs . ( [ angular ] ) and ( [ bo ] ) respectively . all results shown in this figure are averages over five pin configurations at temperature @xmath98k . at this temperature the liquid is unstable , and in any case all liquid correlation functions are featureless , so that case is not shown . the ( purple ) triangles correspond to ordered minima obtained from quenching with crystalline initial conditions to @xmath99k and subsequent slow warming , and represent the bond - orientational correlation , @xmath73 . this function appears to saturate at a fairly large value as @xmath17 increases , indicating the presence of long - range bond - orientational order . the ( red ) open circles display @xmath73 for the polycrystalline state with intermediate order , obtained through the procedures described above . this function decays exponentially with distance , as shown by the exponential fit ( dashed line ) , over a distance of few tens in units of @xmath31 . finally , the ( black ) open squares show the results for the `` translational '' correlation function @xmath80 for the ordered minima . the dotted line is an exponential fit to this translational correlation function for @xmath100 , showing that the decay at longer distances is clearly slower than exponential ( possibly a power - law ) . > from the overall examination of data such as those shown in these figures , we can reach the following conclusions : quenching with uniform initial conditions to temperatures above or slightly below @xmath101 leads to very disordered states , with very short range correlations and no structure , except for vortices at and near the pinning centers . these minima become unstable upon slow cooling : one then obtains minima of the third kind , discussed below . they clearly must be identified with the liquid phase , specifically the interstitial liquid ( il ) phase discussed in the introduction . the second kind of minima are obtained by quenching with crystalline initial conditions to any temperature below , or slightly above , @xmath101 . these minima can then be cooled , without losing their character , but they melt into the il upon sufficient warming . the states thus obtained are obviously nearly crystalline , with the reservation that the order is not truly long range , but has a slow decay . this is most evident in the results for @xmath80 seen in fig . the bond - orientational order is nearly perfect . defects are limited to isolated clusters . this state must therefore be identified as a bragg glass ( brg ) . finally , we have the states obtained as described above , by slow cooling of the il state , which can also be obtained by quenching with uniform initial conditions to a temperature below the il state stability limit . either procedure yields , for any pin configuration , states that at a given @xmath0 differ only slightly in free energy or density configuration . the states do differ somewhat more , however , for different pin configurations . the voronoi construction conclusively shows ( see fig . [ fig4 ] ) that these states are polycrystalline . the grain boundaries are formed by dislocation chains . for any pin configuration , these grain boundaries survive thermal cycling across @xmath101 , but if sufficiently warmed up , these minima melt , the melting beginning locally at the grain boundaries ( see sec [ props ] below ) . the bond - orientational correlation function for these minima has an intermediate range . this , and also the observation that these states are not unique ( as mentioned above , slightly different states are reached depending on the cooling or quenching protocol ) , clearly indicate a glassy state . we therefore identify it with the bose glass ( bog ) which has been experimentally@xcite and numerically@xcite shown to be polycrystalline . in this section , we describe in detail how the properties of the low - temperature `` solid - like '' condensed phases represented by the brg and bog types of minima defined in the preceding section vary as the temperature is changed . the high - temperature liquid phase represented by the il - type minima is not very interesting from the point of view of its temperature dependence : in the temperature range we have considered , this phase exhibits a liquid - like ( nearly uniform ) density distribution except in the immediate vicinity of the columnar pins , at each of which a vortex is trapped . these trapped vortices would eventually get delocalized at higher temperatures . this happens beyond the upper limit of the temperature range ( 16.8k @xmath102 18.8k ) we have considered here . to study how the properties of a local minimum of the free energy change as the temperature is varied , we have `` followed '' minima as the temperature changes : for example , starting with a minimum obtained by quenching to the lowest temperature of 16.8k , we `` follow '' that minimum to higher temperatures by increasing the temperature in small steps ( usually taken to be 0.2k ) and finding a new minimum at the higher temperature by running the minimization routine with the configuration at the minimum obtained at the previous temperature as the initial state . this procedure leads to a new minimum of the same type as long as the minimum remains locally stable if the temperature is increased to values substantially higher than @xmath101 , where the brg and bog minima become unstable , this procedure leads then to the il minima . we have also carried out `` cooling '' runs where the temperature was decreased in small steps , starting from a minimum obtained at a relatively high temperature . when the il minima become unstable , bog states are obtained . as long as the minimum under consideration did not become unstable in the range of temperatures considered in the runs , we did not find any substantial difference between the results obtained in the `` heating '' and cooling runs ( color online ) . temperature dependence of the order parameter @xmath103 as defined in eq . ( [ op ] ) for three kinds of minima , averaged over five samples , with @xmath104 and @xmath54 . results for the brg , bog and il minima are shown by ( red ) plus signs , ( green ) crosses and ( blue ) asterisks , respectively . ] to characterize the density distribution at a minimum , we looked at `` global '' quantities such as the structure factor @xmath63 , an example of which is shown above in fig . the @xmath0-dependent information contained in @xmath63 is , however , difficult to display in plots . we therefore introduce a closely related `` order parameter '' @xmath103 defined as @xmath105 where @xmath106 is the largest value of the structure factor @xmath63 averaged over the six @xmath107-vectors related by lattice symmetry to each @xmath107 . by definition , the order parameter @xmath103 is equal to unity in a state with perfect crystalline order ( triangular lattice with @xmath108-function peaks ) . since no long - range crystalline order is expected or found in either one of the brg and bog phases , the value of @xmath103 should go to zero at all temperatures in the thermodynamic limit . however , the infinite size limit is reached very slowly in the glassy phases , and for the finite - size systems considered here , this quantity provides a convenient measure of the degree of local order present at the minima . we show in fig . [ fig6 ] the results for the order parameter @xmath103 , averaged over five different pin configurations , for samples with 4096 vortices and 64 pins . the results for the brg , bog and il minima are shown by ( red ) plus signs , ( green ) crosses and ( blue ) asterisks , respectively . only two data points are shown for the il minimum because it becomes unstable at lower temperatures . for all three kinds of minima , the value of @xmath103 decreases with increasing @xmath0 , as expected . the rate of change is largest for the brg minima , and smallest for the il minima . however , the differences among the three kinds of minima in the degree of local order remain quite clear at all the temperatures considered . we have also obtained brg - type minima for several ( @xmath109 ) samples with 1024 vortices and 16 pins . the values of @xmath103 obtained from an average over these smaller samples are found to be only about 6% larger than those obtained for the 4096-vortex samples at the corresponding temperature . this result implies that the translational correlation function at the brg minima falls off very slowly with distance . this is consistent with our interpretation of these minima as representing the brg phase . ( color online ) . peak density plots for the bog minimum of a sample with @xmath104 and @xmath54 ( the sample is the same as the one for which results are shown in figs . [ fig3 ] and [ fig4 ] ) at two temperatures : @xmath0 = 17.4k ( top panel ) and @xmath0 = 17.8k ( bottom panel ) . the symbols and color scheme used here are the same as those in fig . [ fig3].,title="fig : " ] ( color online ) . peak density plots for the bog minimum of a sample with @xmath104 and @xmath54 ( the sample is the same as the one for which results are shown in figs . [ fig3 ] and [ fig4 ] ) at two temperatures : @xmath0 = 17.4k ( top panel ) and @xmath0 = 17.8k ( bottom panel ) . the symbols and color scheme used here are the same as those in fig . [ fig3].,title="fig : " ] we also examined the temperature dependence of the detailed density distribution at the minima ( obtained from `` peak density '' plots similar to those shown in fig . [ fig3 ] ) and their defect structure obtained from voronoi plots such as those in fig . [ fig4 ] . examination of the peak - density plots reveals more information about how the density distribution at the minima changes with temperature . in fig . [ fig7 ] , we have shown peak - density plots at two temperatures ( 17.4k in the top panel and 17.8k in the bottom panel ) for the bog minimum of the same sample for which a similar plot at 18.2k is shown in the middle panel of fig . the symbols and color scheme used in these plots are the same as those in fig . it is clear from these plots that the typical values of the local peak densities decrease ( the vortices become less localized ) as the temperature increases . the largest values of the local peak density occur near the pinning centers and the smallest values appear near the grain boundaries that separate different crystalline regions . this is physically reasonable the disruption of local crystalline order near the grain boundaries should make the vortices in such regions more delocalized . at the relatively low temperature of 17.4k , there are very few local density peaks where the peak density is lower than @xmath110 ( such peaks are indicated by ( red ) circles in the plot ) . as the temperature is increased to 17.8k , the number of such peaks increases , and this trend continues as @xmath0 is increased further , as can be seen in the middle panel of fig . [ fig3 ] where the results for @xmath111 are shown . it is also clear from these plots that the spatial regions where the low peak densities occur remain roughly unchanged as the temperature increases as noted above , these regions are strongly correlated with the locations of the grain boundaries . these observations indicate that the vortices in the interior of the crystalline grains remain in a `` solid '' state as the temperature is increased to a value close to @xmath101 , while those in the neighborhood of the grain boundaries begin to `` melt '' ( get delocalized ) at a lower temperature . this `` inhomogeneity '' of the melting process will be discussed in more detain in section [ inhomog ] . we also studied the temperature dependence of the number of topological defects present at the minima . this number increases slowly with increasing @xmath0 , and then exhibits a sudden jump as liquid - like regions ( characterized by low values of the local peak densities ) appear near the grain boundaries at temperatures close to @xmath101 . as noted in sec . [ minima ] above , our method of obtaining the defect structure using the voronoi construction becomes somewhat less reliable when liquid - like regions begin to appear . due to this difficulty in obtaining reliable results for the defect structure and statistics at relatively high temperatures , we have not carried out a quantitative analysis of the dependence of these quantities on the temperature . the gradual decrease in the values of the local peak densities with increasing temperature is also found in the brg minima , but on the average the vortices remain more strongly localized at the brg minima than at the corresponding bog ones . the strong correlation between low values of the local peak density and the location of topological defects is found at the brg minima too . the main difference between brg and bog minima is that the defects are more randomly distributed at the brg minima : they do not line up along grain boundaries as they do at the bog minima . for this reason , the regions of low peak density appear at fairly random locations at the brg minima . the total number of topological defects at the brg minima remains smaller than that at corresponding bog minima at all temperatures . as the temperature approaches @xmath101 , liquid - like regions appear in parts of the sample where the defect density is large . this is illustrated in the plots in the top panels of figs . [ fig3 ] and [ fig4 ] . thus , our investigation of the temperature dependence of the structure of the brg and bog minima confirms that these minima retain their topological structure as @xmath0 is increased toward @xmath101 and even beyond ( provided they remain stable ) . the degree of localization of the vortices decreases with increasing @xmath0 and liquid - like regions with nearly delocalized vortices begin to appear at temperatures close to @xmath101 . however , even at such temperatures , the brg and bog type minima are clearly distinguishable from one another and from the il - type minima , as illustrated in figs [ fig3 ] , [ fig4 ] and [ fig6 ] . as discussed in the preceding subsections , we find three kinds of coexisting , locally stable minima of the free energy at temperatures close to @xmath101 . two kinds ( brg and bog ) of local minima are found at temperatures substantially lower than @xmath101 , and only the il minimum is stable if @xmath0 is much higher than @xmath101 . in our mean - field description , the thermodynamically stable phase at a particular temperature corresponds to the minimum with the lowest free energy . therefore , crossings of the free energies of different kinds of minima correspond to first - order phase transitions in our description . the il minima are expected to have the lowest free energy at high temperatures and the solid - like brg or bog minima should represent the globally stable phase at low temperatures . to determine how this `` freezing '' transition takes place , it is necessary to examine the dependence of the free energies of these different kinds of minima on the temperature @xmath0 . ( color online ) . temperature dependence of the dimensionless free energies of different local minima of a sample with @xmath104 and @xmath54 ( the sample is the same as the one for which results are shown in figs . [ fig1 ] , [ fig3 ] , [ fig4 ] and [ fig7 ] ) . the data for the brg , bog and il minima are shown by the ( green ) crosses and dashed line , ( blue ) asterisks and dotted line and the ( red ) plus signs and solid line , respectively . the lines are guides to the eye . ] in fig . [ fig8 ] , we have shown the results for the free energies of different minima of a sample with @xmath104 and @xmath54 . this sample is the same as the one for which results are shown in figs . [ fig1 ] , [ fig3 ] , [ fig4 ] , and [ fig7 ] . a similar plot , showing the same general behavior for a different sample , may be found in ref . . the brg minimum clearly has the lowest free energy at low temperatures ( while we have shown data for @xmath112 , we have checked that this remains true at lower temperatures ) , while the il minimum is the one with the lowest free energy at high temperatures . the interesting feature that emerges from data as that shown in this figure is that the bog minimum has the lowest free energy in an intermediate temperature range of small width ( between 18.0k and 18.3k for this sample ) , indicating that the melting of the low - temperature solid phase to the high - temperature il phase occurs in two distinct steps : the brg phase that is the thermodynamically stable one at low temperatures undergoes a first - order transition into a bog phase as the temperature is increased , and then this bog phase melts into the il phase via a second first - order transition at a slightly higher temperature . this two - step melting behavior is one of our main results . ( color online ) . results for a sample with @xmath113 and @xmath55 . voronoi plots for the brg and bog minima at 18.0k are shown in the top and middle panels , respectively . the symbols and color scheme used in these plots are the same as those in fig . the bottom panel shows the temperature dependence of the free energies of the brg ( blue line and squares ) , bog ( red line and circles ) and il ( black line and triangles ) minima , respectively . the lines are guides to the eye . , title="fig : " ] ( color online ) . results for a sample with @xmath113 and @xmath55 . voronoi plots for the brg and bog minima at 18.0k are shown in the top and middle panels , respectively . the symbols and color scheme used in these plots are the same as those in fig . the bottom panel shows the temperature dependence of the free energies of the brg ( blue line and squares ) , bog ( red line and circles ) and il ( black line and triangles ) minima , respectively . the lines are guides to the eye . , title="fig : " ] ( color online ) . results for a sample with @xmath113 and @xmath55 . voronoi plots for the brg and bog minima at 18.0k are shown in the top and middle panels , respectively . the symbols and color scheme used in these plots are the same as those in fig . the bottom panel shows the temperature dependence of the free energies of the brg ( blue line and squares ) , bog ( red line and circles ) and il ( black line and triangles ) minima , respectively . the lines are guides to the eye . , title="fig : " ] the same qualitative behavior , indicating the occurrence of two separate first - order transitions , is found in all the 4096-vortex samples we have studied at pin concentration @xmath53 ( @xmath54 ) . the average value of the temperature interval in which the bog phase has the lowest free energy is about 0.42k . this width exhibits fairly large sample - to - sample variations , ranging between about 0.1k in one sample to a maximum of 1.2k . as the system is cooled from the high - temperature liquid phase , it undergoes a first - order transition into a polycrystalline bog phase . such a transition has been observed @xcite in experiments on bscco samples with a small concentration of columnar pins . the value of the upper ( bog to il ) transition lies between 18.2k and 18.3k in all the 4096-pin samples we have studied . these values are quite close to the first - order melting temperature @xmath101 of the same system in the absence of pins @xcite . our results , thus , are consistent with the experimental observation @xcite of a weak dependence of the freezing temperature of the vortex liquid on the pin concentration @xmath2 for small values of @xmath2 . in addition , our work predicts a second first - order transition to a more ordered brg phase at a slightly lower temperature . for smaller samples at the same @xmath53 concentration ( @xmath114 with @xmath55 ) we did not always find the bog minima : the minimization procedure that led to the bog minima in the samples with @xmath104 often converged to minima of the brg type in the smaller samples . this is because the typical size of the crystalline grains at the bog minima at this pin concentration is of the order of the sample size for 1024-vortex samples . this can be seen by comparing the middle panel of fig . [ fig9 ] , where we have shown the voronoi plot for the bog minimum obtained for a @xmath114 sample , with the voronoi plot in the middle panel of fig . [ fig4 ] , which is for the same @xmath0 and @xmath2 , but a larger sample with 4096 vortices . one can plainly see that the domain size is comparable to the system size of the smaller samples . however , for the 1024-vortex samples where we found bog - type minima , the behavior of the free energies was found to be very similar to that shown in fig . an example of such behavior is shown in the bottom panel of fig , [ fig9 ] . the two - step melting transition found in the larger systems is found here also , indicating that this is the generic behavior . we have also carried out preliminary studies of the phase diagram for a slightly higher value of the pin concentration , @xmath56 . we find the same qualitative behavior , namely the occurrence of two - step melting , with a larger difference between the two transition temperatures . we therefore conclude that the two - step melting transition we have found is a characteristic feature of our model of layered superconductors with a small concentration of columnar pins . ( color online ) . the pinning free energy ( see text ) averaged over five samples with @xmath104 and @xmath54 . results for the brg and bog minima are shown by ( red ) triangles and ( black ) circles , respectively . the solid lines are straight lines joining the points . ] since a first - order transition is not characterized by power - law behaviors of thermodynamic quantities with universal exponents , the usual finite - size scaling analysis of numerical data for continuous transitions does not apply to our work . however , we have examined the dependence of the magnitudes of various discontinuous changes at the transitions on sample size . from the results for the free energy as a function of the temperature , we have calculated the entropy jump per vortex at the first - order transitions . the entropy change at the brg - bog ( lower temperature ) transition is found to be @xmath115 per vortex ( @xmath116 is the boltzmann constant ) , and the corresponding change at the bog - il ( higher temperature ) transition has a slightly higher value , @xmath117 per vortex . the sum of these two entropy jumps is slightly smaller than the entropy change ( @xmath118 per vortex ) at the single first - order melting transition found @xcite in the same system in the absence of pinning . all these results are physically reasonable . the difference between the degrees of order in the brg and bog minima is smaller than that between the bog and il minima , suggesting that the entropy jump at the lower transition should be smaller than that at the upper one . also , the low - temperature bog phase of the system in the presence of pinning is less ordered than the crystalline phase of the pure system , and the il phase is slightly more ordered than the vortex liquid in the system without pinning ( this is due to the local order of the vortices near the pinning centers which persists in the il phase ) . therefore , the net change of entropy in going from the bog phase to the il phase should be smaller than the entropy jump at the melting transition in the pure system . a comparison of our results for two sample sizes ( @xmath119 and 1024 ) does not show any appreciable dependence of the entropy changes on the sample size . we , therefore , conclude that there is no indication of any significant change in our phase diagram as the sample size is increased . since our mean - field treatment ignores the effects of fluctuations , it is important to address the question of whether one or both of the transitions found would become continuous if fluctuations were included . however , there are very few examples of such fluctuation - driven continuous transitions in three dimensions . in our calculations , the effects of the electromagnetic interaction among vortices on different layers are included . so , we expect our results regarding the nature of the transition to remain valid if fluctuations were included . this conclusion is supported by the result that our density functional theory provides a _ quantitatively _ a correct account @xcite of the first - order melting of the vortex lattice in the pure system . also , the transition in the presence of a small concentration of columnar defects is known to be first - order both experimentally @xcite and from simulations @xcite . the appearance of a sliver of the bog phase in our phase diagram may be qualitatively understood as arising from a competition between the elastic and pinning parts of the free energy . the elastic ( free ) energy plays a dominant role in the brg minima : the effect of the randomly located pinning centers is accommodated in this structure by small displacements of the vortices from their ideal lattice positions towards the nearest pinning center . where the occupation of a pinning center by a vortex would require a large displacement of the vortex , the pinning center is _ not _ fully occupied . for this reason , the number of pinning centers occupied by vortices at a brg minimum is always slightly lower than the total number of pinning centers . at the corresponding bog minima , on the other hand , the pinning centers are always occupied ( except in very rare cases where two pinning centers are located very close to each other ) . since the bog minima are obtained from liquid - like initial conditions , the starting point has fully occupied pinning centers , and vortices localized in small crystalline patches in their immediate vicinity ( see , for example , the bottom panel of fig . [ fig3 ] which shows such crystalline patches surrounding the pinning centers ) . the crystalline orientation of vortices around a vortex - binding pin site depends on the local arrangement of the pins.@xcite this orientation is , in general , different in different regions of the sample . these crystalline patches grow as the temperature is reduced , and eventually meet one another at grain boundaries to form a polycrystalline bog minimum . it is clear that the pinning centers are better accommodated in this structure than in the corresponding brg structure . on the other hand , the creation of grain boundaries costs elastic energy . thus , the bog minima are expected to have lower pinning energy but higher elastic energy than the brg ones for the same pin configuration . the elastic energy dominates over the pinning energy at low temperatures in our low pin - concentration samples . this is why the brg phase is globally stable at low @xmath0 . both these components of the free energy decrease in magnitude as the temperature is increased . the softening of the lattice near the melting transition causes the elastic energy to decrease faster than the pinning energy . this makes the pinning component of the free energy more important than the elastic part near @xmath101 , thereby making the total free energy of the bog minima ( which , as discussed above , have lower pinning energy ) lower than that of the bog minima . the bog to il transition at a slightly higher temperature is driven by the usual entropic mechanism . we can substantiate this qualitative explanation by evaluating the pinning component of the free energy , as defined in eq . ( [ pin ] ) , for the brg and bog minima . the results of our calculation , averaged over five samples ( each with 4096 vortices and 64 pins ) , are shown in fig . [ fig10 ] . the pinning energy is negative for both kinds of minima , as expected . the absolute value of the pinning energy of the bog minima shows a smooth ( nearly linear ) decrease as the temperature is increased . this is because both the value of the parameter @xmath20 ( see eq . ( [ single ] ) ) that determines the depth of the pining potential , and the height of the local density peak at a pinning center decrease with increasing @xmath0 . the plot for the brg minima shows a similar but much slower behavior , still monotonic or nearly so : it is not clear whether the very shallow minimum near @xmath0 = 17.6k is significant . in some of the samples , the total number of occupied pining centers increases by a small amount near this temperature , thereby reducing the value of the total pinning energy . this may reflect a better accommodation of the pinning centers by the lattice , which softens as the temperature is increased . this plot clearly demonstrates that the pinning centers are better accommodated at the bog minima . the difference in the pinning energies of the two kinds of minima decreases with increasing @xmath0 , but the difference in the elastic component of the free energy decreases faster ( this is clear from our results for the total free energy ) due to a softening of the elastic constants with increasing temperature . the overall effect is a crossing of the free energies of the two kinds of minima near the melting transition . quantitatively , however , the values of the two parts of the free energy and their dependence on @xmath0 are determined by the material parameters of the superconductor and the properties of the pinning centers . since several experimental studies@xcite of the effects of irradiation - induced columnar pinning on the mixed state of bscco exist in the literature , we have used parameter values appropriate for this system . for other layered superconductors , the bog phase might occur over a wider or narrower ( even vanishing ) range . as mentioned in section [ props ] , the density distribution in both brg and bog minima is very inhomogeneous : at temperatures close to @xmath101 there are liquid - like regions , characterized by low values of the local peak densities in parts of the sample . in this subsection , we show that this inhomogeneity leads to a spatial variation of a `` local melting temperature '' , defined below . as mentioned in the introduction , such spatial variations of a local melting temperature have been deduced from measurements of the local magnetization in bscco samples with random point@xcite and columnar pinning@xcite . since we are dealing with time averaged densities , it is clear that the value of @xmath120 at a local peak of the density field provides a measure of the degree of localization of the vortex whose average position corresponds to the location of the density peak . a high ( low ) value of the local peak density implies strong ( weak ) localization . smaller values of the local peak density imply mobile , liquid - like behavior . the value of the local density is , of course , equal to @xmath43 everywhere in the liquid state in the absence of pinning . the presence of pinning centers causes the local density to vary in space , but in the liquid state this variation does not lead to local peaks higher than about @xmath121 ( excluding the vortices localized at the pinning centers ) . a similar result was also obtained in previous studies @xcite of vortices in the presence of pinning , where it was found that values of the peak density lower than about @xmath121 correspond to the liquid state . we , therefore , take the value @xmath122 of the local peak density as separating solid- and liquid - like behaviors . ( color online ) . determination of the local melting temperatures in different regions of a sample . the top panel , at @xmath93k and for the bog minimum , shows the three different regions ( a , b and c ) considered in the calculation . the positions of local density peaks in these regions are indicated by ( red ) plus signs ( region a ) , ( blue ) crosses ( region b ) and ( green ) circles ( region c ) . the black dots represent the positions of the local density peaks in the other regions , and the ( black ) circles show the locations of the pinning centers . the bottom panel shows the dependence of the average local peak density @xmath123 ( normalized by the liquid density @xmath43 ) calculated for these regions on the temperature @xmath0 . data for regions a , b and c are respectively shown by ( red ) triangles , ( blue ) squares , and ( green ) circles . the solid lines are guides to the eye . , title="fig : " ] ( color online ) . determination of the local melting temperatures in different regions of a sample . the top panel , at @xmath93k and for the bog minimum , shows the three different regions ( a , b and c ) considered in the calculation . the positions of local density peaks in these regions are indicated by ( red ) plus signs ( region a ) , ( blue ) crosses ( region b ) and ( green ) circles ( region c ) . the black dots represent the positions of the local density peaks in the other regions , and the ( black ) circles show the locations of the pinning centers . the bottom panel shows the dependence of the average local peak density @xmath123 ( normalized by the liquid density @xmath43 ) calculated for these regions on the temperature @xmath0 . data for regions a , b and c are respectively shown by ( red ) triangles , ( blue ) squares , and ( green ) circles . the solid lines are guides to the eye . , title="fig : " ] using this criterion , we can determine whether a small region of the sample at a given minimum is in a locally `` solid '' or `` liquid '' state . to do this , we define a quantity @xmath123 as the average of the local peak densities in a small region containing @xmath124 vortices ( see fig . [ fig11 ] ) . the very high local density peaks representing vortices trapped at pinning centers are not included in this average . values of @xmath123 substantially larger than @xmath122 indicate solid - like behavior in the region under consideration , while substantially lower values of @xmath123 suggest a locally melted region . to determine how the local melting temperature varies from one part of the sample to another , we have studied the temperature dependence of @xmath123 for different regions of the sample . typical results are shown in fig . [ fig11 ] for the pin configuration for which we have earlier shown detailed results in several figures . in the top panel , where the positions of the local density peaks in the bog minimum at @xmath93k and the locations of the pinning centers are shown , we have indicated three regions for which the average local peak density @xmath123 was calculated . the local density peaks in these regions are indicated by ( red ) plus signs ( region a ) , ( blue ) crosses ( region b ) and ( green ) circles ( region c ) , while the black dots represent the positions of the local density peaks in the other regions . the bottom panel of fig . [ fig11 ] shows the dependence of the @xmath123 s calculated for these three regions on the temperature @xmath0 . at each value of @xmath0 , the minimum with the lowest free energy at that temperature was used in the calculation of @xmath123 . ( color online ) . percolation and melting ( see text ) . the ( red ) plus signs denote the locations of liquid - like local density peaks ( peak height smaller than @xmath121 ) , and the ( blue ) circles indicate the solid - like ones ( peak height greater than @xmath121 ) . the top panel is for the bog minimum of a 4096-vortex sample at 18.2k and the bottom panel is for the il minimum of the same sample at 18.4k . the thermodynamic transition between the bog and il phases takes place between these two temperatures . , title="fig : " ] ( color online ) . percolation and melting ( see text ) . the ( red ) plus signs denote the locations of liquid - like local density peaks ( peak height smaller than @xmath121 ) , and the ( blue ) circles indicate the solid - like ones ( peak height greater than @xmath121 ) . the top panel is for the bog minimum of a 4096-vortex sample at 18.2k and the bottom panel is for the il minimum of the same sample at 18.4k . the thermodynamic transition between the bog and il phases takes place between these two temperatures . , title="fig : " ] it is clear from the plot and from similar ones for other pin configurations ( one of which was shown in ref . ) that the `` local melting temperature '' , operationally defined as the temperature at which @xmath123 drops from values well above @xmath122 to values clearly below , varies from region to region . the range over which the local melting temperature varies is comparable to that found in the experiments @xcite . the values of the local melting temperature are strongly correlated with the local pin structure and the resulting defect structure of the vortex solid . region b of the sample does not have any pinning center and is located across a grain boundary of the bog minimum . as noted in section [ props ] , regions near grain boundaries appear to melt at temperatures that are slightly lower than the global transition temperature determined by the crossing of free energies . this is why the local melting temperature for region b is the lowest . this temperature corresponds to the transition from the brg to the bog state . in region a the vortices form a nearly perfect crystalline arrangement with no topological defects . the local melting temperature measured in this region is , as a consequence , close to that of the pure system . region c contains a cluster of pinning centers , and the relatively large value of @xmath123 for this region at temperatures higher than the bog to il transition temperature reflects the local solid - like structure of vortices situated near pinning centers . thus , the spatial variation of the local transition temperature is closely correlated with the `` pinning landscape '' of the sample . we have found a second way of correlating the melting transition with the local density structure of the free energy minima . this second way is based on a previous study@xcite of the melting of the vortex lattice in the presence of periodic pinning , where it was found that the melting transition corresponds to the onset of percolation of liquid - like regions defined using the peak - density criterion mentioned above . we focus for this purpose on the upper transition between the bog and il phases . we classify vortices represented by local peaks of the density as solid - like or liquid - like , depending on whether the density at the local peak is higher or lower than @xmath121 . we then check whether the regions containing liquid - like vortices percolate across the sample . we find , as in the earlier study , that the melting transition coincides with the occurrence of percolation of the liquid - like regions . typical results are shown in fig . [ fig12 ] where the top panel shown the locations of solid- and liquid - like local density peaks at a bog minimum obtained at 18.2k ( this minimum has the lowest free energy at this temperature ) , and the bottom panel shows a similar plot for the il minimum of the same sample at 18.4k ( the il minimum is the one with the lowest free energy at this temperature , so that the melting transition in this sample occurs between 18.2k and 18.4k ) . the liquid - like regions do not percolate at 18.2k , whereas they do at the higher temperature of 18.4k . thus , the melting transition in this sample also corresponds to the occurrence of percolation for the liquid - like regions . similar behavior was found in the other samples we have studied . this observation provides a convenient way of approximately locating the transition point . this may be useful in other situations where the method of locating the transition temperature from a crossing of free energies may not be easily implementable ( e.g. at higher pin concentrations where the melting transition is expected to become continuous ) . we have presented here the results of a detailed investigation of the structural and thermodynamic properties of a system of vortices in a highly anisotropic layered superconductor with a small concentration of randomly placed columnar pinning centers . both the external magnetic field and the columnar pins are assumed to be perpendicular to the superconducting layers . our method , based on numerical minimization of the appropriate free - energy functional , allows us to obtain very detailed information about the density distribution in the different free energy minima ( which allows us to reliably identify the phases corresponding to these minima ) , and to map out the phase diagram of the system . there are several salient results of our study . the first one is the occurrence of a topologically ordered brg phase at low temperatures . while the occurrence of a low - temperature brg phase in superconductors with a low concentration of random point pinning centers is well - established now , relatively little is known about the existence of such a phase in superconductors with random columnar pins . our results are consistent with those of a recent numerical study @xcite of a similar system . it is clear from our work that the brg minima represent a phase distinct from the polycrystalline bog phase also found in our study . we can not conclusively rule out the possibility that free dislocations would appear at the nearly crystalline minima at length scales much longer than those considered in our numerical study . if this should happen , then the `` hexatic glass '' phase suggested in some earlier theoretical studies @xcite would become a possible candidate for describing the brg minima found in our study . this phase , however , would be distinct from the bog . our second important result is the occurrence of a two - step melting transition : we find that the low - temperature brg phase transforms into a polycrystalline bog phase as the temperature is increased , and this bog phase then melts into the high - temperature il at a slightly higher temperature . this conclusion about the occurrence of two distinct transitions would remain valid even if the true nature of the low - temperature phase turns out to be slightly different from a bragg glass : our work shows that the brg and bog minima are quite distinct from each other . the possibility of occurrence of a two - step melting transition of the vortex lattice in systems with random point pinning has been suggested earlier @xcite . our work provides support to this suggestion . to our knowledge , the second ( lower @xmath0 ) transition between the bog and brg phases has not been observed in experiments on layered superconductors with a small concentration of random columnar pins . this may be due to strong metastability : the bog minimum into which the il is expected to freeze as the temperature is decreased remains locally stable at temperatures lower than that at which its free energy crosses that of the brg minimum , suggesting that it would be difficult to see in experiments the transition to the globally stable brg phase . the situation here may be similar to that found in a recent experimental study@xcite of a low-@xmath125 superconductor with weak point pinning which is expected to exhibit a brg phase at low @xmath0 . it is , however , found in the experiment that the vortex solid obtained by cooling the sample in the presence of the external magnetic field has a polycrystalline structure , indicating that the metastability of this disordered state prevents the system from reaching the more ordered ( brg ) equilibrium state at low temperatures . in our numerical work , the brg minima were obtained by performing the free - energy minimization from an initial configuration with crystalline order . it is not clear how a similar procedure can be adopted in experimental studies . a low - temperature brg phase has been observed in a recent simulation@xcite of a model of htsc with a small concentration of columnar pinning centers . however , this simulation finds a single first - order transition between the brg and il phases at low pin concentrations : the small intermediate region of bog phase found in our study is not observed . this is probably due to the smallness of the system sizes ( @xmath126 100 vortex lines ) used in the simulation . as discussed in sec . [ phasediag ] above , the polycrystalline bog minima are found only if the sample size is larger than the typical size of the crystalline domains : only the brg minimum is found at low temperatures if this condition is not satisfied . since the crystalline domains become large at small pin concentrations , it is quite likely that a simulation with small system sizes and low pin concentration would not see the bog phase . another possibility is that a narrow `` two - phase '' region found in ref . near the brg melting transition actually corresponds to the intermediate bog phase found in our study . a third possibility is that the intermediate bog phase , which arises due to a competition between the elastic and pinning components of the free energy ( see sec . [ phasediag ] where it is shown that the pinning energy favors the bog phase ) , does not appear in the simulation of ref . because the pins are assumed to be weak in that work . our study also illustrates the spatial inhomogeneity of the melting process in the presence of disorder : we have found that a `` local '' melting temperature defined using a criterion based on the degree of localization of the vortices shows considerable spatial variation . this spatial variation is strongly correlated with the pinning landscape associated with the random spatial location of the pinning centers . our results about the spatial inhomogeneity of the local melting temperature are consistent with those of recent experiments @xcite on superconductors with pinning disorder . these results establish the usefulness of our numerical method in dealing with the problem of vortex matter in the presence of random pinning . it would be interesting to examine the extent to which our results depend on the values of the parameters appearing in the free energy functional . it would also be clearly useful to carry out similar studies of other related problems , such as the complete phase diagram of systems with random columnar pins in the @xmath127 plane , and the phase behavior of systems with random point pinning . some of these investigations are currently in progress . g. blatter , m.v . feigelman , v. b. geshkenbein , a. i. larkin , and v. m. vinokur , rev . phys . * 66 * , 1125 ( 1994 ) . . de gennes , _ superconductivity of metals and alloys _ , addison - 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we study the melting transition of the low - temperature vortex solid in strongly anisotropic layered superconductors with a concentration of random columnar pinning centers small enough so that the areal density of the pins is much less than that of the vortex lines . both the external magnetic field and the columnar pins are assumed to be oriented perpendicular to the layers our method , involving numerical minimization of a model free energy functional , yields not only the free energy values at the local minima of the functional but also the detailed density distribution of the system at each minimum : this allows us to study in detail the structure of the different phases . we find that at these pin concentrations and low temperatures , the thermodynamically stable state is a topologically ordered bragg glass . this nearly crystalline state melts into an interstitial liquid ( a liquid in which a small fraction of vortex lines remain localized at the pinning centers ) in two steps , so that the bragg glass and the liquid are separated by a narrow phase that we identify from analysis of its density structure as a polycrystalline bose glass . both the bragg glass to bose glass and the bose glass to interstitial liquid transitions are first - order . we also find that a local melting temperature defined using a criterion based on the degree of localization of the vortex lines exhibits spatial variations similar to those observed in recent experiments .

<s>[INST]the mixed phase of type - ii superconductors with random pinning is generally regarded to be an archetypal test system for the study of the effects of quenched disorder on the structure and melting of solids . in this phase , magnetic flux penetrates the sample as quantized vortex lines which form a special physical system known as `` vortex matter '' . the fascinating equilibrium and dynamical properties of vortex matter in the mixed phase of high - temperature superconductors ( htscs ) have prompted considerable experimental and theoretical attention for more than a decade ( see ref . for an early review ) . the mixed phase of htscs is strongly affected by the presence of pinning centers , either intrinsic or artificially generated . understanding the effects of pinning in these systems is basic for practical applications because pinning strongly influences the value of the critical current @xcite . the vortex lines in a pure type - ii superconductor form a triangular lattice ( the abrikosov lattice ) at low temperatures . because of enhanced thermal fluctuations in highly anisotropic , layered htscs , the abrikosov lattice in very pure samples , in a magnetic field perpendicular to the layers ( the field will be assumed to be in this direction throughout our discussion ) , undergoes a first - order melting transition@xcite into a resistive vortex liquid ( vl ) as the temperature @xmath0 increases . random pinning destroys the long - range translational order of the abrikosov lattice and leads to the occurrence of a variety of glassy phases at low @xmath0 . it is now generally accepted that in systems with random point pinning , a topologically ordered low - temperature phase with quasi - long - range translational order ( denoted as the `` bragg glass '' ( brg ) phase ) occurs at low fields if the pinning disorder is sufficiently weak . this has been established theoretically @xcite as well as experimentally ( see e.g. ref . ) . the possibility of an amorphous vortex glass ( vg ) phase , with nonlinear voltage - current characteristics and vanishing resistance in the zero - current limit , in systems with strong pinning ( or at high magnetic fields where the effects of pinning disorder are enhanced ) was suggested by fisher@xcite ( see also ref . ) . however , in spite of extensive investigations , the existence of a true vg phase ( i.e. , an amorphous glassy phase thermodynamically distinct from the high - temperature vl ) in systems with uncorrelated point pinning remains very controversial : different calculations @xcite lead to different conclusions and the experimental situation@xcite is similarly contradictory . a variety of `` glassy '' behavior has been reported in different experiments ( see ref . and references therein ) near the first - order melting transition of the brg phase of both conventional superconductors and htscs with point pinning . it has been suggested@xcite that these observations may be understood if it is assumed that the melting of the brg phase occurs in two steps : the brg first transforms into a `` multidomain '' glassy phase that melts into the usual vl at a slightly higher @xmath0 . columnar pinning defects can be produced for example as damage tracks arising from heavy - ion bombardment . the technological importance of these extended defects oriented parallel to the direction of the external magnetic field has been long recognized@xcite : they are highly effective in increasing the critical current by localizing vortex lines along their length . heavy - ion irradiation produces a random array of parallel columnar defects each of which can trap one or more vortices at low temperatures . the effects of such random arrays of extended defects , oriented perpendicular to the superconducting layers , on the properties of the mixed phase of htscs have been extensively studied experimentally@xcite . the same question has also been examined theoretically@xcite and numerically@xcite . when the columnar pinning is strong , and their concentration exceeds that of the vortex lines , a so - called `` strong '' bose glass ( bog ) phase with nearly all the vortex lines localized at the pinning centers occurs@xcite at low @xmath0 . this phase is strongly disordered with very short - range translational and bond - orientational correlations . the behavior in this regime is fairly well - understood in terms of a mapping@xcite of the thermodynamics of the system to the quantum mechanical properties of a two - dimensional system of interacting bosons in a random potential . much less is known about the behavior in the dilute pin limit where the concentration of pins is much smaller than that of vortex lines . in such systems , one expects@xcite a `` weak '' bog phase at low temperatures , with a small fraction of vortex lines localized strongly at the pinning centers and the remaining ones localized relatively weakly in the interstitial region between pinning centers . as the temperature is increased , this phase should@xcite melt into an interstitial liquid ( il ) . in the il phase , some of the vortices remain trapped at the pinning centers , while the other , interstitial ones , form a liquid . the pinned vortices are expected@xcite to delocalize , thereby forming the usual vl , at a crossover occuring at a higher temperature . the melting transition of the `` weak '' bog phase into the il is predicted@xcite to be first - order for small pin concentrations , whereas the `` strong '' bog to vl transition occurring for large pin concentrations is known@xcite to be a continuous one . a first - order melting transition of the `` weak '' bog phase has been observed@xcite in recent experiments on samples of @xmath1 ( bscco ) with a small concentration of columnar pins . the bog phase in these systems is found@xcite to have a polycrystalline structure with ordered vortex crystallites of different orientations embedded in the interstitial region between vortices pinned at the columnar defects . if the pin concentration is sufficiently small , the melting of this bog phase upon increasing the temperature occurs into an il phase with a fraction of vortex lines remaining pinned at the defects . these pinned vortices delocalize at a higher temperature@xcite . the temperature at which the first - order bog to il transition occurs is@xcite very close to the melting temperature of the same system without the columnar pins , if the pin concentration is small . as the pin concentration is increased , the melting temperature increases and the transition eventually becomes continuous . the difference between the melting temperature and the temperature at which the pinned vortices in the il phase delocalizes decreases and eventually goes to zero as the pin concentration increases . another interesting feature , found experimentally for both point@xcite and columnar@xcite pinning , is that the melting of the low @xmath0 `` solid '' phase is `` inhomogeneous '' in that it occurs locally over a range of temperatures : the local transition temperature , which can be measured from the local magnetization , is different in different regions of the sample . this inhomogeneity of the local melting temperature is believed@xcite to be closely related to the local arrangement of the specific pinning centers ( the so - called `` pinning landscape '' ) in each sample studied . the polycrystalline nature of the bog phase for small pin concentrations has also been observed in simulations@xcite . recent numerical work@xcite indicates that a brg phase , with topological order , may also exist in such systems provided that the pin concentration is sufficiently small . in these simulations , the brg phase is found to melt into the il phase via a first - order transition as the temperature is increased . as the pin concentration is increased beyond a critical value , the brg phase disappears@xcite and a low - temperature bog phase with a continuous bog to il transition upon increasing the temperature is found@xcite . in this paper , we approach these problems through a different numerical method . we consider a layered , strongly anisotropic superconductor ( such as bscco ) with a dilute random array of columnar defects oriented perpendicular to the layers , and with a magnetic field applied parallel to the columnar pins . we describe the equilibrium properties of this system in terms of vortex density variables , using a free energy functional of the ramakrishnan - yussouff@xcite ( ry ) form . we numericall minimize a spatially discretized version of this free energy functional and obtain the vortex density configuration at each local minimum . analysis of these density configurations , both in terms of a variety of correlation functions and by direct visualization of the arrangement of the vortices ( vortex positions are identified with those of local peaks of the vortex density ) , allows us to identify the nature of the phases corresponding to different local minima of the free energy . comparison of the values of the free energy at the minima as the temperature varies yields the transition temperatures . a similar procedure has been successfully employed for the case of a regular array@xcite of columnar pinning centers . we find in our study that that a bragg glass phase exists at low temperatures for samples with a small concentration of columnar pins . we will present evidence for this phase from our analysis of the vortex density and associated correlation functions . upon warming , this phase melts into what we show to be an insterstitial liquid ( il ) phase , but the melting is shown@xcite to occur in two steps : the brg and il phases are separated , over a narrow temperature range , by an intermediate phase which exhibits a multi - domain polycrystalline structure . we show that this intermediate phase should be identified as a bose glass ( bog ) . the temperature of the upper ( bog to il ) transition is approximately independent of the columnar pin concentration @xmath2 , at the low @xmath2 values studied . both the brg to bog and the bog to il transitions are found to be first - order . we also find that a local melting temperature can be suitably defined using a criterion based on the degree of localization of the vortices , and that its behavior ( in particular , its spatial variation ) is quite consistent with what is seen in experiments@xcite . the value of the local melting temperature is strongly correlated with the presence of topological defects ( dislocations ) in the vortex solid which , in turn , is correlated with the local arrangement of the pinning centers . we also show that the transition to the il phase corresponds to a percolation of regions containing liquid - like ( delocalized ) vortices across the sample . after this introduction , we discuss our definitions , model and numerical methods in the next section . then in section [ results ] we present our results . we discuss first the free energy minima and their study through the use of tools such as correlation functions , local peak - density plots , and voronoi construction for the lattice formed by local density peaks . these tools allow the identification of the phases at each free energy minimum , as we shall show . then we derive the phase diagram and show that indeed the brg and il phases are separated by a thin sliver of bog . finally , our results for the nature of the local melting are displayed and discussed . a brief conclusions section recapitulates the main points of the paper and discusses them in the context of existing results . the general procedures that we use are quite similar to those employed in previous work on a regular array of columnar pins@xcite . we will therefore give here only a brief summary , emphasizing the details that are different in the random case considered here . the system we study is a layered superconductor in the extreme anisotropic limit , that is , with vanishing josephson coupling between layers , which are then coupled via the electromagnetic interaction only . this limit is appropriate for the bi- and tl- based htsc compounds in a large region of the magnetic field ( @xmath3)@xmath0 plane . in this work , we will use material parameter values appropriate to bscco . with these assumptions , one can write the energy of a system of `` pancake '' vortices residing in the layers as a sum of anisotropic two - body interactions . for straight columnar pins normal to the layers , the pinning potential is the same in every layer . it is then possible to write the free energy as a functional of the _ time averaged _ areal vortex density @xmath4 : @xmath5-f_0=f_{ry}[\rho]+f_p[\rho ] . \label{fe}\ ] ] where @xmath6 is the free energy corresponding to a uniform vortex liquid of density @xmath7 ( @xmath8 is the magnetic induction and @xmath9 the superconducting flux quantum ) . the first term in the right - hand side of eq . ( [ fe ] ) is the free energy functional in the absence of pinning . as explained above we use for this free energy the ry@xcite functional , which is known@xcite to give a quantitatively accurate description of the vortex - lattice melting transition in the absence of pinning . it is of the form : @xmath10 & = & \int d^2r\left[\rho({\bf r } ) \ { \ln(\rho({\bf r}))-\ln ( \rho_0)\ } - \delta\rho({\bf r})\right ] \nonumber \\ & -&\frac{1}{2}\int d^2r \int d^2r^\prime \,\tilde{c}(|{\bf r } - { \bf r}^\prime | ) \delta\rho({\bf r } ) \delta\rho({\bf r}^\prime ) . \label{ryfe}\end{aligned}\ ] ] here @xmath11 is the inverse temperature , @xmath12 , and @xmath13 is the usual direct pair correlation function@xcite which may be written as a sum over layers : @xmath14 , with @xmath15 ( where @xmath16 is the layer separation and @xmath17 the in - layer distance ) being the corresponding direct pair correlation function of a layered liquid of pancake vortices . the direct correlation function , which is needed as input in our free energy , can be accurately calculated in a number of ways . we will use here the results of the hypernetted chain calculation of ref . . in general , the results in the limit considered depend on the values of the in - plane london penetration length @xmath18 , the interlayer spacing @xmath19 and a dimensionless coupling parameter @xmath20 given by : @xmath21 for bscco we will take @xmath22 , and we will assume a standard two - fluid temperature dependence for @xmath18 with @xmath23 and @xmath24k ( at zero field ) . the second term in the right - hand side of eq . ( [ fe ] ) represents the pinning and is of the form : @xmath25 = \int d^2r v_p({\bf r } ) \delta\rho({\bf r } ) . \label{pin}\ ] ] where @xmath26 is the pinning potential which can be written as @xmath27 with the sum extending over the planar positions of the random pinning centers . we take the potential @xmath28 corresponding to a single pinning center to be of the usual truncated parabolic form:@xcite @xmath29\theta(r_0-r ) \label{single}\ ] ] where @xmath30 is the range . the basic length in the problem , which we will use as our unit of length unless otherwise indicated , is @xmath31 , defined by the relation @xmath32 . we choose @xmath30 to be @xmath33 and take the dimensionless constant @xmath34 , for which value , as previously shown,@xcite each pinning center traps approximately one vortex in bscco , in the temperature range of interest . this range is determined by the following considerations . we will keep the field fixed at @xmath35 t , and vary the temperature . the melting temperature of the unpinned lattice is then @xmath36k@xcite , and we , therefore , consider the neighborhood of this temperature . then one has , to a very good approximation @xmath37 ( with the temperature in kelvin ) , while @xmath38 . to carry out our numerical calculations , we discretize the density variables on a computational triangular grid of lattice spacing @xmath39 , containing @xmath40 sites . we take the spacing @xmath39 to be @xmath41 in our calculations , where @xmath42 is the equilibrium lattice constant of the vortex lattice in the temperature range considered at the indicated field . this value , as pointed out in ref . , is slightly higher than that of a triangular vortex lattice of density @xmath43 , which is @xmath44 . we define at each site @xmath45 on this computational lattice a variable @xmath46 , with @xmath47 , where @xmath48 is the area of each computational unit cell . results reported here are for @xmath49 , which , for the chosen value of @xmath39 , corresponds to including @xmath50 4096 vortices in the calculation . preliminary and confirmatory results at @xmath51 ( 1024 vortices ) were also obtained . a number of pinning sites ( @xmath52 ) are put , at random , on some of the computational lattice sites . the results presented here , which correspond to the dilute limit , will be primarily for a pin concentration @xmath2 of @xmath53 , that is , a number of pins @xmath54 at @xmath49 ( or @xmath55 at @xmath51 ) . some preliminary results for @xmath56 ( @xmath57 at @xmath49 , or @xmath58 at @xmath51 ) will also be discussed briefly . with random pins , the results depend on the particular random pin configuration and averaging over different such configurations is required . the dependence is however not strong : as we shall see , averaging over five to ten configurations is enough to make statistical errors sufficiently small for our purposes . to perform our studies , we numerically minimize the discretized free energy with respect to the @xmath40 discretized density variables @xmath59 . to do so , the interaction term in the right side of eq . ( [ ryfe ] ) must be repeatedly evaluated , and since this term is of a convolution form , this is most efficiently done in momentum space , through the use of efficient fast fourier transform ( fft ) routines . this avoids having to evaluate this term as a double sum which would be computationally much more cumbersome than performing the direct and inverse fft s . in performing the minimization , one must keep in mind that the variables @xmath59 must be nonnegative . this precludes the use of many efficient minimization algorithms . we use a procedure@xcite that ensures that this constraint is satisfied . numerical minimization is performed starting with an appropriate initial condition for the density variables . as explained in sec . [ results ] below , different local minima may be found , at the same field and temperature , depending on the initial conditions . these minima correspond to different phases . the minimization procedure yields not only the value of the free energy at each minimum but also the detailed vortex density configuration at the minimum found , i.e. the values of the set @xmath59 at the minimum . it is then straightforward to analyze the actual density configuration in several ways . it is also possible to evaluate any desired density correlations . the nature of the phase corresponding to each local minimum of the free energy can be inferred from such analysis . the ( mean - field ) phase diagram is then obtained from a comparison of the free energies of the different minima as the temperature @xmath0 is varied . the results of carrying out this program are discussed below . as explained above , minima of the free energy are found by starting the minimization process with appropriate initial conditions . we use three different kinds of initial conditions . the first kind is a uniform density ( @xmath60 for all @xmath61 ) , corresponding to a completely disordered liquid state . this is typically used to obtain , as we shall see , liquid - like states at temperatures near the equilibrium melting temperature of the pure vortex lattice , which is@xcite @xmath62k for the value of @xmath8 considered here . the second kind corresponds to a crystalline initial state , with values of @xmath59 as obtained in ref . for the pure vortex lattice . in our system with a spatially varying random pinning potential , the pinning energy of such a crystalline density configuration depends on the choice of the computational lattice sites at which the periodic local peaks of the density are located . we take , among all possible choices equivalent by symmetry operations in the computational lattice , the one for which the pinning energy is lowest for the specific pinning configuration under consideration . these initial conditions are used to obtain ordered states at lower temperatures . finally , states originally obtained by either of these two procedures can be slowly warmed up , or cooled down : in this case the initial conditions are simply the final state obtained at the previous temperature . as one warms up or cools down a state , its nature in general changes : liquid configurations may become unstable upon cooling and ordered configurations upon warming . whichever initial conditions one uses , a local minimum of the free energy is eventually found . at a given temperature , in general several local minima with different density configurations , characterized by the values of the set of @xmath59 variables , are obtained . the minimum with the lowest free energy represents , at a given @xmath0 , the true equilibrium state . it is obviously necessary to develop systematic procedures to identify the structure of each of these diverse minima . since we have access to the full set of density variables at the computational lattice sites , we have at our disposal a variety of methods to achieve that goal . the first is to calculate the density correlations , e.g. the structure factor @xmath63 : @xmath64 where @xmath65 is the discrete fourier transform of the set @xmath59 . equivalently , one can consider the fourier transform of @xmath63 , which is the two - point spatial correlation function @xmath66 of the time - averaged local density . we will present here results for @xmath63 , considered as a function of the vector @xmath67 , and for the angularly averaged spatial density correlation function , @xmath68 . it is also very useful to consider the spatial structure formed by the _ vortices _ at low temperatures . for this purpose we have extracted from @xmath59 the local peak densities . we say that the density locally peaks at site @xmath61 if the value of @xmath46 at @xmath69 is higher than that at any other computational lattice site within a distance @xmath70 from @xmath61 , where , as defined above , @xmath71 is the equilibrium spacing of the unpinned vortex lattice . as expected , we find that at low - temperature solid - like minima where the vortices are strongly localized , the number of local density peaks matches the number of vortices @xmath72 . the positions of these peaks determine what we will call the `` vortex lattice '' . much useful information about the spatial structure of this vortex lattice may be obtained by plotting directly the local density values at the vortex lattice points . an excellent , and complementary , alternative to help elucidate the degree of vortex lattice order is to carry out a voronoi construction : we recall that in the voronoi construction one determines cells around each lattice point by a wigner - seitz procedure . in a perfect crystal , all the resulting wigner - seitz cells are identical , while in the general case the cells can have different sizes and shapes . the number of sides of the wigner - seitz cell surrounding a lattice point is identified with the number of `` nearest neighbors '' of that lattice point , and the difference between this number and the average ( six in our case ) marks the position of defects ( disclinations ) . we will make use of such plots below . since we will be concerned not only about translational , but also with orientational order , we will also examine the bond - orientational correlation function @xmath73 in the vortex lattice defined as : [ angular ] @xmath74 where the angular brackets denote overall average over the vortex lattice and the field @xmath75 is given by : @xmath76\ ] ] with @xmath77 being the angle that the bond connecting a vortex at @xmath78 to its @xmath45-th neighbor makes with a fixed axis , and @xmath79 is the number of neighbors of the vortex at @xmath78 . it is also possible , and as we shall see , useful , to define what we will call a `` translational correlation function '' in the vortex lattice in a way that is quite analogous to the definition of @xmath73 . this function , which we denote as @xmath80 , is defined by an equation identical to the right - hand side of eq . ( [ ang1 ] ) , but with the field @xmath81 being defined as @xmath82 where @xmath83 is a reciprocal lattice vector of the triangular vortex lattice in the absence of pinning . we will consider here only the case where @xmath83 is a shortest nonzero reciprocal lattice vector and average over the results obtained for the six equivalent @xmath84 s . ( color online ) the static structure factor @xmath63 ( see eq . ( [ sofk ] ) ) for three local minima obtained at @xmath85k for the same pin configuration . the ( red ) circles are for a state identified , from the overall evidence ( see text ) , as a bragg glass ( brg ) , the ( blue ) triangles are for a bose glass ( bog ) state , and the ( green ) crosses are for an insterstitial liquid ( il ) . the vertical lines are guides to the eye . ] our identification of the different phases is based on analysis of all this information . we show some of the results in the next few figures . these all correspond to samples with 64 pins and 4096 vortices . first , in fig . [ fig1 ] , we show the structure factor , as defined in eq . ( [ sofk ] ) . the three sets of results shown there are for local free energy minima at the same temperature , @xmath85k , obtained with different initial conditions of the three kinds described above , and the same pin configuration . other pin configurations yield very similar results ( a different example is shown in fig . 1c of ref . ) . the green symbols correspond to the free energy minimum obtained by starting with uniform initial conditions . clearly , the structure factor is completely featureless and liquid - like in this case the absolute value of @xmath86 never exceeds five . the red circles are for a local minimum obtained with initial conditions corresponding to the best crystalline state , as explained above , for this pin configuration . the structure factor now exhibits typical ordered behavior , highlighted by six sharp bragg - like peaks which are emphasized by the added vertical lines in the figure . finally , the blue triangles correspond to a minimum obtained by first `` quenching '' with uniform initial conditions to a relatively low temperature ( 16.8k ) where the liquid - like state is found not to be stable , and then slowly warming , at 0.2k temperature intervals , back up to 18.4k . as one can see , the @xmath63 for this minimum has an intermediate structure , with several relatively well - defined peaks , more than six in number , whose heights are considerably lower than those of the peaks found for the ordered minimum . ( color online ) . the angularly averaged density correlation function @xmath68 plotted at the same temperature as in fig . [ fig1 ] as a function of dimensionless distance . the results are this time averaged over five different pin configurations . the results for the bog and il minima are shown in the top panel . the ( blue ) dotted line plot with higher peaks corresponds to bog minima and the ( green ) light grey plot with fewer and lower peaks to il minima . the bottom panel displays the results for the brg minima . the vertical and horizontal scales are the same in the two panels and the color scheme is the same as that in fig . [ fig1].,title="fig : " ] ( color online ) . the angularly averaged density correlation function @xmath68 plotted at the same temperature as in fig . [ fig1 ] as a function of dimensionless distance . the results are this time averaged over five different pin configurations . the results for the bog and il minima are shown in the top panel . the ( blue ) dotted line plot with higher peaks corresponds to bog minima and the ( green ) light grey plot with fewer and lower peaks to il minima . the bottom panel displays the results for the brg minima . the vertical and horizontal scales are the same in the two panels and the color scheme is the same as that in fig . [ fig1].,title="fig : " ] in fig . [ fig2 ] , results for the angularly averaged density correlation function @xmath68 are displayed . these results are for minima obtained at the same temperature , and using the same initial condition procedures , as those for the data shown in fig . [ fig1 ] however , the results shown here are averages over five different pin configurations . the nearly flat ( green ) curve in the top panel corresponds to minima obtained from quenches with uniform initial conditions , the ( red ) curve with the well - defined peaks shown in the bottom panel corresponds to minima obtained with crystalline initial conditions , and the ( blue ) curve with the intermediate peaks shown in the top panel is for minima obtained by quenching with uniform initial conditions to a low temperature and subsequent slow warming ( very similar results can alternatively be obtained by slowly cooling a high - temperature liquid - like minimum to a temperature where it is unstable ) . one can see then that the results for @xmath68 are fully consistent with those found in fig . [ fig1 ] : the minimum obtained from uniform initial conditions is fully disordered , while that obtained from crystalline initial conditions exhibits a large degree of crystalline order . for the the third kind of minima , we find some degree of intermediate range order . ( color online ) . local peak densities at three different local minima of the free energy . the positions of the local density peaks and the values of the density at these peaks are displayed according to the following scheme : ( cyan ) solid circles : peaks with @xmath87 , ( red ) circles : @xmath88 , ( blue ) squares : @xmath89 , ( green ) plus signs : @xmath90 , and ( purple ) triangles : @xmath91 . blank areas , found mainly in the bottom panel , correspond to regions where no local peaks are found . the temperature is 18.2k in all panels , which all correspond to the same pin configuration as that for the results in fig.[fig1 ] . pin locations are indicated by ( black ) asterisks . from top to bottom , the results displayed correspond respectively to ordered ( identified as brg ) , intermediate ( bog ) and disordered ( il ) minima . , title="fig : " ] ( color online ) . local peak densities at three different local minima of the free energy . the positions of the local density peaks and the values of the density at these peaks are displayed according to the following scheme : ( cyan ) solid circles : peaks with @xmath87 , ( red ) circles : @xmath88 , ( blue ) squares : @xmath89 , ( green ) plus signs : @xmath90 , and ( purple ) triangles : @xmath91 . blank areas , found mainly in the bottom panel , correspond to regions where no local peaks are found . the temperature is 18.2k in all panels , which all correspond to the same pin configuration as that for the results in fig.[fig1 ] . pin locations are indicated by ( black ) asterisks . from top to bottom , the results displayed correspond respectively to ordered ( identified as brg ) , intermediate ( bog ) and disordered ( il ) minima . , title="fig : " ] ( color online ) . local peak densities at three different local minima of the free energy . the positions of the local density peaks and the values of the density at these peaks are displayed according to the following scheme : ( cyan ) solid circles : peaks with @xmath87 , ( red ) circles : @xmath88 , ( blue ) squares : @xmath89 , ( green ) plus signs : @xmath90 , and ( purple ) triangles : @xmath91 . blank areas , found mainly in the bottom panel , correspond to regions where no local peaks are found . the temperature is 18.2k in all panels , which all correspond to the same pin configuration as that for the results in fig.[fig1 ] . pin locations are indicated by ( black ) asterisks . from top to bottom , the results displayed correspond respectively to ordered ( identified as brg ) , intermediate ( bog ) and disordered ( il ) minima . , title="fig : " ] we next examine the structure of the minima in terms of the `` vortex lattice '' found by the procedure explained above . sample results are shown in fig . [ fig3 ] , all for the same pin configuration , at the temperature @xmath92k . results for three minima , obtained from the same procedures and initial conditions as the three minima in the previous two figures , are shown . the positions of the local density peaks and the values of the density at these peaks are displayed through a symbol and color coding scheme described in the caption of the figure . blank regions denote areas where no local peak was found using the algorithm described above : such areas are mostly found only in the most disordered case ( uniform initial conditions ) . we see that the results are quite consistent with those obtained from the previous correlation functions : quenching with the appropriate crystalline initial conditions leads to a fairly well - ordered ( but not perfectly ordered ) lattice , while from uniform initial conditions , one obtains a rather disordered , liquid - like structure where the density is nearly uniform and close to @xmath43 , except near the pinning centers at each of which one vortex is trapped . an intermediate result , on the whole more solid than liquid - like , but definitely disordered , is obtained through the slow warming or cooling scheme . ( color online ) . voronoi plots for the three cases for which density plots are shown in fig . [ fig3 ] , except that the temperature is now @xmath93k . the ( black ) dots denote lattice sites with six neighbors , the ( red ) triangles denote five - fold coordinated sites , and the ( green ) solid circles , seven - fold coordinated sites . rarely occurring four - fold and eight - fold coordinated sites are indicated by ( blue ) squares and ( purple ) inverted triangles , respectively . sites surrounded by black circles denote locations of pinning centers . see text for explanations.,title="fig : " ] ( color online ) . voronoi plots for the three cases for which density plots are shown in fig . [ fig3 ] , except that the temperature is now @xmath93k . the ( black ) dots denote lattice sites with six neighbors , the ( red ) triangles denote five - fold coordinated sites , and the ( green ) solid circles , seven - fold coordinated sites . rarely occurring four - fold and eight - fold coordinated sites are indicated by ( blue ) squares and ( purple ) inverted triangles , respectively . sites surrounded by black circles denote locations of pinning centers . see text for explanations.,title="fig : " ] ( color online ) . voronoi plots for the three cases for which density plots are shown in fig . [ fig3 ] , except that the temperature is now @xmath93k . the ( black ) dots denote lattice sites with six neighbors , the ( red ) triangles denote five - fold coordinated sites , and the ( green ) solid circles , seven - fold coordinated sites . rarely occurring four - fold and eight - fold coordinated sites are indicated by ( blue ) squares and ( purple ) inverted triangles , respectively . sites surrounded by black circles denote locations of pinning centers . see text for explanations.,title="fig : " ] to better gauge the degree of disorder present in each case , we construct , in fig . [ fig4 ] , the corresponding voronoi plots . to display the behavior in a more obvious way , the temperature in these plots is lower by @xmath94k than that of the plots in fig . as mentioned above , sites with number of nearest neighbors ( @xmath79 ) different from six represent the locations of disclinations . in the solid - like minima ( top two panels of fig . [ fig4 ] ) , nearly all the sites with @xmath95 have @xmath96 or @xmath97 ( the disclinations have unit `` charge '' ) . also , six- and seven - coordinates sites , indicated respectively by ( red ) triangles and ( green ) solid circles in the plots , always occur in nearest - neighbor pairs . such pairs correspond to dislocations . in the first panel , which displays the results for the most ordered state obtained from crystalline initial configurations , we see that the number of dislocations , while nonzero , is quite small and that they form fairly isolated small clusters , each of which has zero net burgers vector . these defect clusters occur near the pinning centers and they represent the local disruption of crystalline order due to the pinning . in the second panel , which shows the results for the minimum with intermediate order , the dislocations are organized to form well - defined grain boundaries that separate crystallites with different orientations . as a result of this polycrystalline structure , both translational and bond - orientational correlations are short - range . performing the same construction for other pin configurations ( results for a different pin configuration are shown in fig.1b of ref . ) , one finds that the crystallite arrangement depends on the pin configuration , as one would expect . the grain boundaries tend to lie away from pinning centers , which makes sense physically . finally , in the last panel , which shows the results for the minimum obtained from uniform initial conditions , the high degree of disorder is evident . the voronoi construction shown in this panel is not very meaningful because our method of obtaining the vortex positions is not reliable for liquid - like minima . the identification of the position of a vortex with that of a local peak of the density field is justified only when the peak is sharp . this is the case in the solid - like minima , but not so in the liquid - like minima with low peak densities . we have shown here the results for the liquid - like minimum only for the purpose of illustrating the difference between the structure of this minimum and those of the more ordered ones . for this minimum , we find a very large number of defects , and it is difficult to determine whether disclinations of opposite `` charge '' always pair up to form dislocations . inspection of the defect distribution suggests the presence of free disclinations , but not conclusively . the total number of local peaks of the density field in liquid - like minima turns out to be substantially smaller than the expected number of vortices . this problem is not present at the solid - like minima where nearly all the vortices are strongly localized . ( color online ) . bond - orientational correlation function @xmath73 as defined in eq . ( [ angular ] ) , and `` translational '' correlation function , @xmath80 , see eq . ( [ bo ] ) . these are results averaged over five pin configurations , at @xmath98k . the ( purple ) triangles and ( red ) circles denote @xmath73 for ordered ( brg ) and polycrystalline ( bog ) minima ( liquid - like minima are not stable at this lower @xmath0 ) respectively . the black squares are @xmath80 for the brg minima . the dashed line is an exponential fit to @xmath73 for the bog minima . the dotted line is a similar exponential fit to @xmath80 for the brg minima at small distances , showing that the decay is slower than exponential for large values of @xmath17 . the solid lines connecting symbols are guides to the eye . ] next , we show in fig . [ fig5 ] examples of the bond - orientational and `` translational '' correlation functions , @xmath73 and @xmath80 as defined in eqs . ( [ angular ] ) and ( [ bo ] ) respectively . all results shown in this figure are averages over five pin configurations at temperature @xmath98k . at this temperature the liquid is unstable , and in any case all liquid correlation functions are featureless , so that case is not shown . the ( purple ) triangles correspond to ordered minima obtained from quenching with crystalline initial conditions to @xmath99k and subsequent slow warming , and represent the bond - orientational correlation , @xmath73 . this function appears to saturate at a fairly large value as @xmath17 increases , indicating the presence of long - range bond - orientational order . the ( red ) open circles display @xmath73 for the polycrystalline state with intermediate order , obtained through the procedures described above . this function decays exponentially with distance , as shown by the exponential fit ( dashed line ) , over a distance of few tens in units of @xmath31 . finally , the ( black ) open squares show the results for the `` translational '' correlation function @xmath80 for the ordered minima . the dotted line is an exponential fit to this translational correlation function for @xmath100 , showing that the decay at longer distances is clearly slower than exponential ( possibly a power - law ) . > from the overall examination of data such as those shown in these figures , we can reach the following conclusions : quenching with uniform initial conditions to temperatures above or slightly below @xmath101 leads to very disordered states , with very short range correlations and no structure , except for vortices at and near the pinning centers . these minima become unstable upon slow cooling : one then obtains minima of the third kind , discussed below . they clearly must be identified with the liquid phase , specifically the interstitial liquid ( il ) phase discussed in the introduction . the second kind of minima are obtained by quenching with crystalline initial conditions to any temperature below , or slightly above , @xmath101 . these minima can then be cooled , without losing their character , but they melt into the il upon sufficient warming . the states thus obtained are obviously nearly crystalline , with the reservation that the order is not truly long range , but has a slow decay . this is most evident in the results for @xmath80 seen in fig . the bond - orientational order is nearly perfect . defects are limited to isolated clusters . this state must therefore be identified as a bragg glass ( brg ) . finally , we have the states obtained as described above , by slow cooling of the il state , which can also be obtained by quenching with uniform initial conditions to a temperature below the il state stability limit . either procedure yields , for any pin configuration , states that at a given @xmath0 differ only slightly in free energy or density configuration . the states do differ somewhat more , however , for different pin configurations . the voronoi construction conclusively shows ( see fig . [ fig4 ] ) that these states are polycrystalline . the grain boundaries are formed by dislocation chains . for any pin configuration , these grain boundaries survive thermal cycling across @xmath101 , but if sufficiently warmed up , these minima melt , the melting beginning locally at the grain boundaries ( see sec [ props ] below ) . the bond - orientational correlation function for these minima has an intermediate range . this , and also the observation that these states are not unique ( as mentioned above , slightly different states are reached depending on the cooling or quenching protocol ) , clearly indicate a glassy state . we therefore identify it with the bose glass ( bog ) which has been experimentally@xcite and numerically@xcite shown to be polycrystalline . in this section , we describe in detail how the properties of the low - temperature `` solid - like '' condensed phases represented by the brg and bog types of minima defined in the preceding section vary as the temperature is changed . the high - temperature liquid phase represented by the il - type minima is not very interesting from the point of view of its temperature dependence : in the temperature range we have considered , this phase exhibits a liquid - like ( nearly uniform ) density distribution except in the immediate vicinity of the columnar pins , at each of which a vortex is trapped . these trapped vortices would eventually get delocalized at higher temperatures . this happens beyond the upper limit of the temperature range ( 16.8k @xmath102 18.8k ) we have considered here . to study how the properties of a local minimum of the free energy change as the temperature is varied , we have `` followed '' minima as the temperature changes : for example , starting with a minimum obtained by quenching to the lowest temperature of 16.8k , we `` follow '' that minimum to higher temperatures by increasing the temperature in small steps ( usually taken to be 0.2k ) and finding a new minimum at the higher temperature by running the minimization routine with the configuration at the minimum obtained at the previous temperature as the initial state . this procedure leads to a new minimum of the same type as long as the minimum remains locally stable if the temperature is increased to values substantially higher than @xmath101 , where the brg and bog minima become unstable , this procedure leads then to the il minima . we have also carried out `` cooling '' runs where the temperature was decreased in small steps , starting from a minimum obtained at a relatively high temperature . when the il minima become unstable , bog states are obtained . as long as the minimum under consideration did not become unstable in the range of temperatures considered in the runs , we did not find any substantial difference between the results obtained in the `` heating '' and cooling runs ( color online ) . temperature dependence of the order parameter @xmath103 as defined in eq . ( [ op ] ) for three kinds of minima , averaged over five samples , with @xmath104 and @xmath54 . results for the brg , bog and il minima are shown by ( red ) plus signs , ( green ) crosses and ( blue ) asterisks , respectively . ] to characterize the density distribution at a minimum , we looked at `` global '' quantities such as the structure factor @xmath63 , an example of which is shown above in fig . the @xmath0-dependent information contained in @xmath63 is , however , difficult to display in plots . we therefore introduce a closely related `` order parameter '' @xmath103 defined as @xmath105 where @xmath106 is the largest value of the structure factor @xmath63 averaged over the six @xmath107-vectors related by lattice symmetry to each @xmath107 . by definition , the order parameter @xmath103 is equal to unity in a state with perfect crystalline order ( triangular lattice with @xmath108-function peaks ) . since no long - range crystalline order is expected or found in either one of the brg and bog phases , the value of @xmath103 should go to zero at all temperatures in the thermodynamic limit . however , the infinite size limit is reached very slowly in the glassy phases , and for the finite - size systems considered here , this quantity provides a convenient measure of the degree of local order present at the minima . we show in fig . [ fig6 ] the results for the order parameter @xmath103 , averaged over five different pin configurations , for samples with 4096 vortices and 64 pins . the results for the brg , bog and il minima are shown by ( red ) plus signs , ( green ) crosses and ( blue ) asterisks , respectively . only two data points are shown for the il minimum because it becomes unstable at lower temperatures . for all three kinds of minima , the value of @xmath103 decreases with increasing @xmath0 , as expected . the rate of change is largest for the brg minima , and smallest for the il minima . however , the differences among the three kinds of minima in the degree of local order remain quite clear at all the temperatures considered . we have also obtained brg - type minima for several ( @xmath109 ) samples with 1024 vortices and 16 pins . the values of @xmath103 obtained from an average over these smaller samples are found to be only about 6% larger than those obtained for the 4096-vortex samples at the corresponding temperature . this result implies that the translational correlation function at the brg minima falls off very slowly with distance . this is consistent with our interpretation of these minima as representing the brg phase . ( color online ) . peak density plots for the bog minimum of a sample with @xmath104 and @xmath54 ( the sample is the same as the one for which results are shown in figs . [ fig3 ] and [ fig4 ] ) at two temperatures : @xmath0 = 17.4k ( top panel ) and @xmath0 = 17.8k ( bottom panel ) . the symbols and color scheme used here are the same as those in fig . [ fig3].,title="fig : " ] ( color online ) . peak density plots for the bog minimum of a sample with @xmath104 and @xmath54 ( the sample is the same as the one for which results are shown in figs . [ fig3 ] and [ fig4 ] ) at two temperatures : @xmath0 = 17.4k ( top panel ) and @xmath0 = 17.8k ( bottom panel ) . the symbols and color scheme used here are the same as those in fig . [ fig3].,title="fig : " ] we also examined the temperature dependence of the detailed density distribution at the minima ( obtained from `` peak density '' plots similar to those shown in fig . [ fig3 ] ) and their defect structure obtained from voronoi plots such as those in fig . [ fig4 ] . examination of the peak - density plots reveals more information about how the density distribution at the minima changes with temperature . in fig . [ fig7 ] , we have shown peak - density plots at two temperatures ( 17.4k in the top panel and 17.8k in the bottom panel ) for the bog minimum of the same sample for which a similar plot at 18.2k is shown in the middle panel of fig . the symbols and color scheme used in these plots are the same as those in fig . it is clear from these plots that the typical values of the local peak densities decrease ( the vortices become less localized ) as the temperature increases . the largest values of the local peak density occur near the pinning centers and the smallest values appear near the grain boundaries that separate different crystalline regions . this is physically reasonable the disruption of local crystalline order near the grain boundaries should make the vortices in such regions more delocalized . at the relatively low temperature of 17.4k , there are very few local density peaks where the peak density is lower than @xmath110 ( such peaks are indicated by ( red ) circles in the plot ) . as the temperature is increased to 17.8k , the number of such peaks increases , and this trend continues as @xmath0 is increased further , as can be seen in the middle panel of fig . [ fig3 ] where the results for @xmath111 are shown . it is also clear from these plots that the spatial regions where the low peak densities occur remain roughly unchanged as the temperature increases as noted above , these regions are strongly correlated with the locations of the grain boundaries . these observations indicate that the vortices in the interior of the crystalline grains remain in a `` solid '' state as the temperature is increased to a value close to @xmath101 , while those in the neighborhood of the grain boundaries begin to `` melt '' ( get delocalized ) at a lower temperature . this `` inhomogeneity '' of the melting process will be discussed in more detain in section [ inhomog ] . we also studied the temperature dependence of the number of topological defects present at the minima . this number increases slowly with increasing @xmath0 , and then exhibits a sudden jump as liquid - like regions ( characterized by low values of the local peak densities ) appear near the grain boundaries at temperatures close to @xmath101 . as noted in sec . [ minima ] above , our method of obtaining the defect structure using the voronoi construction becomes somewhat less reliable when liquid - like regions begin to appear . due to this difficulty in obtaining reliable results for the defect structure and statistics at relatively high temperatures , we have not carried out a quantitative analysis of the dependence of these quantities on the temperature . the gradual decrease in the values of the local peak densities with increasing temperature is also found in the brg minima , but on the average the vortices remain more strongly localized at the brg minima than at the corresponding bog ones . the strong correlation between low values of the local peak density and the location of topological defects is found at the brg minima too . the main difference between brg and bog minima is that the defects are more randomly distributed at the brg minima : they do not line up along grain boundaries as they do at the bog minima . for this reason , the regions of low peak density appear at fairly random locations at the brg minima . the total number of topological defects at the brg minima remains smaller than that at corresponding bog minima at all temperatures . as the temperature approaches @xmath101 , liquid - like regions appear in parts of the sample where the defect density is large . this is illustrated in the plots in the top panels of figs . [ fig3 ] and [ fig4 ] . thus , our investigation of the temperature dependence of the structure of the brg and bog minima confirms that these minima retain their topological structure as @xmath0 is increased toward @xmath101 and even beyond ( provided they remain stable ) . the degree of localization of the vortices decreases with increasing @xmath0 and liquid - like regions with nearly delocalized vortices begin to appear at temperatures close to @xmath101 . however , even at such temperatures , the brg and bog type minima are clearly distinguishable from one another and from the il - type minima , as illustrated in figs [ fig3 ] , [ fig4 ] and [ fig6 ] . as discussed in the preceding subsections , we find three kinds of coexisting , locally stable minima of the free energy at temperatures close to @xmath101 . two kinds ( brg and bog ) of local minima are found at temperatures substantially lower than @xmath101 , and only the il minimum is stable if @xmath0 is much higher than @xmath101 . in our mean - field description , the thermodynamically stable phase at a particular temperature corresponds to the minimum with the lowest free energy . therefore , crossings of the free energies of different kinds of minima correspond to first - order phase transitions in our description . the il minima are expected to have the lowest free energy at high temperatures and the solid - like brg or bog minima should represent the globally stable phase at low temperatures . to determine how this `` freezing '' transition takes place , it is necessary to examine the dependence of the free energies of these different kinds of minima on the temperature @xmath0 . ( color online ) . temperature dependence of the dimensionless free energies of different local minima of a sample with @xmath104 and @xmath54 ( the sample is the same as the one for which results are shown in figs . [ fig1 ] , [ fig3 ] , [ fig4 ] and [ fig7 ] ) . the data for the brg , bog and il minima are shown by the ( green ) crosses and dashed line , ( blue ) asterisks and dotted line and the ( red ) plus signs and solid line , respectively . the lines are guides to the eye . ] in fig . [ fig8 ] , we have shown the results for the free energies of different minima of a sample with @xmath104 and @xmath54 . this sample is the same as the one for which results are shown in figs . [ fig1 ] , [ fig3 ] , [ fig4 ] , and [ fig7 ] . a similar plot , showing the same general behavior for a different sample , may be found in ref . . the brg minimum clearly has the lowest free energy at low temperatures ( while we have shown data for @xmath112 , we have checked that this remains true at lower temperatures ) , while the il minimum is the one with the lowest free energy at high temperatures . the interesting feature that emerges from data as that shown in this figure is that the bog minimum has the lowest free energy in an intermediate temperature range of small width ( between 18.0k and 18.3k for this sample ) , indicating that the melting of the low - temperature solid phase to the high - temperature il phase occurs in two distinct steps : the brg phase that is the thermodynamically stable one at low temperatures undergoes a first - order transition into a bog phase as the temperature is increased , and then this bog phase melts into the il phase via a second first - order transition at a slightly higher temperature . this two - step melting behavior is one of our main results . ( color online ) . results for a sample with @xmath113 and @xmath55 . voronoi plots for the brg and bog minima at 18.0k are shown in the top and middle panels , respectively . the symbols and color scheme used in these plots are the same as those in fig . the bottom panel shows the temperature dependence of the free energies of the brg ( blue line and squares ) , bog ( red line and circles ) and il ( black line and triangles ) minima , respectively . the lines are guides to the eye . , title="fig : " ] ( color online ) . results for a sample with @xmath113 and @xmath55 . voronoi plots for the brg and bog minima at 18.0k are shown in the top and middle panels , respectively . the symbols and color scheme used in these plots are the same as those in fig . the bottom panel shows the temperature dependence of the free energies of the brg ( blue line and squares ) , bog ( red line and circles ) and il ( black line and triangles ) minima , respectively . the lines are guides to the eye . , title="fig : " ] ( color online ) . results for a sample with @xmath113 and @xmath55 . voronoi plots for the brg and bog minima at 18.0k are shown in the top and middle panels , respectively . the symbols and color scheme used in these plots are the same as those in fig . the bottom panel shows the temperature dependence of the free energies of the brg ( blue line and squares ) , bog ( red line and circles ) and il ( black line and triangles ) minima , respectively . the lines are guides to the eye . , title="fig : " ] the same qualitative behavior , indicating the occurrence of two separate first - order transitions , is found in all the 4096-vortex samples we have studied at pin concentration @xmath53 ( @xmath54 ) . the average value of the temperature interval in which the bog phase has the lowest free energy is about 0.42k . this width exhibits fairly large sample - to - sample variations , ranging between about 0.1k in one sample to a maximum of 1.2k . as the system is cooled from the high - temperature liquid phase , it undergoes a first - order transition into a polycrystalline bog phase . such a transition has been observed @xcite in experiments on bscco samples with a small concentration of columnar pins . the value of the upper ( bog to il ) transition lies between 18.2k and 18.3k in all the 4096-pin samples we have studied . these values are quite close to the first - order melting temperature @xmath101 of the same system in the absence of pins @xcite . our results , thus , are consistent with the experimental observation @xcite of a weak dependence of the freezing temperature of the vortex liquid on the pin concentration @xmath2 for small values of @xmath2 . in addition , our work predicts a second first - order transition to a more ordered brg phase at a slightly lower temperature . for smaller samples at the same @xmath53 concentration ( @xmath114 with @xmath55 ) we did not always find the bog minima : the minimization procedure that led to the bog minima in the samples with @xmath104 often converged to minima of the brg type in the smaller samples . this is because the typical size of the crystalline grains at the bog minima at this pin concentration is of the order of the sample size for 1024-vortex samples . this can be seen by comparing the middle panel of fig . [ fig9 ] , where we have shown the voronoi plot for the bog minimum obtained for a @xmath114 sample , with the voronoi plot in the middle panel of fig . [ fig4 ] , which is for the same @xmath0 and @xmath2 , but a larger sample with 4096 vortices . one can plainly see that the domain size is comparable to the system size of the smaller samples . however , for the 1024-vortex samples where we found bog - type minima , the behavior of the free energies was found to be very similar to that shown in fig . an example of such behavior is shown in the bottom panel of fig , [ fig9 ] . the two - step melting transition found in the larger systems is found here also , indicating that this is the generic behavior . we have also carried out preliminary studies of the phase diagram for a slightly higher value of the pin concentration , @xmath56 . we find the same qualitative behavior , namely the occurrence of two - step melting , with a larger difference between the two transition temperatures . we therefore conclude that the two - step melting transition we have found is a characteristic feature of our model of layered superconductors with a small concentration of columnar pins . ( color online ) . the pinning free energy ( see text ) averaged over five samples with @xmath104 and @xmath54 . results for the brg and bog minima are shown by ( red ) triangles and ( black ) circles , respectively . the solid lines are straight lines joining the points . ] since a first - order transition is not characterized by power - law behaviors of thermodynamic quantities with universal exponents , the usual finite - size scaling analysis of numerical data for continuous transitions does not apply to our work . however , we have examined the dependence of the magnitudes of various discontinuous changes at the transitions on sample size . from the results for the free energy as a function of the temperature , we have calculated the entropy jump per vortex at the first - order transitions . the entropy change at the brg - bog ( lower temperature ) transition is found to be @xmath115 per vortex ( @xmath116 is the boltzmann constant ) , and the corresponding change at the bog - il ( higher temperature ) transition has a slightly higher value , @xmath117 per vortex . the sum of these two entropy jumps is slightly smaller than the entropy change ( @xmath118 per vortex ) at the single first - order melting transition found @xcite in the same system in the absence of pinning . all these results are physically reasonable . the difference between the degrees of order in the brg and bog minima is smaller than that between the bog and il minima , suggesting that the entropy jump at the lower transition should be smaller than that at the upper one . also , the low - temperature bog phase of the system in the presence of pinning is less ordered than the crystalline phase of the pure system , and the il phase is slightly more ordered than the vortex liquid in the system without pinning ( this is due to the local order of the vortices near the pinning centers which persists in the il phase ) . therefore , the net change of entropy in going from the bog phase to the il phase should be smaller than the entropy jump at the melting transition in the pure system . a comparison of our results for two sample sizes ( @xmath119 and 1024 ) does not show any appreciable dependence of the entropy changes on the sample size . we , therefore , conclude that there is no indication of any significant change in our phase diagram as the sample size is increased . since our mean - field treatment ignores the effects of fluctuations , it is important to address the question of whether one or both of the transitions found would become continuous if fluctuations were included . however , there are very few examples of such fluctuation - driven continuous transitions in three dimensions . in our calculations , the effects of the electromagnetic interaction among vortices on different layers are included . so , we expect our results regarding the nature of the transition to remain valid if fluctuations were included . this conclusion is supported by the result that our density functional theory provides a _ quantitatively _ a correct account @xcite of the first - order melting of the vortex lattice in the pure system . also , the transition in the presence of a small concentration of columnar defects is known to be first - order both experimentally @xcite and from simulations @xcite . the appearance of a sliver of the bog phase in our phase diagram may be qualitatively understood as arising from a competition between the elastic and pinning parts of the free energy . the elastic ( free ) energy plays a dominant role in the brg minima : the effect of the randomly located pinning centers is accommodated in this structure by small displacements of the vortices from their ideal lattice positions towards the nearest pinning center . where the occupation of a pinning center by a vortex would require a large displacement of the vortex , the pinning center is _ not _ fully occupied . for this reason , the number of pinning centers occupied by vortices at a brg minimum is always slightly lower than the total number of pinning centers . at the corresponding bog minima , on the other hand , the pinning centers are always occupied ( except in very rare cases where two pinning centers are located very close to each other ) . since the bog minima are obtained from liquid - like initial conditions , the starting point has fully occupied pinning centers , and vortices localized in small crystalline patches in their immediate vicinity ( see , for example , the bottom panel of fig . [ fig3 ] which shows such crystalline patches surrounding the pinning centers ) . the crystalline orientation of vortices around a vortex - binding pin site depends on the local arrangement of the pins.@xcite this orientation is , in general , different in different regions of the sample . these crystalline patches grow as the temperature is reduced , and eventually meet one another at grain boundaries to form a polycrystalline bog minimum . it is clear that the pinning centers are better accommodated in this structure than in the corresponding brg structure . on the other hand , the creation of grain boundaries costs elastic energy . thus , the bog minima are expected to have lower pinning energy but higher elastic energy than the brg ones for the same pin configuration . the elastic energy dominates over the pinning energy at low temperatures in our low pin - concentration samples . this is why the brg phase is globally stable at low @xmath0 . both these components of the free energy decrease in magnitude as the temperature is increased . the softening of the lattice near the melting transition causes the elastic energy to decrease faster than the pinning energy . this makes the pinning component of the free energy more important than the elastic part near @xmath101 , thereby making the total free energy of the bog minima ( which , as discussed above , have lower pinning energy ) lower than that of the bog minima . the bog to il transition at a slightly higher temperature is driven by the usual entropic mechanism . we can substantiate this qualitative explanation by evaluating the pinning component of the free energy , as defined in eq . ( [ pin ] ) , for the brg and bog minima . the results of our calculation , averaged over five samples ( each with 4096 vortices and 64 pins ) , are shown in fig . [ fig10 ] . the pinning energy is negative for both kinds of minima , as expected . the absolute value of the pinning energy of the bog minima shows a smooth ( nearly linear ) decrease as the temperature is increased . this is because both the value of the parameter @xmath20 ( see eq . ( [ single ] ) ) that determines the depth of the pining potential , and the height of the local density peak at a pinning center decrease with increasing @xmath0 . the plot for the brg minima shows a similar but much slower behavior , still monotonic or nearly so : it is not clear whether the very shallow minimum near @xmath0 = 17.6k is significant . in some of the samples , the total number of occupied pining centers increases by a small amount near this temperature , thereby reducing the value of the total pinning energy . this may reflect a better accommodation of the pinning centers by the lattice , which softens as the temperature is increased . this plot clearly demonstrates that the pinning centers are better accommodated at the bog minima . the difference in the pinning energies of the two kinds of minima decreases with increasing @xmath0 , but the difference in the elastic component of the free energy decreases faster ( this is clear from our results for the total free energy ) due to a softening of the elastic constants with increasing temperature . the overall effect is a crossing of the free energies of the two kinds of minima near the melting transition . quantitatively , however , the values of the two parts of the free energy and their dependence on @xmath0 are determined by the material parameters of the superconductor and the properties of the pinning centers . since several experimental studies@xcite of the effects of irradiation - induced columnar pinning on the mixed state of bscco exist in the literature , we have used parameter values appropriate for this system . for other layered superconductors , the bog phase might occur over a wider or narrower ( even vanishing ) range . as mentioned in section [ props ] , the density distribution in both brg and bog minima is very inhomogeneous : at temperatures close to @xmath101 there are liquid - like regions , characterized by low values of the local peak densities in parts of the sample . in this subsection , we show that this inhomogeneity leads to a spatial variation of a `` local melting temperature '' , defined below . as mentioned in the introduction , such spatial variations of a local melting temperature have been deduced from measurements of the local magnetization in bscco samples with random point@xcite and columnar pinning@xcite . since we are dealing with time averaged densities , it is clear that the value of @xmath120 at a local peak of the density field provides a measure of the degree of localization of the vortex whose average position corresponds to the location of the density peak . a high ( low ) value of the local peak density implies strong ( weak ) localization . smaller values of the local peak density imply mobile , liquid - like behavior . the value of the local density is , of course , equal to @xmath43 everywhere in the liquid state in the absence of pinning . the presence of pinning centers causes the local density to vary in space , but in the liquid state this variation does not lead to local peaks higher than about @xmath121 ( excluding the vortices localized at the pinning centers ) . a similar result was also obtained in previous studies @xcite of vortices in the presence of pinning , where it was found that values of the peak density lower than about @xmath121 correspond to the liquid state . we , therefore , take the value @xmath122 of the local peak density as separating solid- and liquid - like behaviors . ( color online ) . determination of the local melting temperatures in different regions of a sample . the top panel , at @xmath93k and for the bog minimum , shows the three different regions ( a , b and c ) considered in the calculation . the positions of local density peaks in these regions are indicated by ( red ) plus signs ( region a ) , ( blue ) crosses ( region b ) and ( green ) circles ( region c ) . the black dots represent the positions of the local density peaks in the other regions , and the ( black ) circles show the locations of the pinning centers . the bottom panel shows the dependence of the average local peak density @xmath123 ( normalized by the liquid density @xmath43 ) calculated for these regions on the temperature @xmath0 . data for regions a , b and c are respectively shown by ( red ) triangles , ( blue ) squares , and ( green ) circles . the solid lines are guides to the eye . , title="fig : " ] ( color online ) . determination of the local melting temperatures in different regions of a sample . the top panel , at @xmath93k and for the bog minimum , shows the three different regions ( a , b and c ) considered in the calculation . the positions of local density peaks in these regions are indicated by ( red ) plus signs ( region a ) , ( blue ) crosses ( region b ) and ( green ) circles ( region c ) . the black dots represent the positions of the local density peaks in the other regions , and the ( black ) circles show the locations of the pinning centers . the bottom panel shows the dependence of the average local peak density @xmath123 ( normalized by the liquid density @xmath43 ) calculated for these regions on the temperature @xmath0 . data for regions a , b and c are respectively shown by ( red ) triangles , ( blue ) squares , and ( green ) circles . the solid lines are guides to the eye . , title="fig : " ] using this criterion , we can determine whether a small region of the sample at a given minimum is in a locally `` solid '' or `` liquid '' state . to do this , we define a quantity @xmath123 as the average of the local peak densities in a small region containing @xmath124 vortices ( see fig . [ fig11 ] ) . the very high local density peaks representing vortices trapped at pinning centers are not included in this average . values of @xmath123 substantially larger than @xmath122 indicate solid - like behavior in the region under consideration , while substantially lower values of @xmath123 suggest a locally melted region . to determine how the local melting temperature varies from one part of the sample to another , we have studied the temperature dependence of @xmath123 for different regions of the sample . typical results are shown in fig . [ fig11 ] for the pin configuration for which we have earlier shown detailed results in several figures . in the top panel , where the positions of the local density peaks in the bog minimum at @xmath93k and the locations of the pinning centers are shown , we have indicated three regions for which the average local peak density @xmath123 was calculated . the local density peaks in these regions are indicated by ( red ) plus signs ( region a ) , ( blue ) crosses ( region b ) and ( green ) circles ( region c ) , while the black dots represent the positions of the local density peaks in the other regions . the bottom panel of fig . [ fig11 ] shows the dependence of the @xmath123 s calculated for these three regions on the temperature @xmath0 . at each value of @xmath0 , the minimum with the lowest free energy at that temperature was used in the calculation of @xmath123 . ( color online ) . percolation and melting ( see text ) . the ( red ) plus signs denote the locations of liquid - like local density peaks ( peak height smaller than @xmath121 ) , and the ( blue ) circles indicate the solid - like ones ( peak height greater than @xmath121 ) . the top panel is for the bog minimum of a 4096-vortex sample at 18.2k and the bottom panel is for the il minimum of the same sample at 18.4k . the thermodynamic transition between the bog and il phases takes place between these two temperatures . , title="fig : " ] ( color online ) . percolation and melting ( see text ) . the ( red ) plus signs denote the locations of liquid - like local density peaks ( peak height smaller than @xmath121 ) , and the ( blue ) circles indicate the solid - like ones ( peak height greater than @xmath121 ) . the top panel is for the bog minimum of a 4096-vortex sample at 18.2k and the bottom panel is for the il minimum of the same sample at 18.4k . the thermodynamic transition between the bog and il phases takes place between these two temperatures . , title="fig : " ] it is clear from the plot and from similar ones for other pin configurations ( one of which was shown in ref . ) that the `` local melting temperature '' , operationally defined as the temperature at which @xmath123 drops from values well above @xmath122 to values clearly below , varies from region to region . the range over which the local melting temperature varies is comparable to that found in the experiments @xcite . the values of the local melting temperature are strongly correlated with the local pin structure and the resulting defect structure of the vortex solid . region b of the sample does not have any pinning center and is located across a grain boundary of the bog minimum . as noted in section [ props ] , regions near grain boundaries appear to melt at temperatures that are slightly lower than the global transition temperature determined by the crossing of free energies . this is why the local melting temperature for region b is the lowest . this temperature corresponds to the transition from the brg to the bog state . in region a the vortices form a nearly perfect crystalline arrangement with no topological defects . the local melting temperature measured in this region is , as a consequence , close to that of the pure system . region c contains a cluster of pinning centers , and the relatively large value of @xmath123 for this region at temperatures higher than the bog to il transition temperature reflects the local solid - like structure of vortices situated near pinning centers . thus , the spatial variation of the local transition temperature is closely correlated with the `` pinning landscape '' of the sample . we have found a second way of correlating the melting transition with the local density structure of the free energy minima . this second way is based on a previous study@xcite of the melting of the vortex lattice in the presence of periodic pinning , where it was found that the melting transition corresponds to the onset of percolation of liquid - like regions defined using the peak - density criterion mentioned above . we focus for this purpose on the upper transition between the bog and il phases . we classify vortices represented by local peaks of the density as solid - like or liquid - like , depending on whether the density at the local peak is higher or lower than @xmath121 . we then check whether the regions containing liquid - like vortices percolate across the sample . we find , as in the earlier study , that the melting transition coincides with the occurrence of percolation of the liquid - like regions . typical results are shown in fig . [ fig12 ] where the top panel shown the locations of solid- and liquid - like local density peaks at a bog minimum obtained at 18.2k ( this minimum has the lowest free energy at this temperature ) , and the bottom panel shows a similar plot for the il minimum of the same sample at 18.4k ( the il minimum is the one with the lowest free energy at this temperature , so that the melting transition in this sample occurs between 18.2k and 18.4k ) . the liquid - like regions do not percolate at 18.2k , whereas they do at the higher temperature of 18.4k . thus , the melting transition in this sample also corresponds to the occurrence of percolation for the liquid - like regions . similar behavior was found in the other samples we have studied . this observation provides a convenient way of approximately locating the transition point . this may be useful in other situations where the method of locating the transition temperature from a crossing of free energies may not be easily implementable ( e.g. at higher pin concentrations where the melting transition is expected to become continuous ) . we have presented here the results of a detailed investigation of the structural and thermodynamic properties of a system of vortices in a highly anisotropic layered superconductor with a small concentration of randomly placed columnar pinning centers . both the external magnetic field and the columnar pins are assumed to be perpendicular to the superconducting layers . our method , based on numerical minimization of the appropriate free - energy functional , allows us to obtain very detailed information about the density distribution in the different free energy minima ( which allows us to reliably identify the phases corresponding to these minima ) , and to map out the phase diagram of the system . there are several salient results of our study . the first one is the occurrence of a topologically ordered brg phase at low temperatures . while the occurrence of a low - temperature brg phase in superconductors with a low concentration of random point pinning centers is well - established now , relatively little is known about the existence of such a phase in superconductors with random columnar pins . our results are consistent with those of a recent numerical study @xcite of a similar system . it is clear from our work that the brg minima represent a phase distinct from the polycrystalline bog phase also found in our study . we can not conclusively rule out the possibility that free dislocations would appear at the nearly crystalline minima at length scales much longer than those considered in our numerical study . if this should happen , then the `` hexatic glass '' phase suggested in some earlier theoretical studies @xcite would become a possible candidate for describing the brg minima found in our study . this phase , however , would be distinct from the bog . our second important result is the occurrence of a two - step melting transition : we find that the low - temperature brg phase transforms into a polycrystalline bog phase as the temperature is increased , and this bog phase then melts into the high - temperature il at a slightly higher temperature . this conclusion about the occurrence of two distinct transitions would remain valid even if the true nature of the low - temperature phase turns out to be slightly different from a bragg glass : our work shows that the brg and bog minima are quite distinct from each other . the possibility of occurrence of a two - step melting transition of the vortex lattice in systems with random point pinning has been suggested earlier @xcite . our work provides support to this suggestion . to our knowledge , the second ( lower @xmath0 ) transition between the bog and brg phases has not been observed in experiments on layered superconductors with a small concentration of random columnar pins . this may be due to strong metastability : the bog minimum into which the il is expected to freeze as the temperature is decreased remains locally stable at temperatures lower than that at which its free energy crosses that of the brg minimum , suggesting that it would be difficult to see in experiments the transition to the globally stable brg phase . the situation here may be similar to that found in a recent experimental study@xcite of a low-@xmath125 superconductor with weak point pinning which is expected to exhibit a brg phase at low @xmath0 . it is , however , found in the experiment that the vortex solid obtained by cooling the sample in the presence of the external magnetic field has a polycrystalline structure , indicating that the metastability of this disordered state prevents the system from reaching the more ordered ( brg ) equilibrium state at low temperatures . in our numerical work , the brg minima were obtained by performing the free - energy minimization from an initial configuration with crystalline order . it is not clear how a similar procedure can be adopted in experimental studies . a low - temperature brg phase has been observed in a recent simulation@xcite of a model of htsc with a small concentration of columnar pinning centers . however , this simulation finds a single first - order transition between the brg and il phases at low pin concentrations : the small intermediate region of bog phase found in our study is not observed . this is probably due to the smallness of the system sizes ( @xmath126 100 vortex lines ) used in the simulation . as discussed in sec . [ phasediag ] above , the polycrystalline bog minima are found only if the sample size is larger than the typical size of the crystalline domains : only the brg minimum is found at low temperatures if this condition is not satisfied . since the crystalline domains become large at small pin concentrations , it is quite likely that a simulation with small system sizes and low pin concentration would not see the bog phase . another possibility is that a narrow `` two - phase '' region found in ref . near the brg melting transition actually corresponds to the intermediate bog phase found in our study . a third possibility is that the intermediate bog phase , which arises due to a competition between the elastic and pinning components of the free energy ( see sec . [ phasediag ] where it is shown that the pinning energy favors the bog phase ) , does not appear in the simulation of ref . because the pins are assumed to be weak in that work . our study also illustrates the spatial inhomogeneity of the melting process in the presence of disorder : we have found that a `` local '' melting temperature defined using a criterion based on the degree of localization of the vortices shows considerable spatial variation . this spatial variation is strongly correlated with the pinning landscape associated with the random spatial location of the pinning centers . our results about the spatial inhomogeneity of the local melting temperature are consistent with those of recent experiments @xcite on superconductors with pinning disorder . these results establish the usefulness of our numerical method in dealing with the problem of vortex matter in the presence of random pinning . it would be interesting to examine the extent to which our results depend on the values of the parameters appearing in the free energy functional . it would also be clearly useful to carry out similar studies of other related problems , such as the complete phase diagram of systems with random columnar pins in the @xmath127 plane , and the phase behavior of systems with random point pinning . some of these investigations are currently in progress . g. blatter , m.v . feigelman , v. b. geshkenbein , a. i. larkin , and v. m. vinokur , rev . phys . * 66 * , 1125 ( 1994 ) . . de gennes , _ superconductivity of metals and alloys _ , addison - 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temperature vortex solid in strongly anisotropic layered superconductors with a concentration of random columnar pinning centers small enough so that the areal density of the pins is much less than that of the vortex lines . both the external magnetic field and the columnar pins are assumed to be oriented perpendicular to the layers our method , involving numerical minimization of a model free energy functional , yields not only the free energy values at the local minima of the functional but also the detailed density distribution of the system at each minimum : this allows us to study in detail the structure of the different phases . we find that at these pin concentrations and low temperatures , the thermodynamically stable state is a topologically ordered bragg glass . this nearly crystalline state melts into an interstitial liquid ( a liquid in which a small fraction of vortex lines remain localized at the pinning centers ) in two steps , so that the bragg glass and the liquid are separated by a narrow phase that we identify from analysis of its density structure as a polycrystalline bose glass . both the bragg glass to bose glass and the bose glass to interstitial liquid transitions are first - order . we also find that a local melting temperature defined using a criterion based on the degree of localization of the vortex lines exhibits spatial variations similar to those observed in recent experiments . </s>

lunit de soins intensifs ( usi ) , on aspire souvent les scrtions respiratoires des patients intubs ou trachostomiss . des tudes antrieures ont dmontr une importante variation des pratiques daspiration , et mme si les donnes actuelles nappuient pas le rinage systmatique par solution physiologique normale ( spn ) , les donnes empiriques rvlent que leur utilisation serait courante . examiner les pratiques daspiration des infirmires et des inhalothrapeutes lusi de six hpitaux de lontario et sattarder particulirement lutilisation de la spn . les chercheurs ont distribu un sondage auto - administr de 24 questions 180 participants ( 90 infirmires et 90 inalhothrapeutes ) qui travaillaient lusi de six hpitaux de lontario . les groupes dinfirmires et dinhalothrapeutes prsentaient surtout des similarits , tous deux dclarant une forte utilisation du spn . les deux groupes observaient des effets secondaires aprs ladministration du spn , laspiration entranant une diminution de la saturation en oxygne , une agitation des patients et une augmentation du volume de scrtions . bon nombre des participants des deux groupes ne connaissaient pas de protocoles daspiration ou dutilisation de la spn lusi . certains rpondants prcisaient quils procdaient laspiration systmatique des patients sous ventilation mcanique plutt que dattendre les besoins . les infirmires et les inhalothrapeutes continuent dadministrer un spn malgr les directives cliniques fondes sur des donnes probantes indiquant quelle peut tre nfaste au patient . la formation professionnelle de ces deux groupes demploys de lusi devrait sattarder sur les pratiques exemplaires en matire daspiration des sondes trachales en gnral et de ladministration de spn en particulier . a survey was used to gather information from rns and rrts working in icus at six hospitals in ontario . the survey was entitled suctioning an artificial airway in the icu , and requested specific information about the practice and knowledge of participants with respect to the use of nsi before endotracheal suctioning , as well as other suctioning practices . a 24-question survey was developed by the authors and then reviewed by a small group of health professionals before finalization and being sent to participants . this small review group consisted of two rrts who worked outside the geographical area being surveyed , one rn who was responsible for research in an icu and one physician with research experience . the questions in the survey were developed based on a review of the peer - reviewed scientific literature and finalized from input from the small review group . the questionnaire comprised four sections that collected data regarding : demographics ; normal ( intubated ) patient care practices within the icu ; practices relating to nsi before suctioning ; and influences on individual practice . the survey was mailed to managers in six icus at community hospitals within 50 km of the trillium health centre ( mississauga , ontario ) . managers informed their staff about the survey via e - mail or in meetings and the questionnaires were left in staff rooms for any interested parties to complete . the goal was to have a total of 90 rns and 90 rrts complete the surveys . surveys were returned to the principal investigator by a postage - paid envelope provided with the questionnaire . participation was voluntary and no identifying information was collected , ensuring anonymity ; responses were confidential and not disclosed to the unit managers . descriptive statistics were calculated for each question , both as a total and based on respondent professional group . comparative statistics between rrt and rn responses was performed using a pearson test ; p<0.05 was considered to be statistically significant . spss version 20 ( ibm corporation , usa ) was used to perform data analysis . the present study , which was considered to be minimal risk , was approved by the school of biomedical sciences ethics in human research committee of charles sturt university ( burlington , ontario ) and the trillium health centre s ethics committee . a survey was used to gather information from rns and rrts working in icus at six hospitals in ontario . the survey was entitled suctioning an artificial airway in the icu , and requested specific information about the practice and knowledge of participants with respect to the use of nsi before endotracheal suctioning , as well as other suctioning practices . a 24-question survey was developed by the authors and then reviewed by a small group of health professionals before finalization and being sent to participants . this small review group consisted of two rrts who worked outside the geographical area being surveyed , one rn who was responsible for research in an icu and one physician with research experience . the questions in the survey were developed based on a review of the peer - reviewed scientific literature and finalized from input from the small review group . the questionnaire comprised four sections that collected data regarding : demographics ; normal ( intubated ) patient care practices within the icu ; practices relating to nsi before suctioning ; and influences on individual practice . the survey was mailed to managers in six icus at community hospitals within 50 km of the trillium health centre ( mississauga , ontario ) . managers informed their staff about the survey via e - mail or in meetings and the questionnaires were left in staff rooms for any interested parties to complete . the goal was to have a total of 90 rns and 90 rrts complete the surveys . surveys were returned to the principal investigator by a postage - paid envelope provided with the questionnaire . participation was voluntary and no identifying information was collected , ensuring anonymity ; responses were confidential and not disclosed to the unit managers . descriptive statistics were calculated for each question , both as a total and based on respondent professional group . comparative statistics between rrt and rn responses was performed using a pearson test ; p<0.05 was considered to be statistically significant . spss version 20 ( ibm corporation , usa ) was used to perform data analysis . the present study , which was considered to be minimal risk , was approved by the school of biomedical sciences ethics in human research committee of charles sturt university ( burlington , ontario ) and the trillium health centre s ethics committee . surveys were distributed to 90 rns and 90 rrts employed at six icus in ontario . of these , 83 completed surveys were received from rns and 87 from rrts , corresponding to a response rate of 94% and 97% , respectively . overall , approximately one - half ( 48% ) of the respondents had a baccalaureate degree as their highest level of education , with only 2% of respondents having a master s or doctoral degree ; the remaining respondents possessed a diploma . most individuals in each group held either a degree or diploma ; however , there no significance differences between the groups : diploma rn 44% , rrt 56% ( p=0.219 ) ; degree rn 57% , rrt 43% ( p=0.065 ) . no rns held a master s or doctoral degree compared with 5% of rrts ( p=0.122 ) . most respondents had graduated between 2000 and 2010 ( 40% ) , followed by graduation in the periods 1990 to 1999 ( 33% ) , 1980 to 1989 ( 18% ) and before 1980 ( 9% ) . one - half ( 50% ) of the respondents had been working in the icu 10 years . of the remainder , approximately equal numbers had worked from two to five years and six to 10 years ( 26% and 21% , respectively ) ; those who had worked in the icu for < 1 year accounted for 3% of respondents . almost all ( there was no statistically significant difference between the rns and rrts in terms of year of graduation ( p=0.263 ) or years working in the icu ( p=0.773 ) . the type of humidification used for ventilated patients in the icus employing respondents was split between those using heat and moisture exchanger ( rn 31% , rrt 41% ) , and both heat and moisture exchanger and heated chamber ( rn 68% , rrt 59% ) ; only one respondent reported use of heated chamber only . there were few statistically significant differences between these two groups with regard to questions relating to artificial airways suctioning practice ( table 1 ) . differences were observed in awareness of ventilator - assisted pneumonia rates , routine preoxygenation of patients , awareness of protocols for mouth care and checking of endotracheal tube cuff pressures . during a shift , suctioning frequency was primarily as necessary ( prn ) ; however , the data also showed that rrts and , to a lesser extent , rns were also suctioning on 2 h or 4 h schedules ( p=0.003 ) . for rns , prn frequency was 91.6% versus 71.3% for rrts with remaining responses for rns 6.0% 4 h and 2.4% 2 h compared with 17.2% 4 h and 11.5% 2 h for rrts . when asked about frequency of use of nsi before suctioning , there was a statistically significant difference between the responses from rns and rrts ( p=0.014 ) . of the rrts , 11.5% indicated that they never used nsi , 49.4% used it rarely , 36.8% frequently and 2.3% always . in contrast , rns indicated that nsi was used in all patients at least some of the time , with 57.8% rarely using nsi , 41.0% frequently and 1.2% always ( no rns indicted they never used nsi ) . those who responded that they use nsi were asked further questions about instillation practices ( how the normal saline was prepared , why instillation was used , what effects they noted following instillation and what influenced suctioning practices ) . the majority ( 97.5% of rrts , 96.4% of rns ) of respondents used sterile nebulae to prepare the normal saline . the remaining ( 3.6% ) rns used a pre - drawn syringe although the rrts drew the syringe themselves ( 2.5% ) . the volume of saline used was similar between groups , with most using 1 ml to 2 ml ( rrt 50.0% ; rn 41% ) , or 3 ml to 5 ml ( rrt 46.2% ; rn 51.8% ) ; the remaining respondents used > 5 ml . most respondents suctioned the airways immediately following the nsi ( rrt 79.2% ; rn 67.1% ) . the remainder waited up to 1 min ( rrt 16.9% ; rn 30.5% ) or 1 min to 2 min ( rrt 3.9% ; rn 2.4% ) . respondents were also asked why they used nsi before suctioning ( figure 1 ) and whether they had observed any effects following nsi ( figure 2 ) . most respondents had multiple reasons for using nsi and all had observed 1 adverse effect(s ) on patient(s ) following nsi . the only statistically significant differences between the two groups were in relation to the use of nsi to thin secretions ( rrt 10.3% versus rn 1.2% ; p=0.018 ) and that nsi increased the volume of secretions ( rrt 29.6% versus rn 8.9% ; p=0.001 ) . the greatest influence on both rns and rrts practice was reported to be ebp guidelines followed by initial training and continuing education ( figure 3 ) . there was no statistically significant difference between the two groups in this area ( p=0.220 ) . when asked whether they had attended any training or workshops that discussed suctioning of mechanically ventilated patients , no ( 45.3% overall ; rrt 34.5% versus rn 56.6% ; p=0.005 ) followed by yes , but it was more than a year ago ( rrt 32.25 versus rn 16.9% ; p=0.022 ) . approximately 16% overall ( rrt 19.5% versus rn 13.3% ; p=0.306 ) reported they had attended training in the past 12 months , where suction was discussed and the remainder could not recall whether it was discussed ( rn 13% versus rrt 14% ) . in the present study investigating suctioning practices of icu rns and rrts , there were few demographic or practice differences between the two professional groups . most rns and rrts reported that they routinely suctioned mechanically ventilated patients and almost all respondents were aware of icu protocols regarding checking of endotracheal tube cuff pressures and oral hygiene . this was not the case for suctioning protocols in general and specifically related to nsi before suction . it was beyond the scope of the present study to investigate the documentation held in each icu and , hence , it is unknown whether lack of knowledge of particular protocols reflects a lack of protocols or a lack of individual awareness of protocols . that the do nt know responses for the question relating to knowledge of nsi protocols was double that for other protocols ( 47% for rns and 40% for rrts ) may suggest that this is an area that is not discussed within the icu . despite the lack of evidence for benefits of nsi before suctioning ( and concerns about possible adverse effects ) , that this practice is not a recommendation in current clinical practice guidelines and a lack of knowledge about icu protocols regarding nsi , all rns and 89.5% of rrts in the present study used nsi before suction at least some of the time . the most frequent reasons given for using nsi were to clear a mucous plug and/or to loosen secretions . respondents also witnessed a range of adverse effects including decreased oxygenation , patient discomfort , increased heart rate and/or increased volume of secretions . the high level of nsi use reported in the present study is consistent with that reported previously ( 9,20,21 ) ; however , in contrast to the study by schwenker et al ( 20 ) , we report a lower level of combined always and frequent use of nsi . always + frequent use by 83% of rns and 75% of rrts , compared with 42.2% of rns and 39.1% of rrts in the present study . this may suggest a shift away from more routine use of nsi and toward the recommendations of the aarc that routine use of normal saline instillation before endotracheal suction should not be performed ( 18 ) . an interesting finding from our study was that 8.4% of rns and 28.7% of rrts appeared to suction patients on a regular basis ( other than prn ) . it is unclear whether this reflects a misunderstanding of the question ( perhaps the option responses other than prn were seen as an estimate of actual practice ) or whether suctioning was performed at these times regardless of need . a lack of knowledge in icu rns regarding endotracheal tube suctioning has been reported by both day et al ( 21 ) and negro et al ( 22 ) . although the study by day et al ( 21 ) was small ( n=16 ) , the study reported by negro et al ( 22 ) was larger ( n=247 ) . icu nurses from 11 italian hospitals were surveyed on their knowledge of the 2010 aarc clinical practice guidelines and found only 58% of questions were answered correctly . these authors also reported higher knowledge by more experienced nurses ; however , only 2.5% answered nine of the 10 questions correctly . according to some authors , there continues to be a large discrepancy between ebp and actual practice ( 23 ) , and beechey ( 24 ) suggested that many nursing and respiratory therapy practices are still based on experience and routine , rather than on evidence , and that a gap between knowledge ( scientific evidence ) and practice still exists . a large study involving 1665 rns and rrts at 27 sites in the united states found that 83% of respondents did not base their suctioning practice on evidence - based protocols , instead relying on their basic educational programs or the routine practice of their colleagues ( 7 ) . the results of the current study are consistent with these findings and suggest that in the icus participating in the present study , best practice was followed in some suctioning practice areas ( eg , oral care ) ; however , there are gaps between best practice and actual practice in other areas . implementing changes to practices within health care can be complex and much has been written about implementing ebps into a range of health areas . although there is consensus that ebp can improve the effectiveness and efficiency of health care , and improve patient outcomes , there can be significant challenges in adopting practices . competing workload pressures , institutional and individual resistance to change , lack of ebp champions , poor change management processes and lack of access to quality information can act as barriers to implementation , even among those most willing to adopt new practices ( 2527 ) . critical to many implementation strategies is building knowledge in the topic of interest ( 28 ) . although there is limited literature specifically relating to improving adoption of ebps in endotracheal suctioning practice , both mckillop ( 29 ) and day et al ( 21 ) have demonstrated knowledge and practice improvements following interventions . although the methods used by the two studies were different ( mckillop : best practice information checklists ; day et al : structured teaching program ) both programs aimed to increase participant awareness of current best practice . it is a concern in the current study that while approximately one - half of the respondents in both groups stated that they were influenced by ebp protocols or guidelines , there is a gap between best practice and self - reported practice . in addition , less than one - half recalled attending training or workshops covering endotracheal suction practice in the recent past . this is a training gap and an opportunity for the profession or employers to improve the quality of care and , hence , patient outcomes within the icu . there were several limitations to the present study ; specifically , the geographical proximity of participants working within 50 km of the mississauga hospital . the participants may have received their formal education at the same institutions and clinical sites , which may have influenced their practice . the number of participants ( n=180 ) does not constitute a large study and may be viewed as a limitation . the present study identified a gap between what is considered best practice and what is used within groups of community hospital icus . this highlights the need for greater education for both rns and rrts with respect to endotracheal tube suctioning generally and , specifically , with regard to the use of nsi . the routine practice of nsi before suctioning an artificial airway is not recommended and may be detrimental to patients ; however , current practice guidelines do not describe the conditions under which nsi may be used . the risk may outweigh the benefit and , as such , should be carefully considered before engaging in this practice . lack of clarity regarding best practice will contribute to inappropriate and , possibly , unsafe procedures , which in turn reduces the quality of care and increases the potential of poor patient outcomes . suctioning of an artificial airway is not a benign procedure and , as such , health care providers must be aware of the potential complications and side effects .

clinical practice guidelines are , in large part , developed from high - quality data obtained from evidence - based practice . their aim is to optimize treatment efficiency and effectiveness , and to improve the clinical decision - making process . although largely adhered to , studies have reported disparities between clinical guidelines and what is actually practised . this study investigated one such practice that is not supported by current evidence but , paradoxically , is believed to be common in the intensive care unit .

<s>[INST]lunit de soins intensifs ( usi ) , on aspire souvent les scrtions respiratoires des patients intubs ou trachostomiss . des tudes antrieures ont dmontr une importante variation des pratiques daspiration , et mme si les donnes actuelles nappuient pas le rinage systmatique par solution physiologique normale ( spn ) , les donnes empiriques rvlent que leur utilisation serait courante . examiner les pratiques daspiration des infirmires et des inhalothrapeutes lusi de six hpitaux de lontario et sattarder particulirement lutilisation de la spn . les chercheurs ont distribu un sondage auto - administr de 24 questions 180 participants ( 90 infirmires et 90 inalhothrapeutes ) qui travaillaient lusi de six hpitaux de lontario . les groupes dinfirmires et dinhalothrapeutes prsentaient surtout des similarits , tous deux dclarant une forte utilisation du spn . les deux groupes observaient des effets secondaires aprs ladministration du spn , laspiration entranant une diminution de la saturation en oxygne , une agitation des patients et une augmentation du volume de scrtions . bon nombre des participants des deux groupes ne connaissaient pas de protocoles daspiration ou dutilisation de la spn lusi . certains rpondants prcisaient quils procdaient laspiration systmatique des patients sous ventilation mcanique plutt que dattendre les besoins . les infirmires et les inhalothrapeutes continuent dadministrer un spn malgr les directives cliniques fondes sur des donnes probantes indiquant quelle peut tre nfaste au patient . la formation professionnelle de ces deux groupes demploys de lusi devrait sattarder sur les pratiques exemplaires en matire daspiration des sondes trachales en gnral et de ladministration de spn en particulier . a survey was used to gather information from rns and rrts working in icus at six hospitals in ontario . the survey was entitled suctioning an artificial airway in the icu , and requested specific information about the practice and knowledge of participants with respect to the use of nsi before endotracheal suctioning , as well as other suctioning practices . a 24-question survey was developed by the authors and then reviewed by a small group of health professionals before finalization and being sent to participants . this small review group consisted of two rrts who worked outside the geographical area being surveyed , one rn who was responsible for research in an icu and one physician with research experience . the questions in the survey were developed based on a review of the peer - reviewed scientific literature and finalized from input from the small review group . the questionnaire comprised four sections that collected data regarding : demographics ; normal ( intubated ) patient care practices within the icu ; practices relating to nsi before suctioning ; and influences on individual practice . the survey was mailed to managers in six icus at community hospitals within 50 km of the trillium health centre ( mississauga , ontario ) . managers informed their staff about the survey via e - mail or in meetings and the questionnaires were left in staff rooms for any interested parties to complete . the goal was to have a total of 90 rns and 90 rrts complete the surveys . surveys were returned to the principal investigator by a postage - paid envelope provided with the questionnaire . participation was voluntary and no identifying information was collected , ensuring anonymity ; responses were confidential and not disclosed to the unit managers . descriptive statistics were calculated for each question , both as a total and based on respondent professional group . comparative statistics between rrt and rn responses was performed using a pearson test ; p<0.05 was considered to be statistically significant . spss version 20 ( ibm corporation , usa ) was used to perform data analysis . the present study , which was considered to be minimal risk , was approved by the school of biomedical sciences ethics in human research committee of charles sturt university ( burlington , ontario ) and the trillium health centre s ethics committee . a survey was used to gather information from rns and rrts working in icus at six hospitals in ontario . the survey was entitled suctioning an artificial airway in the icu , and requested specific information about the practice and knowledge of participants with respect to the use of nsi before endotracheal suctioning , as well as other suctioning practices . a 24-question survey was developed by the authors and then reviewed by a small group of health professionals before finalization and being sent to participants . this small review group consisted of two rrts who worked outside the geographical area being surveyed , one rn who was responsible for research in an icu and one physician with research experience . the questions in the survey were developed based on a review of the peer - reviewed scientific literature and finalized from input from the small review group . the questionnaire comprised four sections that collected data regarding : demographics ; normal ( intubated ) patient care practices within the icu ; practices relating to nsi before suctioning ; and influences on individual practice . the survey was mailed to managers in six icus at community hospitals within 50 km of the trillium health centre ( mississauga , ontario ) . managers informed their staff about the survey via e - mail or in meetings and the questionnaires were left in staff rooms for any interested parties to complete . the goal was to have a total of 90 rns and 90 rrts complete the surveys . surveys were returned to the principal investigator by a postage - paid envelope provided with the questionnaire . participation was voluntary and no identifying information was collected , ensuring anonymity ; responses were confidential and not disclosed to the unit managers . descriptive statistics were calculated for each question , both as a total and based on respondent professional group . comparative statistics between rrt and rn responses was performed using a pearson test ; p<0.05 was considered to be statistically significant . spss version 20 ( ibm corporation , usa ) was used to perform data analysis . the present study , which was considered to be minimal risk , was approved by the school of biomedical sciences ethics in human research committee of charles sturt university ( burlington , ontario ) and the trillium health centre s ethics committee . surveys were distributed to 90 rns and 90 rrts employed at six icus in ontario . of these , 83 completed surveys were received from rns and 87 from rrts , corresponding to a response rate of 94% and 97% , respectively . overall , approximately one - half ( 48% ) of the respondents had a baccalaureate degree as their highest level of education , with only 2% of respondents having a master s or doctoral degree ; the remaining respondents possessed a diploma . most individuals in each group held either a degree or diploma ; however , there no significance differences between the groups : diploma rn 44% , rrt 56% ( p=0.219 ) ; degree rn 57% , rrt 43% ( p=0.065 ) . no rns held a master s or doctoral degree compared with 5% of rrts ( p=0.122 ) . most respondents had graduated between 2000 and 2010 ( 40% ) , followed by graduation in the periods 1990 to 1999 ( 33% ) , 1980 to 1989 ( 18% ) and before 1980 ( 9% ) . one - half ( 50% ) of the respondents had been working in the icu 10 years . of the remainder , approximately equal numbers had worked from two to five years and six to 10 years ( 26% and 21% , respectively ) ; those who had worked in the icu for < 1 year accounted for 3% of respondents . almost all ( there was no statistically significant difference between the rns and rrts in terms of year of graduation ( p=0.263 ) or years working in the icu ( p=0.773 ) . the type of humidification used for ventilated patients in the icus employing respondents was split between those using heat and moisture exchanger ( rn 31% , rrt 41% ) , and both heat and moisture exchanger and heated chamber ( rn 68% , rrt 59% ) ; only one respondent reported use of heated chamber only . there were few statistically significant differences between these two groups with regard to questions relating to artificial airways suctioning practice ( table 1 ) . differences were observed in awareness of ventilator - assisted pneumonia rates , routine preoxygenation of patients , awareness of protocols for mouth care and checking of endotracheal tube cuff pressures . during a shift , suctioning frequency was primarily as necessary ( prn ) ; however , the data also showed that rrts and , to a lesser extent , rns were also suctioning on 2 h or 4 h schedules ( p=0.003 ) . for rns , prn frequency was 91.6% versus 71.3% for rrts with remaining responses for rns 6.0% 4 h and 2.4% 2 h compared with 17.2% 4 h and 11.5% 2 h for rrts . when asked about frequency of use of nsi before suctioning , there was a statistically significant difference between the responses from rns and rrts ( p=0.014 ) . of the rrts , 11.5% indicated that they never used nsi , 49.4% used it rarely , 36.8% frequently and 2.3% always . in contrast , rns indicated that nsi was used in all patients at least some of the time , with 57.8% rarely using nsi , 41.0% frequently and 1.2% always ( no rns indicted they never used nsi ) . those who responded that they use nsi were asked further questions about instillation practices ( how the normal saline was prepared , why instillation was used , what effects they noted following instillation and what influenced suctioning practices ) . the majority ( 97.5% of rrts , 96.4% of rns ) of respondents used sterile nebulae to prepare the normal saline . the remaining ( 3.6% ) rns used a pre - drawn syringe although the rrts drew the syringe themselves ( 2.5% ) . the volume of saline used was similar between groups , with most using 1 ml to 2 ml ( rrt 50.0% ; rn 41% ) , or 3 ml to 5 ml ( rrt 46.2% ; rn 51.8% ) ; the remaining respondents used > 5 ml . most respondents suctioned the airways immediately following the nsi ( rrt 79.2% ; rn 67.1% ) . the remainder waited up to 1 min ( rrt 16.9% ; rn 30.5% ) or 1 min to 2 min ( rrt 3.9% ; rn 2.4% ) . respondents were also asked why they used nsi before suctioning ( figure 1 ) and whether they had observed any effects following nsi ( figure 2 ) . most respondents had multiple reasons for using nsi and all had observed 1 adverse effect(s ) on patient(s ) following nsi . the only statistically significant differences between the two groups were in relation to the use of nsi to thin secretions ( rrt 10.3% versus rn 1.2% ; p=0.018 ) and that nsi increased the volume of secretions ( rrt 29.6% versus rn 8.9% ; p=0.001 ) . the greatest influence on both rns and rrts practice was reported to be ebp guidelines followed by initial training and continuing education ( figure 3 ) . there was no statistically significant difference between the two groups in this area ( p=0.220 ) . when asked whether they had attended any training or workshops that discussed suctioning of mechanically ventilated patients , no ( 45.3% overall ; rrt 34.5% versus rn 56.6% ; p=0.005 ) followed by yes , but it was more than a year ago ( rrt 32.25 versus rn 16.9% ; p=0.022 ) . approximately 16% overall ( rrt 19.5% versus rn 13.3% ; p=0.306 ) reported they had attended training in the past 12 months , where suction was discussed and the remainder could not recall whether it was discussed ( rn 13% versus rrt 14% ) . in the present study investigating suctioning practices of icu rns and rrts , there were few demographic or practice differences between the two professional groups . most rns and rrts reported that they routinely suctioned mechanically ventilated patients and almost all respondents were aware of icu protocols regarding checking of endotracheal tube cuff pressures and oral hygiene . this was not the case for suctioning protocols in general and specifically related to nsi before suction . it was beyond the scope of the present study to investigate the documentation held in each icu and , hence , it is unknown whether lack of knowledge of particular protocols reflects a lack of protocols or a lack of individual awareness of protocols . that the do nt know responses for the question relating to knowledge of nsi protocols was double that for other protocols ( 47% for rns and 40% for rrts ) may suggest that this is an area that is not discussed within the icu . despite the lack of evidence for benefits of nsi before suctioning ( and concerns about possible adverse effects ) , that this practice is not a recommendation in current clinical practice guidelines and a lack of knowledge about icu protocols regarding nsi , all rns and 89.5% of rrts in the present study used nsi before suction at least some of the time . the most frequent reasons given for using nsi were to clear a mucous plug and/or to loosen secretions . respondents also witnessed a range of adverse effects including decreased oxygenation , patient discomfort , increased heart rate and/or increased volume of secretions . the high level of nsi use reported in the present study is consistent with that reported previously ( 9,20,21 ) ; however , in contrast to the study by schwenker et al ( 20 ) , we report a lower level of combined always and frequent use of nsi . always + frequent use by 83% of rns and 75% of rrts , compared with 42.2% of rns and 39.1% of rrts in the present study . this may suggest a shift away from more routine use of nsi and toward the recommendations of the aarc that routine use of normal saline instillation before endotracheal suction should not be performed ( 18 ) . an interesting finding from our study was that 8.4% of rns and 28.7% of rrts appeared to suction patients on a regular basis ( other than prn ) . it is unclear whether this reflects a misunderstanding of the question ( perhaps the option responses other than prn were seen as an estimate of actual practice ) or whether suctioning was performed at these times regardless of need . a lack of knowledge in icu rns regarding endotracheal tube suctioning has been reported by both day et al ( 21 ) and negro et al ( 22 ) . although the study by day et al ( 21 ) was small ( n=16 ) , the study reported by negro et al ( 22 ) was larger ( n=247 ) . icu nurses from 11 italian hospitals were surveyed on their knowledge of the 2010 aarc clinical practice guidelines and found only 58% of questions were answered correctly . these authors also reported higher knowledge by more experienced nurses ; however , only 2.5% answered nine of the 10 questions correctly . according to some authors , there continues to be a large discrepancy between ebp and actual practice ( 23 ) , and beechey ( 24 ) suggested that many nursing and respiratory therapy practices are still based on experience and routine , rather than on evidence , and that a gap between knowledge ( scientific evidence ) and practice still exists . a large study involving 1665 rns and rrts at 27 sites in the united states found that 83% of respondents did not base their suctioning practice on evidence - based protocols , instead relying on their basic educational programs or the routine practice of their colleagues ( 7 ) . the results of the current study are consistent with these findings and suggest that in the icus participating in the present study , best practice was followed in some suctioning practice areas ( eg , oral care ) ; however , there are gaps between best practice and actual practice in other areas . implementing changes to practices within health care can be complex and much has been written about implementing ebps into a range of health areas . although there is consensus that ebp can improve the effectiveness and efficiency of health care , and improve patient outcomes , there can be significant challenges in adopting practices . competing workload pressures , institutional and individual resistance to change , lack of ebp champions , poor change management processes and lack of access to quality information can act as barriers to implementation , even among those most willing to adopt new practices ( 2527 ) . critical to many implementation strategies is building knowledge in the topic of interest ( 28 ) . although there is limited literature specifically relating to improving adoption of ebps in endotracheal suctioning practice , both mckillop ( 29 ) and day et al ( 21 ) have demonstrated knowledge and practice improvements following interventions . although the methods used by the two studies were different ( mckillop : best practice information checklists ; day et al : structured teaching program ) both programs aimed to increase participant awareness of current best practice . it is a concern in the current study that while approximately one - half of the respondents in both groups stated that they were influenced by ebp protocols or guidelines , there is a gap between best practice and self - reported practice . in addition , less than one - half recalled attending training or workshops covering endotracheal suction practice in the recent past . this is a training gap and an opportunity for the profession or employers to improve the quality of care and , hence , patient outcomes within the icu . there were several limitations to the present study ; specifically , the geographical proximity of participants working within 50 km of the mississauga hospital . the participants may have received their formal education at the same institutions and clinical sites , which may have influenced their practice . the number of participants ( n=180 ) does not constitute a large study and may be viewed as a limitation . the present study identified a gap between what is considered best practice and what is used within groups of community hospital icus . this highlights the need for greater education for both rns and rrts with respect to endotracheal tube suctioning generally and , specifically , with regard to the use of nsi . the routine practice of nsi before suctioning an artificial airway is not recommended and may be detrimental to patients ; however , current practice guidelines do not describe the conditions under which nsi may be used . the risk may outweigh the benefit and , as such , should be carefully considered before engaging in this practice . lack of clarity regarding best practice will contribute to inappropriate and , possibly , unsafe procedures , which in turn reduces the quality of care and increases the potential of poor patient outcomes . suctioning of an artificial airway is not a benign procedure and , as such , health care providers must be aware of the potential complications and side effects .[/INST]clinical practice guidelines are , in large part , developed from high - quality data obtained from evidence - based practice . their aim is to optimize treatment efficiency and effectiveness , and to improve the clinical decision - making process . although largely adhered to , studies have reported disparities between clinical guidelines and what is actually practised . this study investigated one such practice that is not supported by current evidence but , paradoxically , is believed to be common in the intensive care unit .</s>

between 1972 and 1974 , community - dwelling residents living in rancho bernardo , california , 3079 years of age , were invited to participate in a study of heart disease risk factors ; 82% enrolled . nearly all were middle- to upper - middle class and relatively well - educated . since the study was approved by the institutional review board of the university of california san diego , and all participants gave written informed consent . of the 1,781 participants who attended the 19921996 visits , 39 were excluded for insufficient stored plasma for fetuin - a determination and 27 for missing covariates , resulting in sample sizes of 672 men and 1,043 women for the prevalent diabetes analysis . of these 1,715 participants , 241 were lost to follow - up for incident diabetes . on average , participants lost to follow - up were older ( 79.8 vs. 70.0 years , p = 0.008 ) and had lower age - adjusted fetuin - a levels at baseline ( 0.489 vs. 0.523 g / l , p < 0.001 ) compared with those followed ; 82% of loss to follow - up was caused by death . these individuals , as well as those with prevalent diabetes at baseline ( n = 242 ) , were excluded , resulting in sample sizes of 477 men and 782 women for the incident diabetes analysis . during the 19921996 clinic visits , information regarding medical history , medication use , physical activity , alcohol consumption , and current smoking was obtained through standard questionnaires . current medication use was validated by examination of pills and prescriptions brought to the clinic for that purpose . bmi and waist - to - hip ratio ( whr ) were used as estimates of overall and central adiposity , respectively . percent body fat was determined by full body dual energy x - ray absorptiometry scan . blood pressures were measured twice while participants were seated , according to the hypertension detection and follow - up program protocol ( 19 ) , and the mean used in the analyses . a 75-g oral glucose tolerance test was administered between 0730 and 1100 h after a minimum 8-h overnight fast . blood samples were drawn by venipuncture at 0 and 2 h , and serum and plasma were separated and frozen at 70c . plasma glucose was measured by the glucose oxidase method , and insulin concentration was determined by radioimmunoassay in a diabetes research laboratory . fetuin - a concentrations were measured in duplicate in 2010 from archived fasting edta plasma samples with a human elisa kit ( epitope diagnostics , san diego , ca ) . this assay uses a two - site sandwich technique with polyclonal antibodies that bind different epitopes of human fetuin - a . intra- and interassay coefficients of variation were 2.44.7% and 9.59.9% , respectively , for the set of assays used for the present sample . impaired fasting glucose ( ifg ) was defined as a fasting plasma glucose level of 100125 mg / dl and impaired glucose tolerance ( igt ) as a 2-h postchallenge glucose level of 140199 mg / dl . prevalent diabetes was defined by self - report of physician diagnosis , fasting plasma glucose 126 mg / dl , 2-h postchallenge glucose 200 mg / dl , or use of diabetes medications . incident diabetes was defined as any of the prevalent diabetes criteria with the exception of postchallenge glucose , which was not available at follow - up . incident diabetes was assessed at five follow - up clinic visits and by four mailed questionnaires over a maximum 15-year follow - up period . prevalent cardiovascular disease ( cvd ) was defined as physician - diagnosed myocardial infarction , coronary artery revascularization , congestive heart failure , stroke or transient ischemic attack , carotid artery surgery , peripheral arterial surgery , or physician - diagnosed intermittent claudication . the metabolic syndrome was defined according to 2002 adult treatment panel iii criteria ( 20 ) . kidney function was assessed by the estimated glomerular filtration rate ( egfr ) based on the modification of diet in renal disease equation ( 21 ) and by the albumin - to - creatinine ratio ( acr ) . the homeostasis model assessment for insulin resistance ( homa - ir ) insulin resistance was defined as a homa - ir > 75th percentile for the study population . initial combined analyses revealed strong interactions for sex and fetuin - a for both prevalent ( p = 0.007 ) and incident ( p = 0.020 ) diabetes ; therefore , all analyses were stratified by sex . fetuin - a concentration was entered into models as a first - order continuous variable after screening for thresholds and curvilinear associations . the association between fetuin - a and baseline characteristics was evaluated by pearson correlation coefficient . hdl cholesterol , triglyceride , aspartate transaminase ( ast ) , and alanine transaminase ( alt ) levels were log - transformed to reduce the influence of outliers ; reported values are geometric means and interquartile ranges . the age - adjusted association of fetuin - a with baseline glycemic status was assessed by ancova . the association of fetuin - a with prevalent diabetes was determined by logistic regression ; the association with incident diabetes was assessed by cox proportional hazards regressions . the first adjusted for age and use of oral estrogens ( on the basis of our earlier studies that showed higher fetuin - a levels in women taking oral estrogens versus those not taking estrogens ) . the second added adjustment for adiposity and lifestyle , and the third added other diabetes risk factors . separate secondary models tested the influence of potential confounders and mediators by adding each variable separately to the fully adjusted base model . biologically plausible effect modifiers were individually tested by interaction terms on a multiplicative scale in both the logistic and the proportional hazards regression models . all p values presented are two - tailed , with p < 0.05 considered statistically significant for all analyses , including the interaction terms . data were analyzed using stata version 12.0 ( stata corp . , college station , tx ) and spss version 15 ( ibm corporation , chicago , il ) statistical software . between 1972 and 1974 , community - dwelling residents living in rancho bernardo , california , 3079 years of age , were invited to participate in a study of heart disease risk factors ; 82% enrolled . nearly all were middle- to upper - middle class and relatively well - educated . since the study was approved by the institutional review board of the university of california san diego , and all participants gave written informed consent . of the 1,781 participants who attended the 19921996 visits , 39 were excluded for insufficient stored plasma for fetuin - a determination and 27 for missing covariates , resulting in sample sizes of 672 men and 1,043 women for the prevalent diabetes analysis . of these 1,715 participants , 241 were lost to follow - up for incident diabetes . on average , participants lost to follow - up were older ( 79.8 vs. 70.0 years , p = 0.008 ) and had lower age - adjusted fetuin - a levels at baseline ( 0.489 vs. 0.523 g / l , p < 0.001 ) compared with those followed ; 82% of loss to follow - up was caused by death . these individuals , as well as those with prevalent diabetes at baseline ( n = 242 ) , were excluded , resulting in sample sizes of 477 men and 782 women for the incident diabetes analysis . during the 19921996 clinic visits , information regarding medical history , medication use , physical activity , alcohol consumption , and current smoking was obtained through standard questionnaires . current medication use was validated by examination of pills and prescriptions brought to the clinic for that purpose . bmi and waist - to - hip ratio ( whr ) were used as estimates of overall and central adiposity , respectively . percent body fat was determined by full body dual energy x - ray absorptiometry scan . blood pressures were measured twice while participants were seated , according to the hypertension detection and follow - up program protocol ( 19 ) , and the mean used in the analyses . a 75-g oral glucose tolerance test was administered between 0730 and 1100 h after a minimum 8-h overnight fast . blood samples were drawn by venipuncture at 0 and 2 h , and serum and plasma were separated and frozen at 70c . plasma glucose was measured by the glucose oxidase method , and insulin concentration was determined by radioimmunoassay in a diabetes research laboratory . fetuin - a concentrations were measured in duplicate in 2010 from archived fasting edta plasma samples with a human elisa kit ( epitope diagnostics , san diego , ca ) . this assay uses a two - site sandwich technique with polyclonal antibodies that bind different epitopes of human fetuin - a . intra- and interassay coefficients of variation were 2.44.7% and 9.59.9% , respectively , for the set of assays used for the present sample . impaired fasting glucose ( ifg ) was defined as a fasting plasma glucose level of 100125 mg / dl and impaired glucose tolerance ( igt ) as a 2-h postchallenge glucose level of 140199 mg / dl . prevalent diabetes was defined by self - report of physician diagnosis , fasting plasma glucose 126 mg / dl , 2-h postchallenge glucose 200 mg / dl , or use of diabetes medications . incident diabetes was defined as any of the prevalent diabetes criteria with the exception of postchallenge glucose , which was not available at follow - up . incident diabetes was assessed at five follow - up clinic visits and by four mailed questionnaires over a maximum 15-year follow - up period . prevalent cardiovascular disease ( cvd ) was defined as physician - diagnosed myocardial infarction , coronary artery revascularization , congestive heart failure , stroke or transient ischemic attack , carotid artery surgery , peripheral arterial surgery , or physician - diagnosed intermittent claudication . the metabolic syndrome was defined according to 2002 adult treatment panel iii criteria ( 20 ) . kidney function was assessed by the estimated glomerular filtration rate ( egfr ) based on the modification of diet in renal disease equation ( 21 ) and by the albumin - to - creatinine ratio ( acr ) . the homeostasis model assessment for insulin resistance ( homa - ir ) insulin resistance was defined as a homa - ir > 75th percentile for the study population . initial combined analyses revealed strong interactions for sex and fetuin - a for both prevalent ( p = 0.007 ) and incident ( p = 0.020 ) diabetes ; therefore , all analyses were stratified by sex . fetuin - a concentration was entered into models as a first - order continuous variable after screening for thresholds and curvilinear associations . the association between fetuin - a and baseline characteristics was evaluated by pearson correlation coefficient . hdl cholesterol , triglyceride , aspartate transaminase ( ast ) , and alanine transaminase ( alt ) levels were log - transformed to reduce the influence of outliers ; reported values are geometric means and interquartile ranges . the age - adjusted association of fetuin - a with baseline glycemic status was assessed by ancova . the association of fetuin - a with prevalent diabetes was determined by logistic regression ; the association with incident diabetes was assessed by cox proportional hazards regressions . the first adjusted for age and use of oral estrogens ( on the basis of our earlier studies that showed higher fetuin - a levels in women taking oral estrogens versus those not taking estrogens ) . the second added adjustment for adiposity and lifestyle , and the third added other diabetes risk factors . separate secondary models tested the influence of potential confounders and mediators by adding each variable separately to the fully adjusted base model . biologically plausible effect modifiers were individually tested by interaction terms on a multiplicative scale in both the logistic and the proportional hazards regression models . all p values presented are two - tailed , with p < 0.05 considered statistically significant for all analyses , including the interaction terms . data were analyzed using stata version 12.0 ( stata corp . , college station , tx ) and spss version 15 ( ibm corporation , chicago , il ) statistical software . the mean age of the 1,715 participants was 71.3 years ; 61% ( n = 1,043 ) were women of whom 401 ( 38% ) reported current oral estrogen therapy . g / l ) , intermediate for women not taking oral estrogens ( 0.51 , 0.440.58 ) , and lowest for men ( 0.50 , 0.440.56 ) ( p < 0.001 for all comparisons ) . baseline characteristics and the correlation of individual variables with fetuin - a levels are shown in table 1 . in general , fetuin - a associations were similar for men and women . triglycerides , total cholesterol , bmi , and waist circumference showed the strongest positive associations with fetuin - a , whereas age and hdl cholesterol showed the strongest negative associations . men and women with the metabolic syndrome had higher fetuin - a levels , whereas those with prevalent cvd had lower fetuin - a levels . baseline characteristics figure 1 shows age - adjusted fetuin - a levels by glucose tolerance status at baseline ( fig . 1a ) and in nondiabetic participants in whom incident diabetes did and did not develop during follow - up ( fig . compared with women with normal glucose tolerance ( ngt ) , age - adjusted levels of fetuin - a were elevated in women with isolated igt ( p = 0.019 ) or igt plus ifg ( p = 0.030 ) and were highest in women with prevalent diabetes ( p < 0.001 ) . fetuin - a levels did not differ by ifg in women ( p = 0.81 ) and did not vary by any measure of glucose tolerance status in men . baseline fetuin - a levels were also significantly higher in women ( p = 0.008 ) , but not men , in whom incident diabetes developed during follow - up compared with those who remained diabetes free ( fig . mean ( sem ) age - adjusted fetuin - a levels by glycemic status ( a ) and by incident diabetes status ( b ) in women ( ) and men ( ) . number of women with each status : ngt = 578 , ifg = 75 , igt = 204 , igt + ifg = 72 , prevalent diabetes = 129 , no diabetes = 750 , and incident diabetes = 32 . number of men with each status : ngt = 294 , ifg = 96 , igt = 109 , igt + ifg = 72 , prevalent diabetes = 113 , no diabetes = 424 , and incident diabetes = 53 . * p < 0.05 versus ngt , * * p < 0.01 versus ngt ( a ) or no diabetes ( b ) . at baseline , 113 ( 17% ) overall , 42% ( n = 102 ) of prevalent cases were based on postchallenge glucose alone , 4% ( n = 9 ) on fasting glucose alone , and 38% ( n = 92 ) only on self - report of physician diagnosis ; the remaining 16% ( n = 39 ) were based on more than one criterion . during the median 9.1-year follow - up , incident diabetes developed in 32 women and 53 men . overall , 33% ( n = 26 ) of incident cases were based on fasting plasma glucose , 13% ( n = 11 ) on the use of diabetes medications , and 52% ( n = 44 ) on self - report of physician diagnosis ; four cases were based on combined criteria . the distribution of diagnostic categories that identified cases of prevalent and incident diabetes did not differ significantly by sex ( p > 0.17 ) , although the proportion of prevalent cases identified by postchallenge glucose alone was higher in women than in men ( 48 vs. 35% , p = 0.047 ) . table 2 presents odds ratios ( ors ) for prevalent diabetes and hazard ratios ( hrs ) for incident diabetes per sd ( 0.10 each sd higher fetuin - a level was associated with a 79% greater odds of prevalent diabetes and a 66% greater risk of incident diabetes , adjusting for age and oral estrogen therapy . risk estimates for women were only modestly attenuated in sequential models that added adjustment for alcohol consumption , current smoking , exercise , bmi , and whr ( model 2 ) and other diabetes risk factors ( triglycerides , hdl cholesterol , and systolic and diastolic blood pressures ) ( model 3 ) . in contrast , among men , a positive association was suggested in age - adjusted models , but risk estimates were attenuated to one in multivariable models . g / l ) greater fetuin - a level in secondary models , individually adding adjustment for homa - ir , fasting plasma glucose , 2-h postchallenge glucose , egfr , acr , albumin , or liver enzymes ( alt , ast , and -glutamyl transpeptidase [ ggt ] ) to the multivariable base model ( model 3 ) had minimal influence on results in either sex , with one exception . in women , separate added adjustment for height and percent fat mass did not alter results for either diabetes outcome in either sex ( data not shown ) . next we examined whether the associations of fetuin - a with prevalent and incident diabetes differed across strata of selected risk factors ( table 3 ) . for women , the association of fetuin - a with prevalent diabetes was stronger for those with insulin resistance compared with those without ( p for interaction = 0.041 ) . g / l ) higher fetuin - a level was associated with a nearly fourfold higher risk of incident diabetes in women with fasting glucose > 100 mg / dl , but this was not significantly related to diabetes risk in women with lower fasting glucose levels ( p for interaction = 0.039 ) . there was no statistical evidence of effect modification by age , prevalent cvd , or oral estrogen therapy . among men , the association of fetuin - a with prevalent and incident diabetes was similar across all subgroups except for prevalent cvd status . g / l ) higher fetuin - a level was associated with a 70% greater odds of prevalent diabetes for men with prevalent cvd but was not related to prevalent diabetes among men without known cvd ( p for interaction = 0.022 ) . effect modifiers of the fetuin - a association with prevalent and incident diabetes for women and men the mean age of the 1,715 participants was 71.3 years ; 61% ( n = 1,043 ) were women of whom 401 ( 38% ) reported current oral estrogen therapy . g / l ) , intermediate for women not taking oral estrogens ( 0.51 , 0.440.58 ) , and lowest for men ( 0.50 , 0.440.56 ) ( p < 0.001 for all comparisons ) . baseline characteristics and the correlation of individual variables with fetuin - a levels are shown in table 1 . in general , fetuin - a associations were similar for men and women . triglycerides , total cholesterol , bmi , and waist circumference showed the strongest positive associations with fetuin - a , whereas age and hdl cholesterol showed the strongest negative associations . men and women with the metabolic syndrome had higher fetuin - a levels , whereas those with prevalent cvd had lower fetuin - a levels . figure 1 shows age - adjusted fetuin - a levels by glucose tolerance status at baseline ( fig . 1a ) and in nondiabetic participants in whom incident diabetes did and did not develop during follow - up ( fig . 1b ) . compared with women with normal glucose tolerance ( ngt ) , age - adjusted levels of fetuin - a were elevated in women with isolated igt ( p = 0.019 ) or igt plus ifg ( p = 0.030 ) and were highest in women with prevalent diabetes ( p < 0.001 ) . fetuin - a levels did not differ by ifg in women ( p = 0.81 ) and did not vary by any measure of glucose tolerance status in men . baseline fetuin - a levels were also significantly higher in women ( p = 0.008 ) , but not men , in whom incident diabetes developed during follow - up compared with those who remained diabetes free ( fig . mean ( sem ) age - adjusted fetuin - a levels by glycemic status ( a ) and by incident diabetes status ( b ) in women ( ) and men ( ) . number of women with each status : ngt = 578 , ifg = 75 , igt = 204 , igt + ifg = 72 , prevalent diabetes = 129 , no diabetes = 750 , and incident diabetes = 32 . number of men with each status : ngt = 294 , ifg = 96 , igt = 109 , igt + ifg = 72 , prevalent diabetes = 113 , no diabetes = 424 , and incident diabetes = 53 . * p < 0.05 versus ngt , * * p < 0.01 versus ngt ( a ) or no diabetes ( b ) . at baseline , 113 ( 17% ) men and 129 ( 12% ) women had prevalent diabetes . overall , 42% ( n = 102 ) of prevalent cases were based on postchallenge glucose alone , 4% ( n = 9 ) on fasting glucose alone , and 38% ( n = 92 ) only on self - report of physician diagnosis ; the remaining 16% ( n = 39 ) were based on more than one criterion . during the median 9.1-year follow - up , incident diabetes developed in 32 women and 53 men . overall , 33% ( n = 26 ) of incident cases were based on fasting plasma glucose , 13% ( n = 11 ) on the use of diabetes medications , and 52% ( n = 44 ) on self - report of physician diagnosis ; four cases were based on combined criteria . the distribution of diagnostic categories that identified cases of prevalent and incident diabetes did not differ significantly by sex ( p > 0.17 ) , although the proportion of prevalent cases identified by postchallenge glucose alone was higher in women than in men ( 48 vs. 35% , p = 0.047 ) . table 2 presents odds ratios ( ors ) for prevalent diabetes and hazard ratios ( hrs ) for incident diabetes per sd ( 0.10 each sd higher fetuin - a level was associated with a 79% greater odds of prevalent diabetes and a 66% greater risk of incident diabetes , adjusting for age and oral estrogen therapy . risk estimates for women were only modestly attenuated in sequential models that added adjustment for alcohol consumption , current smoking , exercise , bmi , and whr ( model 2 ) and other diabetes risk factors ( triglycerides , hdl cholesterol , and systolic and diastolic blood pressures ) ( model 3 ) . in contrast , among men , a positive association was suggested in age - adjusted models , but risk estimates were attenuated to one in multivariable models . g / l ) greater fetuin - a level in secondary models , individually adding adjustment for homa - ir , fasting plasma glucose , 2-h postchallenge glucose , egfr , acr , albumin , or liver enzymes ( alt , ast , and -glutamyl transpeptidase [ ggt ] ) to the multivariable base model ( model 3 ) had minimal influence on results in either sex , with one exception . in women , separate added adjustment for height and percent fat mass did not alter results for either diabetes outcome in either sex ( data not shown ) . next we examined whether the associations of fetuin - a with prevalent and incident diabetes differed across strata of selected risk factors ( table 3 ) . for women , the association of fetuin - a with prevalent diabetes was stronger for those with insulin resistance compared with those without ( p for interaction = 0.041 ) . g / l ) higher fetuin - a level was associated with a nearly fourfold higher risk of incident diabetes in women with fasting glucose > 100 mg / dl , but this was not significantly related to diabetes risk in women with lower fasting glucose levels ( p for interaction = 0.039 ) . there was no statistical evidence of effect modification by age , prevalent cvd , or oral estrogen therapy . among men , the association of fetuin - a with prevalent and incident diabetes was similar across all subgroups except for prevalent cvd status . g / l ) higher fetuin - a level was associated with a 70% greater odds of prevalent diabetes for men with prevalent cvd but was not related to prevalent diabetes among men without known cvd ( p for interaction = 0.022 ) . effect modifiers of the fetuin - a association with prevalent and incident diabetes for women and men in this cohort of white community - dwelling older adults , we observed a strong and persistent sex difference in the association of fetuin - a with stages of glucose tolerance , prevalent diabetes , and the development of new diabetes over a median 9-year follow - up . an sd greater fetuin - a level was associated with 66% higher odds of prevalent diabetes and a 79% greater risk of incident diabetes in women but was not related to diabetes in men . this sex difference extended to prediabetic conditions ; women , but not men , with igt had elevated fetuin - a concentrations compared with their counterparts with ngt . these findings were independent of established diabetes risk factors and markers of liver function and chronic kidney disease , with one notable exception : adjustment for postchallenge glucose concentrations attenuated associations with prevalent and incident diabetes in women . evidence of sex differences in the regulation of glucose homeostasis and the primary risk factors for diabetes is accumulating , particularly for older adults . early studies in the rancho bernardo cohort showed that more than one - half of type 2 diabetes cases would be undiagnosed without a glucose tolerance test , that a diagnosis based solely on postchallenge hyperglycemia was more frequent in women than in men ( comprising more than one - half of diabetes diagnoses in women when a glucose tolerance test was included ) , and that older women had more pronounced glucose intolerance but lower fasting glucose concentrations than men ( 9,10,24 ) . a markedly higher prevalence of igt in older women than in older men , contrasted with more ifg in men than in women , has been observed in epidemiologic studies from various countries around the world , including germany ( 25 ) , mauritius ( 6 ) , denmark ( 7 ) , and england ( 26 ) . ( 4 ) observed higher rates of both glucose appearance and glucose disappearance in response to a fixed meal in elderly women than in elderly men . consistent with prior epidemiologic studies ( 2729 ) , fetuin - a levels were positively associated with insulin resistance in both sexes in the current study . several lines of evidence suggest that igt may be a specific link between fetuin - a and type 2 diabetes , especially for older women . first , in this and prior studies ( 30,31 ) , fetuin - a levels are elevated in middle - aged and elderly individuals with isolated igt but are not related to ifg . second , the association of fetuin - a with igt in the current study was only observed in women , and igt is more common in older women than in older men ( 6,7,10,25,26 ) . third , postchallenge glucose was the only risk factor among many tested that explained a significant proportion of the association of fetuin - a with both prevalent and incident diabetes in the women in this study . the apparently dominant role of igt in defining diabetes in older women , whereas ifg seems to be more important for older men , may explain the absence of an association of fetuin - a with diabetes in the men in this study . the sex differences identified in the current study conflict with earlier epidemiologic studies . a link between elevated fetuin - a levels and the development of type 2 diabetes was first reported in 2008 in our pilot study of older white and black adults from the health , aging , and body composition ( health abc ) population ( 17 ) and in a larger study of middle - aged adults from the european prospective investigation into cancer and nutrition ( epic)-potsdam study ( 14 ) . we recently confirmed these early findings with data from the cardiovascular health study among community - dwelling adults aged 65 years . higher fetuin - a levels predicted incident diabetes regardless of sex , race , or prevalent cvd status ( 13 ) . effect modification by sex was also examined in the health abc and epic - potsdam studies , and none was found . the health abc was a pilot study , and the sample size may have been limiting . the epic - potsdam study and cardiovascular health study were not able to exclude prevalent diabetes cases on the basis of postchallenge glucose alone , and incident diabetes cases in epic - potsdam were identified by self - report and examination of medical records without fasting glucose measurements ; thus , undiagnosed cases may have confounded identification of sex differences in these studies . it is also notable that the rancho bernardo study population is distinct in its high degree of racial and socioeconomic homogeneity , which may have reduced sources of confounding and optimized our ability to detect sex differences . consonant with findings from the epic - potsdam study ( 14 ) , the association between circulating fetuin - a and incident diabetes in the current study was modified by fasting glucose levels , but only in women . higher fetuin - a levels were associated with an increased risk of diabetes among women whose fasting glucose levels fell to within the prediabetic range but were not related to diabetes among women with normal glucose levels , suggesting that fetuin - a elevation might be more important later in the progression to diabetes . although evidence from this study along with that from several others strongly suggests that fetuin - a is an independent marker of type 2 diabetes risk in humans , whether the relation is causal is still unknown . the fact that the gene encoding fetuin - a is located on chromosome arm 3q27 , a region mapped as a diabetes susceptibility locus ( 32 ) , supports a role for fetuin - a in the regulation of glucose homeostasis . that plasma fetuin - a levels and protein expression are increased in fatty liver disease ( 29 ) , a strong predictor of diabetes ( 33 ) , also points to a role for fetuin - a in the pathogenesis of diabetes . nonetheless , experimental evidence that selective lowering of fetuin - a levels improves insulin sensitivity and reduces the risk for type 2 diabetes in humans is still lacking . more investigations are needed to determine whether fetuin - a is a viable target for diabetes prevention or treatment . the strengths of this study are its prospective design , the relatively large sample size , inclusion of both sexes , and the availability of measurements of a wide spectrum of potential mediators and confounders . our ability to accurately identify prevalent diabetes cases was enhanced by having postchallenge glucose concentrations at baseline . associations were based on fetuin - a concentrations measured at a single time point ; nonetheless , we identified a strong signal for both prevalent and incident diabetes in women that was robust to statistical adjustment for multiple covariates . because the number of diabetes cases in this study was relatively small , it is possible that the findings , including the sex differences , were due to chance . like most epidemiologic studies , postchallenge glucose levels were not available at follow - up , which may have exerted a stronger limitation on incident diabetes diagnosis in women than in men but is unlikely to account for the sex - specific associations . we also had no information on family history of diabetes , which may have confounded results , but whether this is the case to a greater degree in one sex than the other is not clear ( 34 ) . finally , the majority of participants were white elderly men and women , and the results may not generalize to younger adults or those of different races / ethnicities . in conclusion , higher fetuin - a levels were associated with igt and prevalent and incident type 2 diabetes in community - dwelling older women independent of most established and several emerging diabetes risk factors . fetuin - a levels were not associated with igt or diabetes prevalence and incidence in men . if the findings are substantiated in larger epidemiologic studies with postchallenge glucose levels available , these sex - specific fetuin - a associations may provide new insights into mechanisms responsible for sex differences in glucose homeostasis and diabetes risk with advancing age .

objectivethis study evaluated the sex - specific association of plasma fetuin - a levels with prevalent and incident type 2 diabetes in community - dwelling older adults.research design and methodsparticipants were 684 men and 1,058 women ( median age , 71 years ) whose fetuin - a levels , diabetes prevalence , and diabetes risk factors were evaluated in 19921996 . the participants were followed for incident diabetes through 2010 ( median follow - up , 9 years).resultswomen with impaired glucose tolerance had elevated fetuin - a levels compared with women with normal glucose tolerance ( p = 0.019 ) , but fetuin - a levels were not elevated in women with impaired fasting glucose . fetuin - a did not vary by glucose tolerance status in men . there were significant interactions of fetuin - a by sex for prevalent ( p = 0.007 ) and incident ( p = 0.020 ) diabetes . for women , each sd ( 0.10 g / l ) higher fetuin - a level was associated with a higher odds of prevalent diabetes ( odds ratio [ or ] 1.79 , 95% ci 1.472.17 ) and greater risk of incident diabetes ( hazard ratio [ hr ] 1.66 , 95% ci 1.182.34 ) , adjusting for age and estrogen therapy . these associations were not materially altered by adjustment for diabetes risk factors but were attenuated by adjusting for postchallenge glucose levels . among men , although positive associations with prevalent ( or 1.15 [ 0.941.41 ] ) and incident ( hr 1.24 [ 0.931.65 ] ) diabetes were suggested in age - adjusted models , risk estimates attenuated to one after multivariable adjustment.conclusionshigher fetuin - a concentrations were independently associated with an increased risk of developing type 2 diabetes in older women but were not related to diabetes risk in older men . fetuin - a may provide novel insights into mechanisms underlying sex differences in glucose homeostasis and diabetes risk in old age .

<s>[INST]between 1972 and 1974 , community - dwelling residents living in rancho bernardo , california , 3079 years of age , were invited to participate in a study of heart disease risk factors ; 82% enrolled . nearly all were middle- to upper - middle class and relatively well - educated . since the study was approved by the institutional review board of the university of california san diego , and all participants gave written informed consent . of the 1,781 participants who attended the 19921996 visits , 39 were excluded for insufficient stored plasma for fetuin - a determination and 27 for missing covariates , resulting in sample sizes of 672 men and 1,043 women for the prevalent diabetes analysis . of these 1,715 participants , 241 were lost to follow - up for incident diabetes . on average , participants lost to follow - up were older ( 79.8 vs. 70.0 years , p = 0.008 ) and had lower age - adjusted fetuin - a levels at baseline ( 0.489 vs. 0.523 g / l , p < 0.001 ) compared with those followed ; 82% of loss to follow - up was caused by death . these individuals , as well as those with prevalent diabetes at baseline ( n = 242 ) , were excluded , resulting in sample sizes of 477 men and 782 women for the incident diabetes analysis . during the 19921996 clinic visits , information regarding medical history , medication use , physical activity , alcohol consumption , and current smoking was obtained through standard questionnaires . current medication use was validated by examination of pills and prescriptions brought to the clinic for that purpose . bmi and waist - to - hip ratio ( whr ) were used as estimates of overall and central adiposity , respectively . percent body fat was determined by full body dual energy x - ray absorptiometry scan . blood pressures were measured twice while participants were seated , according to the hypertension detection and follow - up program protocol ( 19 ) , and the mean used in the analyses . a 75-g oral glucose tolerance test was administered between 0730 and 1100 h after a minimum 8-h overnight fast . blood samples were drawn by venipuncture at 0 and 2 h , and serum and plasma were separated and frozen at 70c . plasma glucose was measured by the glucose oxidase method , and insulin concentration was determined by radioimmunoassay in a diabetes research laboratory . fetuin - a concentrations were measured in duplicate in 2010 from archived fasting edta plasma samples with a human elisa kit ( epitope diagnostics , san diego , ca ) . this assay uses a two - site sandwich technique with polyclonal antibodies that bind different epitopes of human fetuin - a . intra- and interassay coefficients of variation were 2.44.7% and 9.59.9% , respectively , for the set of assays used for the present sample . impaired fasting glucose ( ifg ) was defined as a fasting plasma glucose level of 100125 mg / dl and impaired glucose tolerance ( igt ) as a 2-h postchallenge glucose level of 140199 mg / dl . prevalent diabetes was defined by self - report of physician diagnosis , fasting plasma glucose 126 mg / dl , 2-h postchallenge glucose 200 mg / dl , or use of diabetes medications . incident diabetes was defined as any of the prevalent diabetes criteria with the exception of postchallenge glucose , which was not available at follow - up . incident diabetes was assessed at five follow - up clinic visits and by four mailed questionnaires over a maximum 15-year follow - up period . prevalent cardiovascular disease ( cvd ) was defined as physician - diagnosed myocardial infarction , coronary artery revascularization , congestive heart failure , stroke or transient ischemic attack , carotid artery surgery , peripheral arterial surgery , or physician - diagnosed intermittent claudication . the metabolic syndrome was defined according to 2002 adult treatment panel iii criteria ( 20 ) . kidney function was assessed by the estimated glomerular filtration rate ( egfr ) based on the modification of diet in renal disease equation ( 21 ) and by the albumin - to - creatinine ratio ( acr ) . the homeostasis model assessment for insulin resistance ( homa - ir ) insulin resistance was defined as a homa - ir > 75th percentile for the study population . initial combined analyses revealed strong interactions for sex and fetuin - a for both prevalent ( p = 0.007 ) and incident ( p = 0.020 ) diabetes ; therefore , all analyses were stratified by sex . fetuin - a concentration was entered into models as a first - order continuous variable after screening for thresholds and curvilinear associations . the association between fetuin - a and baseline characteristics was evaluated by pearson correlation coefficient . hdl cholesterol , triglyceride , aspartate transaminase ( ast ) , and alanine transaminase ( alt ) levels were log - transformed to reduce the influence of outliers ; reported values are geometric means and interquartile ranges . the age - adjusted association of fetuin - a with baseline glycemic status was assessed by ancova . the association of fetuin - a with prevalent diabetes was determined by logistic regression ; the association with incident diabetes was assessed by cox proportional hazards regressions . the first adjusted for age and use of oral estrogens ( on the basis of our earlier studies that showed higher fetuin - a levels in women taking oral estrogens versus those not taking estrogens ) . the second added adjustment for adiposity and lifestyle , and the third added other diabetes risk factors . separate secondary models tested the influence of potential confounders and mediators by adding each variable separately to the fully adjusted base model . biologically plausible effect modifiers were individually tested by interaction terms on a multiplicative scale in both the logistic and the proportional hazards regression models . all p values presented are two - tailed , with p < 0.05 considered statistically significant for all analyses , including the interaction terms . data were analyzed using stata version 12.0 ( stata corp . , college station , tx ) and spss version 15 ( ibm corporation , chicago , il ) statistical software . between 1972 and 1974 , community - dwelling residents living in rancho bernardo , california , 3079 years of age , were invited to participate in a study of heart disease risk factors ; 82% enrolled . nearly all were middle- to upper - middle class and relatively well - educated . since the study was approved by the institutional review board of the university of california san diego , and all participants gave written informed consent . of the 1,781 participants who attended the 19921996 visits , 39 were excluded for insufficient stored plasma for fetuin - a determination and 27 for missing covariates , resulting in sample sizes of 672 men and 1,043 women for the prevalent diabetes analysis . of these 1,715 participants , 241 were lost to follow - up for incident diabetes . on average , participants lost to follow - up were older ( 79.8 vs. 70.0 years , p = 0.008 ) and had lower age - adjusted fetuin - a levels at baseline ( 0.489 vs. 0.523 g / l , p < 0.001 ) compared with those followed ; 82% of loss to follow - up was caused by death . these individuals , as well as those with prevalent diabetes at baseline ( n = 242 ) , were excluded , resulting in sample sizes of 477 men and 782 women for the incident diabetes analysis . during the 19921996 clinic visits , information regarding medical history , medication use , physical activity , alcohol consumption , and current smoking was obtained through standard questionnaires . current medication use was validated by examination of pills and prescriptions brought to the clinic for that purpose . bmi and waist - to - hip ratio ( whr ) were used as estimates of overall and central adiposity , respectively . percent body fat was determined by full body dual energy x - ray absorptiometry scan . blood pressures were measured twice while participants were seated , according to the hypertension detection and follow - up program protocol ( 19 ) , and the mean used in the analyses . a 75-g oral glucose tolerance test was administered between 0730 and 1100 h after a minimum 8-h overnight fast . blood samples were drawn by venipuncture at 0 and 2 h , and serum and plasma were separated and frozen at 70c . plasma glucose was measured by the glucose oxidase method , and insulin concentration was determined by radioimmunoassay in a diabetes research laboratory . fetuin - a concentrations were measured in duplicate in 2010 from archived fasting edta plasma samples with a human elisa kit ( epitope diagnostics , san diego , ca ) . this assay uses a two - site sandwich technique with polyclonal antibodies that bind different epitopes of human fetuin - a . intra- and interassay coefficients of variation were 2.44.7% and 9.59.9% , respectively , for the set of assays used for the present sample . impaired fasting glucose ( ifg ) was defined as a fasting plasma glucose level of 100125 mg / dl and impaired glucose tolerance ( igt ) as a 2-h postchallenge glucose level of 140199 mg / dl . prevalent diabetes was defined by self - report of physician diagnosis , fasting plasma glucose 126 mg / dl , 2-h postchallenge glucose 200 mg / dl , or use of diabetes medications . incident diabetes was defined as any of the prevalent diabetes criteria with the exception of postchallenge glucose , which was not available at follow - up . incident diabetes was assessed at five follow - up clinic visits and by four mailed questionnaires over a maximum 15-year follow - up period . prevalent cardiovascular disease ( cvd ) was defined as physician - diagnosed myocardial infarction , coronary artery revascularization , congestive heart failure , stroke or transient ischemic attack , carotid artery surgery , peripheral arterial surgery , or physician - diagnosed intermittent claudication . the metabolic syndrome was defined according to 2002 adult treatment panel iii criteria ( 20 ) . kidney function was assessed by the estimated glomerular filtration rate ( egfr ) based on the modification of diet in renal disease equation ( 21 ) and by the albumin - to - creatinine ratio ( acr ) . the homeostasis model assessment for insulin resistance ( homa - ir ) insulin resistance was defined as a homa - ir > 75th percentile for the study population . initial combined analyses revealed strong interactions for sex and fetuin - a for both prevalent ( p = 0.007 ) and incident ( p = 0.020 ) diabetes ; therefore , all analyses were stratified by sex . fetuin - a concentration was entered into models as a first - order continuous variable after screening for thresholds and curvilinear associations . the association between fetuin - a and baseline characteristics was evaluated by pearson correlation coefficient . hdl cholesterol , triglyceride , aspartate transaminase ( ast ) , and alanine transaminase ( alt ) levels were log - transformed to reduce the influence of outliers ; reported values are geometric means and interquartile ranges . the age - adjusted association of fetuin - a with baseline glycemic status was assessed by ancova . the association of fetuin - a with prevalent diabetes was determined by logistic regression ; the association with incident diabetes was assessed by cox proportional hazards regressions . the first adjusted for age and use of oral estrogens ( on the basis of our earlier studies that showed higher fetuin - a levels in women taking oral estrogens versus those not taking estrogens ) . the second added adjustment for adiposity and lifestyle , and the third added other diabetes risk factors . separate secondary models tested the influence of potential confounders and mediators by adding each variable separately to the fully adjusted base model . biologically plausible effect modifiers were individually tested by interaction terms on a multiplicative scale in both the logistic and the proportional hazards regression models . all p values presented are two - tailed , with p < 0.05 considered statistically significant for all analyses , including the interaction terms . data were analyzed using stata version 12.0 ( stata corp . , college station , tx ) and spss version 15 ( ibm corporation , chicago , il ) statistical software . the mean age of the 1,715 participants was 71.3 years ; 61% ( n = 1,043 ) were women of whom 401 ( 38% ) reported current oral estrogen therapy . g / l ) , intermediate for women not taking oral estrogens ( 0.51 , 0.440.58 ) , and lowest for men ( 0.50 , 0.440.56 ) ( p < 0.001 for all comparisons ) . baseline characteristics and the correlation of individual variables with fetuin - a levels are shown in table 1 . in general , fetuin - a associations were similar for men and women . triglycerides , total cholesterol , bmi , and waist circumference showed the strongest positive associations with fetuin - a , whereas age and hdl cholesterol showed the strongest negative associations . men and women with the metabolic syndrome had higher fetuin - a levels , whereas those with prevalent cvd had lower fetuin - a levels . baseline characteristics figure 1 shows age - adjusted fetuin - a levels by glucose tolerance status at baseline ( fig . 1a ) and in nondiabetic participants in whom incident diabetes did and did not develop during follow - up ( fig . compared with women with normal glucose tolerance ( ngt ) , age - adjusted levels of fetuin - a were elevated in women with isolated igt ( p = 0.019 ) or igt plus ifg ( p = 0.030 ) and were highest in women with prevalent diabetes ( p < 0.001 ) . fetuin - a levels did not differ by ifg in women ( p = 0.81 ) and did not vary by any measure of glucose tolerance status in men . baseline fetuin - a levels were also significantly higher in women ( p = 0.008 ) , but not men , in whom incident diabetes developed during follow - up compared with those who remained diabetes free ( fig . mean ( sem ) age - adjusted fetuin - a levels by glycemic status ( a ) and by incident diabetes status ( b ) in women ( ) and men ( ) . number of women with each status : ngt = 578 , ifg = 75 , igt = 204 , igt + ifg = 72 , prevalent diabetes = 129 , no diabetes = 750 , and incident diabetes = 32 . number of men with each status : ngt = 294 , ifg = 96 , igt = 109 , igt + ifg = 72 , prevalent diabetes = 113 , no diabetes = 424 , and incident diabetes = 53 . * p < 0.05 versus ngt , * * p < 0.01 versus ngt ( a ) or no diabetes ( b ) . at baseline , 113 ( 17% ) overall , 42% ( n = 102 ) of prevalent cases were based on postchallenge glucose alone , 4% ( n = 9 ) on fasting glucose alone , and 38% ( n = 92 ) only on self - report of physician diagnosis ; the remaining 16% ( n = 39 ) were based on more than one criterion . during the median 9.1-year follow - up , incident diabetes developed in 32 women and 53 men . overall , 33% ( n = 26 ) of incident cases were based on fasting plasma glucose , 13% ( n = 11 ) on the use of diabetes medications , and 52% ( n = 44 ) on self - report of physician diagnosis ; four cases were based on combined criteria . the distribution of diagnostic categories that identified cases of prevalent and incident diabetes did not differ significantly by sex ( p > 0.17 ) , although the proportion of prevalent cases identified by postchallenge glucose alone was higher in women than in men ( 48 vs. 35% , p = 0.047 ) . table 2 presents odds ratios ( ors ) for prevalent diabetes and hazard ratios ( hrs ) for incident diabetes per sd ( 0.10 each sd higher fetuin - a level was associated with a 79% greater odds of prevalent diabetes and a 66% greater risk of incident diabetes , adjusting for age and oral estrogen therapy . risk estimates for women were only modestly attenuated in sequential models that added adjustment for alcohol consumption , current smoking , exercise , bmi , and whr ( model 2 ) and other diabetes risk factors ( triglycerides , hdl cholesterol , and systolic and diastolic blood pressures ) ( model 3 ) . in contrast , among men , a positive association was suggested in age - adjusted models , but risk estimates were attenuated to one in multivariable models . g / l ) greater fetuin - a level in secondary models , individually adding adjustment for homa - ir , fasting plasma glucose , 2-h postchallenge glucose , egfr , acr , albumin , or liver enzymes ( alt , ast , and -glutamyl transpeptidase [ ggt ] ) to the multivariable base model ( model 3 ) had minimal influence on results in either sex , with one exception . in women , separate added adjustment for height and percent fat mass did not alter results for either diabetes outcome in either sex ( data not shown ) . next we examined whether the associations of fetuin - a with prevalent and incident diabetes differed across strata of selected risk factors ( table 3 ) . for women , the association of fetuin - a with prevalent diabetes was stronger for those with insulin resistance compared with those without ( p for interaction = 0.041 ) . g / l ) higher fetuin - a level was associated with a nearly fourfold higher risk of incident diabetes in women with fasting glucose > 100 mg / dl , but this was not significantly related to diabetes risk in women with lower fasting glucose levels ( p for interaction = 0.039 ) . there was no statistical evidence of effect modification by age , prevalent cvd , or oral estrogen therapy . among men , the association of fetuin - a with prevalent and incident diabetes was similar across all subgroups except for prevalent cvd status . g / l ) higher fetuin - a level was associated with a 70% greater odds of prevalent diabetes for men with prevalent cvd but was not related to prevalent diabetes among men without known cvd ( p for interaction = 0.022 ) . effect modifiers of the fetuin - a association with prevalent and incident diabetes for women and men the mean age of the 1,715 participants was 71.3 years ; 61% ( n = 1,043 ) were women of whom 401 ( 38% ) reported current oral estrogen therapy . g / l ) , intermediate for women not taking oral estrogens ( 0.51 , 0.440.58 ) , and lowest for men ( 0.50 , 0.440.56 ) ( p < 0.001 for all comparisons ) . baseline characteristics and the correlation of individual variables with fetuin - a levels are shown in table 1 . in general , fetuin - a associations were similar for men and women . triglycerides , total cholesterol , bmi , and waist circumference showed the strongest positive associations with fetuin - a , whereas age and hdl cholesterol showed the strongest negative associations . men and women with the metabolic syndrome had higher fetuin - a levels , whereas those with prevalent cvd had lower fetuin - a levels . figure 1 shows age - adjusted fetuin - a levels by glucose tolerance status at baseline ( fig . 1a ) and in nondiabetic participants in whom incident diabetes did and did not develop during follow - up ( fig . 1b ) . compared with women with normal glucose tolerance ( ngt ) , age - adjusted levels of fetuin - a were elevated in women with isolated igt ( p = 0.019 ) or igt plus ifg ( p = 0.030 ) and were highest in women with prevalent diabetes ( p < 0.001 ) . fetuin - a levels did not differ by ifg in women ( p = 0.81 ) and did not vary by any measure of glucose tolerance status in men . baseline fetuin - a levels were also significantly higher in women ( p = 0.008 ) , but not men , in whom incident diabetes developed during follow - up compared with those who remained diabetes free ( fig . mean ( sem ) age - adjusted fetuin - a levels by glycemic status ( a ) and by incident diabetes status ( b ) in women ( ) and men ( ) . number of women with each status : ngt = 578 , ifg = 75 , igt = 204 , igt + ifg = 72 , prevalent diabetes = 129 , no diabetes = 750 , and incident diabetes = 32 . number of men with each status : ngt = 294 , ifg = 96 , igt = 109 , igt + ifg = 72 , prevalent diabetes = 113 , no diabetes = 424 , and incident diabetes = 53 . * p < 0.05 versus ngt , * * p < 0.01 versus ngt ( a ) or no diabetes ( b ) . at baseline , 113 ( 17% ) men and 129 ( 12% ) women had prevalent diabetes . overall , 42% ( n = 102 ) of prevalent cases were based on postchallenge glucose alone , 4% ( n = 9 ) on fasting glucose alone , and 38% ( n = 92 ) only on self - report of physician diagnosis ; the remaining 16% ( n = 39 ) were based on more than one criterion . during the median 9.1-year follow - up , incident diabetes developed in 32 women and 53 men . overall , 33% ( n = 26 ) of incident cases were based on fasting plasma glucose , 13% ( n = 11 ) on the use of diabetes medications , and 52% ( n = 44 ) on self - report of physician diagnosis ; four cases were based on combined criteria . the distribution of diagnostic categories that identified cases of prevalent and incident diabetes did not differ significantly by sex ( p > 0.17 ) , although the proportion of prevalent cases identified by postchallenge glucose alone was higher in women than in men ( 48 vs. 35% , p = 0.047 ) . table 2 presents odds ratios ( ors ) for prevalent diabetes and hazard ratios ( hrs ) for incident diabetes per sd ( 0.10 each sd higher fetuin - a level was associated with a 79% greater odds of prevalent diabetes and a 66% greater risk of incident diabetes , adjusting for age and oral estrogen therapy . risk estimates for women were only modestly attenuated in sequential models that added adjustment for alcohol consumption , current smoking , exercise , bmi , and whr ( model 2 ) and other diabetes risk factors ( triglycerides , hdl cholesterol , and systolic and diastolic blood pressures ) ( model 3 ) . in contrast , among men , a positive association was suggested in age - adjusted models , but risk estimates were attenuated to one in multivariable models . g / l ) greater fetuin - a level in secondary models , individually adding adjustment for homa - ir , fasting plasma glucose , 2-h postchallenge glucose , egfr , acr , albumin , or liver enzymes ( alt , ast , and -glutamyl transpeptidase [ ggt ] ) to the multivariable base model ( model 3 ) had minimal influence on results in either sex , with one exception . in women , separate added adjustment for height and percent fat mass did not alter results for either diabetes outcome in either sex ( data not shown ) . next we examined whether the associations of fetuin - a with prevalent and incident diabetes differed across strata of selected risk factors ( table 3 ) . for women , the association of fetuin - a with prevalent diabetes was stronger for those with insulin resistance compared with those without ( p for interaction = 0.041 ) . g / l ) higher fetuin - a level was associated with a nearly fourfold higher risk of incident diabetes in women with fasting glucose > 100 mg / dl , but this was not significantly related to diabetes risk in women with lower fasting glucose levels ( p for interaction = 0.039 ) . there was no statistical evidence of effect modification by age , prevalent cvd , or oral estrogen therapy . among men , the association of fetuin - a with prevalent and incident diabetes was similar across all subgroups except for prevalent cvd status . g / l ) higher fetuin - a level was associated with a 70% greater odds of prevalent diabetes for men with prevalent cvd but was not related to prevalent diabetes among men without known cvd ( p for interaction = 0.022 ) . effect modifiers of the fetuin - a association with prevalent and incident diabetes for women and men in this cohort of white community - dwelling older adults , we observed a strong and persistent sex difference in the association of fetuin - a with stages of glucose tolerance , prevalent diabetes , and the development of new diabetes over a median 9-year follow - up . an sd greater fetuin - a level was associated with 66% higher odds of prevalent diabetes and a 79% greater risk of incident diabetes in women but was not related to diabetes in men . this sex difference extended to prediabetic conditions ; women , but not men , with igt had elevated fetuin - a concentrations compared with their counterparts with ngt . these findings were independent of established diabetes risk factors and markers of liver function and chronic kidney disease , with one notable exception : adjustment for postchallenge glucose concentrations attenuated associations with prevalent and incident diabetes in women . evidence of sex differences in the regulation of glucose homeostasis and the primary risk factors for diabetes is accumulating , particularly for older adults . early studies in the rancho bernardo cohort showed that more than one - half of type 2 diabetes cases would be undiagnosed without a glucose tolerance test , that a diagnosis based solely on postchallenge hyperglycemia was more frequent in women than in men ( comprising more than one - half of diabetes diagnoses in women when a glucose tolerance test was included ) , and that older women had more pronounced glucose intolerance but lower fasting glucose concentrations than men ( 9,10,24 ) . a markedly higher prevalence of igt in older women than in older men , contrasted with more ifg in men than in women , has been observed in epidemiologic studies from various countries around the world , including germany ( 25 ) , mauritius ( 6 ) , denmark ( 7 ) , and england ( 26 ) . ( 4 ) observed higher rates of both glucose appearance and glucose disappearance in response to a fixed meal in elderly women than in elderly men . consistent with prior epidemiologic studies ( 2729 ) , fetuin - a levels were positively associated with insulin resistance in both sexes in the current study . several lines of evidence suggest that igt may be a specific link between fetuin - a and type 2 diabetes , especially for older women . first , in this and prior studies ( 30,31 ) , fetuin - a levels are elevated in middle - aged and elderly individuals with isolated igt but are not related to ifg . second , the association of fetuin - a with igt in the current study was only observed in women , and igt is more common in older women than in older men ( 6,7,10,25,26 ) . third , postchallenge glucose was the only risk factor among many tested that explained a significant proportion of the association of fetuin - a with both prevalent and incident diabetes in the women in this study . the apparently dominant role of igt in defining diabetes in older women , whereas ifg seems to be more important for older men , may explain the absence of an association of fetuin - a with diabetes in the men in this study . the sex differences identified in the current study conflict with earlier epidemiologic studies . a link between elevated fetuin - a levels and the development of type 2 diabetes was first reported in 2008 in our pilot study of older white and black adults from the health , aging , and body composition ( health abc ) population ( 17 ) and in a larger study of middle - aged adults from the european prospective investigation into cancer and nutrition ( epic)-potsdam study ( 14 ) . we recently confirmed these early findings with data from the cardiovascular health study among community - dwelling adults aged 65 years . higher fetuin - a levels predicted incident diabetes regardless of sex , race , or prevalent cvd status ( 13 ) . effect modification by sex was also examined in the health abc and epic - potsdam studies , and none was found . the health abc was a pilot study , and the sample size may have been limiting . the epic - potsdam study and cardiovascular health study were not able to exclude prevalent diabetes cases on the basis of postchallenge glucose alone , and incident diabetes cases in epic - potsdam were identified by self - report and examination of medical records without fasting glucose measurements ; thus , undiagnosed cases may have confounded identification of sex differences in these studies . it is also notable that the rancho bernardo study population is distinct in its high degree of racial and socioeconomic homogeneity , which may have reduced sources of confounding and optimized our ability to detect sex differences . consonant with findings from the epic - potsdam study ( 14 ) , the association between circulating fetuin - a and incident diabetes in the current study was modified by fasting glucose levels , but only in women . higher fetuin - a levels were associated with an increased risk of diabetes among women whose fasting glucose levels fell to within the prediabetic range but were not related to diabetes among women with normal glucose levels , suggesting that fetuin - a elevation might be more important later in the progression to diabetes . although evidence from this study along with that from several others strongly suggests that fetuin - a is an independent marker of type 2 diabetes risk in humans , whether the relation is causal is still unknown . the fact that the gene encoding fetuin - a is located on chromosome arm 3q27 , a region mapped as a diabetes susceptibility locus ( 32 ) , supports a role for fetuin - a in the regulation of glucose homeostasis . that plasma fetuin - a levels and protein expression are increased in fatty liver disease ( 29 ) , a strong predictor of diabetes ( 33 ) , also points to a role for fetuin - a in the pathogenesis of diabetes . nonetheless , experimental evidence that selective lowering of fetuin - a levels improves insulin sensitivity and reduces the risk for type 2 diabetes in humans is still lacking . more investigations are needed to determine whether fetuin - a is a viable target for diabetes prevention or treatment . the strengths of this study are its prospective design , the relatively large sample size , inclusion of both sexes , and the availability of measurements of a wide spectrum of potential mediators and confounders . our ability to accurately identify prevalent diabetes cases was enhanced by having postchallenge glucose concentrations at baseline . associations were based on fetuin - a concentrations measured at a single time point ; nonetheless , we identified a strong signal for both prevalent and incident diabetes in women that was robust to statistical adjustment for multiple covariates . because the number of diabetes cases in this study was relatively small , it is possible that the findings , including the sex differences , were due to chance . like most epidemiologic studies , postchallenge glucose levels were not available at follow - up , which may have exerted a stronger limitation on incident diabetes diagnosis in women than in men but is unlikely to account for the sex - specific associations . we also had no information on family history of diabetes , which may have confounded results , but whether this is the case to a greater degree in one sex than the other is not clear ( 34 ) . finally , the majority of participants were white elderly men and women , and the results may not generalize to younger adults or those of different races / ethnicities . in conclusion , higher fetuin - a levels were associated with igt and prevalent and incident type 2 diabetes in community - dwelling older women independent of most established and several emerging diabetes risk factors . fetuin - a levels were not associated with igt or diabetes prevalence and incidence in men . if the findings are substantiated in larger epidemiologic studies with postchallenge glucose levels available , these sex - specific fetuin - a associations may provide new insights into mechanisms responsible for sex differences in glucose homeostasis and diabetes risk with advancing age .[/INST]objectivethis study evaluated the sex - specific association of plasma fetuin - a levels with prevalent and incident type 2 diabetes in community - dwelling older adults.research design and methodsparticipants were 684 men and 1,058 women ( median age , 71 years ) whose fetuin - a levels , diabetes prevalence , and diabetes risk factors were evaluated in 19921996 . the participants were followed for incident diabetes through 2010 ( median follow - up , 9 years).resultswomen with impaired glucose tolerance had elevated fetuin - a levels compared with women with normal glucose tolerance ( p = 0.019 ) , but fetuin - a levels were not elevated in women with impaired fasting glucose . fetuin - a did not vary by glucose tolerance status in men . there were significant interactions of fetuin - a by sex for prevalent ( p = 0.007 ) and incident ( p = 0.020 ) diabetes . for women , each sd ( 0.10 g / l ) higher fetuin - a level was associated with a higher odds of prevalent diabetes ( odds ratio [ or ] 1.79 , 95% ci 1.472.17 ) and greater risk of incident diabetes ( hazard ratio [ hr ] 1.66 , 95% ci 1.182.34 ) , adjusting for age and estrogen therapy . these associations were not materially altered by adjustment for diabetes risk factors but were attenuated by adjusting for postchallenge glucose levels . among men , although positive associations with prevalent ( or 1.15 [ 0.941.41 ] ) and incident ( hr 1.24 [ 0.931.65 ] ) diabetes were suggested in age - adjusted models , risk estimates attenuated to one after multivariable adjustment.conclusionshigher fetuin - a concentrations were independently associated with an increased risk of developing type 2 diabetes in older women but were not related to diabetes risk in older men . fetuin - a may provide novel insights into mechanisms underlying sex differences in glucose homeostasis and diabetes risk in old age .</s>

Charles Krupa / AP Republican Sen. Scott Brown of shakes hands with supporters during his re-election campaign kick-off event in Worcester, Massachusetts, Jan. 19, 2012. From its start, the race for Ted Kennedy’s old Senate seat seemed destined to be one of most expensive political battles in Massachusetts history. Challenger Elizabeth Warren, bank-scolding darling of the left, and Scott Brown, the Tea Party pinup who swept into office in early 2010 to strip President Obama of his congressional supermajority, are both candidates of national stature. It’s a rare and precious Red seat in a Blue state. Nothing less than control of the Senate may hang in the balance. And so the money has poured in. Last week, Warren raised more than $1 million in 24 hours, a feat Brown pulled off three days running during his first bid; each raised huge amounts, $5.7 million and $3.2 million respectively, in the final quarter of 2011. The Bay overfloweth, and that’s before you start counting the money being spent by third-party groups. The League of Conservation Voters and the League of Women Voters have combined to spend some $3 million on issue ads that are critical of Brown. Crossroads GPS, the behemoth Republican super PAC founded by Karl Rove, has aired spots criticizing Warren, for her “extreme” alignment with the Occupy protesters and for glad-handing bankers during her stint at the Treasury Department. On Monday, however, Warren and Brown signed an unusual agreement to stem the influence of outside money. It marks the first attempt at an explicit multilateral disarmament of super PACs and their ilk since the landmark Citizens United vs. FEC Supreme Court case remade campaign finance law in 2010. Its success, or its failure, could help answer a looming question in American politics: with campaign spending now enshrined as free speech, are we capable of extracting our elections from the swamp of moneyed interests even when we really want to? In recent weeks Warren and Brown have been jostling over the issue of third-party spending, each trying to claim the mantle of political purity. “I’m pleased Professor Warren has joined with me in signing my People’s Pledge,” Scott Brown said Monday after putting pen to a tweaked version of the agreement the Warren campaign had sent over. “This is a great victory for the people of Massachusetts, and a bold statement that puts super PACs and other third parties on notice that their interference in this race will not be tolerated,” Warren said. In the most direct sense, their detente is symbolic. By law, campaigns cannot forbid super PACs from buying airtime any more than they can instruct them to run ads; the ban on coordination cuts both ways. Public finger-wagging is the extent of what’s allowed — but in the past, finger wagging has had its success. In 2007, Senator Barack Obama successfully cowed primary rival John Edwards by accusing him of lying when he said he was powerless to call off the independent attack ad dogs. “The fact is this is somebody who worked for John Edwards, for the last who-knows-how-many years, who’s a good friend and colleague of Edwards, who’s now running a 527 that is running ads on behalf of John Edwards,” he said. “You’re telling me he has no influence over him? That’s not true.” In the 2008 general election, Obama and John McCain both discouraged outside groups from spending on their behalves, directing donors to give to the campaigns instead. It worked. Even now, post-Citizens United, public discouragement has played a role. Newt Gingrich recently expressed disapproval of some of the ads a super PAC run by his former aide aired against Mitt Romney, and the group seemed responsive to his public cues. Warren and Brown have made their public disapproval of third-party spending well known, but they’re also trying something novel. In addition to sending letters to TV stations and advocacy groups requesting a halt to the deluge of paid media, they’ve devised an enforcement mechanism: the Brown and Warren campaigns will monitor outside spending and donate 50% of the value of each TV, cable, satellite or radio buy on their behalf to a charity of their rival’s choosing. Too many ads touting a candidate or lashing her rival and the official campaign is kaput. “I think it’s an interesting and commendable effort,” says Paul Ryan, a lawyer for the Campaign Legal Center, which supports stricter campaign finance regulations. “But I’m not entirely convinced it will be effective.” Ryan says the agreement’s bounds will likely be tested by issue ads, which target candidates on specific policy positions, and which spending groups frequently use to skirt limits on direct candidate advocacy under tax law. The pledge makes explicit mention of such ads, but the line between issue ad and candidate ad is blurry. Though no group has explicitly rejected the pledge, the League of Women Voters came close Monday, insisting that their advertising targeted lawmakers, not political candidates. “The League’s ads ran in April of 2011 in Massachusetts and Missouri, and were issue ads aimed at holding public officials accountable for their votes in Congress,” said national President Elisabeth MacNamara. “These ads were not in support or opposition of any candidate but in support of the Clean Air Act. The League does not support or oppose any candidates or parties.” The ads in question castigated Brown for voting against increased emission standards. It’s not clear if the LWV will run more like it in the coming year. American Crossroads, the national Republican group, registered a different sort of complaint. “Because the agreement allows union phone banks, direct mail, and get-out-the-vote drives – all union core specialties,” president and CEO Steven Law said, “Warren’s latest agreement has loopholes the Teamsters could drive a truck though, the longshoremen could steer a ship through, the machinists could fly a plane through, and government unions could drive forklifts of paperwork through.” Ryan, of the Campaign Legal Center, says Law’s points are valid — although, he notes, there’s nothing to stop Crossroads, or others, from spending their money on their own ground game instead of broadcast advertising. Indeed, one possible consequence of the Brown-Warren pact and others like it is that super PACs may become more involved in direct mail, phone banking and other traditional campaign tactics. Some groups are heeding Brown and Warren’s call. The League of Conservation Voters, which ran a bruising campaign against Brown over environmental issues, appeared to cede the issue in a Monday statement, albeit not without taking a parting shot and leaving the door open to more ads. “While we cannot take directions from any candidate on our independent activities,” Senior Vice President of Campaigns Navin Nayak said, “we are inclined to respect the People’s Pledge agreed to by Elizabeth Warren and Scott Brown and we hope that Scott Brown will honor his end of the deal when Crossroads and the Koch Brothers inevitably break it.” Only one outside spending group, Rethink Brown, a union-backed super PAC, explicitly stated its intention to withdraw from the airwaves, while fighting on “[t]hrough our website… the news media, social media and other means of modern campaigning.” As Law noted, there is already well-established election-influencing machinery for unions to fund off-air. Even if all the varied interests were to fall in line, the ceasefire would be a fragile one. John Kerry and Bill Weld made a similar pact in Massachusetts’ Senate race in 1996, swearing to stop at $5 million in ads a piece, but the agreement fell apart at the climax of the campaign. Fred Wertheimer of Democracy 21, a nonpartisan campaign-finance-reform group, says there’s nothing preventing a large, last minute third-party ad buy from deciding the 2012 race. “This is hard-nose politics,” he says, skeptical that independent expenditure groups will stick to the campaigns’ rules if they see an opportunity to win. “If it costs the candidates some, that’s not a problem.” In most races, the interests of donors, supporters and campaigns closely align. Even advocacy groups, eager to curry favor or access with politicians once they reach elected office, have reason to follow the candidates’ lead. But it’s not happening in Massachusetts. Not yet. Pledge or no, in a campaign this big, outside money isn’t so easily disentangled. ||||| CBS/Getty Images Republican Sen. Scott Brown of Massachusetts and his Democratic challenger Elizabeth Warren have entered into a super PAC pact. The two candidates have agreed to discourage outside groups like super PACs from airing ads in their high-profile race. The agreement came after Brown called on Warren to denounce the millions in outside advertising flooding Massachusetts media on her behalf. For instance, the League of Conservation Voters spent nearly $2 million attacking Brown's record. On the other side, the group Crossroads GPS attacked Warren in a seven-figure ad campaign targeting four Democratic Senate candidates. In a statement today, Brown called his agreement with Warren to discourage such ads "a great victory for the people of Massachusetts, and a bold statement that puts Super PACs and other third parties on notice that their interference in this race will not be tolerated." Political candidates are already barred from coordinating with super PACs that run ads on their behalf. Nevertheless, the pledge commits Brown and Warren to paying a price if groups run negative ads on their behalf. The pledge says that if an outside group does run an ad attacking either Brown or Warren, the other candidate must pay 50 percent of the ads' cost to a charity of the targeted candidates' choice. Even without the help of third parties, Brown and Warren have plenty of cash to spend on their campaigns. After an impressive fundraising year in 2011, Warren's campaign holds just over $6 million in cash on hand, the Boston Globe reports, while the incumbent Brown has $12.8 million in his campaign account.

– Scott Brown and Elizabeth Warren are rivals in a sure-to-be-bitterly-contested race for Ted Kennedy's old Senate seat, but they both want super PACs to stay out of it: The rivals yesterday entered into a pact discouraging outside groups from airing ads on their behalf; both Brown and Warren agreed to pay 50% of the ads' cost to a charity chosen by their rival if any such ads do air, CBS News reports. In a statement, Brown called the pact "a great victory for the people of Massachusetts, and a bold statement that puts super PACs and other third parties on notice that their interference in this race will not be tolerated." But Time notes that the agreement may not work, particularly because super PACs may be able to skirt it by airing "issue ads" rather than "candidate ads." The line between the two types is blurry, since issue ads still target candidates on their policy positions. It's also possible that super PACs will simply spend more on other types of campaigning, including phone banking and direct mail.

<s>[INST]Charles Krupa / AP Republican Sen. Scott Brown of shakes hands with supporters during his re-election campaign kick-off event in Worcester, Massachusetts, Jan. 19, 2012. From its start, the race for Ted Kennedy’s old Senate seat seemed destined to be one of most expensive political battles in Massachusetts history. Challenger Elizabeth Warren, bank-scolding darling of the left, and Scott Brown, the Tea Party pinup who swept into office in early 2010 to strip President Obama of his congressional supermajority, are both candidates of national stature. It’s a rare and precious Red seat in a Blue state. Nothing less than control of the Senate may hang in the balance. And so the money has poured in. Last week, Warren raised more than $1 million in 24 hours, a feat Brown pulled off three days running during his first bid; each raised huge amounts, $5.7 million and $3.2 million respectively, in the final quarter of 2011. The Bay overfloweth, and that’s before you start counting the money being spent by third-party groups. The League of Conservation Voters and the League of Women Voters have combined to spend some $3 million on issue ads that are critical of Brown. Crossroads GPS, the behemoth Republican super PAC founded by Karl Rove, has aired spots criticizing Warren, for her “extreme” alignment with the Occupy protesters and for glad-handing bankers during her stint at the Treasury Department. On Monday, however, Warren and Brown signed an unusual agreement to stem the influence of outside money. It marks the first attempt at an explicit multilateral disarmament of super PACs and their ilk since the landmark Citizens United vs. FEC Supreme Court case remade campaign finance law in 2010. Its success, or its failure, could help answer a looming question in American politics: with campaign spending now enshrined as free speech, are we capable of extracting our elections from the swamp of moneyed interests even when we really want to? In recent weeks Warren and Brown have been jostling over the issue of third-party spending, each trying to claim the mantle of political purity. “I’m pleased Professor Warren has joined with me in signing my People’s Pledge,” Scott Brown said Monday after putting pen to a tweaked version of the agreement the Warren campaign had sent over. “This is a great victory for the people of Massachusetts, and a bold statement that puts super PACs and other third parties on notice that their interference in this race will not be tolerated,” Warren said. In the most direct sense, their detente is symbolic. By law, campaigns cannot forbid super PACs from buying airtime any more than they can instruct them to run ads; the ban on coordination cuts both ways. Public finger-wagging is the extent of what’s allowed — but in the past, finger wagging has had its success. In 2007, Senator Barack Obama successfully cowed primary rival John Edwards by accusing him of lying when he said he was powerless to call off the independent attack ad dogs. “The fact is this is somebody who worked for John Edwards, for the last who-knows-how-many years, who’s a good friend and colleague of Edwards, who’s now running a 527 that is running ads on behalf of John Edwards,” he said. “You’re telling me he has no influence over him? That’s not true.” In the 2008 general election, Obama and John McCain both discouraged outside groups from spending on their behalves, directing donors to give to the campaigns instead. It worked. Even now, post-Citizens United, public discouragement has played a role. Newt Gingrich recently expressed disapproval of some of the ads a super PAC run by his former aide aired against Mitt Romney, and the group seemed responsive to his public cues. Warren and Brown have made their public disapproval of third-party spending well known, but they’re also trying something novel. In addition to sending letters to TV stations and advocacy groups requesting a halt to the deluge of paid media, they’ve devised an enforcement mechanism: the Brown and Warren campaigns will monitor outside spending and donate 50% of the value of each TV, cable, satellite or radio buy on their behalf to a charity of their rival’s choosing. Too many ads touting a candidate or lashing her rival and the official campaign is kaput. “I think it’s an interesting and commendable effort,” says Paul Ryan, a lawyer for the Campaign Legal Center, which supports stricter campaign finance regulations. “But I’m not entirely convinced it will be effective.” Ryan says the agreement’s bounds will likely be tested by issue ads, which target candidates on specific policy positions, and which spending groups frequently use to skirt limits on direct candidate advocacy under tax law. The pledge makes explicit mention of such ads, but the line between issue ad and candidate ad is blurry. Though no group has explicitly rejected the pledge, the League of Women Voters came close Monday, insisting that their advertising targeted lawmakers, not political candidates. “The League’s ads ran in April of 2011 in Massachusetts and Missouri, and were issue ads aimed at holding public officials accountable for their votes in Congress,” said national President Elisabeth MacNamara. “These ads were not in support or opposition of any candidate but in support of the Clean Air Act. The League does not support or oppose any candidates or parties.” The ads in question castigated Brown for voting against increased emission standards. It’s not clear if the LWV will run more like it in the coming year. American Crossroads, the national Republican group, registered a different sort of complaint. “Because the agreement allows union phone banks, direct mail, and get-out-the-vote drives – all union core specialties,” president and CEO Steven Law said, “Warren’s latest agreement has loopholes the Teamsters could drive a truck though, the longshoremen could steer a ship through, the machinists could fly a plane through, and government unions could drive forklifts of paperwork through.” Ryan, of the Campaign Legal Center, says Law’s points are valid — although, he notes, there’s nothing to stop Crossroads, or others, from spending their money on their own ground game instead of broadcast advertising. Indeed, one possible consequence of the Brown-Warren pact and others like it is that super PACs may become more involved in direct mail, phone banking and other traditional campaign tactics. Some groups are heeding Brown and Warren’s call. The League of Conservation Voters, which ran a bruising campaign against Brown over environmental issues, appeared to cede the issue in a Monday statement, albeit not without taking a parting shot and leaving the door open to more ads. “While we cannot take directions from any candidate on our independent activities,” Senior Vice President of Campaigns Navin Nayak said, “we are inclined to respect the People’s Pledge agreed to by Elizabeth Warren and Scott Brown and we hope that Scott Brown will honor his end of the deal when Crossroads and the Koch Brothers inevitably break it.” Only one outside spending group, Rethink Brown, a union-backed super PAC, explicitly stated its intention to withdraw from the airwaves, while fighting on “[t]hrough our website… the news media, social media and other means of modern campaigning.” As Law noted, there is already well-established election-influencing machinery for unions to fund off-air. Even if all the varied interests were to fall in line, the ceasefire would be a fragile one. John Kerry and Bill Weld made a similar pact in Massachusetts’ Senate race in 1996, swearing to stop at $5 million in ads a piece, but the agreement fell apart at the climax of the campaign. Fred Wertheimer of Democracy 21, a nonpartisan campaign-finance-reform group, says there’s nothing preventing a large, last minute third-party ad buy from deciding the 2012 race. “This is hard-nose politics,” he says, skeptical that independent expenditure groups will stick to the campaigns’ rules if they see an opportunity to win. “If it costs the candidates some, that’s not a problem.” In most races, the interests of donors, supporters and campaigns closely align. Even advocacy groups, eager to curry favor or access with politicians once they reach elected office, have reason to follow the candidates’ lead. But it’s not happening in Massachusetts. Not yet. Pledge or no, in a campaign this big, outside money isn’t so easily disentangled. ||||| CBS/Getty Images Republican Sen. Scott Brown of Massachusetts and his Democratic challenger Elizabeth Warren have entered into a super PAC pact. The two candidates have agreed to discourage outside groups like super PACs from airing ads in their high-profile race. The agreement came after Brown called on Warren to denounce the millions in outside advertising flooding Massachusetts media on her behalf. For instance, the League of Conservation Voters spent nearly $2 million attacking Brown's record. On the other side, the group Crossroads GPS attacked Warren in a seven-figure ad campaign targeting four Democratic Senate candidates. In a statement today, Brown called his agreement with Warren to discourage such ads "a great victory for the people of Massachusetts, and a bold statement that puts Super PACs and other third parties on notice that their interference in this race will not be tolerated." Political candidates are already barred from coordinating with super PACs that run ads on their behalf. Nevertheless, the pledge commits Brown and Warren to paying a price if groups run negative ads on their behalf. The pledge says that if an outside group does run an ad attacking either Brown or Warren, the other candidate must pay 50 percent of the ads' cost to a charity of the targeted candidates' choice. Even without the help of third parties, Brown and Warren have plenty of cash to spend on their campaigns. After an impressive fundraising year in 2011, Warren's campaign holds just over $6 million in cash on hand, the Boston Globe reports, while the incumbent Brown has $12.8 million in his campaign account.[/INST]– Scott Brown and Elizabeth Warren are rivals in a sure-to-be-bitterly-contested race for Ted Kennedy's old Senate seat, but they both want super PACs to stay out of it: The rivals yesterday entered into a pact discouraging outside groups from airing ads on their behalf; both Brown and Warren agreed to pay 50% of the ads' cost to a charity chosen by their rival if any such ads do air, CBS News reports. In a statement, Brown called the pact "a great victory for the people of Massachusetts, and a bold statement that puts super PACs and other third parties on notice that their interference in this race will not be tolerated." But Time notes that the agreement may not work, particularly because super PACs may be able to skirt it by airing "issue ads" rather than "candidate ads." The line between the two types is blurry, since issue ads still target candidates on their policy positions. It's also possible that super PACs will simply spend more on other types of campaigning, including phone banking and direct mail.</s>

primary dermal melanoma ( pdm ) has been proposed as a specific subtype of melanoma [ 1 , 2 ] . such a skin lesion is confined to the dermis and/or subcutaneous fat , showing no connections with the overlying epidermis and simulating a melanoma metastasis . pdm should be differentiated from primary nodular melanoma , cutaneous metastatic melanoma and clear cell sarcoma , due to its excellent prognosis as compared to that of patients with these three latter diseases [ 2 , 3 , 4 ] . generally , a diagnosis of pdm should be considered in all patients with a solitary melanoma confined to the dermis and subcutaneous tissue when there is no evidence of a primary tumour or disease at other sites following appropriate staging studies . this uncommon clinical entity is reported in the literature with an incidence ranging between 0.4 and 0.9% . among the main pathways which have been found to be involved in melanomagenesis , including those inducing cell proliferation ( proliferative pathways ) , overcoming cell senescence ( senescence pathway ) or affecting apoptosis ( apoptotic pathways ) , molecular characterization of pdm lesions revealed lower expression levels of p53 and cyclin d1 proteins as well as an up - regulation of the ckit gene . we report a case of pdm in a 72-year - old caucasian woman who had a peculiar history of multiple previous malignancies . a molecular characterization of the lesion was performed . a 72-year - old caucasian woman came to our attention for a right paravertebral purplish - red nodular lesion on the back , with a few focal pigmentations and a small semilunar perinodular area of brownish pigmentation ( fig . the differential diagnosis included , in this case , basal cell carcinoma , malignant melanoma , vascular lesions , epidermoid carcinoma and dermatofibroma . the patient 's clinical history was characterized by multiple tumours , including bilateral metachronous breast cancer for which she had undergone bilateral mastectomy and axillary lymphadenectomy , clear cell renal cell carcinoma , uterine fibromatosis and intestinal polyposis with low- and high - grade dysplasia . despite the macroscopic aspect which suggested pigmented basal cell carcinoma , the possibility of the lesion being melanocytic made us opt for an excisional biopsy with a 2-mm margin . the skin lesion specimen showed a poorly differentiated neoplastic dermal infiltration with morphological aspects of melanocytic proliferation ( fig . the tumour cells displayed round or oval shapes with brisk mitotic activity , and they were arranged in a nodular architecture with rounded margins . lymphocytic and plasmacellular infiltration of the lesion was observed , without formation of lymphoid nodules . an intraepidermal component , ulceration and regression aspects were not evident , even with an examination of multiple sections ; a preexisting nevus , spindle neoplastic cells or bands of mature intercellular collagen were also not found . the neoplastic cells demonstrated melanocytic - type immunohistochemistry ( s100 protein and hmb-45 positive ) . the absence of intraepidermal atypical melanocytes is compatible with metastatic malignant melanoma or pdm. desmoplastic melanoma was excluded on the basis of cytology and because of the lack of a desmoplastic reaction , while nodular melanoma was excluded due to the absence of an intraepidermal component . with the aim of identifying a possible primary lesion , the following tests were performed : dermatological examination ; total body ct ; ophthalmologic examination ; pancolonoscopy ; ear , nose and throat examination ; esophagogastroduodenoscopy , and gynaecological examination . no evidence of another primary melanoma was found ; however , a parallel finding of frontal meningioma was noted . the absence of another primary lesion led us to make the diagnosis of pdm per exclusionem . the second surgical step included the excision of the biopsy scar with 2-cm margins and sentinel lymph node biopsy . the preoperative lymphoscintigraphy showed 3 areas of uptake 2 of them involving the soft tissue at the level of the posterior pillar of both the axillae , and the remaining 1 in the left paravertebral area , adjacent to the previous surgical site . however , only a single sentinel node presenting micrometastasis of melanoma was found in the latter area . a bilateral axillary ultrasound examination was performed to investigate the areas of lymphoscintigraphic uptake ; subsequently , the patient underwent an additional surgical procedure for the removal of a lymph node with ambiguous ultrasonographic features found within the residual left axillary fatty tissue ( the patient had had ipsilateral axillary lymphadenectomy several years before for breast cancer ) . the histological examination of the specimen revealed adipose tissue and a lymph node with reactive patterns . melanomas on skin not chronically exposed to the sun such as the anatomical location of the skin lesion in our case have been reported to usually carry either a mutated nras gene or mutated braf gene or concurrently mutated braf and pten genes . furthermore , the coexistence of additional tumours in our patient was a strong indication to either investigate the cdkn2a and tp53 genes , which have been demonstrated to be involved in multiple cancer pathogenesis and predisposition , or assess the occurrence of the e318k sequence variation in the mitf ( microphthalmia - associated transcription factor ) oncogene , which has been reported in patients with an association between melanoma and renal cancer . finally , the mutation analysis was carried out in the ckit gene , which has been demonstrated to be involved in pdm pathogenesis . genomic dna was isolated from a peripheral blood sample and tumour tissue , using standard methods . the full coding sequences and splice junctions of p16 ( exons 1 , 2 and 3 ) , p14 ( exon 1 ) and pten ( exons 19 ) genes as well as the most frequently affected exons of nras / kras ( 23 ) , braf ( 15 ) , ckit ( 9 , 11 , 13 , 17 and 18 ) and tp53 ( 58 ) genes were screened for mutations on somatic dna isolated from paraffin - embedded tumour tissue samples by directly sequencing the amplified pcr products through an automated fluorescence - cycle sequencer ( abi prism 3130 , applied biosystems , foster city , calif . mutation analysis was also carried out on germline dna obtained from peripheral blood of the patient , as previously described [ 8 , 9 ] . no mutation was identified in such crucial genes involved in melanoma susceptibility and pathogenesis . in particular , alteration of the cdkn2a gene , encoding p16 , which is the main component of the cyclind1-rb pathway , and p14 , which has been functionally linked to the mdm2-p53 pathway , have been widely reported as the most common causes of inherited susceptibility to melanoma at the germline level , participating also in melanoma progression at the somatic level [ 10 , 11 ] . lack of tp53 mutations in melanoma cells from our patient 's tissues is consistent with the absence of involvement of both the p16-cyclind1-rb and p14-mdm2-tp53 cascades in the pathogenesis of such lesions . analogously , activation of both the mapk - erk pathway ( including the cascade of nras / kras , braf , mek1/2 , and erk1/2 proteins ) , a major signaling cascade deputed to the control of cell growth and proliferation , and the pten - dependent pathway ( including the pi3k and akt effectors ) , committed to regulate cell survival and apoptosis , were not involved in inducing the malignant transformation in our case . as a further confirmation that genetic alterations in such major pathways played no role in pathogenesis in our pdm case , a wild - type ckit variant ( this gene has been demonstrated to indeed recruit and activate a number of intracellular signalling pathways implicated in melanocytic transformation and progression , including the pi3k - akt and mapk pathways ) as well as the absence of the mitf e318k variant were observed here . therefore , one could speculate that the cascade of alterations underlying melanomagenesis may be due to additional low - frequency genetic and molecular events in our patient . dermal or subcutaneous metastasis of melanoma of unknown primary origin , according to the 2002 ajcc ( american joint committee on cancer ) staging guidelines , is classified as stage iv m1a disease and has a poor prognosis ( 5-year survival rate 18.8% ) . nevertheless , small series of dermal or subcutaneous solitary lesions have been reported with consistently better recurrence and survival rates , depending on the thickness and presence of ulceration . in 2004 , swetter et al . reported a series of 5 patients with such lesions and speculated that those were cases of a distinct subtype of melanoma and should be referred to by the term primary dermal melanoma . it is , therefore , of utmost importance to differentiate pdm from a solitary dermal or subcutaneous metastasis of melanoma . some authors speculate that the tumour may arise from nonepidermal melanocytes or intradermal nevi , while others believe that it is an epidermally regressed primary [ 13 , 14 ] . despite the existence of some evidence in favour of one or the other theory , none has been demonstrated definitely . given the rarity of pdm and the small number of cases reported , demographic information and data on the anatomic sites most commonly involved are inconsistent . in a series of 101 solitary dermal melanomas , did not find any site - related differences which might explain the generally better prognosis of these tumours . from the clinical point of view , a thorough dermatological examination of the skin and of the visible mucosae as well as gynaecological and ophthalmological examinations , a pancolonoscopy and a total body ct should be performed to look for and possibly exclude hidden primaries . the role of sentinel lymph node biopsy in clinical management is not yet clear , but it seems to be useful for the detection of micrometastasis , as occurred in our case . the possibility that such melanomas may show a distinct genetic pattern prompted us to also undertake a genetic analysis . the patient also had a history of multiple previous malignancies that could have been a clue for a genetic predisposition . the genetic analysis performed at both the germline and somatic levels in our patient revealed that the main genes responsible for the susceptibility and pathogenesis of melanoma , respectively , were not affected . this suggests that alternative , low - frequency altered genes / pathways may be involved . a more comprehensive genetic profiling based on microarray technology will be helpful in making correlations between molecular signatures and clinical features ; to date , gene expression arrays have been employed in such a melanoma classification . nevertheless , the advancements of biotechnology , mostly represented by next - generation sequencing approaches , will provide even more reliable tools for detailed gene - based analyses , allowing physicians to better characterize molecular biomarkers in order to achieve a more accurate diagnosis as well as predict prognosis and response to treatment in patients with melanoma . the differential diagnosis between pdm and isolated metastatic melanoma is generally performed per exclusionem and is based on the negativity of clinical findings and imaging studies for primary lesions . this distinction is important because 5-year survival rates in pdm are consistently higher than in metastatic cases ( 80100 vs. 520% , respectively ) .

introductionprimary dermal melanoma ( pdm ) is a recently described clinical entity accounting for less than 1% of all melanomas . histologically , it is located in the dermis or subcutaneous tissue , and it shows no connections with the overlying epidermis . the differential diagnosis is principally made along with that of metastatic cutaneous melanoma.case reporta 72-year - old caucasian woman with a history of multiple cancers ( metachronous bilateral breast cancer , meningioma , clear cell renal cell carcinoma , uterine fibromatosis and intestinal adenomatous polyposis ) , came to our attention with a nodular lesion on her back . after removal of the lesion , the histology report indicated malignant pdm or metastatic malignant melanoma . the clinical and instrumental evaluation of the patient did not reveal any other primary tumour , suggesting the primitive nature of the lesion . the absence of an epithelial component argued for a histological diagnosis of pdm . subsequently , the patient underwent a wide surgical excision with sentinel node biopsy , which was positive for metastatic melanoma . finally , the mutational status was studied in the main genes that regulate proliferation , apoptosis and cellular senescence . no pathogenetic mutations in cdkn2a , braf , nras , kras , ckit , tp53 and pten genes were observed . this suggests that alternative pathways and low - frequency alterations may be involved.conclusionsthe differential diagnosis between pdm and isolated metastatic melanoma depends on the negativity of imaging studies and clinical findings for other primary lesions . this distinction is important because 5-year survival rates in such cases are higher than in metastatic cases ( 80100 vs. 520% , respectively ) .

<s>[INST]primary dermal melanoma ( pdm ) has been proposed as a specific subtype of melanoma [ 1 , 2 ] . such a skin lesion is confined to the dermis and/or subcutaneous fat , showing no connections with the overlying epidermis and simulating a melanoma metastasis . pdm should be differentiated from primary nodular melanoma , cutaneous metastatic melanoma and clear cell sarcoma , due to its excellent prognosis as compared to that of patients with these three latter diseases [ 2 , 3 , 4 ] . generally , a diagnosis of pdm should be considered in all patients with a solitary melanoma confined to the dermis and subcutaneous tissue when there is no evidence of a primary tumour or disease at other sites following appropriate staging studies . this uncommon clinical entity is reported in the literature with an incidence ranging between 0.4 and 0.9% . among the main pathways which have been found to be involved in melanomagenesis , including those inducing cell proliferation ( proliferative pathways ) , overcoming cell senescence ( senescence pathway ) or affecting apoptosis ( apoptotic pathways ) , molecular characterization of pdm lesions revealed lower expression levels of p53 and cyclin d1 proteins as well as an up - regulation of the ckit gene . we report a case of pdm in a 72-year - old caucasian woman who had a peculiar history of multiple previous malignancies . a molecular characterization of the lesion was performed . a 72-year - old caucasian woman came to our attention for a right paravertebral purplish - red nodular lesion on the back , with a few focal pigmentations and a small semilunar perinodular area of brownish pigmentation ( fig . the differential diagnosis included , in this case , basal cell carcinoma , malignant melanoma , vascular lesions , epidermoid carcinoma and dermatofibroma . the patient 's clinical history was characterized by multiple tumours , including bilateral metachronous breast cancer for which she had undergone bilateral mastectomy and axillary lymphadenectomy , clear cell renal cell carcinoma , uterine fibromatosis and intestinal polyposis with low- and high - grade dysplasia . despite the macroscopic aspect which suggested pigmented basal cell carcinoma , the possibility of the lesion being melanocytic made us opt for an excisional biopsy with a 2-mm margin . the skin lesion specimen showed a poorly differentiated neoplastic dermal infiltration with morphological aspects of melanocytic proliferation ( fig . the tumour cells displayed round or oval shapes with brisk mitotic activity , and they were arranged in a nodular architecture with rounded margins . lymphocytic and plasmacellular infiltration of the lesion was observed , without formation of lymphoid nodules . an intraepidermal component , ulceration and regression aspects were not evident , even with an examination of multiple sections ; a preexisting nevus , spindle neoplastic cells or bands of mature intercellular collagen were also not found . the neoplastic cells demonstrated melanocytic - type immunohistochemistry ( s100 protein and hmb-45 positive ) . the absence of intraepidermal atypical melanocytes is compatible with metastatic malignant melanoma or pdm. desmoplastic melanoma was excluded on the basis of cytology and because of the lack of a desmoplastic reaction , while nodular melanoma was excluded due to the absence of an intraepidermal component . with the aim of identifying a possible primary lesion , the following tests were performed : dermatological examination ; total body ct ; ophthalmologic examination ; pancolonoscopy ; ear , nose and throat examination ; esophagogastroduodenoscopy , and gynaecological examination . no evidence of another primary melanoma was found ; however , a parallel finding of frontal meningioma was noted . the absence of another primary lesion led us to make the diagnosis of pdm per exclusionem . the second surgical step included the excision of the biopsy scar with 2-cm margins and sentinel lymph node biopsy . the preoperative lymphoscintigraphy showed 3 areas of uptake 2 of them involving the soft tissue at the level of the posterior pillar of both the axillae , and the remaining 1 in the left paravertebral area , adjacent to the previous surgical site . however , only a single sentinel node presenting micrometastasis of melanoma was found in the latter area . a bilateral axillary ultrasound examination was performed to investigate the areas of lymphoscintigraphic uptake ; subsequently , the patient underwent an additional surgical procedure for the removal of a lymph node with ambiguous ultrasonographic features found within the residual left axillary fatty tissue ( the patient had had ipsilateral axillary lymphadenectomy several years before for breast cancer ) . the histological examination of the specimen revealed adipose tissue and a lymph node with reactive patterns . melanomas on skin not chronically exposed to the sun such as the anatomical location of the skin lesion in our case have been reported to usually carry either a mutated nras gene or mutated braf gene or concurrently mutated braf and pten genes . furthermore , the coexistence of additional tumours in our patient was a strong indication to either investigate the cdkn2a and tp53 genes , which have been demonstrated to be involved in multiple cancer pathogenesis and predisposition , or assess the occurrence of the e318k sequence variation in the mitf ( microphthalmia - associated transcription factor ) oncogene , which has been reported in patients with an association between melanoma and renal cancer . finally , the mutation analysis was carried out in the ckit gene , which has been demonstrated to be involved in pdm pathogenesis . genomic dna was isolated from a peripheral blood sample and tumour tissue , using standard methods . the full coding sequences and splice junctions of p16 ( exons 1 , 2 and 3 ) , p14 ( exon 1 ) and pten ( exons 19 ) genes as well as the most frequently affected exons of nras / kras ( 23 ) , braf ( 15 ) , ckit ( 9 , 11 , 13 , 17 and 18 ) and tp53 ( 58 ) genes were screened for mutations on somatic dna isolated from paraffin - embedded tumour tissue samples by directly sequencing the amplified pcr products through an automated fluorescence - cycle sequencer ( abi prism 3130 , applied biosystems , foster city , calif . mutation analysis was also carried out on germline dna obtained from peripheral blood of the patient , as previously described [ 8 , 9 ] . no mutation was identified in such crucial genes involved in melanoma susceptibility and pathogenesis . in particular , alteration of the cdkn2a gene , encoding p16 , which is the main component of the cyclind1-rb pathway , and p14 , which has been functionally linked to the mdm2-p53 pathway , have been widely reported as the most common causes of inherited susceptibility to melanoma at the germline level , participating also in melanoma progression at the somatic level [ 10 , 11 ] . lack of tp53 mutations in melanoma cells from our patient 's tissues is consistent with the absence of involvement of both the p16-cyclind1-rb and p14-mdm2-tp53 cascades in the pathogenesis of such lesions . analogously , activation of both the mapk - erk pathway ( including the cascade of nras / kras , braf , mek1/2 , and erk1/2 proteins ) , a major signaling cascade deputed to the control of cell growth and proliferation , and the pten - dependent pathway ( including the pi3k and akt effectors ) , committed to regulate cell survival and apoptosis , were not involved in inducing the malignant transformation in our case . as a further confirmation that genetic alterations in such major pathways played no role in pathogenesis in our pdm case , a wild - type ckit variant ( this gene has been demonstrated to indeed recruit and activate a number of intracellular signalling pathways implicated in melanocytic transformation and progression , including the pi3k - akt and mapk pathways ) as well as the absence of the mitf e318k variant were observed here . therefore , one could speculate that the cascade of alterations underlying melanomagenesis may be due to additional low - frequency genetic and molecular events in our patient . dermal or subcutaneous metastasis of melanoma of unknown primary origin , according to the 2002 ajcc ( american joint committee on cancer ) staging guidelines , is classified as stage iv m1a disease and has a poor prognosis ( 5-year survival rate 18.8% ) . nevertheless , small series of dermal or subcutaneous solitary lesions have been reported with consistently better recurrence and survival rates , depending on the thickness and presence of ulceration . in 2004 , swetter et al . reported a series of 5 patients with such lesions and speculated that those were cases of a distinct subtype of melanoma and should be referred to by the term primary dermal melanoma . it is , therefore , of utmost importance to differentiate pdm from a solitary dermal or subcutaneous metastasis of melanoma . some authors speculate that the tumour may arise from nonepidermal melanocytes or intradermal nevi , while others believe that it is an epidermally regressed primary [ 13 , 14 ] . despite the existence of some evidence in favour of one or the other theory , none has been demonstrated definitely . given the rarity of pdm and the small number of cases reported , demographic information and data on the anatomic sites most commonly involved are inconsistent . in a series of 101 solitary dermal melanomas , did not find any site - related differences which might explain the generally better prognosis of these tumours . from the clinical point of view , a thorough dermatological examination of the skin and of the visible mucosae as well as gynaecological and ophthalmological examinations , a pancolonoscopy and a total body ct should be performed to look for and possibly exclude hidden primaries . the role of sentinel lymph node biopsy in clinical management is not yet clear , but it seems to be useful for the detection of micrometastasis , as occurred in our case . the possibility that such melanomas may show a distinct genetic pattern prompted us to also undertake a genetic analysis . the patient also had a history of multiple previous malignancies that could have been a clue for a genetic predisposition . the genetic analysis performed at both the germline and somatic levels in our patient revealed that the main genes responsible for the susceptibility and pathogenesis of melanoma , respectively , were not affected . this suggests that alternative , low - frequency altered genes / pathways may be involved . a more comprehensive genetic profiling based on microarray technology will be helpful in making correlations between molecular signatures and clinical features ; to date , gene expression arrays have been employed in such a melanoma classification . nevertheless , the advancements of biotechnology , mostly represented by next - generation sequencing approaches , will provide even more reliable tools for detailed gene - based analyses , allowing physicians to better characterize molecular biomarkers in order to achieve a more accurate diagnosis as well as predict prognosis and response to treatment in patients with melanoma . the differential diagnosis between pdm and isolated metastatic melanoma is generally performed per exclusionem and is based on the negativity of clinical findings and imaging studies for primary lesions . this distinction is important because 5-year survival rates in pdm are consistently higher than in metastatic cases ( 80100 vs. 520% , respectively ) . [/INST]introductionprimary dermal melanoma ( pdm ) is a recently described clinical entity accounting for less than 1% of all melanomas . histologically , it is located in the dermis or subcutaneous tissue , and it shows no connections with the overlying epidermis . the differential diagnosis is principally made along with that of metastatic cutaneous melanoma.case reporta 72-year - old caucasian woman with a history of multiple cancers ( metachronous bilateral breast cancer , meningioma , clear cell renal cell carcinoma , uterine fibromatosis and intestinal adenomatous polyposis ) , came to our attention with a nodular lesion on her back . after removal of the lesion , the histology report indicated malignant pdm or metastatic malignant melanoma . the clinical and instrumental evaluation of the patient did not reveal any other primary tumour , suggesting the primitive nature of the lesion . the absence of an epithelial component argued for a histological diagnosis of pdm . subsequently , the patient underwent a wide surgical excision with sentinel node biopsy , which was positive for metastatic melanoma . finally , the mutational status was studied in the main genes that regulate proliferation , apoptosis and cellular senescence . no pathogenetic mutations in cdkn2a , braf , nras , kras , ckit , tp53 and pten genes were observed . this suggests that alternative pathways and low - frequency alterations may be involved.conclusionsthe differential diagnosis between pdm and isolated metastatic melanoma depends on the negativity of imaging studies and clinical findings for other primary lesions . this distinction is important because 5-year survival rates in such cases are higher than in metastatic cases ( 80100 vs. 520% , respectively ) .</s>

most subepithelial tumors ( sets ) are asymptomatic and found in only about 0.3% of all endoscopic examinations . owing to limited information about the natural course and malignant potential of sets less than 2 cm in size and the difficulty in targeting and completely resecting such tumors , regular follow - ups rather than resection have been recommended [ 2 - 4 ] . however , according to previous reports , up to 3.7% of gastrointestinal stromal tumors ( gists ) less than 2 cm in size and benign - appearing on endoscopic ultrasonography have a high mitotic index and rapidly increase in size , and hence have a high risk of malignancy . therefore , resection procedures that allow a definitive diagnosis as well as an evaluation of malignant potential are needed . furthermore , complications resulting from repetitive endoscopic procedures that delay diagnosis may arise , and doctor - patient relationships may be influenced by indecisiveness on the part of the physician . surgical approaches for gists in the upper gastrointestinal ( gi ) tract include open surgery and laparoscopic surgery , both of which are more invasive than is endoscopic surgery and potentially lead to several complications . on the other hand , most endoscopic methods , including endoscopic mucosal resection ( emr ) and endoscopic submucosal dissection ( esd ) , are usually only applicable to the submucosal layer of the gastric wall . therefore , many endoscopic surgeries have been developed and attempted . in this article , recent developments in the procedures for treating gists in the upper gi tract are discussed . endoscopic resection is indicated for gists in the upper gi tract that are located in the proper muscle ( pm ) layer and protrude into the endoluminal side . gists arising from the pm layer are not easily , completely , or safely resected via emr or esd alone . owing to the high risk of perforation when resecting sets deep in the gi wall , deep submucosal and muscular dissection around the tumor should be carefully performed . several studies reported high en bloc resection rates ( 64% to 94% ) and low perforation rates ( 0% to 12% ) for esd of gists [ 8 - 10 ] . endoscopic muscularis dissection ( emd ) involves precutting the mucosa that covers the tumor via a longitudinal incision , endoscopically dissecting the tumor away from the submucosal and pm layers , and closing the wound with clips . perforations occurring during dissection are closed by using only endoscopic devices , and a longitudinal incision is usually used during this procedure . emd can be performed within a relatively short period of time , and injuries to the overlying mucosa are minimal , resulting in easier mucosal closure . in 2012 , liu et al . reported that emd completely removed 30 of the 31 tumors ( 96.8% ; 14 esophagus , seven cardia , and 10 stomach tumors ) in their study . the mean size of the set was 22.1 mm , and the procedure required 76.8 minutes ( range , 15 to 330 ) . perforation occurred in four patients ( 12.9% ) , all of whom were managed successfully by using endoscopic devices . endoscopic resection without laparoscopic assistance has recently come to be regarded as a minimally invasive method for treating sets . however , it is not commonly used to resect tumors that have invaded the muscular layer because it requires advanced skill , and the need to suture intentionally perforated holes after resection increases the length of the procedure . in 2012 , inoue et al . proposed an endoscopic submucosal tunnel dissection ( estd ) technique for sets that consisted of five major procedures : ( 1 ) creation of a mucosal entrance 2 to 3 cm in size 5 cm above the tumor ; ( 2 ) creation of a submucosal tunnel to provide endoscopic working space ; ( 3 ) separation of the tumor from the covering submucosa ; ( 4 ) dissection of the tumor away from the pm layer ; and ( 5 ) closure of the mucosal entry after specimen retrieval . successfully resected 10 of 12 sets ( 83.3% ; eight esophagus and four cardia tumors ) by using estd with en bloc resection . the mean resected tumor size was 19.5 mm , and the mean operation time was 48.3 minutes ( range , 30 to 60 ) . the most important advantage of estd is the maintenance of the mucosal integrity of the gi tract . endoscopic full - thickness resection ( eftr ) was designed to resect gastric sets located in the pm layer . it consists of four steps : ( 1 ) circumferential incision around the tumor ; ( 2 ) an incision as far as the subserosal layer along the circumferential incision ; ( 3 ) removal of the tumor including the surrounding pm layer and serosa by using a snare immediately after partial perforation ; and ( 4 ) closure of digestive wall defects by using endoscopic closure devices . zhou et al . successfully used eftr to remove 26 gastric sets originating in the pm layer . the complete resection rate was 100% , the mean operation time was 105 minutes ( range , 60 to 145 ) , and the mean size of the resected lesions was 2.8 cm ( range , 1.2 to 4.5 ) . in the study by ye et al . advances in the over - the - scope clip ( otsc ) system led to the use of otsc devices for removal of sets . was the first to perform a snare resection after clipping with an otsc device , and schmidt et al . developed a device for full - thickness resection . once applied , the otsc device captures the pathologic lesions , and the snare removes intentionally created pseudopolyps . the full - thickness resection device is an endoscopic suturing device that captures the muscularis layer below the pathologic lesion and resects the lesion after submucosal resection . owing to technical advances in endoscopic surgery and increases in the numbers of experienced endoscopists , various endoscopic technologies for resection of gists in the upper gi tract have been developed . the key to improving therapeutic outcomes following endoscopic enucleation of these tumors is to minimize the number of incomplete resections and maximize safety . however , perforations and pseudocapsule injuries , which can increase procedure time and peritoneal seeding , are possible . furthermore , information regarding the use of endoscopy procedures is still limited to case reports and small or pilot series . in the future , large - scale studies in clinical practice are required to accurately assess the efficacy and safety of these procedures .

most gastrointestinal stromal tumors ( gists ) arise from the proper muscle layer of the upper gastrointestinal ( gi ) tract and have a low malignant potential . they are sometimes accompanied by symptoms , but in most cases are detected by chance . endoscopic surgery of subepithelial tumors in the upper gi tract has been actively performed , and its merits include the need for fewer medical devices compared with other surgical procedures and post - resection organ preservation . however , because endoscopic procedures are still limited to small or pilot studies , a multidisciplinary approach combining laparoscopy and endoscopy is needed for more effective and pathologically acceptable management of gists . many new endoscopic surgeries have been developed , and this review describes the current status of and the new approaches for endoscopic surgery of gists in the upper gi tract .

<s>[INST]most subepithelial tumors ( sets ) are asymptomatic and found in only about 0.3% of all endoscopic examinations . owing to limited information about the natural course and malignant potential of sets less than 2 cm in size and the difficulty in targeting and completely resecting such tumors , regular follow - ups rather than resection have been recommended [ 2 - 4 ] . however , according to previous reports , up to 3.7% of gastrointestinal stromal tumors ( gists ) less than 2 cm in size and benign - appearing on endoscopic ultrasonography have a high mitotic index and rapidly increase in size , and hence have a high risk of malignancy . therefore , resection procedures that allow a definitive diagnosis as well as an evaluation of malignant potential are needed . furthermore , complications resulting from repetitive endoscopic procedures that delay diagnosis may arise , and doctor - patient relationships may be influenced by indecisiveness on the part of the physician . surgical approaches for gists in the upper gastrointestinal ( gi ) tract include open surgery and laparoscopic surgery , both of which are more invasive than is endoscopic surgery and potentially lead to several complications . on the other hand , most endoscopic methods , including endoscopic mucosal resection ( emr ) and endoscopic submucosal dissection ( esd ) , are usually only applicable to the submucosal layer of the gastric wall . therefore , many endoscopic surgeries have been developed and attempted . in this article , recent developments in the procedures for treating gists in the upper gi tract are discussed . endoscopic resection is indicated for gists in the upper gi tract that are located in the proper muscle ( pm ) layer and protrude into the endoluminal side . gists arising from the pm layer are not easily , completely , or safely resected via emr or esd alone . owing to the high risk of perforation when resecting sets deep in the gi wall , deep submucosal and muscular dissection around the tumor should be carefully performed . several studies reported high en bloc resection rates ( 64% to 94% ) and low perforation rates ( 0% to 12% ) for esd of gists [ 8 - 10 ] . endoscopic muscularis dissection ( emd ) involves precutting the mucosa that covers the tumor via a longitudinal incision , endoscopically dissecting the tumor away from the submucosal and pm layers , and closing the wound with clips . perforations occurring during dissection are closed by using only endoscopic devices , and a longitudinal incision is usually used during this procedure . emd can be performed within a relatively short period of time , and injuries to the overlying mucosa are minimal , resulting in easier mucosal closure . in 2012 , liu et al . reported that emd completely removed 30 of the 31 tumors ( 96.8% ; 14 esophagus , seven cardia , and 10 stomach tumors ) in their study . the mean size of the set was 22.1 mm , and the procedure required 76.8 minutes ( range , 15 to 330 ) . perforation occurred in four patients ( 12.9% ) , all of whom were managed successfully by using endoscopic devices . endoscopic resection without laparoscopic assistance has recently come to be regarded as a minimally invasive method for treating sets . however , it is not commonly used to resect tumors that have invaded the muscular layer because it requires advanced skill , and the need to suture intentionally perforated holes after resection increases the length of the procedure . in 2012 , inoue et al . proposed an endoscopic submucosal tunnel dissection ( estd ) technique for sets that consisted of five major procedures : ( 1 ) creation of a mucosal entrance 2 to 3 cm in size 5 cm above the tumor ; ( 2 ) creation of a submucosal tunnel to provide endoscopic working space ; ( 3 ) separation of the tumor from the covering submucosa ; ( 4 ) dissection of the tumor away from the pm layer ; and ( 5 ) closure of the mucosal entry after specimen retrieval . successfully resected 10 of 12 sets ( 83.3% ; eight esophagus and four cardia tumors ) by using estd with en bloc resection . the mean resected tumor size was 19.5 mm , and the mean operation time was 48.3 minutes ( range , 30 to 60 ) . the most important advantage of estd is the maintenance of the mucosal integrity of the gi tract . endoscopic full - thickness resection ( eftr ) was designed to resect gastric sets located in the pm layer . it consists of four steps : ( 1 ) circumferential incision around the tumor ; ( 2 ) an incision as far as the subserosal layer along the circumferential incision ; ( 3 ) removal of the tumor including the surrounding pm layer and serosa by using a snare immediately after partial perforation ; and ( 4 ) closure of digestive wall defects by using endoscopic closure devices . zhou et al . successfully used eftr to remove 26 gastric sets originating in the pm layer . the complete resection rate was 100% , the mean operation time was 105 minutes ( range , 60 to 145 ) , and the mean size of the resected lesions was 2.8 cm ( range , 1.2 to 4.5 ) . in the study by ye et al . advances in the over - the - scope clip ( otsc ) system led to the use of otsc devices for removal of sets . was the first to perform a snare resection after clipping with an otsc device , and schmidt et al . developed a device for full - thickness resection . once applied , the otsc device captures the pathologic lesions , and the snare removes intentionally created pseudopolyps . the full - thickness resection device is an endoscopic suturing device that captures the muscularis layer below the pathologic lesion and resects the lesion after submucosal resection . owing to technical advances in endoscopic surgery and increases in the numbers of experienced endoscopists , various endoscopic technologies for resection of gists in the upper gi tract have been developed . the key to improving therapeutic outcomes following endoscopic enucleation of these tumors is to minimize the number of incomplete resections and maximize safety . however , perforations and pseudocapsule injuries , which can increase procedure time and peritoneal seeding , are possible . furthermore , information regarding the use of endoscopy procedures is still limited to case reports and small or pilot series . in the future , large - scale studies in clinical practice are required to accurately assess the efficacy and safety of these procedures .[/INST]most gastrointestinal stromal tumors ( gists ) arise from the proper muscle layer of the upper gastrointestinal ( gi ) tract and have a low malignant potential . they are sometimes accompanied by symptoms , but in most cases are detected by chance . endoscopic surgery of subepithelial tumors in the upper gi tract has been actively performed , and its merits include the need for fewer medical devices compared with other surgical procedures and post - resection organ preservation . however , because endoscopic procedures are still limited to small or pilot studies , a multidisciplinary approach combining laparoscopy and endoscopy is needed for more effective and pathologically acceptable management of gists . many new endoscopic surgeries have been developed , and this review describes the current status of and the new approaches for endoscopic surgery of gists in the upper gi tract .</s>

in 1971 , martinet @xcite showed that every 3-manifold admits a contact structure . but in the subsequent twenty years , through the work of bennequin @xcite and eliashberg @xcite , it became apparent that not all contact structures are created equal in dimension 3 . specifically , contact structures fall into one of two classes : tight or overtwisted . in this new light , what martinet actually showed was that every 3-manifold admits an overtwisted contact structure . in @xcite eliashberg classified overtwisted contact structures on closed 3-manifolds by proving the weak homotopy equivalence of the space of overtwisted contact structures up to isotopy and the space of 2-plane fields up to homotopy hence overtwisted contact structures could now be understood via homotopy theory . on the other hand , it has become apparent that tight contact structures have surprising and deep connections to the topology of 3-manifolds , not limited to homotopy theory . for example , rudolph @xcite and lisca and mati @xcite found connections with slice knots and slice genus , kronheimer and mrowka @xcite found connections with seiberg - witten theory , and eliashberg and thurston @xcite found connections with foliation theory . thus , whether or not every 3-manifold admits a tight contact structure became a central question in 3-dimensional contact topology . the first candidate for a 3-manifold without a tight contact structure was the poincar homology sphere @xmath0 with reverse orientation . the difficulty of constructing a holomorphically fillable contact structure on @xmath1 was highlighted in gompf s paper @xcite . subsequently lisca @xcite , using techniques from seiberg - witten theory , proved that @xmath1 has no symplectically semi - fillable contact structure . in this paper we prove the following nonexistence result . [ thm : main ] there exist no positive tight contact structures on the poincar homology sphere @xmath2 with reverse orientation . this is the first example of a closed 3-manifold which does not carry a positive tight contact structure . let @xmath1 be the poincar homology sphere with reverse orientation . then the connect sum @xmath3 , where @xmath4 is @xmath1 with the opposite orientation , does not carry any tight contact structure , positive or negative . this follows from theorem [ thm : main ] , since a tight structures on a reducible manifold may be decomposed into tight structures on its summands @xcite we assume the reader is familiar with the basics ideas of contact topology in dimension 3 ( see for example @xcite ) . a thorough understanding of @xcite would be helpful but we include a brief summary of the ideas and terminology . the reader might also find @xcite useful for various parts of this section . in this paper the ambient manifold @xmath1 will be an oriented 3-manifold , and the contact structure @xmath5 will be _ positive _ , _ i.e. _ , given by a 1-form @xmath6 with @xmath7 . throughout this section we only consider @xmath8 _ tight_. also , when we refer to _ legendrian curves _ we mean closed curves , in contrast to _ legendrian arcs_. recall an oriented embedded surface @xmath9 in @xmath8 is called if there is a vector field @xmath10 transverse to @xmath9 whose flow preserves @xmath11 perhaps the most important feature of convex surfaces is the _ dividing set_. if @xmath12 is a singular foliation on @xmath9 then a disjoint union of ( properly ) embedded curves @xmath13 is said to @xmath12 if @xmath13 divides @xmath9 into two parts @xmath14 @xmath13 is transverse to @xmath15 and there is a vector field @xmath16 directing @xmath12 and a volume form @xmath17 on @xmath9 such that @xmath18 on @xmath19 and @xmath16 points transversely out of @xmath20 if @xmath6 is a contact 1-form for @xmath5 then the zeros of @xmath21 provide dividing curves for the characteristic foliation @xmath22 it is sometimes useful to keep in mind that the dividing curves are where @xmath10 is tangent to @xmath11 an isotopy @xmath23\to m$ ] of @xmath9 is called if @xmath24 is transversal to @xmath10 for all @xmath25 an important result concerning convex surfaces we will ( implicitly ) be using through out this paper is : [ giroux : main ] let @xmath13 be the dividing set for @xmath26 and @xmath12 another singular foliation on @xmath9 divided by @xmath27 then there is an admissible isotopy @xmath28 of @xmath9 such that @xmath29 @xmath30 and the isotopy is fixed on @xmath27 roughly speaking , this says that the dividing set @xmath13 dictates the geometry of @xmath9 , not the precise characteristic foliation . we will let @xmath31 denote the number of connected components of @xmath13 . if there is any ambiguity , we will also write @xmath32 instead of @xmath13 to denote the dividing set of @xmath9 . let @xmath33 and @xmath34 be compact convex surfaces with legendrian boundary , which intersect transversely along a common boundary legendrian curve @xmath35 . the neighborhood of the common boundary legendrian is locally isomorphic to the neighborhood @xmath36 of @xmath37 with coordinates @xmath38 and contact 1-form @xmath39 , for some @xmath40 . let @xmath41 , @xmath42 , be an annular collar of the boundary component @xmath35 . we may choose our local model so that @xmath43 and @xmath44 ( or the same with @xmath45 and @xmath46 switched ) . assuming the former , if we join @xmath33 and @xmath34 along @xmath47 and round the common edge , the resulting surface is convex , and the dividing curve @xmath48 on @xmath33 will connect to the dividing curve @xmath49 on @xmath34 , where @xmath50 . we now introduce the main idea on which this work is based . let @xmath35 be a legendrian arc . a half - disk @xmath51 is called a @xmath35 if @xmath52 is legendrian and consists of two arcs @xmath53 and @xmath54 such that , if we orient @xmath51 , @xmath55 are both positive ( negative ) elliptic singular points in @xmath56 there is a negative ( positive ) elliptic point along @xmath57 , and the singular points along @xmath54 are all positive ( negative ) and alternate between elliptic and hyperbolic . see figure [ bypass ] . = 1.3 in we also allow for the degenerate case when @xmath35 is a closed curve and the endpoints of @xmath57 are the same ( _ i.e. _ , @xmath58 ) . we refer to such a bypass as a . once an orientation on @xmath51 is fixed , the of the bypass is the sign of the elliptic point on the interior of @xmath59 the reason for the name ` bypass ' is that , instead of traveling along the legendrian arc @xmath35 , we may go around and drive through @xmath60 this has the effect of increasing the twisting of @xmath5 along the legendrian curve . ( here we are using the convention that left twists are negative . ) one can then show : [ thm : bypass ] assume @xmath1 has a convex boundary @xmath9 and there exists a bypass @xmath51 along the legendrian curve @xmath61 then we can find a neighborhood @xmath62 of @xmath63 with @xmath64 , and @xmath65 is related to @xmath32 as shown in figure [ bypassmove ] . = 1.5 in consider a convex torus @xmath66 . if @xmath5 is tight , then one can show that no dividing curve for @xmath66 bounds a disk . thus @xmath67 consists of @xmath68 parallel dividing curves with @xmath69 . assume for now that the dividing curves are all horizontal . using theorem [ giroux : main ] we can isotop @xmath66 so that there is one closed curve of singularities in @xmath70 in each region of @xmath71 these are called and are parallel to the dividing curves . we can further assume all the other leaves of @xmath70 form a 1-parameter family of parallel closed curves transverse to the legendrian divides . these can have any slope not equal to the slope of the dividing curves . a convex torus @xmath66 is said to be in _ standard form _ if @xmath70 has this nongeneric form , consisting of legendrian divides and legendrian ruling curves . suppose @xmath72 and we find a bypass for one of the ruling curves for @xmath66 then we may isotop @xmath66 across the bypass as in theorem [ thm : bypass ] and reduce the number @xmath73 by one . if @xmath74 we have a configuration change as follows : let @xmath66 be a convex torus with @xmath75 and in some basis for @xmath66 the slope of the dividing curves is 0 . if we find a bypass for a ruling curve of slope between @xmath76 and @xmath77 , @xmath78 then after pushing @xmath66 across the bypass the new torus has two dividing curves of slope @xmath79 let @xmath80 be a legendrian curve in @xmath81 we can always find a neighborhood @xmath62 of @xmath80 whose boundary is a convex torus with two dividing curves . the linking of a dividing curve on @xmath82 with @xmath80 is the thurston - bennequin invariant of @xmath83 we call the slope of these dividing curves the _ boundary slope _ of @xmath84 if @xmath80 is not null - homologous , then the framing induced on @xmath80 relative to some pre - assigned trivialization of the normal bundle of @xmath80 will be called the of @xmath83 in contrast to transverse curves , neighborhoods of legendrian curves have a quantifiable thickness no matter how small a ( nice ) neighborhood of a legendrian curve one takes , the boundary slope of the neighborhood is fixed . if @xmath62 is the neighborhood of a legendrian curve with twisting number @xmath85 ( relative to a framing that is already fixed ) , then the slopes of the dividing curves on @xmath86 are @xmath87 . on the other hand , any tight contact structure on the solid torus @xmath88 with boundary slope @xmath87 is contact isotopic to a neighborhood of a legendrian curve with twisting number @xmath89 see @xcite . it is easy to decrease the twisting number inside @xmath62 by adding ` zigzags ' ( see below for an explanation of terminology ) . hence , increasing the twisting number is one way of thickening @xmath62 . we now show how to use bypasses to increase the twisting number of @xmath83 let @xmath80 be a legendrian curve in @xmath1 with a fixed framing . let @xmath62 be a standard neighborhood of @xmath80 and @xmath73 the twisting number of @xmath83 if there exists a bypass attached to a legendrian ruling curve of @xmath82 of slope @xmath90 and @xmath91 then there exists a legendrian curve with larger twisting number isotopic to @xmath83 this lemma is a very useful formulation of the observation that if one has a bypass for a legendrian knot then one can increase its twisting number . now that we see bypasses are useful let us consider how to find them . let @xmath9 be a convex surface with legendrian boundary @xmath92 if the thurston - bennequin invariant of @xmath35 ( or let us say twisting number with respect to @xmath9 ) is negative then we can arrange that all the singularities of @xmath26 along @xmath35 are ( half)-elliptic . moreover we can assume the singular foliation @xmath26 is morse - smale . if @xmath73 is the twisting number of @xmath35 , then @xmath32 intersects @xmath35 at @xmath68 points . in this situation we can use the flow of @xmath16 ( the vector field directing @xmath26 in the definition of the dividing set ) to flow any dividing curve to a legendrian arc on @xmath9 , all of whose singularities are of the same sign . now , starting with a dividing curve @xmath93 with endpoints along @xmath35 isotopic to the boundary of @xmath9 , we push @xmath93 ` back into @xmath9 along @xmath16 ' and eventually arrive at a legendrian arc which cuts a bypass for @xmath35 off of @xmath94 thus to find bypasses we need only look for these @xmath95-compressible dividing curves . we now explore the neighborhood of a legendrian knot in more detail . to this end let @xmath62 be a standard neighborhood of a legendrian knot @xmath80 with a fixed framing so that @xmath96 and @xmath80 has twisting number @xmath97 in this framing . recall this means that @xmath82 is convex with two dividing curves ( and two legendrian divides ) of slope @xmath98 inside of @xmath62 we can isotop @xmath80 ( but not legendrian isotop ) to @xmath99 so as to decrease the twisting number by one . there are actually two different ways to do this . if @xmath80 were a knot in @xmath100 with the standard tight contact structure then this process corresponds to stabilizing the knot ( reducing the thurston - bennequin invariant ) by adding zigzags , and one can do this while increasing or decreasing the rotation number by one . to see how to detect this difference in @xmath62 we do the following : first , fix an orientation on @xmath62 and orient @xmath80 so that @xmath80 and @xmath101 intersect positively . let @xmath102 be a standard neighborhood of @xmath99 . then consider the layer @xmath103=n\backslash n'$ ] , where we set @xmath104 and @xmath105 we assume the legendrian ruling curves are vertical so that @xmath106 $ ] is an annulus with legendrian boundary . note that @xmath107 intersects the dividing curves on @xmath108 @xmath109 times and @xmath110 intersects the dividing curves on @xmath111 @xmath68 times . so there will be a bypass ( in fact just one bypass ) on @xmath112 for @xmath113 if @xmath112 is oriented so that the orientation on @xmath107 agrees with the one chosen above on @xmath80 , then the sign of the bypass is what distinguishes the two possible @xmath99 s . if @xmath93 is a curve on @xmath107 whose slope is not @xmath114 or @xmath115 then we can make the legendrian ruling curves on @xmath116 parallel to @xmath117 later it will be useful to know what the dividing curves on @xmath118 $ ] will look like . the relative euler class in the next paragraph can be useful for this purpose . let @xmath5 be any tight structure on a toric annulus @xmath119 $ ] ( not necessarily the same one as in the above paragraphs ) . assume the boundary is convex and in standard form . let @xmath120 be a section of @xmath121 which is transverse to and twists ( with @xmath5 ) along the legendrian ruling curves . we also take @xmath120 to be tangent to the legendrian divides . we may now form the relative euler class @xmath122 in @xmath123 first note that @xmath122 is unchanged if we perform a @xmath124-small isotopy of @xmath116 so as to alter the slopes of the ruling curve . now given an oriented curve @xmath93 on @xmath125 we can assume the annulus @xmath126 $ ] has legendrian boundary and is also convex . we orient @xmath112 so that it induces the correct orientation on @xmath117 now we have @xmath127 where @xmath128 are the positive and negative regions into which the dividing curves cut @xmath129 this formula follows from proposition 6.6 in @xcite once one observes that @xmath120 may be homotoped in @xmath121 so as to be tangent to and define the correct orientation on @xmath130 we end this section by making precise the notion of _ twisting _ along @xmath131 let @xmath132 be the kernel of @xmath133 on @xmath134 with coordinates @xmath135 . this contact structure is tight . the characteristic foliation on @xmath136 is by lines of a fixed slope . the slope `` decreases '' as @xmath137 moves around @xmath138 in the positive direction . let @xmath139 $ ] be an interval in @xmath140 $ ] so that at one end @xmath141 has slope @xmath114 and at the other end @xmath142 has slope @xmath143 we can @xmath144-perturb @xmath145 and @xmath146 so that they are convex and each has two dividing curves of slope @xmath114 and @xmath147 respectively . let @xmath148 $ ] be the layer between @xmath102 and @xmath62 as in [ layering ] . it is possible to show that @xmath149 $ ] is contactomorphic to @xmath150 with the contact structure constructed above ( see @xcite ) . the slopes of the characteristic foliations on @xmath151 vary from @xmath114 to @xmath115 in @xmath149 $ ] so they do likewise in @xmath152 from this one can conclude that if @xmath62 is a standard neighborhood of a legendrian knot @xmath80 with twist number @xmath73 ( with respect to some fixed framing ) , then for any slope in @xmath153 one can find a torus around @xmath80 whose characteristic foliation has this slope ( note if @xmath154 then @xmath153 means @xmath155 $ ] where @xmath156 is identified with @xmath157 ) . more generally , if @xmath131 $ ] has boundary slopes @xmath158 for @xmath159 , then we may find convex tori parallel to @xmath159 with any slope @xmath160 in @xmath161 $ ] ( if @xmath162 then this means @xmath163\cup [ -\infty , s_0]$ ] ) . this follows from the classification of tight contact structures on @xmath164 in the proof we layer @xmath164 into ` thin ' toric annuli , each of which is isomorphic to @xmath149 $ ] above ( see @xcite ) . consider the seifert fibered space @xmath1 with 3 singular fibers over @xmath165 . @xmath1 is described by the seifert invariants @xmath166 . let @xmath167 , @xmath168 , be the neighborhoods of the singular fibers @xmath169 , isomorphic to @xmath88 and identify @xmath170 with @xmath171 where @xmath172 is a sphere with three punctures . then @xmath173 is given by @xmath174 . we identify @xmath175 , by choosing @xmath176 as the meridional direction , and @xmath177 as the longitudinal direction with respect to the product structure on @xmath167 . we identify @xmath178 by letting @xmath177 be the direction of an @xmath138-fiber , and @xmath176 be the direction given by @xmath179 . let @xmath1 be the poincar homology sphere @xmath2 with reverse orientation . it is a seifert fibered space over @xmath165 with seifert invariants @xmath180 . in the case @xmath181 , we choose @xmath182 . notice there we has some freedom to choose @xmath183 , @xmath184 , since we could have postmultiplied by @xmath185 if we changed our framing for @xmath186 . similarly , let @xmath187 , and @xmath188 . now let @xmath5 be a positive contact structure on @xmath1 . assume @xmath5 is tight . the goal of the paper is to obtain a contradiction by finding overtwisted disks inside @xmath1 . in the first stage of the proof , we will try to thicken neighborhoods @xmath167 of the singular fibers @xmath169 ( we may assume the singular fibers are legendrian after isotopy ) . this is done by maximizing the twisting number @xmath189 among legendrian curves isotopic to @xmath169 , subject to the condition that all three legendrian curves be simultaneously isotopic to @xmath190 . let @xmath167 be a standard tubular neighborhood of @xmath169 with minimal convex boundary and boundary slope @xmath191 ( note this is negative ) . it is useful to note how the dividing curves map under @xmath192 . @xmath193 , @xmath194 , and @xmath195 . therefore , the boundary slopes are @xmath196 , @xmath197 and @xmath198 , when viewed on @xmath199 . .1 in * warning : * we will often call the same surface by different names , such as @xmath200 and @xmath199 . although the surfaces themselves are the same , their _ identifications _ with @xmath201 are not . therefore , when we refer to slopes on @xmath200 , we implicitly invoke the identification of @xmath200 with @xmath201 given in the first paragraph of this section . [ increase ] we can increase @xmath189 so that @xmath202 , @xmath203 , and thicken @xmath167 to @xmath204 so that the slopes of @xmath205 are all infinite . we may modify the legendrian rulings on both @xmath206 and @xmath207 so that they are vertical . take a vertical annulus @xmath208 spanning from a vertical legendrian ruling curve on @xmath206 to a vertical legendrian ruling curve on @xmath207 . here ` vertical ' means ` in the direction of the @xmath138-fibers ' . note @xmath208 intersects the dividing curves on @xmath209 and @xmath210 @xmath211 and @xmath212 times respectively . assume @xmath213 . if @xmath214 , then there exists a bypass ( due to the imbalance ) , attached along a vertical legendrian curve of @xmath206 or @xmath207 . we transform @xmath177 via @xmath215 to use the twist number lemma . @xmath216 , and @xmath217 . the legendrian rulings will have slope @xmath218 and @xmath219 , and , therefore , we may increase the twisting number by 1 if the twisting number is @xmath220 . next , assume @xmath221 and there are no bypasses on the vertical annulus . then we may take @xmath208 to be standard , with vertical rulings , and parallel legendrian divides spanning from @xmath222 to @xmath223 . cutting along @xmath208 and rounding the corners , we obtain the torus boundary of @xmath224 ; if we identify this torus with @xmath201 in the same way as @xmath225 , then the boundary slope is @xmath226 . when @xmath227 , then the slope is @xmath228 , and any legendrian divide gives rise to an overtwisted disk this is because @xmath229 , which corresponds to a slope of @xmath228 on @xmath225 . when @xmath230 , then the slope is @xmath231 , which implies that on the @xmath232 , the twisting in the radial direction is almost @xmath233 . in particular , there exists a convex torus with slope @xmath157 inside @xmath88 , and hence a vertical legendrian curve with zero twisting , obtained as a legendrian divide of the convex torus . any vertical annulus taken from this vertical legendrian to @xmath234 ( or @xmath235 ) will give bypasses . we can now assume @xmath203 . the boundary slopes of @xmath236 and @xmath237 are @xmath228 and @xmath238 , respectively . again look at the vertical annulus @xmath208 spanning from @xmath234 to @xmath235 , with legendrian boundary . there are three possibilities : ( 1 ) there are no bypasses along @xmath107 ( on the @xmath234 side ) in this case , we can cut along the annulus as before , and get boundary component with boundary slope @xmath228 , contradicting tightness . ( 2 ) there is one bypass along @xmath107 cutting along the annulus again , we find that the boundary slope is @xmath239 . this means that the twisting of @xmath240 is large , and that we have a convex torus in standard form with legendrian divides of infinite slope as before . ( 3 ) there are two bypasses . in any case , there exist vertical legendrian curves with twisting number @xmath241 with respect to the framing from the fibers . since @xmath242 , we have bypasses for @xmath186 as well , and we can increase to @xmath202 using the twist number lemma . next , taking a vertical annulus from @xmath234 to one such vertical legendrian curve , we obtain two bypasses for @xmath234 and , similarly , we obtain four bypasses for @xmath235 . by attaching these two bypasses , we obtain a thickening @xmath204 of @xmath167 , @xmath168 , so that @xmath243 has two vertical dividing curves . in the section we use the structure of @xmath244 as a punctured torus bundle over @xmath138 to complete the proof of our main theorem . the strategy is as follows : first we use the bundle structure to increase @xmath245 to 0 by finding a bypass along the boundary of the punctured torus fiber . we then show how to increase @xmath245 to 1 by making the boundary of the punctured torus fiber legendrian with twist number 0 . when @xmath246 the corresponding neighborhood of @xmath247 almost contains an overtwisted disk . by increasing it a little further it does contain one . this will complete the proof of our main theorem . we now describe the fibration as a punctured torus bundle over @xmath138 . in the previous section , @xmath167 was the neighborhood of a legendrian curve @xmath169 with twisting number @xmath189 , and @xmath248 its thickening . write @xmath249 , where @xmath9 is a 3-holed sphere . let @xmath80 be an embedded arc on @xmath9 connecting @xmath250 to @xmath251 , @xmath252 an annulus connecting @xmath250 to @xmath251 , and @xmath253 a neighborhood of @xmath112 in @xmath254 . define @xmath255 , which is @xmath256 with a @xmath164 layer removed from the boundary . let @xmath257 and @xmath258 be meridional disks for @xmath251 and @xmath259 respectively . the slope of @xmath257 on @xmath260 is @xmath228 and the slope of @xmath258 on @xmath261 is @xmath262 thus we can take two copies of @xmath258 and three copies of @xmath257 and glue them together with six copies of @xmath263 to obtain a punctured torus @xmath66 in @xmath264 with boundary on @xmath265 ( see figure [ goodfiber ] . ) parallel copies of @xmath66 will fiber @xmath264 ( and @xmath244 ) as a punctured torus bundle over @xmath266 the slope of @xmath267 on @xmath268 is @xmath269 thus the slope on @xmath270 is 1 , so @xmath66 provides a seifert surface for @xmath271 we can show ( for example by using kirby calculus ) that @xmath272 represented in figure [ fig : surgery](a ) , is diffeomorphic to figure [ fig : surgery](b ) , and that @xmath273 is diffeomorphic to the complement of the right - handed trefoil knot in @xmath274 thus we may identify the monodromy of the punctured torus bundle as @xmath275 we begin by showing that either we can find a bypass for @xmath267 or arrange that the dividing curves on @xmath66 consist of exactly two parallel arcs . if there are no bypasses , then the dividing set must consist of two parallel arcs and an even number , say @xmath279 of closed parallel curves . consider @xmath280 $ ] with @xmath66 identified with @xmath281 here we are viewing @xmath264 as @xmath273 . let @xmath6 be a closed legendrian curve on @xmath66 parallel to the dividing curves . then consider @xmath282 $ ] which we may assume is convex with legendrian boundary . the dividing curves do not intersect @xmath283 , but they intersect @xmath284 at least @xmath285 times . thus we may find a bypass @xmath51 for @xmath286 the inner boundary @xmath287 of a neighborhood of @xmath288 is a convex torus with either a bypass for @xmath289 or two fewer dividing curves than @xmath290 repeating this argument @xmath85 times will result in a bypass for @xmath267 or a convex torus whose dividing set consist of exactly two parallel arcs . now suppose @xmath67 consists of two parallel arcs , since otherwise we are done . then @xmath291 consists of two arcs and @xmath292 consists of the image of these two arcs under the monodromy map for the bundle . let @xmath6 be a closed curve on @xmath293 parallel to the dividing curves , and @xmath294.$ ] we may arrange for @xmath295 to be legendrian and for @xmath296 to be convex . now the dividing curves on @xmath296 do not intersect @xmath283 but intersect @xmath284 at least two times . thus we have a bypass @xmath51 for the dividing curves on @xmath286 assume first that the intersection number is exactly two . then the annulus @xmath296 may be split into two annuli , one of which , call it @xmath297 intersects @xmath298 and contains @xmath51 , which is of degenerate type . the boundary of a small neighborhood of @xmath299 in @xmath300 is an annulus @xmath301 and has dividing curves as shown in figure [ fig : annulus ] . the boundary of @xmath301 sits on @xmath286 if we cut out the annulus in @xmath298 that cobounds a solid torus with @xmath302 glue in @xmath301 , and smooth corners , then the dividing curves on the new @xmath298 are shown in figure [ fig : annulus ] . if the intersection number is greater than two , then simply attach the bypass @xmath51 onto @xmath298 either the new @xmath298 has a bypass , in which case we are done , or we can take a new @xmath296 which has fewer ( but @xmath304 intersections ) . we continue until the intersection number becomes two . [ lem : twist ] we may increase @xmath245 to @xmath241 while keeping @xmath202 and @xmath305 moreover , @xmath234 may be further thickened to @xmath306 so that @xmath307 has dividing curves of slope @xmath277 since we have a bypass on @xmath267 we may apply the twist number lemma to increase the twist number of @xmath247 to @xmath308 so we have two vertical dividing curves on @xmath270 and on @xmath309 they have slope 0 . now repeating the argument in lemma [ increase ] we see that we can arrange @xmath202 and @xmath305 note the dividing curves on @xmath310 and @xmath311 have slope @xmath228 and 0 , respectively . thus taking a vertical annulus between @xmath312 and @xmath209 , we find a vertical bypass along @xmath313 with this bypass we can thicken @xmath234 to @xmath306 whose dividing curves have slope @xmath277 note if we had another bypass along @xmath267 we could increase @xmath245 to 1 and from here we could then find an overtwisted disk ( see below ) . however , we know of no direct way to prove this bypass exists . therefore we use the following strategy , which can be called as ` thinning before thickening ' . notice we have thickened @xmath235 so that @xmath246 ; we will now backtrack by having @xmath235 relinquish some of its thickness ( we peel off a toric annulus from @xmath235 and reattach to @xmath186 and @xmath234 ) , and then thicken again to obtain a contradiction . let @xmath317 be the meridional disk to @xmath167 for @xmath318 if we arrange that the legendrian rulings on @xmath200 are horizontal and the @xmath317 are convex , then @xmath319 and @xmath320 . the dividing sets divide @xmath257 into two regions , one positive and one negative , and @xmath258 into three regions without loss of generality we can assume that , two regions are positive and one is negative . note that the signs of these regions depend on an orientation on the disks . pick an orientation for the fibers of the seifert fibration , and the disks will be oriented so that their intersection with a fiber is positive . note we can write @xmath321 , where @xmath322 is a solid torus with convex boundary and dividing curves of slope @xmath239 ( on @xmath323 ) , @xmath103 $ ] , @xmath324 , and @xmath325 is convex with vertical dividing curves . we do this by stabilizing ( reducing the twist number ) @xmath247 with @xmath315 in @xmath326 in @xmath150 we can find a @xmath327 , say @xmath328 with dividing curves of slope @xmath219 ( which correspond to vertical dividing curves from the point of view of @xmath329 ) . by performing the correct stabilization we can arrange that on a convex annulus in @xmath330 $ ] of slope @xmath331 with legendrian boundary on @xmath332 and @xmath333 there is a negative bypass along the boundary component on @xmath334 we can use this bypass to thicken @xmath167 , @xmath42 , to @xmath204 so that @xmath335 have vertical slopes . using the relative euler class we can easily see that each meridional disk @xmath336 in @xmath248 has an extra positive region . specifically , if @xmath337 is the relative euler class on @xmath338 ( as defined in section [ section : convexity ] ) and @xmath339 and @xmath340 are the horizontal and vertical curves on @xmath341 then one may easily compute that @xmath342)= 1 $ ] and @xmath343)=0.$ ] thus @xmath344)=1 $ ] where @xmath93 is the boundary of the meridional disk in @xmath345 from this and equation [ eqn : formula ] , we can conclude that the dividing curves are as in figure [ anndivides ] ( a ) , and hence a convex meridional disk in @xmath251 will have one negative and two positive regions in the complement of the dividing curves . similarly , a convex meridional disk in @xmath250 will have one negative and three positive regions since a relative euler class argument will show its intersection with @xmath346 is shown in figure [ anndivides ] ( b ) we would now like to piece these meridional disks together to form a punctured torus fiber for @xmath348 , but to do this we first need to understand the complement of the singular fibers . recall all the boundary slopes of @xmath349 are infinite . take @xmath350 , which we assume is convex with legendrian boundary . all the boundary components of @xmath9 have exactly two half - elliptic points . we argue that if there is a @xmath95-compressible dividing arc ( as in ( b ) , ( c ) , ( d ) ) on @xmath9 , then @xmath1 is overtwisted . the @xmath95-compressible dividing arc implies the existence of a bypass ( of degenerate type ) along some @xmath351 . hence , there exists a layer @xmath352 with one boundary component @xmath351 and boundary slopes @xmath241 and @xmath157 . however , since there are vertical legendrian curves with twisting number 0 outside of @xmath353 , we obtain another layer @xmath354 , this time with boundary slopes @xmath157 and @xmath241 . therefore , @xmath355 has too much radial twisting , and is overtwisted . the only possible configuration without a @xmath95-compressible dividing arc is ( a ) . we cut @xmath347 along @xmath9 , round the edges , and examine the dividing curves on the boundary of the resulting genus 2 handlebody . we then cut along the meridional disks of the handlebody , which we may assume have legendrian boundary , and eventually obtain a 3-ball . since each meridional disk of the handlebody intersects the dividing set only twice , the configuration of dividing curves on the meridional disks is unique . therefore the initial configuration of dividing curves on @xmath9 uniquely determines the tight structure on @xmath347 . the lemma implies that the tight structure on @xmath347 is a translation - invariant tight structure on @xmath164 with infinite boundary slopes , with the standard neighborhood of a vertical legendrian curve with zero twisting removed . we view this @xmath164 ( minus @xmath88 ) as the region between @xmath359 and @xmath360 ( minus @xmath358 ) . we may think of the @xmath361-factor as being quite small , and then isotop one of the legendrian divides on @xmath359 to one of the legendrian divides on @xmath360 and finally identify small neighborhoods ( in the tori ) of these divides . we may then isotop @xmath362 , @xmath42 , away from these neighborhoods so that the meridional disk @xmath363 in @xmath204 has legendrian boundary . forming the fiber @xmath66 in the fibration of @xmath364 from three copies of @xmath257 and two copies of @xmath258 , we can arrange that @xmath267 is legendrian and the dividing curves on @xmath66 are as in figure [ goodfiber ] . thus there are six bypasses for @xmath303 we can use these to increase the twisting number of @xmath267 to 0 ( _ i.e. _ , @xmath267 will be a legendrian divide on some thickening of @xmath270 ) which corresponds to an increase of @xmath245 to 1 . thus the slope of the dividing curves on @xmath365 is @xmath366 . now repeat the argument in lemma [ increase ] take a vertical annulus from @xmath367 to @xmath368 , and start with @xmath369 small . since the denominator of @xmath366 is never equal to @xmath211 , we eventually arrive at @xmath305 this implies the existence of a vertical bypass for @xmath368 , with which we can increase the slope of the dividing curves on @xmath365 to @xmath370 . thus the legendrian divide on our thickened solid torus bounds a meridional disk in @xmath235 , so we have found an overtwisted disk . this completes the proof of the main theorem .

we exhibit a 3-manifold which admits no tight contact structure .

<s>[INST]in 1971 , martinet @xcite showed that every 3-manifold admits a contact structure . but in the subsequent twenty years , through the work of bennequin @xcite and eliashberg @xcite , it became apparent that not all contact structures are created equal in dimension 3 . specifically , contact structures fall into one of two classes : tight or overtwisted . in this new light , what martinet actually showed was that every 3-manifold admits an overtwisted contact structure . in @xcite eliashberg classified overtwisted contact structures on closed 3-manifolds by proving the weak homotopy equivalence of the space of overtwisted contact structures up to isotopy and the space of 2-plane fields up to homotopy hence overtwisted contact structures could now be understood via homotopy theory . on the other hand , it has become apparent that tight contact structures have surprising and deep connections to the topology of 3-manifolds , not limited to homotopy theory . for example , rudolph @xcite and lisca and mati @xcite found connections with slice knots and slice genus , kronheimer and mrowka @xcite found connections with seiberg - witten theory , and eliashberg and thurston @xcite found connections with foliation theory . thus , whether or not every 3-manifold admits a tight contact structure became a central question in 3-dimensional contact topology . the first candidate for a 3-manifold without a tight contact structure was the poincar homology sphere @xmath0 with reverse orientation . the difficulty of constructing a holomorphically fillable contact structure on @xmath1 was highlighted in gompf s paper @xcite . subsequently lisca @xcite , using techniques from seiberg - witten theory , proved that @xmath1 has no symplectically semi - fillable contact structure . in this paper we prove the following nonexistence result . [ thm : main ] there exist no positive tight contact structures on the poincar homology sphere @xmath2 with reverse orientation . this is the first example of a closed 3-manifold which does not carry a positive tight contact structure . let @xmath1 be the poincar homology sphere with reverse orientation . then the connect sum @xmath3 , where @xmath4 is @xmath1 with the opposite orientation , does not carry any tight contact structure , positive or negative . this follows from theorem [ thm : main ] , since a tight structures on a reducible manifold may be decomposed into tight structures on its summands @xcite we assume the reader is familiar with the basics ideas of contact topology in dimension 3 ( see for example @xcite ) . a thorough understanding of @xcite would be helpful but we include a brief summary of the ideas and terminology . the reader might also find @xcite useful for various parts of this section . in this paper the ambient manifold @xmath1 will be an oriented 3-manifold , and the contact structure @xmath5 will be _ positive _ , _ i.e. _ , given by a 1-form @xmath6 with @xmath7 . throughout this section we only consider @xmath8 _ tight_. also , when we refer to _ legendrian curves _ we mean closed curves , in contrast to _ legendrian arcs_. recall an oriented embedded surface @xmath9 in @xmath8 is called if there is a vector field @xmath10 transverse to @xmath9 whose flow preserves @xmath11 perhaps the most important feature of convex surfaces is the _ dividing set_. if @xmath12 is a singular foliation on @xmath9 then a disjoint union of ( properly ) embedded curves @xmath13 is said to @xmath12 if @xmath13 divides @xmath9 into two parts @xmath14 @xmath13 is transverse to @xmath15 and there is a vector field @xmath16 directing @xmath12 and a volume form @xmath17 on @xmath9 such that @xmath18 on @xmath19 and @xmath16 points transversely out of @xmath20 if @xmath6 is a contact 1-form for @xmath5 then the zeros of @xmath21 provide dividing curves for the characteristic foliation @xmath22 it is sometimes useful to keep in mind that the dividing curves are where @xmath10 is tangent to @xmath11 an isotopy @xmath23\to m$ ] of @xmath9 is called if @xmath24 is transversal to @xmath10 for all @xmath25 an important result concerning convex surfaces we will ( implicitly ) be using through out this paper is : [ giroux : main ] let @xmath13 be the dividing set for @xmath26 and @xmath12 another singular foliation on @xmath9 divided by @xmath27 then there is an admissible isotopy @xmath28 of @xmath9 such that @xmath29 @xmath30 and the isotopy is fixed on @xmath27 roughly speaking , this says that the dividing set @xmath13 dictates the geometry of @xmath9 , not the precise characteristic foliation . we will let @xmath31 denote the number of connected components of @xmath13 . if there is any ambiguity , we will also write @xmath32 instead of @xmath13 to denote the dividing set of @xmath9 . let @xmath33 and @xmath34 be compact convex surfaces with legendrian boundary , which intersect transversely along a common boundary legendrian curve @xmath35 . the neighborhood of the common boundary legendrian is locally isomorphic to the neighborhood @xmath36 of @xmath37 with coordinates @xmath38 and contact 1-form @xmath39 , for some @xmath40 . let @xmath41 , @xmath42 , be an annular collar of the boundary component @xmath35 . we may choose our local model so that @xmath43 and @xmath44 ( or the same with @xmath45 and @xmath46 switched ) . assuming the former , if we join @xmath33 and @xmath34 along @xmath47 and round the common edge , the resulting surface is convex , and the dividing curve @xmath48 on @xmath33 will connect to the dividing curve @xmath49 on @xmath34 , where @xmath50 . we now introduce the main idea on which this work is based . let @xmath35 be a legendrian arc . a half - disk @xmath51 is called a @xmath35 if @xmath52 is legendrian and consists of two arcs @xmath53 and @xmath54 such that , if we orient @xmath51 , @xmath55 are both positive ( negative ) elliptic singular points in @xmath56 there is a negative ( positive ) elliptic point along @xmath57 , and the singular points along @xmath54 are all positive ( negative ) and alternate between elliptic and hyperbolic . see figure [ bypass ] . = 1.3 in we also allow for the degenerate case when @xmath35 is a closed curve and the endpoints of @xmath57 are the same ( _ i.e. _ , @xmath58 ) . we refer to such a bypass as a . once an orientation on @xmath51 is fixed , the of the bypass is the sign of the elliptic point on the interior of @xmath59 the reason for the name ` bypass ' is that , instead of traveling along the legendrian arc @xmath35 , we may go around and drive through @xmath60 this has the effect of increasing the twisting of @xmath5 along the legendrian curve . ( here we are using the convention that left twists are negative . ) one can then show : [ thm : bypass ] assume @xmath1 has a convex boundary @xmath9 and there exists a bypass @xmath51 along the legendrian curve @xmath61 then we can find a neighborhood @xmath62 of @xmath63 with @xmath64 , and @xmath65 is related to @xmath32 as shown in figure [ bypassmove ] . = 1.5 in consider a convex torus @xmath66 . if @xmath5 is tight , then one can show that no dividing curve for @xmath66 bounds a disk . thus @xmath67 consists of @xmath68 parallel dividing curves with @xmath69 . assume for now that the dividing curves are all horizontal . using theorem [ giroux : main ] we can isotop @xmath66 so that there is one closed curve of singularities in @xmath70 in each region of @xmath71 these are called and are parallel to the dividing curves . we can further assume all the other leaves of @xmath70 form a 1-parameter family of parallel closed curves transverse to the legendrian divides . these can have any slope not equal to the slope of the dividing curves . a convex torus @xmath66 is said to be in _ standard form _ if @xmath70 has this nongeneric form , consisting of legendrian divides and legendrian ruling curves . suppose @xmath72 and we find a bypass for one of the ruling curves for @xmath66 then we may isotop @xmath66 across the bypass as in theorem [ thm : bypass ] and reduce the number @xmath73 by one . if @xmath74 we have a configuration change as follows : let @xmath66 be a convex torus with @xmath75 and in some basis for @xmath66 the slope of the dividing curves is 0 . if we find a bypass for a ruling curve of slope between @xmath76 and @xmath77 , @xmath78 then after pushing @xmath66 across the bypass the new torus has two dividing curves of slope @xmath79 let @xmath80 be a legendrian curve in @xmath81 we can always find a neighborhood @xmath62 of @xmath80 whose boundary is a convex torus with two dividing curves . the linking of a dividing curve on @xmath82 with @xmath80 is the thurston - bennequin invariant of @xmath83 we call the slope of these dividing curves the _ boundary slope _ of @xmath84 if @xmath80 is not null - homologous , then the framing induced on @xmath80 relative to some pre - assigned trivialization of the normal bundle of @xmath80 will be called the of @xmath83 in contrast to transverse curves , neighborhoods of legendrian curves have a quantifiable thickness no matter how small a ( nice ) neighborhood of a legendrian curve one takes , the boundary slope of the neighborhood is fixed . if @xmath62 is the neighborhood of a legendrian curve with twisting number @xmath85 ( relative to a framing that is already fixed ) , then the slopes of the dividing curves on @xmath86 are @xmath87 . on the other hand , any tight contact structure on the solid torus @xmath88 with boundary slope @xmath87 is contact isotopic to a neighborhood of a legendrian curve with twisting number @xmath89 see @xcite . it is easy to decrease the twisting number inside @xmath62 by adding ` zigzags ' ( see below for an explanation of terminology ) . hence , increasing the twisting number is one way of thickening @xmath62 . we now show how to use bypasses to increase the twisting number of @xmath83 let @xmath80 be a legendrian curve in @xmath1 with a fixed framing . let @xmath62 be a standard neighborhood of @xmath80 and @xmath73 the twisting number of @xmath83 if there exists a bypass attached to a legendrian ruling curve of @xmath82 of slope @xmath90 and @xmath91 then there exists a legendrian curve with larger twisting number isotopic to @xmath83 this lemma is a very useful formulation of the observation that if one has a bypass for a legendrian knot then one can increase its twisting number . now that we see bypasses are useful let us consider how to find them . let @xmath9 be a convex surface with legendrian boundary @xmath92 if the thurston - bennequin invariant of @xmath35 ( or let us say twisting number with respect to @xmath9 ) is negative then we can arrange that all the singularities of @xmath26 along @xmath35 are ( half)-elliptic . moreover we can assume the singular foliation @xmath26 is morse - smale . if @xmath73 is the twisting number of @xmath35 , then @xmath32 intersects @xmath35 at @xmath68 points . in this situation we can use the flow of @xmath16 ( the vector field directing @xmath26 in the definition of the dividing set ) to flow any dividing curve to a legendrian arc on @xmath9 , all of whose singularities are of the same sign . now , starting with a dividing curve @xmath93 with endpoints along @xmath35 isotopic to the boundary of @xmath9 , we push @xmath93 ` back into @xmath9 along @xmath16 ' and eventually arrive at a legendrian arc which cuts a bypass for @xmath35 off of @xmath94 thus to find bypasses we need only look for these @xmath95-compressible dividing curves . we now explore the neighborhood of a legendrian knot in more detail . to this end let @xmath62 be a standard neighborhood of a legendrian knot @xmath80 with a fixed framing so that @xmath96 and @xmath80 has twisting number @xmath97 in this framing . recall this means that @xmath82 is convex with two dividing curves ( and two legendrian divides ) of slope @xmath98 inside of @xmath62 we can isotop @xmath80 ( but not legendrian isotop ) to @xmath99 so as to decrease the twisting number by one . there are actually two different ways to do this . if @xmath80 were a knot in @xmath100 with the standard tight contact structure then this process corresponds to stabilizing the knot ( reducing the thurston - bennequin invariant ) by adding zigzags , and one can do this while increasing or decreasing the rotation number by one . to see how to detect this difference in @xmath62 we do the following : first , fix an orientation on @xmath62 and orient @xmath80 so that @xmath80 and @xmath101 intersect positively . let @xmath102 be a standard neighborhood of @xmath99 . then consider the layer @xmath103=n\backslash n'$ ] , where we set @xmath104 and @xmath105 we assume the legendrian ruling curves are vertical so that @xmath106 $ ] is an annulus with legendrian boundary . note that @xmath107 intersects the dividing curves on @xmath108 @xmath109 times and @xmath110 intersects the dividing curves on @xmath111 @xmath68 times . so there will be a bypass ( in fact just one bypass ) on @xmath112 for @xmath113 if @xmath112 is oriented so that the orientation on @xmath107 agrees with the one chosen above on @xmath80 , then the sign of the bypass is what distinguishes the two possible @xmath99 s . if @xmath93 is a curve on @xmath107 whose slope is not @xmath114 or @xmath115 then we can make the legendrian ruling curves on @xmath116 parallel to @xmath117 later it will be useful to know what the dividing curves on @xmath118 $ ] will look like . the relative euler class in the next paragraph can be useful for this purpose . let @xmath5 be any tight structure on a toric annulus @xmath119 $ ] ( not necessarily the same one as in the above paragraphs ) . assume the boundary is convex and in standard form . let @xmath120 be a section of @xmath121 which is transverse to and twists ( with @xmath5 ) along the legendrian ruling curves . we also take @xmath120 to be tangent to the legendrian divides . we may now form the relative euler class @xmath122 in @xmath123 first note that @xmath122 is unchanged if we perform a @xmath124-small isotopy of @xmath116 so as to alter the slopes of the ruling curve . now given an oriented curve @xmath93 on @xmath125 we can assume the annulus @xmath126 $ ] has legendrian boundary and is also convex . we orient @xmath112 so that it induces the correct orientation on @xmath117 now we have @xmath127 where @xmath128 are the positive and negative regions into which the dividing curves cut @xmath129 this formula follows from proposition 6.6 in @xcite once one observes that @xmath120 may be homotoped in @xmath121 so as to be tangent to and define the correct orientation on @xmath130 we end this section by making precise the notion of _ twisting _ along @xmath131 let @xmath132 be the kernel of @xmath133 on @xmath134 with coordinates @xmath135 . this contact structure is tight . the characteristic foliation on @xmath136 is by lines of a fixed slope . the slope `` decreases '' as @xmath137 moves around @xmath138 in the positive direction . let @xmath139 $ ] be an interval in @xmath140 $ ] so that at one end @xmath141 has slope @xmath114 and at the other end @xmath142 has slope @xmath143 we can @xmath144-perturb @xmath145 and @xmath146 so that they are convex and each has two dividing curves of slope @xmath114 and @xmath147 respectively . let @xmath148 $ ] be the layer between @xmath102 and @xmath62 as in [ layering ] . it is possible to show that @xmath149 $ ] is contactomorphic to @xmath150 with the contact structure constructed above ( see @xcite ) . the slopes of the characteristic foliations on @xmath151 vary from @xmath114 to @xmath115 in @xmath149 $ ] so they do likewise in @xmath152 from this one can conclude that if @xmath62 is a standard neighborhood of a legendrian knot @xmath80 with twist number @xmath73 ( with respect to some fixed framing ) , then for any slope in @xmath153 one can find a torus around @xmath80 whose characteristic foliation has this slope ( note if @xmath154 then @xmath153 means @xmath155 $ ] where @xmath156 is identified with @xmath157 ) . more generally , if @xmath131 $ ] has boundary slopes @xmath158 for @xmath159 , then we may find convex tori parallel to @xmath159 with any slope @xmath160 in @xmath161 $ ] ( if @xmath162 then this means @xmath163\cup [ -\infty , s_0]$ ] ) . this follows from the classification of tight contact structures on @xmath164 in the proof we layer @xmath164 into ` thin ' toric annuli , each of which is isomorphic to @xmath149 $ ] above ( see @xcite ) . consider the seifert fibered space @xmath1 with 3 singular fibers over @xmath165 . @xmath1 is described by the seifert invariants @xmath166 . let @xmath167 , @xmath168 , be the neighborhoods of the singular fibers @xmath169 , isomorphic to @xmath88 and identify @xmath170 with @xmath171 where @xmath172 is a sphere with three punctures . then @xmath173 is given by @xmath174 . we identify @xmath175 , by choosing @xmath176 as the meridional direction , and @xmath177 as the longitudinal direction with respect to the product structure on @xmath167 . we identify @xmath178 by letting @xmath177 be the direction of an @xmath138-fiber , and @xmath176 be the direction given by @xmath179 . let @xmath1 be the poincar homology sphere @xmath2 with reverse orientation . it is a seifert fibered space over @xmath165 with seifert invariants @xmath180 . in the case @xmath181 , we choose @xmath182 . notice there we has some freedom to choose @xmath183 , @xmath184 , since we could have postmultiplied by @xmath185 if we changed our framing for @xmath186 . similarly , let @xmath187 , and @xmath188 . now let @xmath5 be a positive contact structure on @xmath1 . assume @xmath5 is tight . the goal of the paper is to obtain a contradiction by finding overtwisted disks inside @xmath1 . in the first stage of the proof , we will try to thicken neighborhoods @xmath167 of the singular fibers @xmath169 ( we may assume the singular fibers are legendrian after isotopy ) . this is done by maximizing the twisting number @xmath189 among legendrian curves isotopic to @xmath169 , subject to the condition that all three legendrian curves be simultaneously isotopic to @xmath190 . let @xmath167 be a standard tubular neighborhood of @xmath169 with minimal convex boundary and boundary slope @xmath191 ( note this is negative ) . it is useful to note how the dividing curves map under @xmath192 . @xmath193 , @xmath194 , and @xmath195 . therefore , the boundary slopes are @xmath196 , @xmath197 and @xmath198 , when viewed on @xmath199 . .1 in * warning : * we will often call the same surface by different names , such as @xmath200 and @xmath199 . although the surfaces themselves are the same , their _ identifications _ with @xmath201 are not . therefore , when we refer to slopes on @xmath200 , we implicitly invoke the identification of @xmath200 with @xmath201 given in the first paragraph of this section . [ increase ] we can increase @xmath189 so that @xmath202 , @xmath203 , and thicken @xmath167 to @xmath204 so that the slopes of @xmath205 are all infinite . we may modify the legendrian rulings on both @xmath206 and @xmath207 so that they are vertical . take a vertical annulus @xmath208 spanning from a vertical legendrian ruling curve on @xmath206 to a vertical legendrian ruling curve on @xmath207 . here ` vertical ' means ` in the direction of the @xmath138-fibers ' . note @xmath208 intersects the dividing curves on @xmath209 and @xmath210 @xmath211 and @xmath212 times respectively . assume @xmath213 . if @xmath214 , then there exists a bypass ( due to the imbalance ) , attached along a vertical legendrian curve of @xmath206 or @xmath207 . we transform @xmath177 via @xmath215 to use the twist number lemma . @xmath216 , and @xmath217 . the legendrian rulings will have slope @xmath218 and @xmath219 , and , therefore , we may increase the twisting number by 1 if the twisting number is @xmath220 . next , assume @xmath221 and there are no bypasses on the vertical annulus . then we may take @xmath208 to be standard , with vertical rulings , and parallel legendrian divides spanning from @xmath222 to @xmath223 . cutting along @xmath208 and rounding the corners , we obtain the torus boundary of @xmath224 ; if we identify this torus with @xmath201 in the same way as @xmath225 , then the boundary slope is @xmath226 . when @xmath227 , then the slope is @xmath228 , and any legendrian divide gives rise to an overtwisted disk this is because @xmath229 , which corresponds to a slope of @xmath228 on @xmath225 . when @xmath230 , then the slope is @xmath231 , which implies that on the @xmath232 , the twisting in the radial direction is almost @xmath233 . in particular , there exists a convex torus with slope @xmath157 inside @xmath88 , and hence a vertical legendrian curve with zero twisting , obtained as a legendrian divide of the convex torus . any vertical annulus taken from this vertical legendrian to @xmath234 ( or @xmath235 ) will give bypasses . we can now assume @xmath203 . the boundary slopes of @xmath236 and @xmath237 are @xmath228 and @xmath238 , respectively . again look at the vertical annulus @xmath208 spanning from @xmath234 to @xmath235 , with legendrian boundary . there are three possibilities : ( 1 ) there are no bypasses along @xmath107 ( on the @xmath234 side ) in this case , we can cut along the annulus as before , and get boundary component with boundary slope @xmath228 , contradicting tightness . ( 2 ) there is one bypass along @xmath107 cutting along the annulus again , we find that the boundary slope is @xmath239 . this means that the twisting of @xmath240 is large , and that we have a convex torus in standard form with legendrian divides of infinite slope as before . ( 3 ) there are two bypasses . in any case , there exist vertical legendrian curves with twisting number @xmath241 with respect to the framing from the fibers . since @xmath242 , we have bypasses for @xmath186 as well , and we can increase to @xmath202 using the twist number lemma . next , taking a vertical annulus from @xmath234 to one such vertical legendrian curve , we obtain two bypasses for @xmath234 and , similarly , we obtain four bypasses for @xmath235 . by attaching these two bypasses , we obtain a thickening @xmath204 of @xmath167 , @xmath168 , so that @xmath243 has two vertical dividing curves . in the section we use the structure of @xmath244 as a punctured torus bundle over @xmath138 to complete the proof of our main theorem . the strategy is as follows : first we use the bundle structure to increase @xmath245 to 0 by finding a bypass along the boundary of the punctured torus fiber . we then show how to increase @xmath245 to 1 by making the boundary of the punctured torus fiber legendrian with twist number 0 . when @xmath246 the corresponding neighborhood of @xmath247 almost contains an overtwisted disk . by increasing it a little further it does contain one . this will complete the proof of our main theorem . we now describe the fibration as a punctured torus bundle over @xmath138 . in the previous section , @xmath167 was the neighborhood of a legendrian curve @xmath169 with twisting number @xmath189 , and @xmath248 its thickening . write @xmath249 , where @xmath9 is a 3-holed sphere . let @xmath80 be an embedded arc on @xmath9 connecting @xmath250 to @xmath251 , @xmath252 an annulus connecting @xmath250 to @xmath251 , and @xmath253 a neighborhood of @xmath112 in @xmath254 . define @xmath255 , which is @xmath256 with a @xmath164 layer removed from the boundary . let @xmath257 and @xmath258 be meridional disks for @xmath251 and @xmath259 respectively . the slope of @xmath257 on @xmath260 is @xmath228 and the slope of @xmath258 on @xmath261 is @xmath262 thus we can take two copies of @xmath258 and three copies of @xmath257 and glue them together with six copies of @xmath263 to obtain a punctured torus @xmath66 in @xmath264 with boundary on @xmath265 ( see figure [ goodfiber ] . ) parallel copies of @xmath66 will fiber @xmath264 ( and @xmath244 ) as a punctured torus bundle over @xmath266 the slope of @xmath267 on @xmath268 is @xmath269 thus the slope on @xmath270 is 1 , so @xmath66 provides a seifert surface for @xmath271 we can show ( for example by using kirby calculus ) that @xmath272 represented in figure [ fig : surgery](a ) , is diffeomorphic to figure [ fig : surgery](b ) , and that @xmath273 is diffeomorphic to the complement of the right - handed trefoil knot in @xmath274 thus we may identify the monodromy of the punctured torus bundle as @xmath275 we begin by showing that either we can find a bypass for @xmath267 or arrange that the dividing curves on @xmath66 consist of exactly two parallel arcs . if there are no bypasses , then the dividing set must consist of two parallel arcs and an even number , say @xmath279 of closed parallel curves . consider @xmath280 $ ] with @xmath66 identified with @xmath281 here we are viewing @xmath264 as @xmath273 . let @xmath6 be a closed legendrian curve on @xmath66 parallel to the dividing curves . then consider @xmath282 $ ] which we may assume is convex with legendrian boundary . the dividing curves do not intersect @xmath283 , but they intersect @xmath284 at least @xmath285 times . thus we may find a bypass @xmath51 for @xmath286 the inner boundary @xmath287 of a neighborhood of @xmath288 is a convex torus with either a bypass for @xmath289 or two fewer dividing curves than @xmath290 repeating this argument @xmath85 times will result in a bypass for @xmath267 or a convex torus whose dividing set consist of exactly two parallel arcs . now suppose @xmath67 consists of two parallel arcs , since otherwise we are done . then @xmath291 consists of two arcs and @xmath292 consists of the image of these two arcs under the monodromy map for the bundle . let @xmath6 be a closed curve on @xmath293 parallel to the dividing curves , and @xmath294.$ ] we may arrange for @xmath295 to be legendrian and for @xmath296 to be convex . now the dividing curves on @xmath296 do not intersect @xmath283 but intersect @xmath284 at least two times . thus we have a bypass @xmath51 for the dividing curves on @xmath286 assume first that the intersection number is exactly two . then the annulus @xmath296 may be split into two annuli , one of which , call it @xmath297 intersects @xmath298 and contains @xmath51 , which is of degenerate type . the boundary of a small neighborhood of @xmath299 in @xmath300 is an annulus @xmath301 and has dividing curves as shown in figure [ fig : annulus ] . the boundary of @xmath301 sits on @xmath286 if we cut out the annulus in @xmath298 that cobounds a solid torus with @xmath302 glue in @xmath301 , and smooth corners , then the dividing curves on the new @xmath298 are shown in figure [ fig : annulus ] . if the intersection number is greater than two , then simply attach the bypass @xmath51 onto @xmath298 either the new @xmath298 has a bypass , in which case we are done , or we can take a new @xmath296 which has fewer ( but @xmath304 intersections ) . we continue until the intersection number becomes two . [ lem : twist ] we may increase @xmath245 to @xmath241 while keeping @xmath202 and @xmath305 moreover , @xmath234 may be further thickened to @xmath306 so that @xmath307 has dividing curves of slope @xmath277 since we have a bypass on @xmath267 we may apply the twist number lemma to increase the twist number of @xmath247 to @xmath308 so we have two vertical dividing curves on @xmath270 and on @xmath309 they have slope 0 . now repeating the argument in lemma [ increase ] we see that we can arrange @xmath202 and @xmath305 note the dividing curves on @xmath310 and @xmath311 have slope @xmath228 and 0 , respectively . thus taking a vertical annulus between @xmath312 and @xmath209 , we find a vertical bypass along @xmath313 with this bypass we can thicken @xmath234 to @xmath306 whose dividing curves have slope @xmath277 note if we had another bypass along @xmath267 we could increase @xmath245 to 1 and from here we could then find an overtwisted disk ( see below ) . however , we know of no direct way to prove this bypass exists . therefore we use the following strategy , which can be called as ` thinning before thickening ' . notice we have thickened @xmath235 so that @xmath246 ; we will now backtrack by having @xmath235 relinquish some of its thickness ( we peel off a toric annulus from @xmath235 and reattach to @xmath186 and @xmath234 ) , and then thicken again to obtain a contradiction . let @xmath317 be the meridional disk to @xmath167 for @xmath318 if we arrange that the legendrian rulings on @xmath200 are horizontal and the @xmath317 are convex , then @xmath319 and @xmath320 . the dividing sets divide @xmath257 into two regions , one positive and one negative , and @xmath258 into three regions without loss of generality we can assume that , two regions are positive and one is negative . note that the signs of these regions depend on an orientation on the disks . pick an orientation for the fibers of the seifert fibration , and the disks will be oriented so that their intersection with a fiber is positive . note we can write @xmath321 , where @xmath322 is a solid torus with convex boundary and dividing curves of slope @xmath239 ( on @xmath323 ) , @xmath103 $ ] , @xmath324 , and @xmath325 is convex with vertical dividing curves . we do this by stabilizing ( reducing the twist number ) @xmath247 with @xmath315 in @xmath326 in @xmath150 we can find a @xmath327 , say @xmath328 with dividing curves of slope @xmath219 ( which correspond to vertical dividing curves from the point of view of @xmath329 ) . by performing the correct stabilization we can arrange that on a convex annulus in @xmath330 $ ] of slope @xmath331 with legendrian boundary on @xmath332 and @xmath333 there is a negative bypass along the boundary component on @xmath334 we can use this bypass to thicken @xmath167 , @xmath42 , to @xmath204 so that @xmath335 have vertical slopes . using the relative euler class we can easily see that each meridional disk @xmath336 in @xmath248 has an extra positive region . specifically , if @xmath337 is the relative euler class on @xmath338 ( as defined in section [ section : convexity ] ) and @xmath339 and @xmath340 are the horizontal and vertical curves on @xmath341 then one may easily compute that @xmath342)= 1 $ ] and @xmath343)=0.$ ] thus @xmath344)=1 $ ] where @xmath93 is the boundary of the meridional disk in @xmath345 from this and equation [ eqn : formula ] , we can conclude that the dividing curves are as in figure [ anndivides ] ( a ) , and hence a convex meridional disk in @xmath251 will have one negative and two positive regions in the complement of the dividing curves . similarly , a convex meridional disk in @xmath250 will have one negative and three positive regions since a relative euler class argument will show its intersection with @xmath346 is shown in figure [ anndivides ] ( b ) we would now like to piece these meridional disks together to form a punctured torus fiber for @xmath348 , but to do this we first need to understand the complement of the singular fibers . recall all the boundary slopes of @xmath349 are infinite . take @xmath350 , which we assume is convex with legendrian boundary . all the boundary components of @xmath9 have exactly two half - elliptic points . we argue that if there is a @xmath95-compressible dividing arc ( as in ( b ) , ( c ) , ( d ) ) on @xmath9 , then @xmath1 is overtwisted . the @xmath95-compressible dividing arc implies the existence of a bypass ( of degenerate type ) along some @xmath351 . hence , there exists a layer @xmath352 with one boundary component @xmath351 and boundary slopes @xmath241 and @xmath157 . however , since there are vertical legendrian curves with twisting number 0 outside of @xmath353 , we obtain another layer @xmath354 , this time with boundary slopes @xmath157 and @xmath241 . therefore , @xmath355 has too much radial twisting , and is overtwisted . the only possible configuration without a @xmath95-compressible dividing arc is ( a ) . we cut @xmath347 along @xmath9 , round the edges , and examine the dividing curves on the boundary of the resulting genus 2 handlebody . we then cut along the meridional disks of the handlebody , which we may assume have legendrian boundary , and eventually obtain a 3-ball . since each meridional disk of the handlebody intersects the dividing set only twice , the configuration of dividing curves on the meridional disks is unique . therefore the initial configuration of dividing curves on @xmath9 uniquely determines the tight structure on @xmath347 . the lemma implies that the tight structure on @xmath347 is a translation - invariant tight structure on @xmath164 with infinite boundary slopes , with the standard neighborhood of a vertical legendrian curve with zero twisting removed . we view this @xmath164 ( minus @xmath88 ) as the region between @xmath359 and @xmath360 ( minus @xmath358 ) . we may think of the @xmath361-factor as being quite small , and then isotop one of the legendrian divides on @xmath359 to one of the legendrian divides on @xmath360 and finally identify small neighborhoods ( in the tori ) of these divides . we may then isotop @xmath362 , @xmath42 , away from these neighborhoods so that the meridional disk @xmath363 in @xmath204 has legendrian boundary . forming the fiber @xmath66 in the fibration of @xmath364 from three copies of @xmath257 and two copies of @xmath258 , we can arrange that @xmath267 is legendrian and the dividing curves on @xmath66 are as in figure [ goodfiber ] . thus there are six bypasses for @xmath303 we can use these to increase the twisting number of @xmath267 to 0 ( _ i.e. _ , @xmath267 will be a legendrian divide on some thickening of @xmath270 ) which corresponds to an increase of @xmath245 to 1 . thus the slope of the dividing curves on @xmath365 is @xmath366 . now repeat the argument in lemma [ increase ] take a vertical annulus from @xmath367 to @xmath368 , and start with @xmath369 small . since the denominator of @xmath366 is never equal to @xmath211 , we eventually arrive at @xmath305 this implies the existence of a vertical bypass for @xmath368 , with which we can increase the slope of the dividing curves on @xmath365 to @xmath370 . thus the legendrian divide on our thickened solid torus bounds a meridional disk in @xmath235 , so we have found an overtwisted disk . this completes the proof of the main theorem .[/INST] we exhibit a 3-manifold which admits no tight contact structure . </s>

heavy - ion collisions provide a possibility to study the properties of nuclear matter in conditions that are vastly different than reported in normal nuclei @xcite . considerable progress has been made recently in determining the equation of state of nuclear matter from heavy ion reaction data @xcite . a prominent role among available observables is played by the collective flow . much theoretical and experimental efforts have been made to the study of collective flow in hics @xcite . the elliptic flow has proven to be one of the most fruitful probes for extracting the eos and the dynamics of heavy - ion collisions . the parameter of elliptic flow is quantified by the second - order fourier coefficient @xcite from the azimuthal distribution of detected particles at midrapidity as : @xmath2 where @xmath3 is the azimuthal angle of emitted particle momentum relative to the x axis . positive values for @xmath4 @xmath5 @xmath6 reflect a preferential in - plane emission , whereas negative values of @xmath4 @xmath5 @xmath6 reflect a preferential out - of - plane emission . yu - ming zheng _ et al . , _ @xcite studied the proton elliptic flow in the collisions of @xmath7 at energies from 30 to 100 mev / nucleon . they showed that , with increasing incident energy , the elliptic flow shows a transition from positive to negative values . its magnitude was found to depend on both nuclear equation of state ( eos ) as well as on the nucleon - nucleon scattering cross - section . on the other hand , d. persram _ et al . , _ @xcite have shown , for the first time , the effect of parameter - free self - consistent calculation of nucleon - nucleon in - medium scattering cross - section implemented buu model on different flows . their results favored in - medium cross - section compared to free one . et al . , _ @xcite have investigated the elliptic flow in heavy - ion collisions at energies from several tens to several hundreds of mev / nucleon . they showed that , soft nuclear equation of state and incident energy dependent in - medium nucleon - nucleon cross - sections are required to describe the excitation function of the elliptic flow at intermediate energies . our study is performed within the framework of iqmd @xcite model where hadrons propagate with hamilton equations of motion : @xmath8 with @xmath9 the baryon - baryon potential @xmath10 , in the above relation , reads as : @xmath11\nonumber\\ & & + ~t_{3}\frac{exp(|\vec{r}^\prime-\vec{r}|/\mu)}{(|\vec{r}^\prime-\vec{r}|/\mu)}~+~\frac{z_{i}z_{j}e^{2}}{|\vec{r}^\prime -\vec{r}|}\nonumber\\ & & + t_{6}\frac{1}{\varrho_0}t_3^{i}t_3^{j}\delta(\vec{r_i}^\prime -\vec{r_j } ) . \label{s1}\end{aligned}\ ] ] here @xmath12 and @xmath13 denote the charges of @xmath14 and @xmath15 baryon , and @xmath16 , @xmath17 are their respective @xmath18 components ( i.e. 1/2 for protons and -1/2 for neutrons ) . meson potential consists of coulomb interaction only . the binary nucleon - nucleon collisions are included by employing the collision term of well known vuu - buu equation . during the propagation , two nucleons are supposed to suffer a binary collision if the distance between their centroids @xmath19 `` type '' denotes the ingoing collision partners ( n - n , n-@xmath20 , n-@xmath21 , .. ) . in addition , pauli blocking ( of the final state ) of baryons is taken into account by checking the phase space densities in the final states . for the present analysis , simulations are carried out for two sets of the reaction using soft equation of state . for the first case , the mass of the colliding nuclei is fixed to be 124 units and for the second set , the mass of the colliding nuclei is fixed to be 40 units . in other words , we study , the reactions of @xmath0 , where @xmath22 = ( @xmath23 , @xmath24 , @xmath25 , @xmath26 and @xmath27 ) , respectively . the second set corresponds to : @xmath28 , where @xmath29 = ( @xmath30 , @xmath31 , @xmath32 , @xmath33 and @xmath34 ) , respectively . the phase space generated by the iqmd model has been analyzed using the minimum spanning tree ( mst ) @xcite method . the elliptical flow is defined as the average difference between the square of x and y components of the particles transverse momentum . mathematically , it can be written as : @xmath35 where @xmath36 and @xmath37 are the x and y components of the momentum . the positive value of elliptical flow describes the eccentricity of an ellipse - like distribution and indicates in - plane enhancement of the particle emission . on the other hand , a negative value of @xmath38 shows the squeeze - out effects perpendicular to the reaction plane . obviously , zero value corresponds to an isotropic distribution . generally , for a meaningful understanding @xmath4 @xmath38 @xmath6 is extracted from the mid - rapidity region only . naturally , mid - rapidity region ( -0.1 @xmath39 @xmath40 @xmath39 0.1 ) corresponds to the collision ( participant ) zone and hence signifies compressed matter . on the other hand , @xmath40 @xmath41 0 corresponds to the spectator zone , ( @xmath40 @xmath4 -0.1 ) corresponds to target like ( tl ) matter and ( @xmath40 @xmath6 0.1 ) corresponds to projectile like ( pl ) matter . transverse momentum dependence of the elliptical flow , summed over the entire rapidity distribution , at @xmath42 = 0.5 for three different reactions at 50 ( left ) and 100 ( right ) mev / nucleon . ] transverse momentum dependence of the elliptical flow , summed over the entire rapidity distribution , at @xmath42 = 0.5 for three different reactions at 50 ( left ) and 100 ( right ) mev / nucleon . ] to study the effect of charge asymmetry on the elliptical flow as a function of @xmath4 @xmath43 @xmath6 , ( where @xmath4 @xmath43 @xmath6 is transverse momentum of particle and is given by @xmath44 ) . we display , final state elliptical flow in fig.1 and 2 for free particles ( a = 1 ) ( upper panel ) , lmf s ( 2 @xmath39 a @xmath39 4)(middle ) and imf s ( 5 @xmath39 a @xmath39 @xmath45/6 ) ( lower panel ) at an incident energy e = 50 mev / nucleon ( left ) and e = 100 mev / nucleon ( right ) for the reactions of @xmath0 , where m = 47 and 59 ( in fig.1 ) and @xmath28 , where n = 14 and 23 ( in fig.2 ) . here elliptical flow is summed over all rapidity bins . figs.1 and 2 reveal : + ( a ) gaussian shape is obtained for @xmath4 @xmath38 @xmath6 in all cases . note that the elliptical flow is integrated over the entire rapidity range . this gaussian shaped behavior is quite similar to the one reported by colona and di toro et al . , @xcite . + ( b ) peak of the gaussian shifts towards lower value of @xmath4 @xmath43 @xmath6 for the heavier fragments . this is because the free nucleons and lmf s feel the mean field directly , while heavy fragments have weaker sensitivity @xcite . + ( c ) the neutron rich systems @xmath46 and @xmath47 exhibit weaker squeeze - out flow compared to the neutron deficient reactions @xmath48 and @xmath49 . our findings are in agreement with zhang et al . , @xcite where a neutron rich system was found to exhibits weaker squeeze - out flow . transverse momentum dependence of the elliptical flow at e = 100 mev / nucleon for two different cross - sections for the reaction @xmath46 . ] same as fig.3 but for the reaction @xmath48 . ] same as fig.3 but for the reaction @xmath47 . ] same as fig.3 but for the reaction @xmath49 . ] to study the effect of isospin dependence of cross - section and charge asymmetry on the elliptical flow , we display in figs.3 - 6 , the transverse momentum dependence of elliptical flow for the reactions of @xmath46 , @xmath48 , @xmath47 and @xmath49 . we divided total elliptical flow into contributions from target - like ( tl ) ( left panels ) , mid - rapidity ( middle panels ) and projectile - like ( pl ) ( right panels ) particles at e = 100 mev / nucleon . the upper , middle and bottom panels represent the free nucleons , lmf s and imf s . these figures reveal following points : + ( a ) @xmath4 @xmath38 @xmath6 is sensitive to different nucleon - nucleon cross - sections . weaker squeeze - out flow is observed in the case of isospin independent cross - section . this happens because in the case of isospin dependent cross - section , neutron - proton cross - section is three times larger compared to neutron - neutron and proton - proton cross - section that will enhance binary collisions . these findings are in agreement with ref . + ( b ) comparison of figs . 3 @xmath50 4 and figs . 5 @xmath50 6 indicates significant dependence of @xmath4 @xmath38 @xmath6 on the charge asymmetry of colliding pairs . our findings are also supported by zhang et al . + ( c ) closer looks to these figures help us to understand the origin of these isospin effects . from the figures , it is clear that percentage change is maximum in the case of mid - rapidity region for both isospin dependent and isospin independent cross - section . indicating that isospin effects originates from mid - rapidity region . + variation of elliptical flow with energy for the reactions @xmath0 , where @xmath22 = ( @xmath23 , @xmath24 , @xmath25 , @xmath26 and @xmath27 ) . ] variation of elliptical flow with energy for the reactions @xmath28 , where @xmath29 = ( @xmath30 , @xmath31 , @xmath32 , @xmath33 and @xmath34 ) . ] in figs . 7 and 8 , we display the variation of excitation function of elliptical flow @xmath4 @xmath38 @xmath6 for free nucleons , lmf s and imf s for mid - rapidity region using same set of the reactions considered earlier . we note : + ( a ) the elliptical flow turns negative with beam energy . this is because spectators move faster after @xmath4 @xmath38 @xmath6 reaches a minimum value @xcite . the energy at which this behavior changes is found to decrease with the size of the fragment . this means that the flow of heavier fragments is larger than that of lmf s and free nucleons at all beam energies . these findings are in agreement with ref . + ( b ) there occurs a transition from in - plane emission to out - of - plane . this is due to the fact that the contribution of participant zone dominates the reaction in midrapidity region leading to the transition from in - plane to out - of - plane . in other words , participant zone is primarily responsible for the transition from in - plane to out - of - plane . the energy at which this transition observed is dubbed as transition energy @xmath51 . + transition energies ( @xmath51 in mev / nucleon ) for elliptical flow as a function of n / z . ] now to study the effect of charge asymmetry on the transition energy of free nucleons , lmf s and imf s , we show in fig.9 , the transition energy as a function of n / z for two sets of reaction . from both the figures , it is clear that transition energy remains almost constant with increase in the n / z of the system . + the energy dependence of elliptical flow for the reaction @xmath52 . ] to further strengthen our interpretation of the results of elliptical flow @xmath4 @xmath38 @xmath6 , we display in fig.10 a comparison of theoretical results of elliptical flow with experimental data extracted by the indra@xmath53(gsi+ganil ) collaboration @xcite . here simulations are performed for the reaction @xmath52 with @xmath54 reduced by 20@xmath55 . it is worth mentioning that the results with above choice of cross - section are in good agreement with the experimental data of ref . the choice of reduced cross - section has also been motivated by ref . @xcite as well as many previous studies @xcite . using the isospin dependent quantum molecular dynamics model , we have studied the effect of charge asymmetry and isospin dependent cross - section on different aspects of elliptical flow . here simulations have been carried out for @xmath0 , where m = ( 47 , 50 , 53 , 57 and 59 ) and @xmath1 , where n= ( 14 , 16 , 18 , 21 and 23 ) . our study shows that elliptical flow is observed to be strongly dependent on the isospin - dependent cross - section . the transition energy remains almost constant with increase in n / z of the system . the comparison with experimental data of indra@xmath53(gsi+ganil ) collaboration supports our findings . moreover , our results of @xmath56 will be of great use for the experimentalists working at scc500 at vecc kolkata ( india ) . + b. a. li , c. m. ko , and w. bauer , int . j. mod e * 7 * , 147(1998 ) . h. stocker and w. greiner , phys . rep . * 137 * , 277(1986 ) . j. lukasik , g. auger , m. l. begemann - blaich _ et al . b * 608 * , 223(2005 ) . s. voloshin and y. zhang , z. phys . c * 70 * , 665(1996 ) . yu - ming zheng , c. m. ko , bao - an li and bin zhang , phys . lett . * 83 * , 2534(1999 ) . d. persram and c. gale phys . c * 65 * , 064611(2002 ) . y. zhang and z. li , phys . c * 74 * , 014602(2006 ) . s. kumar , s. kumar and r. k. puri , phys . c * 81 * , 014611(2010 ) . v. kaur , s. kumar and r. k. puri , phys . b * 697 * , 512(2011 ) . c. hartnack _ et al . j. a * 1 * , 151(1998 ) . m. di toro , v. baran , m. colonna , g. ferini , t. gaitanos , v. greco , j. rizzo , h. h. wolter , nucl . phys . a * 787 * , 585 ( 2007 ) ; m. di toro , v. baran , m. colonna , v. greco , j. phys . g : nucl . part . phys . * 37 * , 083101(2010 ) ; m. di toro , int . j. modern physics e * 17 * , 1989(2008 ) . t. z. tan _ et al . , _ chin . phys . * 16 * , 2676(2007 ) . f. s. zhang , l. w. chen , w. f. li and z. y. zhu , eur . j. a * 9 * , 149(2000 ) . jian - ye liu , wen - jun guo , yong zhong xing and hang liu , nucl . a * 726 * , 123(2003 ) . a. andronic _ et al . , _ nucl . a * 679 * , 765(2001 ) ; ibid phys . b * 612 * , 173(2005 ) . h. y. zhang _ et al . , _ j. phys . g : nucl . part . * 28 * , 2397(2002 ) . j. lukasik , w. trautmann , for the indra and aladin collaborations , arxiv : 0708.2821v1 [ nucl - ex],2007 ; j. lukasik _ et al . , _ international workshop on multifragmentation and related topics , 4 - 7 nov . , iwm 2007 . s. gautam and a. d. sood , phys . rev . c. * 82 * , 014604(2010 ) . f. daffin and w. bauer , arxiv : nucl - th/9809024v1 .

using the isospin dependent quantum molecular dynamics model , we study the effect of charge asymmetry and isospin dependent cross - section on different aspects of elliptical flow . simulations have been carried out for the reactions of @xmath0 , where m = ( 47 , 50 , 53 , 57 and 59 ) and @xmath1 , where n= ( 14 , 16 , 18 , 21 and 23 ) . our study shows that elliptical flow depend strongly on the isospin of cross - section . the transition energy remains almost constant with increase in n / z of the system . a good agreement is obtained with experimental measurements . = 1.5

<s>[INST]heavy - ion collisions provide a possibility to study the properties of nuclear matter in conditions that are vastly different than reported in normal nuclei @xcite . considerable progress has been made recently in determining the equation of state of nuclear matter from heavy ion reaction data @xcite . a prominent role among available observables is played by the collective flow . much theoretical and experimental efforts have been made to the study of collective flow in hics @xcite . the elliptic flow has proven to be one of the most fruitful probes for extracting the eos and the dynamics of heavy - ion collisions . the parameter of elliptic flow is quantified by the second - order fourier coefficient @xcite from the azimuthal distribution of detected particles at midrapidity as : @xmath2 where @xmath3 is the azimuthal angle of emitted particle momentum relative to the x axis . positive values for @xmath4 @xmath5 @xmath6 reflect a preferential in - plane emission , whereas negative values of @xmath4 @xmath5 @xmath6 reflect a preferential out - of - plane emission . yu - ming zheng _ et al . , _ @xcite studied the proton elliptic flow in the collisions of @xmath7 at energies from 30 to 100 mev / nucleon . they showed that , with increasing incident energy , the elliptic flow shows a transition from positive to negative values . its magnitude was found to depend on both nuclear equation of state ( eos ) as well as on the nucleon - nucleon scattering cross - section . on the other hand , d. persram _ et al . , _ @xcite have shown , for the first time , the effect of parameter - free self - consistent calculation of nucleon - nucleon in - medium scattering cross - section implemented buu model on different flows . their results favored in - medium cross - section compared to free one . et al . , _ @xcite have investigated the elliptic flow in heavy - ion collisions at energies from several tens to several hundreds of mev / nucleon . they showed that , soft nuclear equation of state and incident energy dependent in - medium nucleon - nucleon cross - sections are required to describe the excitation function of the elliptic flow at intermediate energies . our study is performed within the framework of iqmd @xcite model where hadrons propagate with hamilton equations of motion : @xmath8 with @xmath9 the baryon - baryon potential @xmath10 , in the above relation , reads as : @xmath11\nonumber\\ & & + ~t_{3}\frac{exp(|\vec{r}^\prime-\vec{r}|/\mu)}{(|\vec{r}^\prime-\vec{r}|/\mu)}~+~\frac{z_{i}z_{j}e^{2}}{|\vec{r}^\prime -\vec{r}|}\nonumber\\ & & + t_{6}\frac{1}{\varrho_0}t_3^{i}t_3^{j}\delta(\vec{r_i}^\prime -\vec{r_j } ) . \label{s1}\end{aligned}\ ] ] here @xmath12 and @xmath13 denote the charges of @xmath14 and @xmath15 baryon , and @xmath16 , @xmath17 are their respective @xmath18 components ( i.e. 1/2 for protons and -1/2 for neutrons ) . meson potential consists of coulomb interaction only . the binary nucleon - nucleon collisions are included by employing the collision term of well known vuu - buu equation . during the propagation , two nucleons are supposed to suffer a binary collision if the distance between their centroids @xmath19 `` type '' denotes the ingoing collision partners ( n - n , n-@xmath20 , n-@xmath21 , .. ) . in addition , pauli blocking ( of the final state ) of baryons is taken into account by checking the phase space densities in the final states . for the present analysis , simulations are carried out for two sets of the reaction using soft equation of state . for the first case , the mass of the colliding nuclei is fixed to be 124 units and for the second set , the mass of the colliding nuclei is fixed to be 40 units . in other words , we study , the reactions of @xmath0 , where @xmath22 = ( @xmath23 , @xmath24 , @xmath25 , @xmath26 and @xmath27 ) , respectively . the second set corresponds to : @xmath28 , where @xmath29 = ( @xmath30 , @xmath31 , @xmath32 , @xmath33 and @xmath34 ) , respectively . the phase space generated by the iqmd model has been analyzed using the minimum spanning tree ( mst ) @xcite method . the elliptical flow is defined as the average difference between the square of x and y components of the particles transverse momentum . mathematically , it can be written as : @xmath35 where @xmath36 and @xmath37 are the x and y components of the momentum . the positive value of elliptical flow describes the eccentricity of an ellipse - like distribution and indicates in - plane enhancement of the particle emission . on the other hand , a negative value of @xmath38 shows the squeeze - out effects perpendicular to the reaction plane . obviously , zero value corresponds to an isotropic distribution . generally , for a meaningful understanding @xmath4 @xmath38 @xmath6 is extracted from the mid - rapidity region only . naturally , mid - rapidity region ( -0.1 @xmath39 @xmath40 @xmath39 0.1 ) corresponds to the collision ( participant ) zone and hence signifies compressed matter . on the other hand , @xmath40 @xmath41 0 corresponds to the spectator zone , ( @xmath40 @xmath4 -0.1 ) corresponds to target like ( tl ) matter and ( @xmath40 @xmath6 0.1 ) corresponds to projectile like ( pl ) matter . transverse momentum dependence of the elliptical flow , summed over the entire rapidity distribution , at @xmath42 = 0.5 for three different reactions at 50 ( left ) and 100 ( right ) mev / nucleon . ] transverse momentum dependence of the elliptical flow , summed over the entire rapidity distribution , at @xmath42 = 0.5 for three different reactions at 50 ( left ) and 100 ( right ) mev / nucleon . ] to study the effect of charge asymmetry on the elliptical flow as a function of @xmath4 @xmath43 @xmath6 , ( where @xmath4 @xmath43 @xmath6 is transverse momentum of particle and is given by @xmath44 ) . we display , final state elliptical flow in fig.1 and 2 for free particles ( a = 1 ) ( upper panel ) , lmf s ( 2 @xmath39 a @xmath39 4)(middle ) and imf s ( 5 @xmath39 a @xmath39 @xmath45/6 ) ( lower panel ) at an incident energy e = 50 mev / nucleon ( left ) and e = 100 mev / nucleon ( right ) for the reactions of @xmath0 , where m = 47 and 59 ( in fig.1 ) and @xmath28 , where n = 14 and 23 ( in fig.2 ) . here elliptical flow is summed over all rapidity bins . figs.1 and 2 reveal : + ( a ) gaussian shape is obtained for @xmath4 @xmath38 @xmath6 in all cases . note that the elliptical flow is integrated over the entire rapidity range . this gaussian shaped behavior is quite similar to the one reported by colona and di toro et al . , @xcite . + ( b ) peak of the gaussian shifts towards lower value of @xmath4 @xmath43 @xmath6 for the heavier fragments . this is because the free nucleons and lmf s feel the mean field directly , while heavy fragments have weaker sensitivity @xcite . + ( c ) the neutron rich systems @xmath46 and @xmath47 exhibit weaker squeeze - out flow compared to the neutron deficient reactions @xmath48 and @xmath49 . our findings are in agreement with zhang et al . , @xcite where a neutron rich system was found to exhibits weaker squeeze - out flow . transverse momentum dependence of the elliptical flow at e = 100 mev / nucleon for two different cross - sections for the reaction @xmath46 . ] same as fig.3 but for the reaction @xmath48 . ] same as fig.3 but for the reaction @xmath47 . ] same as fig.3 but for the reaction @xmath49 . ] to study the effect of isospin dependence of cross - section and charge asymmetry on the elliptical flow , we display in figs.3 - 6 , the transverse momentum dependence of elliptical flow for the reactions of @xmath46 , @xmath48 , @xmath47 and @xmath49 . we divided total elliptical flow into contributions from target - like ( tl ) ( left panels ) , mid - rapidity ( middle panels ) and projectile - like ( pl ) ( right panels ) particles at e = 100 mev / nucleon . the upper , middle and bottom panels represent the free nucleons , lmf s and imf s . these figures reveal following points : + ( a ) @xmath4 @xmath38 @xmath6 is sensitive to different nucleon - nucleon cross - sections . weaker squeeze - out flow is observed in the case of isospin independent cross - section . this happens because in the case of isospin dependent cross - section , neutron - proton cross - section is three times larger compared to neutron - neutron and proton - proton cross - section that will enhance binary collisions . these findings are in agreement with ref . + ( b ) comparison of figs . 3 @xmath50 4 and figs . 5 @xmath50 6 indicates significant dependence of @xmath4 @xmath38 @xmath6 on the charge asymmetry of colliding pairs . our findings are also supported by zhang et al . + ( c ) closer looks to these figures help us to understand the origin of these isospin effects . from the figures , it is clear that percentage change is maximum in the case of mid - rapidity region for both isospin dependent and isospin independent cross - section . indicating that isospin effects originates from mid - rapidity region . + variation of elliptical flow with energy for the reactions @xmath0 , where @xmath22 = ( @xmath23 , @xmath24 , @xmath25 , @xmath26 and @xmath27 ) . ] variation of elliptical flow with energy for the reactions @xmath28 , where @xmath29 = ( @xmath30 , @xmath31 , @xmath32 , @xmath33 and @xmath34 ) . ] in figs . 7 and 8 , we display the variation of excitation function of elliptical flow @xmath4 @xmath38 @xmath6 for free nucleons , lmf s and imf s for mid - rapidity region using same set of the reactions considered earlier . we note : + ( a ) the elliptical flow turns negative with beam energy . this is because spectators move faster after @xmath4 @xmath38 @xmath6 reaches a minimum value @xcite . the energy at which this behavior changes is found to decrease with the size of the fragment . this means that the flow of heavier fragments is larger than that of lmf s and free nucleons at all beam energies . these findings are in agreement with ref . + ( b ) there occurs a transition from in - plane emission to out - of - plane . this is due to the fact that the contribution of participant zone dominates the reaction in midrapidity region leading to the transition from in - plane to out - of - plane . in other words , participant zone is primarily responsible for the transition from in - plane to out - of - plane . the energy at which this transition observed is dubbed as transition energy @xmath51 . + transition energies ( @xmath51 in mev / nucleon ) for elliptical flow as a function of n / z . ] now to study the effect of charge asymmetry on the transition energy of free nucleons , lmf s and imf s , we show in fig.9 , the transition energy as a function of n / z for two sets of reaction . from both the figures , it is clear that transition energy remains almost constant with increase in the n / z of the system . + the energy dependence of elliptical flow for the reaction @xmath52 . ] to further strengthen our interpretation of the results of elliptical flow @xmath4 @xmath38 @xmath6 , we display in fig.10 a comparison of theoretical results of elliptical flow with experimental data extracted by the indra@xmath53(gsi+ganil ) collaboration @xcite . here simulations are performed for the reaction @xmath52 with @xmath54 reduced by 20@xmath55 . it is worth mentioning that the results with above choice of cross - section are in good agreement with the experimental data of ref . the choice of reduced cross - section has also been motivated by ref . @xcite as well as many previous studies @xcite . using the isospin dependent quantum molecular dynamics model , we have studied the effect of charge asymmetry and isospin dependent cross - section on different aspects of elliptical flow . here simulations have been carried out for @xmath0 , where m = ( 47 , 50 , 53 , 57 and 59 ) and @xmath1 , where n= ( 14 , 16 , 18 , 21 and 23 ) . our study shows that elliptical flow is observed to be strongly dependent on the isospin - dependent cross - section . the transition energy remains almost constant with increase in n / z of the system . the comparison with experimental data of indra@xmath53(gsi+ganil ) collaboration supports our findings . moreover , our results of @xmath56 will be of great use for the experimentalists working at scc500 at vecc kolkata ( india ) . + b. a. li , c. m. ko , and w. bauer , int . j. mod e * 7 * , 147(1998 ) . h. stocker and w. greiner , phys . rep . * 137 * , 277(1986 ) . j. lukasik , g. auger , m. l. begemann - blaich _ et al . b * 608 * , 223(2005 ) . s. voloshin and y. zhang , z. phys . c * 70 * , 665(1996 ) . yu - ming zheng , c. m. ko , bao - an li and bin zhang , phys . lett . * 83 * , 2534(1999 ) . d. persram and c. gale phys . c * 65 * , 064611(2002 ) . y. zhang and z. li , phys . c * 74 * , 014602(2006 ) . s. kumar , s. kumar and r. k. puri , phys . c * 81 * , 014611(2010 ) . v. kaur , s. kumar and r. k. puri , phys . b * 697 * , 512(2011 ) . c. hartnack _ et al . j. a * 1 * , 151(1998 ) . m. di toro , v. baran , m. colonna , g. ferini , t. gaitanos , v. greco , j. rizzo , h. h. wolter , nucl . phys . a * 787 * , 585 ( 2007 ) ; m. di toro , v. baran , m. colonna , v. greco , j. phys . g : nucl . part . phys . * 37 * , 083101(2010 ) ; m. di toro , int . j. modern physics e * 17 * , 1989(2008 ) . t. z. tan _ et al . , _ chin . phys . * 16 * , 2676(2007 ) . f. s. zhang , l. w. chen , w. f. li and z. y. zhu , eur . j. a * 9 * , 149(2000 ) . jian - ye liu , wen - jun guo , yong zhong xing and hang liu , nucl . a * 726 * , 123(2003 ) . a. andronic _ et al . , _ nucl . a * 679 * , 765(2001 ) ; ibid phys . b * 612 * , 173(2005 ) . h. y. zhang _ et al . , _ j. phys . g : nucl . part . * 28 * , 2397(2002 ) . j. lukasik , w. trautmann , for the indra and aladin collaborations , arxiv : 0708.2821v1 [ nucl - ex],2007 ; j. lukasik _ et al . , _ international workshop on multifragmentation and related topics , 4 - 7 nov . , iwm 2007 . s. gautam and a. d. sood , phys . rev . c. * 82 * , 014604(2010 ) . f. daffin and w. bauer , arxiv : nucl - th/9809024v1 .[/INST] using the isospin dependent quantum molecular dynamics model , we study the effect of charge asymmetry and isospin dependent cross - section on different aspects of elliptical flow . simulations have been carried out for the reactions of @xmath0 , where m = ( 47 , 50 , 53 , 57 and 59 ) and @xmath1 , where n= ( 14 , 16 , 18 , 21 and 23 ) . our study shows that elliptical flow depend strongly on the isospin of cross - section . the transition energy remains almost constant with increase in n / z of the system . a good agreement is obtained with experimental measurements . = 1.5 </s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Honest Services Restoration Act''. SEC. 2. AMENDMENT TO TITLE 18. (a) In General.--Chapter 63 of title 18, United States Code, is amended by inserting after section 1346 the following: ``Sec. 1346A. Definition of `scheme or artifice to defraud' ``(a) For purposes of this chapter, the term `scheme or artifice to defraud' also includes-- ``(1) a scheme or artifice by a public official to engage in undisclosed self-dealing; or ``(2) a scheme or artifice by officers and directors to engage in undisclosed private self-dealing. ``(b)(1) In subsection (a)(1)-- ``(A) the term `undisclosed self-dealing' means that-- ``(i) a public official performs an official act for the purpose, in whole or in part, of benefitting or furthering a financial interest of-- ``(I) the public official; ``(II) the public official's spouse or minor child; ``(III) a general partner of the public official; ``(IV) a business or organization in which the public official is serving as an employee, officer, director, trustee, or general partner; ``(V) an individual, business, or organization with whom the public official is negotiating for, or has any arrangement concerning, prospective employment or financial compensation; or ``(VI) a person, business, or organization from whom the public official has received a thing of value or a series of things of value, otherwise than as provided by law for the proper discharge of official duty, or by rule or regulation; and ``(ii) the public official knowingly falsifies, conceals, or covers up material information that is required to be disclosed regarding that financial interest by any Federal, State, or local statute, rule, regulation, or charter applicable to the public official, or knowingly fails to disclose material information regarding that financial interest in a manner that is required by any Federal, State, or local statute, rule, regulation, or charter applicable to the public official; ``(B) the term `public official' means an officer, employee, or elected or appointed representative, or person acting for or on behalf of the United States, a State, or subdivision of a State, or any department, agency, or branch thereof, in any official function, under or by authority of any such department agency or branch of Government; ``(C) the term `official act'-- ``(i) includes any act within the range of official duty, and any decision, recommendation, or action on any question, matter, cause, suit, proceeding, or controversy, which may at any time be pending, or which may by law be brought before any public official, in such public official's official capacity or in such official's place of trust or profit; ``(ii) can be a single act, more than one act, or a course of conduct; and ``(iii) includes a decision or recommendation that the Government should not take action; and ``(D) the term `State' includes a State of the United States, the District of Columbia, and any commonwealth, territory, or possession of the United States. ``(2) In subsection (a)(2)-- ``(A) the term `undisclosed private self-dealing' means that-- ``(i) an officer or director performs an act which causes or is intended to cause harm to the officer's or director's employer, and which is undertaken in whole or in part to benefit or further by an actual or intended value of $5,000 or more a financial interest of-- ``(I) the officer or director; ``(II) the officer or director's spouse or minor child; ``(III) a general partner of the officer or director; ``(IV) another business or organization in which the public official is serving as an employee, officer, director, trustee, or general partner; or ``(V) an individual, business, or organization with whom the officer or director is negotiating for, or has any arrangement concerning, prospective employment or financial compensation; and ``(ii) the officer or director knowingly falsifies, conceals, or covers up material information that is required to be disclosed regarding that financial interest by any Federal, State, or local statute, rule, regulation, or charter applicable to the officer or director, or knowingly fails to disclose material information regarding that financial interest in a manner that is required by any Federal, State, or local statute, rule, regulation, or charter applicable to the officer or director; ``(B) the term `employer' includes publicly traded corporations, and private charities under section 501(c)(3) of the Internal Revenue Code of 1986; and ``(C) the term `act' includes a decision or recommendation to take, or not to take action, and can be a single act, more than one act, or a course of conduct.''. (b) Chapter Analysis.--The chapter analysis for chapter 63 of title 18, United States Code, is amended by inserting after the item for section 1346 the following: ``Sec. 1346A. Definition of `scheme or artifice to defraud'.''.

Honest Services Restoration Act - Amends the federal criminal code to expand the definition of "scheme or artifice to defraud," for purposes of fraud offenses, to include: (1) a scheme or artifice by a public official to engage in undisclosed self-dealing; or (2) a scheme or artifice by officers and directors to engage in undisclosed private self-dealing. Defines "undisclosed self-dealing" to mean: (1) performing an official act to benefit or further a financial interest of the public official, a spouse or minor child, a general partner, a business or organization in which the public official is serving as an employee, officer, director, trustee, or general partner, or an individual, business, or organization with whom the public official is negotiating for, or has any arrangement concerning, prospective employment or financial compensation; and (2) knowingly falsifying, concealing, covering up, or failing to disclose material information regarding a financial interest as required by law. Defines "undisclosed private self-dealing" to mean: (1) performing an act which causes or is intended to cause harm to the employer of the officer or director and which is undertaken to benefit or further by an actual or intended value of $5,000 or more a financial interest of the officer or director, a spouse or minor child, a general partner, another business or organization in which the officer or director is serving as an employee, officer, director, trustee, or general partner, or an individual, business, or organization with whom the officer or director is negotiating for, or has any arrangement concerning, prospective employment or financial compensation; and (2) knowingly falsifying, concealing, covering up, or failing to disclose material information regarding a financial interest as required by law.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Honest Services Restoration Act''. SEC. 2. AMENDMENT TO TITLE 18. (a) In General.--Chapter 63 of title 18, United States Code, is amended by inserting after section 1346 the following: ``Sec. 1346A. Definition of `scheme or artifice to defraud' ``(a) For purposes of this chapter, the term `scheme or artifice to defraud' also includes-- ``(1) a scheme or artifice by a public official to engage in undisclosed self-dealing; or ``(2) a scheme or artifice by officers and directors to engage in undisclosed private self-dealing. ``(b)(1) In subsection (a)(1)-- ``(A) the term `undisclosed self-dealing' means that-- ``(i) a public official performs an official act for the purpose, in whole or in part, of benefitting or furthering a financial interest of-- ``(I) the public official; ``(II) the public official's spouse or minor child; ``(III) a general partner of the public official; ``(IV) a business or organization in which the public official is serving as an employee, officer, director, trustee, or general partner; ``(V) an individual, business, or organization with whom the public official is negotiating for, or has any arrangement concerning, prospective employment or financial compensation; or ``(VI) a person, business, or organization from whom the public official has received a thing of value or a series of things of value, otherwise than as provided by law for the proper discharge of official duty, or by rule or regulation; and ``(ii) the public official knowingly falsifies, conceals, or covers up material information that is required to be disclosed regarding that financial interest by any Federal, State, or local statute, rule, regulation, or charter applicable to the public official, or knowingly fails to disclose material information regarding that financial interest in a manner that is required by any Federal, State, or local statute, rule, regulation, or charter applicable to the public official; ``(B) the term `public official' means an officer, employee, or elected or appointed representative, or person acting for or on behalf of the United States, a State, or subdivision of a State, or any department, agency, or branch thereof, in any official function, under or by authority of any such department agency or branch of Government; ``(C) the term `official act'-- ``(i) includes any act within the range of official duty, and any decision, recommendation, or action on any question, matter, cause, suit, proceeding, or controversy, which may at any time be pending, or which may by law be brought before any public official, in such public official's official capacity or in such official's place of trust or profit; ``(ii) can be a single act, more than one act, or a course of conduct; and ``(iii) includes a decision or recommendation that the Government should not take action; and ``(D) the term `State' includes a State of the United States, the District of Columbia, and any commonwealth, territory, or possession of the United States. ``(2) In subsection (a)(2)-- ``(A) the term `undisclosed private self-dealing' means that-- ``(i) an officer or director performs an act which causes or is intended to cause harm to the officer's or director's employer, and which is undertaken in whole or in part to benefit or further by an actual or intended value of $5,000 or more a financial interest of-- ``(I) the officer or director; ``(II) the officer or director's spouse or minor child; ``(III) a general partner of the officer or director; ``(IV) another business or organization in which the public official is serving as an employee, officer, director, trustee, or general partner; or ``(V) an individual, business, or organization with whom the officer or director is negotiating for, or has any arrangement concerning, prospective employment or financial compensation; and ``(ii) the officer or director knowingly falsifies, conceals, or covers up material information that is required to be disclosed regarding that financial interest by any Federal, State, or local statute, rule, regulation, or charter applicable to the officer or director, or knowingly fails to disclose material information regarding that financial interest in a manner that is required by any Federal, State, or local statute, rule, regulation, or charter applicable to the officer or director; ``(B) the term `employer' includes publicly traded corporations, and private charities under section 501(c)(3) of the Internal Revenue Code of 1986; and ``(C) the term `act' includes a decision or recommendation to take, or not to take action, and can be a single act, more than one act, or a course of conduct.''. (b) Chapter Analysis.--The chapter analysis for chapter 63 of title 18, United States Code, is amended by inserting after the item for section 1346 the following: ``Sec. 1346A. Definition of `scheme or artifice to defraud'.''.[/INST]Honest Services Restoration Act - Amends the federal criminal code to expand the definition of "scheme or artifice to defraud," for purposes of fraud offenses, to include: (1) a scheme or artifice by a public official to engage in undisclosed self-dealing; or (2) a scheme or artifice by officers and directors to engage in undisclosed private self-dealing. Defines "undisclosed self-dealing" to mean: (1) performing an official act to benefit or further a financial interest of the public official, a spouse or minor child, a general partner, a business or organization in which the public official is serving as an employee, officer, director, trustee, or general partner, or an individual, business, or organization with whom the public official is negotiating for, or has any arrangement concerning, prospective employment or financial compensation; and (2) knowingly falsifying, concealing, covering up, or failing to disclose material information regarding a financial interest as required by law. Defines "undisclosed private self-dealing" to mean: (1) performing an act which causes or is intended to cause harm to the employer of the officer or director and which is undertaken to benefit or further by an actual or intended value of $5,000 or more a financial interest of the officer or director, a spouse or minor child, a general partner, another business or organization in which the officer or director is serving as an employee, officer, director, trustee, or general partner, or an individual, business, or organization with whom the officer or director is negotiating for, or has any arrangement concerning, prospective employment or financial compensation; and (2) knowingly falsifying, concealing, covering up, or failing to disclose material information regarding a financial interest as required by law.</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Border Improvement and Immigration Act of 1999''. SEC. 2. AMENDMENT OF THE ILLEGAL IMMIGRATION REFORM AND IMMIGRANT RESPONSIBILITY ACT OF 1996. Section 110(a) of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 (8 U.S.C. 1221 note) is amended to read as follows: ``(a) System.-- ``(1) In general.--Subject to paragraph (3), not later than October 15, 1998, the Attorney General shall develop an automated entry and exit control system at air ports-of-entry that will-- ``(A) collect a record of departure for every alien departing the United States and match the record of departure with the record of the alien's arrival in the United States; and ``(B) enable the Attorney General to identify, through on-line searching procedures, lawfully admitted nonimmigrants who remain in the United States beyond the period authorized by the Attorney General. ``(2) Implementation.--The Attorney General shall fully implement the system developed under paragraph (1) at all air ports-of-entry into the United States not later than October 1, 2001. The Attorney General may not implement the system at any land border or seaport. ``(3) Exception.--The system under paragraphs (1) and (2) shall not collect a record of arrival or departure for any alien for whom the documentary requirements in section 212(a)(7)(B) of the Immigration and Nationality Act have been waived by the Attorney General and the Secretary of State under section 212(d)(4)(B) of the Immigration and Nationality Act.''. SEC. 3. REPORT ON AUTOMATED ENTRY-EXIT CONTROL SYSTEM. (a) Requirement.--Not later than 1 year after the date of enactment of this Act, the Attorney General shall submit a report to the Committees on the Judiciary of the Senate and the House of Representatives on the feasibility of developing and implementing an automated entry-exit control system that would collect a record of departure for every alien departing the United States and match the record of departure with the record of the alien's arrival in the United States, including departures and arrivals at the land borders and seaports of the United States. (b) Contents of Report.--Such report shall-- (1) assess the costs and feasibility of various means of operating such an automated entry-exit control system, including exploring-- (A) how, if the automated entry-exit control system were limited to certain aliens arriving at airports, departure records of those aliens could be collected when they depart through a land border or seaport; and (B) the feasibility of the Attorney General, in consultation with the Secretary of State, negotiating reciprocal agreements with the governments of contiguous countries to collect such information on behalf of the United States and share it in an acceptable automated format; (2) consider the various means of developing such a system, including the use of pilot projects if appropriate, and assess which means would be most appropriate in which geographical regions; (3) evaluate how such a system could be implemented without increasing border traffic congestion and border crossing delays and, if any such system would increase border crossing delays, evaluate to what extent such congestion or delays would increase; and (4) estimate the length of time that would be required for any such system to be developed and implemented. SEC. 4. INCREASED RESOURCES FOR BORDER CONTROL AND ENFORCEMENT. (a) Increased Number of INS Inspectors at the Land Borders.--The Attorney General in each of fiscal years 2000, 2001, and 2002 shall increase by not less than 300 the number of full-time immigration inspectors assigned to active duty at the land borders of the United States by the Immigration and Naturalization Service, above the number of such positions for which funds were made available for the preceding fiscal year. The inspectors added under the preceding sentence in each fiscal year shall be assigned equally to the northern and southern borders of the United States. (b) Increased Number of Customs Inspectors at the Land Borders.-- The Secretary of the Treasury in each of fiscal years 2000, 2001, and 2002 shall increase by not less than 150 the number of full-time inspectors assigned to active duty at the land borders of the United States by the Customs Service, above the number of such positions for which funds were made available for the preceding fiscal year. The inspectors added under the preceding sentence in each fiscal year shall be assigned equally to the northern and southern borders of the United States.

Border Improvement and Immigration Act of 1999 - Amends the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 with respect to the automated entry-exit control system to exempt from required recordkeeping: (1) land border and seaport crossings; and (2) aliens for whom certain documentation requirements have been waived by the Attorney General or the Secretary of State. Requires airport implementation of such system by a specified date. Requires the Attorney General to report on the feasibility of implementing an automated entry-exit control system that would include land border and seaport arrivals and departures. Provides for increased numbers of full-time Immigration and Naturalization and Customs inspectors at U.S. land borders, with such inspectors to be equally assigned to the northern and southern borders.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Border Improvement and Immigration Act of 1999''. SEC. 2. AMENDMENT OF THE ILLEGAL IMMIGRATION REFORM AND IMMIGRANT RESPONSIBILITY ACT OF 1996. Section 110(a) of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 (8 U.S.C. 1221 note) is amended to read as follows: ``(a) System.-- ``(1) In general.--Subject to paragraph (3), not later than October 15, 1998, the Attorney General shall develop an automated entry and exit control system at air ports-of-entry that will-- ``(A) collect a record of departure for every alien departing the United States and match the record of departure with the record of the alien's arrival in the United States; and ``(B) enable the Attorney General to identify, through on-line searching procedures, lawfully admitted nonimmigrants who remain in the United States beyond the period authorized by the Attorney General. ``(2) Implementation.--The Attorney General shall fully implement the system developed under paragraph (1) at all air ports-of-entry into the United States not later than October 1, 2001. The Attorney General may not implement the system at any land border or seaport. ``(3) Exception.--The system under paragraphs (1) and (2) shall not collect a record of arrival or departure for any alien for whom the documentary requirements in section 212(a)(7)(B) of the Immigration and Nationality Act have been waived by the Attorney General and the Secretary of State under section 212(d)(4)(B) of the Immigration and Nationality Act.''. SEC. 3. REPORT ON AUTOMATED ENTRY-EXIT CONTROL SYSTEM. (a) Requirement.--Not later than 1 year after the date of enactment of this Act, the Attorney General shall submit a report to the Committees on the Judiciary of the Senate and the House of Representatives on the feasibility of developing and implementing an automated entry-exit control system that would collect a record of departure for every alien departing the United States and match the record of departure with the record of the alien's arrival in the United States, including departures and arrivals at the land borders and seaports of the United States. (b) Contents of Report.--Such report shall-- (1) assess the costs and feasibility of various means of operating such an automated entry-exit control system, including exploring-- (A) how, if the automated entry-exit control system were limited to certain aliens arriving at airports, departure records of those aliens could be collected when they depart through a land border or seaport; and (B) the feasibility of the Attorney General, in consultation with the Secretary of State, negotiating reciprocal agreements with the governments of contiguous countries to collect such information on behalf of the United States and share it in an acceptable automated format; (2) consider the various means of developing such a system, including the use of pilot projects if appropriate, and assess which means would be most appropriate in which geographical regions; (3) evaluate how such a system could be implemented without increasing border traffic congestion and border crossing delays and, if any such system would increase border crossing delays, evaluate to what extent such congestion or delays would increase; and (4) estimate the length of time that would be required for any such system to be developed and implemented. SEC. 4. INCREASED RESOURCES FOR BORDER CONTROL AND ENFORCEMENT. (a) Increased Number of INS Inspectors at the Land Borders.--The Attorney General in each of fiscal years 2000, 2001, and 2002 shall increase by not less than 300 the number of full-time immigration inspectors assigned to active duty at the land borders of the United States by the Immigration and Naturalization Service, above the number of such positions for which funds were made available for the preceding fiscal year. The inspectors added under the preceding sentence in each fiscal year shall be assigned equally to the northern and southern borders of the United States. (b) Increased Number of Customs Inspectors at the Land Borders.-- The Secretary of the Treasury in each of fiscal years 2000, 2001, and 2002 shall increase by not less than 150 the number of full-time inspectors assigned to active duty at the land borders of the United States by the Customs Service, above the number of such positions for which funds were made available for the preceding fiscal year. The inspectors added under the preceding sentence in each fiscal year shall be assigned equally to the northern and southern borders of the United States.[/INST]Border Improvement and Immigration Act of 1999 - Amends the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 with respect to the automated entry-exit control system to exempt from required recordkeeping: (1) land border and seaport crossings; and (2) aliens for whom certain documentation requirements have been waived by the Attorney General or the Secretary of State. Requires airport implementation of such system by a specified date. Requires the Attorney General to report on the feasibility of implementing an automated entry-exit control system that would include land border and seaport arrivals and departures. Provides for increased numbers of full-time Immigration and Naturalization and Customs inspectors at U.S. land borders, with such inspectors to be equally assigned to the northern and southern borders.</s>

despite major advances in pancreatic surgery , pancreatic fistula ( pf ) continues to be a common complication after pancreaticoduodenectomy ( pd ) occurring in 914% of patients even at high volume centers [ 110 ] . classical risk factors associated with pf have been described in the literature and include the following : patient demographics , pancreatic gland texture , pancreatic duct size , pathology of periampullary lesion , anastomotic technique , and surgeon volume [ 1120 ] . this complication with pd continues to occur despite an acknowledged improvement in other types of postoperative complications and declining mortality rates in most large surgical series . as most surgeons realize , the technical challenges of sewing the pancreas to the intestinal tract are formidable . despite these difficulties , if substantial progress in reducing the rate of pf is to be made , improved understanding of the risk factors which predispose to fistula formation seems essential . identifying which glands in which patients are at high risk for a leak can trigger modifications in surgical technique , drainage , and postoperative care to minimize fistula formation . in this study we asked the following questions : first , what preoperative and perioperative factors might predict pf following pancreaticoduodenectomy ? second , what is the effect of pf on outcomes following pancreaticoduodenectomy ? to answer these questions , we analyzed our experience with pd at a high - volume pancreatic referral center and then examined the effect of these variables on the incidence of pf and the clinical outcomes in this group of patients . this is a retrospective review of a case series of consecutive patients who underwent pancreaticoduodenectomy for a broad range of periampullary and pancreatic pathologies between january 1980 and june 2002 at indiana university medical center , a tertiary care academic training hospital in indianapolis , indiana . only patients who had pancreaticoduodenectomy with a remnant , viable pancreatic tail were included for analysis . patients who underwent total pancreatectomy due to positive resection margins or those who had undergone previous distal pancreatic resections prior to their pancreaticoduodenectomy were excluded from this study . pancreatic fistula ( pf ) was defined during the broad range of years in this experience by several definitions . from 1980 to 1985 , a pf was defined as > 10 ml of amylase - rich fluid per day from a surgically placed drain or through a cutaneous site ( around a penrose drain ) after postoperative day 8 and lasting for at least 8 days . from 19852002 our definition was > 50 ml / day of amylase rich fluid after postoperative day 11 and lasting for at least 11 days . since 2005 at our institution , we have used the international study group for pancreatic fistula ( isgpf ) guidelines defining pancreatic fistula as any measurable volume of fluid on or after postoperative day 3 with amylase content greater than 3 times the serum amylase activity ( 21 ) . based on a careful review of the patients medical records during their hospital treatment and postoperative clinical follow - up , pancreatic fistula grades a , b , or c were assigned to each fistula identified as defined in the isgpf guidelines ( see table 1 ) . data were collected and reported in strict compliance with patient confidentiality guidelines put forth by the indiana university - purdue university indianapolis institutional review board . for preoperative variables twelve patient symptoms , physical signs , and associated conditions were included in the database including the following : abdominal pain , back pain , nausea / vomiting , diarrhea , abdominal tenderness , jaundice , diabetes , pancreatitis , abdominal mass , organomegaly , hemepositive stools , and weight loss . the diagnosis of jaundice was based on the presence of scleral icterus on physical examination . the presence of new onset diabetes mellitus was defined as the existence of glucose intolerance necessitating diet modification , oral hyperglycemic drug , or insulin supplementation within two years of the diagnosis of a periampullary pathologic disorder requiring operation . the diagnosis of diarrhea was made if patients reported three or more bowel movements per day or if the total volume of their movements in a day was 0.5 liters or greater . weight loss was quantified by patient history at the time of the preoperative visit . nine preoperative serum chemistries ( total bilirubin , alkaline phosphatase , sgot , total protein , albumin , amylase , glucose , calcium and phosphorous ) , five hematologic parameters ( hematocrit , hemoglobin , white blood cell count , prothrombin time , and partial thromboplastin time ) , and three serum tumor marker values ( cea , ca-19 - 9 , and ca-125 ) were obtained from routine blood draws either in the preoperative clinic or during a hospitalization close to the time of operation . eleven perioperative variables including pre - operative biliary stenting ( endoscopic or percutaneous transhepatic ) , pre - operative transfusion , pre - operative total parenteral nutrition ( tpn ) , pre - operative bowel preparation , estimated intra - operative blood loss ( ml ) , intra- and post - operative transfusions , operative time ( minutes ) , type of resection ( standard versus pylorus preservation ) , type of pancreaticojejunostomy ( invagination or end - to - side duct to mucosa ) , type of intraperitoneal drains used ( penrose or closed suction jackson - pratt drains ) , and gastrostomy tube placement were identified from the patient medical records , anesthesiologist 's records , and the operative reports . all specimens were reviewed by the staff pathologist at indiana university medical center with the majority of specimens also undergoing a secondary review by a dedicated pancreatic pathologist . histopathologic diagnosis , tumor size , tumor differentiation ( well , moderate , poor , none ) , lymph node status ( positive , negative ) , and surgical margin status ( positive , negative ) were routinely reported . margins analyzed included the common bile duct , pancreatic neck , and duodenum or stomach . retroperitoneal ( uncinate ) soft tissue margins were inconsistently analyzed early in this series ( 19802002 ) , but since 2002 , at our facility , standardized retroperitoneal margin assessment and analysis have been carried out based on ajcc guidelines ( 37 ) . clinical outcomes variables that were assessed included the following : in - hospital mortality , overall complications , and specific complications such as cardiopulmonary , delayed gastric emptying ( dge ) , sepsis , wound infection , intra - abdominal abscess , hemorrhage , and hospital length of stay ( los ) . delayed gastric emptying was defined in this cohort as the inability to take a regular diet after postoperative day no . 10 . survival was determined from the most recent encounter at indiana university hospital and was cross - referenced with the clarian cancer registry database and the social security database . twelve surgeons operated on patients included in this study who underwent either pylorus preserving or classic ( hemigastrectomy ) pancreaticoduodenectomy . reconstruction was undertaken with an isoperistaltic limb of jejunum in retrocolic fashion and anastomosed with an end - to - side pancreaticojejunostomy , followed by an end - to - side choledochojejunostomy and an ( antecolic or retrocolic ) end - to - side duodenojejunostomy or gastrojejunostomy . the pancreaticojejunostomy was performed using a duct - to - mucosa anastomosis ( n = 453 ) or , alternatively , an invaginated anastomosis ( n = 52 ) based on surgeon preference . only one surgeon used this technique predominately , accounting for 63% of their total pd . during this period at our institution , the pancreaticojejunostomy and choledochojejunostomy were drained routinely with penrose drains to gravity or closed suction drains . finally , some patients in this series underwent elective gastrostomy for postoperative decompression and alimentation . the association of categorical factors with survival was assessed using the kaplan - meier method ( km ) and was tested using the log - rank test . the association of continuous variables with survival was analyzed using a cox 's proportional hazards regression model and tested via the wald test . analyses were performed with a forward stepwise logistic regression model selection procedure where the probability of inclusion of a factor in the model was set at 20% and the probability of removal factor from the model was 20% . statistical significance was set at p .05 . the mean age was the same in patients with pf ( 58 years ; range 3079 ) compared to those without pf ( 58 years ; range 1593 ) . sixty - five patients underwent pancreaticoduodenectomy in the 1980s with the remainder being performed from 1990 and 2000 . the incidence of pf as a function of time by decade ( 1980 's = 9% ; 1990 's = 6% ; 2000 's = 10% ) or by year ( p = ns ) did not change significantly over the course of the study period . pancreatic fistula was more common in males , with this difference approaching statistical significance in univariate analysis , ( p = .06 ) . of the twelve preoperative patient symptoms tracked , none were associated with a significant difference in the rate of fistula formation ( data not shown ) . notably , a preoperative diagnosis of diabetes was present in a greater proportion of patients who did not have pf ; however , this result was not statistically significant . only serum glucose showed a significant association ( p = .04 ) with pf formation . serum glucose tended to be higher in patients who did not have a pf corroborating the trend in diabetes incidence previously noted . preoperative biliary stenting was done in 211 patients , 68 of whom had percutaneous transhepatic biliary stenting , and 143 had endoscopic stenting . preoperative biliary stenting ( combined percutaneous and endoscopic groups ) showed no significant difference in pf rates when compared to patients who were not preoperatively stented ( 9% stented group ( 20/211 ) versus 8% without stenting ( 26/299 ) ) . when subclassified into percutaneous transhepatic or endoscopic stenting however , a significantly higher incidence of pf was found in the percutaneous transhepatic stent group , 16% ( 11/68 ) compared to endoscopic stent group 6% ( 9/143 ) ( p = .04 ) . information about preoperative mechanical bowel preparation was not tracked in the latter half of our series ; however , among patients in whom preoperative mechanical bowel preparation status was known , a significantly higher incidence of pf was identified in patients who did not undergo mechanical bowel preparation ( 19% ( 6/31 ) versus 6% ( 14/226 ) , p < .02 ) implying that mechanical bowel preparation may be protective against pf . median operative time , however , was comparatively longer in the pf group ( 7 hours versus 5 hours , p < .001 ) . pylorus preserving pancreaticoduodenectomy was performed in 259 patients ( 51% ) and classic pancreaticoduodenectomy was performed in 251 patients ( 49% ) . the incidence of pf was not significantly different according to operation performed ( 11% , ( 28/259 ) pppd versus 7% ( 18/251 ) classic ) . in general , two types of pancreaticojejunostomy reconstruction were performed . a duct - to - mucosa anastomosis was performed in 453 patients , and an invaginated anastomosis , 3 underwent peustow reconstruction of the remnant , and in 2 , the reconstruction was unclear based upon operative records . there was a more than 3x higher incidence of pf in invaginated anastomoses ( 23% ) when compared to duct - to mucosa ( 7% ) , p < .001 . two types of drainage were employed over the course of these operations , closed suction drainage to a bulb suction device usually of the jackson - pratt type , and passive / gravity drainage with a penrose drain . closed suction drainage was used in 269 patients ( 53% ) and passive drainage with a penrose drain was used in 241 patients ( 47% ) with both techniques used continuously throughout this study . there was a significantly higher incidence of pf in patients who underwent closed suction drainage ( 14% ) compared to passive penrose drainage ( 3% ) , p < .001 . placement of a gastrostomy tube was done in 74 patients and was not associated with a comparatively different pf rate . the development of a pf was much more common in patients with the diagnosis of duodenal ( 15% ) or ampullary adenocarcinoma ( 17% ) ( p = .01 and .06 , resp . ) . alternatively , patients with a diagnosis of pancreatitis were less likely to develop a pf ( p = .02 ) . characteristics of the tumor pathology in patients with periampullary adenocarcinoma are provided in table 4 . size of pancreatic lesion measured in longest diameter , tumor differentiation , surgical margin status , and lymph node status were assessed . there was no statistically significant difference in any of these variables and the incidence of pf formation . there was a 4% mortality rate in patients who did not have pf and no mortality in patients who had a pf , a difference that was not statistically significant . there were no differences in rate of complications between patients who had a pf when compared to those who did not ; however , the total number of complications ( number of complications per patient ) was greater in patients who developed a pf . in addition , the type of complications varied according to whether or not a pf was present . the incidence of sepsis ( p < .001 ) , wound infection ( p < .001 ) , and intra - abdominal abscess ( p < the 26% reoperation rate for patients with pf was significantly higher than the 0.4% rate in patients without pf . of the twelve reoperations done in the pf group , eleven were done for complications of the pf and only one was done for a persistent fistula which lasted for greater than 4 months . six reoperations were done prior to the diagnosis of pf for sepsis or a visceral pseudoaneurysm , and six were done in patients following the diagnosis of pf for complications including the following : wound dehiscence ( 1 ) , poor fistula drainage with sepsis ( 3 ) , breakdown of the hepaticojejunostomy ( 1 ) , and persistent fistula > 4 months ( 1 ) . the diagnosis of pf was made on average on postoperative day 8 and these patients experienced longer lengths of hospital stay . the median length of stay in the pf group was 25 days , whereas it was only 12 days in the no pf group ( p < .001 ) . based upon international study group for pancreatic fistula ( isgpf ) grading guidelines , this series included 10 grade a fistulas , 23 grade b fistulas , and 13 grade c fistulas . forty - five of 46 pf ( 98% ) closed without reoperation with a mean time to closure of 34 days ( range 393 days ) . twenty - three patients ( all grade 13 grade c fistulas and 10 grade b fistulas ) were treated with antibiotics . ten patients ( 5 grade c and 5 grade b fistulas ) were treated with octreotide . this timing of closure was not significantly different with / without octreotide treatment ( 39 5 versus 25 5 ) or with / without antibiotic treatment ( 36 5 versus 29 6 ) . thirty - six patients required tpn for an average of 32 days ( range 590 days ) . time to closure was not affected by nutrition route ( enteral versus parenteral ) , daily pf output , or the level of amylase / lipase in the pf fluid analysis . average daily fistula output was 163 26 cc but with a wide range ( 502300 cc ) . computed tomography ( ct ) directed percutaneous drainage of an intra - abdominal fluid collection was required in 11 of 46 patients with a pf . in seven of these patients , notably , there was a trend of delayed fistula closure when patients required percutaneous drainage of any intra - abdominal fluid collection postoperatively ( 42 7 days with versus 30 5 days without , p = .09 ) . a multivariate analysis was performed of all parameters with a forward stepwise logistic regression model ( tables 6(a)6(c ) ) . this analysis indicated that independent predictive factors for the formation of a pf were as follows : invaginated anastomosis ( or 3.30 , p = .01 ) and closed suction drainage ( or 2.24 , p = .05 ) . a diagnosis of pancreatitis ( or 0.22 , p = .05 ) and preoperative endoscopic biliary stenting ( or 0.34 , p = .05 ) were independent protective factors against pf . because the type of drain was highly correlated with individual surgeon , in a separate assessment we performed a multivariate analysis excluding drain type ( table 6(b ) ) . in this analysis , invaginated pancreaticojejunostomy ( or 4.56 , p = .002 ) remained a significant predictive factor of pf and the diagnosis of pancreatitis ( or 0.22 , p = .05 ) remained an independent protective factor . while the presence of an endoscopic stent did not reach significance , the presence of a preoperative percutaneous transhepatic biliary stent ( or 2.43 , p = .07 ) approached significance . a multivariate analysis was also performed on the subgroup of patients with periampullary adenocarcinomas ( table 6(c ) ) . the only independent predictor of pf formation in this group was an invaginated pancreaticojejunostomy ( or 11.8 , p = .0002 ) . female gender ( or 0.238 , p = .03 ) and endoscopic stent ( or 0.194 , p diabetes ( or 0.146 , p = .07 ) demonstrated a trend as a protective factor against pf formation . in this study , we report our experience with pf in a series of 510 consecutive pancreaticoduodenectomies performed over a 22-year period . our incidence of pf was 9% which appears to be comparable to the pf rate of 914% reported in other specialized centers [ 110 ] . it is difficult to compare the incidence and severity of pf without standardization of the diagnosis , terms , and severity of this complication . it is hopeful that the standardized definitions of pf as put forth by the isgpf will likely allow for more equitable comparison among institutions . the risk of pf formation appears to be multifactorial involving demographic , preoperative , intraoperative , and pathologic factors . one prior study has reported that male sex was a significant predictor of pf . in this study , male gender only approached significance as a univariate predictor of pf formation in the overall group of patients undergoing pancreaticoduodenectomy . in our periampullary adenocarcinoma subgroup analysis , females had a lower incidence of pf and these results showed a trend as an independent predictor of pf on multivariate analysis . advanced age cited by some as predictive of pf was not recognized as a predictor in this series [ 23 , 24 ] . a higher incidence of pf was identified in patients who did not undergo mechanical bowel preparation . this association to our knowledge has not been reported before and so is an intriguing finding . perhaps the absence of intestinal succus or stool in the colon minimizes pressure in the jejunum limb translating into reduced pf rates . intraoperative blood loss cited by some as predictive was also not recognized as a significant factor in this series [ 23 , 24 ] . type of pancreaticojejunostomy anastomosis has also been cited by others in the literature to be a predictor of pf . this study showed that the type of pancreaticojejunostomy reconstruction ( invaginated versus end - to - side ) was significantly associated with pf in both the whole group and periampullary adenocarcinoma subanalysis . a recent metaanalysis addressing this particular association found a higher incidence of pf in patients who had invaginated pancreaticojejunostomy ( 26% ) versus a duct - to - mucosa ( 16% ) type of anastomosis . these findings are in contrast to a randomized control trial of 144 patients performed in italy by bassi et al . which showed no significant difference between invaginated and duct - to - mucosa anastomoses in pd . our pancreaticobiliary group is currently participating in a prospective randomized trial with thomas jefferson university to determine whether or not there is a difference in pf rate between invaginated and duct - to - mucosa pancreaticojejunostomy in pd . preoperative biliary stenting has been an area where some groups show an association with pf . a study from hopkins suggests that preoperative stenting is associated with an increased risk of pf formation . on the one hand , preoperative endoscopic stents are actually protective in our subgroup of patients with periampullary adenocarcinoma , while those patients who had preoperative percutaneous transhepatic biliary ( ptb ) stenting showed an increased risk of pf formation . other authors have also shown that preoperative endoscopic stenting decreases the incidence of postoperative pf . our study also suggests that closed suction drainage may be a predictor of pf formation . the memorial sloan kettering group has shown a lower incidence of pf in patients who did not have intraperitoneal drainage following pd . in our series both penrose drains and closed suction drains were used and the penrose drain group showed a lower incidence of pf formation . this finding implies that active suction drainage may have a deleterious effect on pf formation . a confounding factor in our study was that the penrose type drain was used largely by the highest volume surgeon in our series who also had a comparably low pf rate . drain type covaried so tightly with individual surgeons such that it was not possible to separate whether drain type or individual surgeon was more predictive in our multivariate model . one factor which appears to be a consistent is that the texture of the gland is significantly associated with pf formation . stratified patients in a trial according to the texture of the gland and found that patients with a firmer texture gland had a lower incidence of pf . other studies have also supported the association between soft pancreatic gland texture and the risk of pf [ 25 , 30 , 31 ] . our data is indirectly supportive that the texture of the gland is predictive of pf formation in those patients with both duodenal and ampullary adenocarcinomas , who often have a normal ( i.e. , soft ) gland texture ; both had a higher incidence of pf formation in our series but intraoperative assessment of the gland at the time of operation was not available in our retrospective database . other investigators have associated a small pancreatic duct as a contributing factor to pf formation [ 22 , 32 ] . pancreatic duct size was not prospectively tracked in our series of patients although it should be noted that this particular variable is often difficult to separate between soft textures of the gland because typically soft glands also have small pancreatic ducts [ 19 , 22 ] . although not addressed specifically in our analysis , individual surgeons tend to vary widely in their postoperative rate of pf . in particular , two specific surgeons in this series ( out of the 12 participants ) had significantly different pf rates from the average of their remaining peers . one surgeon had a significantly lower incidence of pf ( 4% compared to 14% for all others combined , p < .001 ) while the other surgeon had a significantly higher incidence of pf ( 18% versus 8% for all others combined , p = .04 ) . while these differences were accounted for , in part , by the differences in pancreatic pathology in each surgeon 's cohort , this issue brings up the surgeon as a significant variable in the incidence of pf formation . achilles heel of pancreaticoduodenectomy and novel approaches continue to be put forward to reduce its incidence [ 3336 ] . although historically , pf were associated with a mortality rate of 20 to 40% [ 3 , 7 , 8 ] , current advances in radiologic imaging and interventional radiologic techniques , antibiotics , and critical care medicine have considerably reduced the mortality rates from pf . our data is consistent with this trend since in our series of patients with pf , there were no in - hospital mortalities . nonetheless , pfs continues to cause significant morbidity , prolonged hospital stay , and increased hospital cost . our data supports these observations since patients with pf had a greater total number of complications , a higher incidence of septic complications , and a higher reoperation rate . in addition , our patient 's length of hospital stay was twice that of patients who did not have a pf . based on univariate analyses , gender , diabetes , preoperative glucose level , length of operation , bowel preparation , biliary stenting ( endoscopic versus percutaneous ) , anastomotic technique ( invaginated versus duct - to - mucosa ) , intraperitoneal drain choice ( passive / gravity versus closed - suction ) , and pathology ( pancreatitis , duodenal cancer ) may influence pf formation . in multivariate analyses , invaginated anastomosis , closed suction drainage , and percutaneous biliary stenting all increased the risk of pf while pancreatitis , endoscopic biliary stenting , and female gender conferred protection against pf . the influence of the individual surgeon on pf is also an extremely important factor to consider although difficult to separate from other variables such as gender , pancreatic pathology , or biliary stenting in a retrospectively designed study . in conclusion , in this series the development of pf following pancreaticoduodenectomy was predicted by demographics ( gender ) , preoperative procedures ( biliary stenting ) , intraoperative technique ( anastomosis , drainage , individual surgeon ) , and pancreatic pathology ( pancreatitis ) . outcomes in patients with pf are remarkable for a higher rate of septic complications , an increased incidence of reoperations , and a longer hospital stay without significant difference in overall mortality rate . preoperative biliary stenting , type of pancreaticoenteric anastomosis , and intraperitoneal drain usage are controllable factors in pf formation that surgeons should continue to investigate to reduce its incidence following pd .

pancreatic fistula continues to be a common complication following pd . this study seeks to identify clinical factors which may predict pancreatic fistula ( pf ) and evaluate the effect of pf on outcomes following pancreaticoduodenectomy ( pd ) . we performed a retrospective analysis of a clinical database at an academic tertiary care hospital with a high volume of pancreatic surgery . five hundred ten consecutive patients underwent pd , and pf occurred in 46 patients ( 9% ) . perioperative mortality of patients with pf was 0% . forty - five of 46 pf ( 98% ) closed without reoperation with a mean time to closure of 34 days . patients who developed pf showed a higher incidence of wound infection , intra - abdominal abscess , need for reoperation , and hospital length of stay . multivariate analysis demonstrated an invaginated pancreatic anastomosis and closed suction intraperitoneal drainage were associated with pf whereas a diagnosis of chronic pancreatitis and endoscopic stenting conferred protection . development of pf following pd in this series was predicted by gender , preoperative stenting , pancreatic anastomotic technique , and pancreas pathology . outcomes in patients with pf are remarkable for a higher rate of septic complications , longer hospital stays , but in this study , no increased mortality .

<s>[INST]despite major advances in pancreatic surgery , pancreatic fistula ( pf ) continues to be a common complication after pancreaticoduodenectomy ( pd ) occurring in 914% of patients even at high volume centers [ 110 ] . classical risk factors associated with pf have been described in the literature and include the following : patient demographics , pancreatic gland texture , pancreatic duct size , pathology of periampullary lesion , anastomotic technique , and surgeon volume [ 1120 ] . this complication with pd continues to occur despite an acknowledged improvement in other types of postoperative complications and declining mortality rates in most large surgical series . as most surgeons realize , the technical challenges of sewing the pancreas to the intestinal tract are formidable . despite these difficulties , if substantial progress in reducing the rate of pf is to be made , improved understanding of the risk factors which predispose to fistula formation seems essential . identifying which glands in which patients are at high risk for a leak can trigger modifications in surgical technique , drainage , and postoperative care to minimize fistula formation . in this study we asked the following questions : first , what preoperative and perioperative factors might predict pf following pancreaticoduodenectomy ? second , what is the effect of pf on outcomes following pancreaticoduodenectomy ? to answer these questions , we analyzed our experience with pd at a high - volume pancreatic referral center and then examined the effect of these variables on the incidence of pf and the clinical outcomes in this group of patients . this is a retrospective review of a case series of consecutive patients who underwent pancreaticoduodenectomy for a broad range of periampullary and pancreatic pathologies between january 1980 and june 2002 at indiana university medical center , a tertiary care academic training hospital in indianapolis , indiana . only patients who had pancreaticoduodenectomy with a remnant , viable pancreatic tail were included for analysis . patients who underwent total pancreatectomy due to positive resection margins or those who had undergone previous distal pancreatic resections prior to their pancreaticoduodenectomy were excluded from this study . pancreatic fistula ( pf ) was defined during the broad range of years in this experience by several definitions . from 1980 to 1985 , a pf was defined as > 10 ml of amylase - rich fluid per day from a surgically placed drain or through a cutaneous site ( around a penrose drain ) after postoperative day 8 and lasting for at least 8 days . from 19852002 our definition was > 50 ml / day of amylase rich fluid after postoperative day 11 and lasting for at least 11 days . since 2005 at our institution , we have used the international study group for pancreatic fistula ( isgpf ) guidelines defining pancreatic fistula as any measurable volume of fluid on or after postoperative day 3 with amylase content greater than 3 times the serum amylase activity ( 21 ) . based on a careful review of the patients medical records during their hospital treatment and postoperative clinical follow - up , pancreatic fistula grades a , b , or c were assigned to each fistula identified as defined in the isgpf guidelines ( see table 1 ) . data were collected and reported in strict compliance with patient confidentiality guidelines put forth by the indiana university - purdue university indianapolis institutional review board . for preoperative variables twelve patient symptoms , physical signs , and associated conditions were included in the database including the following : abdominal pain , back pain , nausea / vomiting , diarrhea , abdominal tenderness , jaundice , diabetes , pancreatitis , abdominal mass , organomegaly , hemepositive stools , and weight loss . the diagnosis of jaundice was based on the presence of scleral icterus on physical examination . the presence of new onset diabetes mellitus was defined as the existence of glucose intolerance necessitating diet modification , oral hyperglycemic drug , or insulin supplementation within two years of the diagnosis of a periampullary pathologic disorder requiring operation . the diagnosis of diarrhea was made if patients reported three or more bowel movements per day or if the total volume of their movements in a day was 0.5 liters or greater . weight loss was quantified by patient history at the time of the preoperative visit . nine preoperative serum chemistries ( total bilirubin , alkaline phosphatase , sgot , total protein , albumin , amylase , glucose , calcium and phosphorous ) , five hematologic parameters ( hematocrit , hemoglobin , white blood cell count , prothrombin time , and partial thromboplastin time ) , and three serum tumor marker values ( cea , ca-19 - 9 , and ca-125 ) were obtained from routine blood draws either in the preoperative clinic or during a hospitalization close to the time of operation . eleven perioperative variables including pre - operative biliary stenting ( endoscopic or percutaneous transhepatic ) , pre - operative transfusion , pre - operative total parenteral nutrition ( tpn ) , pre - operative bowel preparation , estimated intra - operative blood loss ( ml ) , intra- and post - operative transfusions , operative time ( minutes ) , type of resection ( standard versus pylorus preservation ) , type of pancreaticojejunostomy ( invagination or end - to - side duct to mucosa ) , type of intraperitoneal drains used ( penrose or closed suction jackson - pratt drains ) , and gastrostomy tube placement were identified from the patient medical records , anesthesiologist 's records , and the operative reports . all specimens were reviewed by the staff pathologist at indiana university medical center with the majority of specimens also undergoing a secondary review by a dedicated pancreatic pathologist . histopathologic diagnosis , tumor size , tumor differentiation ( well , moderate , poor , none ) , lymph node status ( positive , negative ) , and surgical margin status ( positive , negative ) were routinely reported . margins analyzed included the common bile duct , pancreatic neck , and duodenum or stomach . retroperitoneal ( uncinate ) soft tissue margins were inconsistently analyzed early in this series ( 19802002 ) , but since 2002 , at our facility , standardized retroperitoneal margin assessment and analysis have been carried out based on ajcc guidelines ( 37 ) . clinical outcomes variables that were assessed included the following : in - hospital mortality , overall complications , and specific complications such as cardiopulmonary , delayed gastric emptying ( dge ) , sepsis , wound infection , intra - abdominal abscess , hemorrhage , and hospital length of stay ( los ) . delayed gastric emptying was defined in this cohort as the inability to take a regular diet after postoperative day no . 10 . survival was determined from the most recent encounter at indiana university hospital and was cross - referenced with the clarian cancer registry database and the social security database . twelve surgeons operated on patients included in this study who underwent either pylorus preserving or classic ( hemigastrectomy ) pancreaticoduodenectomy . reconstruction was undertaken with an isoperistaltic limb of jejunum in retrocolic fashion and anastomosed with an end - to - side pancreaticojejunostomy , followed by an end - to - side choledochojejunostomy and an ( antecolic or retrocolic ) end - to - side duodenojejunostomy or gastrojejunostomy . the pancreaticojejunostomy was performed using a duct - to - mucosa anastomosis ( n = 453 ) or , alternatively , an invaginated anastomosis ( n = 52 ) based on surgeon preference . only one surgeon used this technique predominately , accounting for 63% of their total pd . during this period at our institution , the pancreaticojejunostomy and choledochojejunostomy were drained routinely with penrose drains to gravity or closed suction drains . finally , some patients in this series underwent elective gastrostomy for postoperative decompression and alimentation . the association of categorical factors with survival was assessed using the kaplan - meier method ( km ) and was tested using the log - rank test . the association of continuous variables with survival was analyzed using a cox 's proportional hazards regression model and tested via the wald test . analyses were performed with a forward stepwise logistic regression model selection procedure where the probability of inclusion of a factor in the model was set at 20% and the probability of removal factor from the model was 20% . statistical significance was set at p .05 . the mean age was the same in patients with pf ( 58 years ; range 3079 ) compared to those without pf ( 58 years ; range 1593 ) . sixty - five patients underwent pancreaticoduodenectomy in the 1980s with the remainder being performed from 1990 and 2000 . the incidence of pf as a function of time by decade ( 1980 's = 9% ; 1990 's = 6% ; 2000 's = 10% ) or by year ( p = ns ) did not change significantly over the course of the study period . pancreatic fistula was more common in males , with this difference approaching statistical significance in univariate analysis , ( p = .06 ) . of the twelve preoperative patient symptoms tracked , none were associated with a significant difference in the rate of fistula formation ( data not shown ) . notably , a preoperative diagnosis of diabetes was present in a greater proportion of patients who did not have pf ; however , this result was not statistically significant . only serum glucose showed a significant association ( p = .04 ) with pf formation . serum glucose tended to be higher in patients who did not have a pf corroborating the trend in diabetes incidence previously noted . preoperative biliary stenting was done in 211 patients , 68 of whom had percutaneous transhepatic biliary stenting , and 143 had endoscopic stenting . preoperative biliary stenting ( combined percutaneous and endoscopic groups ) showed no significant difference in pf rates when compared to patients who were not preoperatively stented ( 9% stented group ( 20/211 ) versus 8% without stenting ( 26/299 ) ) . when subclassified into percutaneous transhepatic or endoscopic stenting however , a significantly higher incidence of pf was found in the percutaneous transhepatic stent group , 16% ( 11/68 ) compared to endoscopic stent group 6% ( 9/143 ) ( p = .04 ) . information about preoperative mechanical bowel preparation was not tracked in the latter half of our series ; however , among patients in whom preoperative mechanical bowel preparation status was known , a significantly higher incidence of pf was identified in patients who did not undergo mechanical bowel preparation ( 19% ( 6/31 ) versus 6% ( 14/226 ) , p < .02 ) implying that mechanical bowel preparation may be protective against pf . median operative time , however , was comparatively longer in the pf group ( 7 hours versus 5 hours , p < .001 ) . pylorus preserving pancreaticoduodenectomy was performed in 259 patients ( 51% ) and classic pancreaticoduodenectomy was performed in 251 patients ( 49% ) . the incidence of pf was not significantly different according to operation performed ( 11% , ( 28/259 ) pppd versus 7% ( 18/251 ) classic ) . in general , two types of pancreaticojejunostomy reconstruction were performed . a duct - to - mucosa anastomosis was performed in 453 patients , and an invaginated anastomosis , 3 underwent peustow reconstruction of the remnant , and in 2 , the reconstruction was unclear based upon operative records . there was a more than 3x higher incidence of pf in invaginated anastomoses ( 23% ) when compared to duct - to mucosa ( 7% ) , p < .001 . two types of drainage were employed over the course of these operations , closed suction drainage to a bulb suction device usually of the jackson - pratt type , and passive / gravity drainage with a penrose drain . closed suction drainage was used in 269 patients ( 53% ) and passive drainage with a penrose drain was used in 241 patients ( 47% ) with both techniques used continuously throughout this study . there was a significantly higher incidence of pf in patients who underwent closed suction drainage ( 14% ) compared to passive penrose drainage ( 3% ) , p < .001 . placement of a gastrostomy tube was done in 74 patients and was not associated with a comparatively different pf rate . the development of a pf was much more common in patients with the diagnosis of duodenal ( 15% ) or ampullary adenocarcinoma ( 17% ) ( p = .01 and .06 , resp . ) . alternatively , patients with a diagnosis of pancreatitis were less likely to develop a pf ( p = .02 ) . characteristics of the tumor pathology in patients with periampullary adenocarcinoma are provided in table 4 . size of pancreatic lesion measured in longest diameter , tumor differentiation , surgical margin status , and lymph node status were assessed . there was no statistically significant difference in any of these variables and the incidence of pf formation . there was a 4% mortality rate in patients who did not have pf and no mortality in patients who had a pf , a difference that was not statistically significant . there were no differences in rate of complications between patients who had a pf when compared to those who did not ; however , the total number of complications ( number of complications per patient ) was greater in patients who developed a pf . in addition , the type of complications varied according to whether or not a pf was present . the incidence of sepsis ( p < .001 ) , wound infection ( p < .001 ) , and intra - abdominal abscess ( p < the 26% reoperation rate for patients with pf was significantly higher than the 0.4% rate in patients without pf . of the twelve reoperations done in the pf group , eleven were done for complications of the pf and only one was done for a persistent fistula which lasted for greater than 4 months . six reoperations were done prior to the diagnosis of pf for sepsis or a visceral pseudoaneurysm , and six were done in patients following the diagnosis of pf for complications including the following : wound dehiscence ( 1 ) , poor fistula drainage with sepsis ( 3 ) , breakdown of the hepaticojejunostomy ( 1 ) , and persistent fistula > 4 months ( 1 ) . the diagnosis of pf was made on average on postoperative day 8 and these patients experienced longer lengths of hospital stay . the median length of stay in the pf group was 25 days , whereas it was only 12 days in the no pf group ( p < .001 ) . based upon international study group for pancreatic fistula ( isgpf ) grading guidelines , this series included 10 grade a fistulas , 23 grade b fistulas , and 13 grade c fistulas . forty - five of 46 pf ( 98% ) closed without reoperation with a mean time to closure of 34 days ( range 393 days ) . twenty - three patients ( all grade 13 grade c fistulas and 10 grade b fistulas ) were treated with antibiotics . ten patients ( 5 grade c and 5 grade b fistulas ) were treated with octreotide . this timing of closure was not significantly different with / without octreotide treatment ( 39 5 versus 25 5 ) or with / without antibiotic treatment ( 36 5 versus 29 6 ) . thirty - six patients required tpn for an average of 32 days ( range 590 days ) . time to closure was not affected by nutrition route ( enteral versus parenteral ) , daily pf output , or the level of amylase / lipase in the pf fluid analysis . average daily fistula output was 163 26 cc but with a wide range ( 502300 cc ) . computed tomography ( ct ) directed percutaneous drainage of an intra - abdominal fluid collection was required in 11 of 46 patients with a pf . in seven of these patients , notably , there was a trend of delayed fistula closure when patients required percutaneous drainage of any intra - abdominal fluid collection postoperatively ( 42 7 days with versus 30 5 days without , p = .09 ) . a multivariate analysis was performed of all parameters with a forward stepwise logistic regression model ( tables 6(a)6(c ) ) . this analysis indicated that independent predictive factors for the formation of a pf were as follows : invaginated anastomosis ( or 3.30 , p = .01 ) and closed suction drainage ( or 2.24 , p = .05 ) . a diagnosis of pancreatitis ( or 0.22 , p = .05 ) and preoperative endoscopic biliary stenting ( or 0.34 , p = .05 ) were independent protective factors against pf . because the type of drain was highly correlated with individual surgeon , in a separate assessment we performed a multivariate analysis excluding drain type ( table 6(b ) ) . in this analysis , invaginated pancreaticojejunostomy ( or 4.56 , p = .002 ) remained a significant predictive factor of pf and the diagnosis of pancreatitis ( or 0.22 , p = .05 ) remained an independent protective factor . while the presence of an endoscopic stent did not reach significance , the presence of a preoperative percutaneous transhepatic biliary stent ( or 2.43 , p = .07 ) approached significance . a multivariate analysis was also performed on the subgroup of patients with periampullary adenocarcinomas ( table 6(c ) ) . the only independent predictor of pf formation in this group was an invaginated pancreaticojejunostomy ( or 11.8 , p = .0002 ) . female gender ( or 0.238 , p = .03 ) and endoscopic stent ( or 0.194 , p diabetes ( or 0.146 , p = .07 ) demonstrated a trend as a protective factor against pf formation . in this study , we report our experience with pf in a series of 510 consecutive pancreaticoduodenectomies performed over a 22-year period . our incidence of pf was 9% which appears to be comparable to the pf rate of 914% reported in other specialized centers [ 110 ] . it is difficult to compare the incidence and severity of pf without standardization of the diagnosis , terms , and severity of this complication . it is hopeful that the standardized definitions of pf as put forth by the isgpf will likely allow for more equitable comparison among institutions . the risk of pf formation appears to be multifactorial involving demographic , preoperative , intraoperative , and pathologic factors . one prior study has reported that male sex was a significant predictor of pf . in this study , male gender only approached significance as a univariate predictor of pf formation in the overall group of patients undergoing pancreaticoduodenectomy . in our periampullary adenocarcinoma subgroup analysis , females had a lower incidence of pf and these results showed a trend as an independent predictor of pf on multivariate analysis . advanced age cited by some as predictive of pf was not recognized as a predictor in this series [ 23 , 24 ] . a higher incidence of pf was identified in patients who did not undergo mechanical bowel preparation . this association to our knowledge has not been reported before and so is an intriguing finding . perhaps the absence of intestinal succus or stool in the colon minimizes pressure in the jejunum limb translating into reduced pf rates . intraoperative blood loss cited by some as predictive was also not recognized as a significant factor in this series [ 23 , 24 ] . type of pancreaticojejunostomy anastomosis has also been cited by others in the literature to be a predictor of pf . this study showed that the type of pancreaticojejunostomy reconstruction ( invaginated versus end - to - side ) was significantly associated with pf in both the whole group and periampullary adenocarcinoma subanalysis . a recent metaanalysis addressing this particular association found a higher incidence of pf in patients who had invaginated pancreaticojejunostomy ( 26% ) versus a duct - to - mucosa ( 16% ) type of anastomosis . these findings are in contrast to a randomized control trial of 144 patients performed in italy by bassi et al . which showed no significant difference between invaginated and duct - to - mucosa anastomoses in pd . our pancreaticobiliary group is currently participating in a prospective randomized trial with thomas jefferson university to determine whether or not there is a difference in pf rate between invaginated and duct - to - mucosa pancreaticojejunostomy in pd . preoperative biliary stenting has been an area where some groups show an association with pf . a study from hopkins suggests that preoperative stenting is associated with an increased risk of pf formation . on the one hand , preoperative endoscopic stents are actually protective in our subgroup of patients with periampullary adenocarcinoma , while those patients who had preoperative percutaneous transhepatic biliary ( ptb ) stenting showed an increased risk of pf formation . other authors have also shown that preoperative endoscopic stenting decreases the incidence of postoperative pf . our study also suggests that closed suction drainage may be a predictor of pf formation . the memorial sloan kettering group has shown a lower incidence of pf in patients who did not have intraperitoneal drainage following pd . in our series both penrose drains and closed suction drains were used and the penrose drain group showed a lower incidence of pf formation . this finding implies that active suction drainage may have a deleterious effect on pf formation . a confounding factor in our study was that the penrose type drain was used largely by the highest volume surgeon in our series who also had a comparably low pf rate . drain type covaried so tightly with individual surgeons such that it was not possible to separate whether drain type or individual surgeon was more predictive in our multivariate model . one factor which appears to be a consistent is that the texture of the gland is significantly associated with pf formation . stratified patients in a trial according to the texture of the gland and found that patients with a firmer texture gland had a lower incidence of pf . other studies have also supported the association between soft pancreatic gland texture and the risk of pf [ 25 , 30 , 31 ] . our data is indirectly supportive that the texture of the gland is predictive of pf formation in those patients with both duodenal and ampullary adenocarcinomas , who often have a normal ( i.e. , soft ) gland texture ; both had a higher incidence of pf formation in our series but intraoperative assessment of the gland at the time of operation was not available in our retrospective database . other investigators have associated a small pancreatic duct as a contributing factor to pf formation [ 22 , 32 ] . pancreatic duct size was not prospectively tracked in our series of patients although it should be noted that this particular variable is often difficult to separate between soft textures of the gland because typically soft glands also have small pancreatic ducts [ 19 , 22 ] . although not addressed specifically in our analysis , individual surgeons tend to vary widely in their postoperative rate of pf . in particular , two specific surgeons in this series ( out of the 12 participants ) had significantly different pf rates from the average of their remaining peers . one surgeon had a significantly lower incidence of pf ( 4% compared to 14% for all others combined , p < .001 ) while the other surgeon had a significantly higher incidence of pf ( 18% versus 8% for all others combined , p = .04 ) . while these differences were accounted for , in part , by the differences in pancreatic pathology in each surgeon 's cohort , this issue brings up the surgeon as a significant variable in the incidence of pf formation . achilles heel of pancreaticoduodenectomy and novel approaches continue to be put forward to reduce its incidence [ 3336 ] . although historically , pf were associated with a mortality rate of 20 to 40% [ 3 , 7 , 8 ] , current advances in radiologic imaging and interventional radiologic techniques , antibiotics , and critical care medicine have considerably reduced the mortality rates from pf . our data is consistent with this trend since in our series of patients with pf , there were no in - hospital mortalities . nonetheless , pfs continues to cause significant morbidity , prolonged hospital stay , and increased hospital cost . our data supports these observations since patients with pf had a greater total number of complications , a higher incidence of septic complications , and a higher reoperation rate . in addition , our patient 's length of hospital stay was twice that of patients who did not have a pf . based on univariate analyses , gender , diabetes , preoperative glucose level , length of operation , bowel preparation , biliary stenting ( endoscopic versus percutaneous ) , anastomotic technique ( invaginated versus duct - to - mucosa ) , intraperitoneal drain choice ( passive / gravity versus closed - suction ) , and pathology ( pancreatitis , duodenal cancer ) may influence pf formation . in multivariate analyses , invaginated anastomosis , closed suction drainage , and percutaneous biliary stenting all increased the risk of pf while pancreatitis , endoscopic biliary stenting , and female gender conferred protection against pf . the influence of the individual surgeon on pf is also an extremely important factor to consider although difficult to separate from other variables such as gender , pancreatic pathology , or biliary stenting in a retrospectively designed study . in conclusion , in this series the development of pf following pancreaticoduodenectomy was predicted by demographics ( gender ) , preoperative procedures ( biliary stenting ) , intraoperative technique ( anastomosis , drainage , individual surgeon ) , and pancreatic pathology ( pancreatitis ) . outcomes in patients with pf are remarkable for a higher rate of septic complications , an increased incidence of reoperations , and a longer hospital stay without significant difference in overall mortality rate . preoperative biliary stenting , type of pancreaticoenteric anastomosis , and intraperitoneal drain usage are controllable factors in pf formation that surgeons should continue to investigate to reduce its incidence following pd .[/INST]pancreatic fistula continues to be a common complication following pd . this study seeks to identify clinical factors which may predict pancreatic fistula ( pf ) and evaluate the effect of pf on outcomes following pancreaticoduodenectomy ( pd ) . we performed a retrospective analysis of a clinical database at an academic tertiary care hospital with a high volume of pancreatic surgery . five hundred ten consecutive patients underwent pd , and pf occurred in 46 patients ( 9% ) . perioperative mortality of patients with pf was 0% . forty - five of 46 pf ( 98% ) closed without reoperation with a mean time to closure of 34 days . patients who developed pf showed a higher incidence of wound infection , intra - abdominal abscess , need for reoperation , and hospital length of stay . multivariate analysis demonstrated an invaginated pancreatic anastomosis and closed suction intraperitoneal drainage were associated with pf whereas a diagnosis of chronic pancreatitis and endoscopic stenting conferred protection . development of pf following pd in this series was predicted by gender , preoperative stenting , pancreatic anastomotic technique , and pancreas pathology . outcomes in patients with pf are remarkable for a higher rate of septic complications , longer hospital stays , but in this study , no increased mortality .</s>

einstein - podolsky - rosen ( epr ) @xcite suggested that quantum mechanics was incomplete and that hidden variables may be needed for completion . this was the subject of an extensive debate with bohr @xcite who denied the existence of such hidden variables using his well known reasoning that is at the basis of the copenhagen interpretation of quantum mechanics . a mathematical non - existence proof for these hidden variables was presented by von neumann within the framework of quantum mechanics . bell @xcite , however , showed that von neumann s proof assumed the simultaneous measurability of certain quantities that could not possibly be simultaneously measured . subsequently bell himself presented a non - existence proof @xcite in form of inequalities that are derived by using more complex assumptions that did not necessarily include simultaneous measurability . the inequalities of bell @xcite are derived by the use of probability theory , in essence by the use of very elementary facts about random variables within the framework pioneered by kolmogorov . the derivation of the inequalities does not involve physics or quantum mechanics , yet the inequalities have assumed an important role for the foundations of quantum mechanics . this role is a consequence of the assumptions for the random variables ( and other possible variables ) that are used to derive the bell inequalities . it is commonly believed that these assumptions are needed and moreover are equivalent to the basic postulates of an objective local " parameter space @xcite . these postulates or conditions encompass einstein - locality and the existence of elements of reality in the sense of mach that co - determine the outcome of measurements . the fact that some results of quantum mechanics violate the bell inequalities has therefore led to the belief that no objective local parameter space can exist that explains all the results of quantum mechanics . subsequent to these discussions experiments were proposed @xcite , @xcite and later realized @xcite that confirmed the theoretical result of quantum mechanics . this seemed to leave only difficult options for theoretical physics such as ( i ) to deny that the microscopic entities of physics have objective reality ( non - existence of objective local parameters ) or ( ii ) to assert that an influence can be propagated faster than the speed of light @xcite . additional options involving the validity of counterfactual reasoning have also been suggested and will be discussed below . we show in this paper that because of the historical sequence of events , viz . the development of bell s theory before the performance of the actual experiments , some very important facts of probability theory have not been considered and/or misinterpreted . these facts are connected with the concept of a probability space that is important to link probability theory and mathematical statistics to the evaluation of actual experiments . we reconsider here these concepts and show that violations of the bell inequalities have a purely mathematical reason , in particular that the bell inequalities represent a special case of theorems given earlier by bass @xcite , vorobev @xcite , @xcite and schell @xcite . these theorems permit us to deduce that , for all the possible bell inequalities to be valid , it is a necessary and sufficient condition that the random variables involved in their proof are defined on one common probability space . beyond this we show that the requirement of the use of one common probability space does not follow from the requirements of objective local spaces and vice versa . in fact , we show that there exist objective local random variables that can not be defined on a common probability space and therefore do not need to obey the bell inequalities . as mentioned , bell has dismissed von neumann s proof that assumed from the start the simultaneous measurability of the observables that correspond to our random variables and that can not be measured simultaneously . our contribution here is that we also dismiss non - existence proofs of certain systems of random variables that need to be defined on one common probability space when it is clear from the outset that these systems of random variables can not be defined on any common probability space . we believe that our results give additional options of explanation for aspect - type experiments without violating relativity or denying objective reality . as outlined above , probability theory provides a probability space and random variables and the link to the statistical treatment of the data from an actual experiment . bell @xcite considered an experimental situation advocated by bohm and aharonov @xcite , and by bohm and hiley @xcite . this proposal was transformed into an actual experiment by aspect et al . @xcite including the suggestion of bell and others that a rapid change of the settings needed to be implemented to accomplish a delayed choice situation @xcite . we develop now an idealized experiment and a probability model for this actual experiment by aspect et al within the framework of kolmogorov . we note that our procedure also applies to other related experiments . we first recall the concepts of a ( discrete ) probability space and of a random variable defined on it . as feller states @xciteif we want to speak about experiments or observations in a theoretical way and without ambiguity , we first must agree on the simple events representing the thinkable outcomes ; _ they define the idealized experiment _ ...... by definition _ every indecomposable result of the ( idealized ) experiment is represented by one , and only one , sample point_. the aggregate of all sample points will be called the _ sample space_. " in our case of the idealized epr experiment , the simple event can be chosen , for example , as the event of sending out one ( and only one ) correlated pair . with this event we associate an element @xmath0 . in order to avoid mathematical technicalities that are not needed for the purpose of our paper we assume that the sample space @xmath1 is at most countable . each simple event @xmath2 is assigned the probability @xmath3 that @xmath0 occurs . @xmath4 is a set function , defined for all subsets of @xmath1 , that satisfies the usual axioms , such as countable additivity and it assigns to @xmath1 the value @xmath5 . the pair @xmath6 is called a probability space . a random variable is a real - valued function on @xmath1 , but if needed it also can assume values in high - dimensional space . we now turn to the specifics of an idealized epr - experiment . a correlated spin pair in the singlet state is sent out from a source in opposite directions toward measurement stations . these stations are characterized by certain randomly and rapidly switched settings which we denote by three dimensional unit vectors @xmath7 . the measurements in the stations are mathematically represented by random variables @xmath8 that may in turn be functions of other random variables e.g. a source parameter @xmath9 that characterizes all the properties of the particles sent out from the source . @xmath10 indicates that the measurements that correspond to the outcomes of random variable @xmath10 have been performed using the setting @xmath11 and similarly for @xmath12 and @xmath13 . we perform three categories of experiments , each with a different pair of setting vectors . the first category is characterized by the vectors @xmath11 in station @xmath14 and @xmath15 in station @xmath16 . according to our notational convention we denote the pair of measurements @xmath17 and the joint probability density of @xmath10 and @xmath12 by @xmath18 . thus @xmath18 is given by @xmath19 @xmath20 the second category of experiments will be characterized by the vectors @xmath11 in @xmath14 and @xmath21 in @xmath16 with the resulting pair of measurements @xmath22 having density @xmath23 , and the third category by the vectors @xmath15 in @xmath14 and @xmath21 in @xmath16 resulting in a pair of measurements @xmath24 with density @xmath25 . the measurement outcomes on both sides need to be completely random and @xmath26 with equal probability , i.e. all three distributions have identical marginals . this is dictated by the rules of quantum mechanics and verified by experiment . from this it follows that the @xmath27 have the center of gravity for their point masses at the origin @xmath28 and @xmath29 the idealized mathematical model with exactly the properties described above and used within the framework of kolmogorov is the basis for all our further considerations and we call it the ma - epr model . we start with an example that illustrates the theorems of bass @xcite and vorobev @xcite for the special case of the ma - epr model . the essential point of these theorems is that , in general , it is not possible to find three random variables @xmath30 and @xmath13 , defined on a common probability space such that the three pairs @xmath31 , @xmath32 , and @xmath33 of random variables have their joint densities equal to @xmath34 and @xmath25 , respectively . hence the notation that is commonly used and that we also introduced in section 2 above is misleading in the sense that it suggests there exist three random variables @xmath30 and @xmath13 that can reproduce the joint densities @xmath18 , @xmath23 and @xmath25 , when in fact they can not . here is a modification of an example of vorobev @xcite . .vorobev - type example @xcite . [ cols="<,>,>,>,>",options="header " , ] it is easy to show that under the assumption of eq([bv1 ] ) the joint pair densities can be expressed in terms of the covariances @xmath35 defined by these pair densities . the pair densities are then given by table [ ta : ob ] ( see also the lemma below ) . note that the covariances @xmath36 do not exceed @xmath37 in absolute value . suppose now that there exist three random variables @xmath38 defined on one common probability space that reproduce the densities @xmath39 in table [ ta : ob ] . then @xmath40 , @xmath41 , and @xmath42 where @xmath43 denotes the expectation value . expressing the entries of table [ ta : ob ] in terms of the eight unknown probabilities @xmath44 will result in a system of twelve linear equations in these eight unknowns that can be solved in an elementary way . in particular , solving this system shows that these eight probabilities can be expressed in terms of the three covariances @xmath45 . it turns out that five of these twelve linear equations are redundant . thus this system has infinitely many solutions . taking into account that the solutions of this system represent probabilities @xmath46 we obtain in a straightforward way that the following four inequalities are necessary and sufficient conditions for the solvability of the consistency problem for the three pair distributions given in table [ ta : ob ] : @xmath47 @xmath48 @xmath49 @xmath50 of course , the necessity part of this conclusion can be shown directly and trivially by modifying the standard proofs of the bell inequality along the lines shown in @xcite . replacing the covariances @xmath51 by the corresponding expectation values , one obtains from eqs.([bvcc2]-[bvcc3 ] ) : @xmath52 and @xmath53 eqs.([bv6 ] ) and ( [ bv7 ] ) give @xmath54 this is , of course , one of the celebrated bell inequalities . five more can be obtained in analogous fashion from eqs.([bvcc1]-[bvcc4 ] ) giving a total of 6 ( 4 choose 2 ) . these can also be obtained by cyclic permutation in eq.([bv8 ] ) and replacing both minus signs by plus signs . bass @xcite proved that for three general pair distributions the consistency problem can be solved if and only if the triple @xmath55 considered as a point in @xmath56 belongs to a certain domain . in the special case we have been considering this domain reduces to the tetrahedron defined by the inequalities of eqs.([bvcc1]-[bvcc4 ] ) . we shall call it the covariance tetrahedron . it is diplayed in fig . [ fig : tetrahedra ] . we formulate now our findings for the ma - epr experiment as a theorem . we first collect a few facts of section 3 above in form of a lemma . lemma : let @xmath57 be a density supported on the four vertices @xmath58 of a square . suppose that @xmath59 then @xmath60 where the sums are extended over the four points @xmath61 . conversely , if @xmath57 satisfies eq.([bvcc6 ] ) then @xmath57 also satisfies eq.([bvcc5 ] ) . set @xmath62 with the same proviso for the sum . then @xmath57 can be expressed in terms of @xmath51 by the equations @xmath63 @xmath64 theorem1 : let @xmath39 be three probability densities satisfying the hypotheses of the lemma with corresponding covariances @xmath65 . then the following statements are equivalent 1 . the point @xmath66 satisfies the system of inequalities eqs.([bvcc1]-[bvcc4 ] ) and therefore belongs to the covariance tetrahedron . the point @xmath55 satisfies the following six bell - type inequalities @xmath67 @xmath68 @xmath69 3 . there exist three random variables @xmath38 defined on a single common probability space with the following properties . the joint probability densities of @xmath70 and @xmath24 are @xmath34 and @xmath25 respectively . in particular , the expectation values equal @xmath71 the covariances equal @xmath72 using eqs.([bvcc10 ] ) and ( [ bvcc12 ] ) one obtains the six bell inequalities for the expectation values @xmath73 . proofs : the proof of the lemma is straightforward . the proof that conditions ( i ) and ( ii ) of theorem1 are equivalent can be done by inspection . the proof that ( iii ) implies ( ii ) or the six bell inequalities obtained from eq.([bvcc10 ] ) and eq.([bvcc12 ] ) can be carried out by a simple modification of the standard proof of the bell inequalities @xcite . finally , the proof that ( i ) implies ( iii ) was outlined at the end of section 3 . we have shown therefore the following . the inequalities of bell are a special case of the theorems of bass and vorobev for the ma - epr experiment . if the 6 bell inequalities are valid then it is possible to find three random variables @xmath30 and @xmath13 , defined on one common probability space that reproduce the three joint pair densities @xmath74 of table [ ta : ob ] and their covariances @xmath75 and @xmath42 . these covariances satisfy the bell inequalities . therefore , if quantum mechanics predicts that , for a given idealized experiment involving random variables @xmath30 and @xmath13 and @xmath76 , @xmath77 , and @xmath78 , one of the six bell inequalities in eq.([bvcc10 ] ) will be violated or equivalently if the point with coordinates @xmath79 does not belong to the covariance tetrahedron of fig . [ fig : tetrahedra ] , then the random variables @xmath30 and @xmath13 , that are supposed to form the basis for the model of this idealized experiment , can not be defined on one common probability space . we note that the work of fine @xcite has already shown the importance of a joint density and therefore of a common probability space in the derivations of bell - type inequalities . the importance of a common probability space was also stressed more recently in @xcite and other publications . in summary , we have shown that the definability of @xmath30 and @xmath13 on one common probability space ( ocps ) is a necessary and sufficient condition for the validity of bell s inequalities and that this condition is of a purely mathematical nature and has nothing to do with the questions of non - locality or counterfactual reasoning that usually surround discussions of the bell inequalities . the condition is , however , related to some of the physics of epr experiments in a variety of ways that will be discussed in section 6 . we add here that other inequalities of similar type such as the clauser - horne - holt - shimony ( chhs ) @xcite inequalities can be treated similarly , although with greater algebraic exertion ( 16 linear equations in 16 unknowns ) . their validity is again a necessary and sufficient reason that all involved random variables are defined on one common probability space . in fact , a theorem analogous to theorem1 above holds , with the covariance tetrahedron replaced by a four - dimensional polytope . this polytope equals the intersection of the four - dimensional parallelepiped , defined by the four chhs inequalities , and the four - dimensional cube with vertices @xmath80 . the details will be published elsewhere . in view of the ocps condition and the theorems of bass and vorobev , the proofs for the bell inequalities as given by bell and others become obvious and at the same time lacking physical justification . consider bell s original proof @xcite . here bell assumes that all random variables @xmath38 are in turn functions of a single random variable @xmath9 . then it is clear that @xmath38 are defined on one common probability space and therefore the inequalities can not be violated by the pair expectation values as explained above . it is clear that no @xmath9 can exist that leads to a violation of the inequalities for purely mathematical reasons as already found by bass much earlier . bell s physical justification is wanting because he attempts to show that the inequalities follow from the fact that @xmath9 does not depend on the settings @xmath81 . in fact , it does not matter on what @xmath9 depends as long as the resulting @xmath30 and @xmath13 are random variables defined on one probability space . we will discuss this in more detail below . other well known proofs @xcite invoke counterfactual " reasoning of the following kind : if , for example , @xmath10 is measured given a certain information that we denote by @xmath82 ( a value that @xmath9 assumes in a given experiment ) and that is carried by the correlated spin pair , then one could have measured with another setting , say @xmath15 and the same @xmath82 . as we have explained in more detail previously @xcite , it is permissible to ask the question of what would have been obtained if the measurement had been performed with a different setting . it is also permissible to hypothesize the existence of an element of reality related to that different setting if that different setting had been chosen . however , to assume then , as is always done in bell type proofs , that all these possible different measurement results are actually contained in the data set of actual outcomes of the idealized experiment is arbitrary and against all the rules of modelling and simulation especially for the particular case of the aspect - type experiment and all other known epr experiments @xcite . naturally , we do not have to pay for all items on a restaurant s menu just because we could have chosen them . we call this latter assumption the extended counterfactual assumption ( eca ) . eca is equivalent to the assumption that @xmath30 and @xmath13 only depend on one random variable @xmath9 and is therefore an assumption , not a proof . as a consequence , eca implies that @xmath30 and @xmath13 are defined on one common probability space . in view of the bass - vorobev theorem it leads to a contradiction from the outset irrespective and independent of any physical considerations a number of physical conditions have been given in the past that have been thought to be necessary and sufficient for the bell inequalities to be valid . most prominently among these conditions ranks the definition of an objective local parameter space @xcite , @xcite . this definition involves several conditions that are automatically fulfilled in our kolmogorovian model as has been outlined before @xcite ; it further implies the existence of elements of reality that contain information related to the spin ( represented by the random variable @xmath9 ) and , most importantly einstein locality . armed with the knowledge that the validity of the bell inequalities as described above is equivalent to the assumption that @xmath38 can be defined on one common probability space , we must now ask the question how this fact can be related to the condition of an objective local parameter space i.e. essentially to einstein locality and the existence of elements of reality . we first deal with the question of the relation between the elements of reality that are carried " by the correlated spin pair and the elements @xmath0 of a probability space . part of the work around the bell theorem concentrates on the question whether elements of reality that determine ( or at least co - determine ) the outcome of the spin measurement can exist . is not @xmath0 such an element of reality and do we not assume then its existence to start with ? the answer is that the @xmath0 s represent only a necessary tool to count and average all measurements correctly . whether or not the outcome of a single measurement is the causal consequence of an element of reality is , at this point , not discussed . the symbol @xmath0 represents just the choice of the goddess tyche ( fortuna ) for the given experiment . of course , if an element of reality exists , @xmath0 can just represent this element . the question of whether such elements of reality can exist in nature and do explain the epr experiments was , of course , a subject of the einstein - bohr debate and is also subject of our discussion here . to explore this question using the bell inequalities we need to explore whether there exist physical reasons that demand the definition of @xmath38 on one probability space . a very important and broadly applicable physical reason for the definition of @xmath38 on one common probability space arises for the case in which all random variables are characterized only by the information emanating from a common source . if in addition this information is stochastically independent of the settings ( delayed choice arguments ) , then in line with our notational convention @xmath38 are completely determined by one random variable @xmath9 corresponding to the elements of reality @xmath82 . these elements of reality can be viewed as the value the random variable @xmath9 assumes for the experiment that we denoted by @xmath0 i.e. we have the relation @xmath83 . the settings may , of course , also be treated as random variables and may be defined on a separate probability space . however , because @xmath9 and the settings are stochastically independent , all random variables can be defined on one common probability space namely the product space . we have discussed details of these facts in @xcite . under these conditions the bell inequalities will hold and the mathematical model obeying these conditions is in contradiction to quantum mechanics . we will show in the next section how this contradiction can be resolved by still using a classical space - time framework and just adding time and setting dependent equipment random variables in addition to the source random variable @xmath9 . we would like to emphasize , however , that even though the system consisting of source parameters only correctly can be ruled out , this fact does not necessarily have anything to do with einstein locality . for example , we can introduce a source parameter represented by a random variable @xmath84 that operates only if the settings @xmath85 and @xmath21 are employed and @xmath84 knows " of these settings by action at a distance . similarly we admit a completely different source parameter @xmath86 that operates and operates only if the three different settings @xmath87 and @xmath88 are going to be chosen . again @xmath86 knows " of these settings @xmath89 , @xmath88 by action at a distance . as long as @xmath84 is a random variable defined on some probability space and @xmath86 is a random variable defined on some possibly different probability space , the bell inequalities formed as before for the settings @xmath85 , @xmath21 respectively for @xmath89,@xmath88 are valid in spite of the assumption of action at a distance . thus a contradiction exists between the results of quantum mechanics and the physical assumptions that have just been described and that appear , on the surface , to be very general . this contradiction has therefore been explained by some authors invoking violations of einstein locality @xcite . others have given more reasonable , albeit noncommittal , explanations by postulating that ( i ) the elements of reality simply do not exist and/or ( ii ) there exists a contextuality " as discussed in @xcite . different contexts of measurements provide then different probability spaces . there were also other choices to explain the difficult situation such as ( iii ) counterfactual reasoning was held responsible for the difficulties @xcite . as we have shown , no counterfactual reasoning is necessary to derive the inequalities and the extended counterfactual reasoning ( eca ) described above is flawed from the viewpoint of mathematical modelling . we will show in the next section that explanations ( i ) and ( ii ) can , in principle , be reformulated in such a way as to have a natural explanation in the space - time of relativity . we note that ( i ) and ( ii ) contain in essence bohr s interpretation : the spin is determined in the moment of measurement and , with respect to measurements in any of the two wings of the experiment , there is essentially the question of an influence on the very conditions which define the possible types of prediction ... " @xcite . as the basis for our reasoning in this section , we will assume or postulate certain properties for the parameters and random variables of the probability theory that are in harmony with special relativity . we define with each basic experiment that corresponds to an element @xmath0 of the probability space a pair of light - cones corresponding to locations and time at which the experiments are performed as shown in fig [ fig : lightcones ] . the elements of reality and the corresponding random variables of the mathematical model are permitted to be functions of the space - time coordinates of the respective light - cones . as parameter random variables we admit not only source parameters but also equipment parameters for each measurement station . what we introduce below is a dependence of the equipment parameters of a given station on the setting vector in the light - cone of that station and an additional dependence on the time of measurement of a clock in the inertial frame of the equipment . all we need to achieve is to derive a model for ma - epr within the space - time of relativity that is not refuted by bell - type inequalities and agrees with ( i ) and ( ii ) in spirit ( if not the letter ) . for this it is only necessary to find an einstein local model with random variables @xmath38 that can not be defined on one common probability space . to show that this is possible we revert to the standard notation using the settings as subscripts and denoting the functions in the two experimental wings by @xmath90 on one side and @xmath91 on the other . we continue to permit all functions to be functions of a source parameter @xmath9 which may have a time dependence e.g. @xmath9 may depend on the time of emission of the correlated pair . however , we also add equipment random variables . of course , equipment parameters have been discussed before in many research articles . but none of them considered the role of time dependencies of these equipment parameters except our work ( see @xcite ) . we permit that the probability densities of these additional random variables depend on the time of measurement @xmath92 as shown by a local clock and also to depend on the local setting . we indicate this latter fact by denoting the additional random variable e.g. for setting @xmath11 by @xmath93 we then have @xmath94 and similar for the other settings and the @xmath12 s on the other side e.g. @xmath95 . notice that all light - cones for different measurement times may contain different @xmath93 even though the setting is the same . no matter how a probabilistic model is conceived , different light - cones can certainly support different probability distributions for the elements of reality . assume now that as in the aspect - type experiment the settings on each side are sequentially changed . because according to relativity this change of settings to take place requires a time interval of length bounded away from 0 by a positive constant @xmath96 , all light - cone pairs of a sequence of measurements are different and each such experiment may be on a different probability space with a different density of the involved random variables . furthermore , let @xmath97 be an element of a probability space that determines the random times of measurement i.e. @xmath98 is the actual measurement time of a given experiment . we now show that physical reasons , derived from the framework of relativity only , necessitate the involvement of different probability spaces if one postulates the existence of time and setting dependent einstein local equipment parameters . theorem2 : assume that there exist a source parameter @xmath9 and equipment parameters @xmath99 and @xmath100 such that @xmath99 and @xmath100 not only depend on the setting vectors @xmath101 and @xmath21 , respectively , but also on the time @xmath92 of a given measurement . here we consider @xmath92 to be a random variable @xmath102 . thus @xmath103 the source parameter @xmath104 is permitted to depend on emission time . we assume further that the random variables corresponding to the measurements of spin @xmath105 and @xmath106 all equal to @xmath26 are functions of the source parameter and of the equipment parameters @xmath99 and @xmath100 . then , under the assumption that the velocity of light in vacuo is an upper limit for the velocities by which the settings can be changed , there is no probability space on which all of @xmath107 @xmath108 @xmath109 @xmath110 can be consistently defined . proof : let @xmath111 be any time interval of length @xmath112 . let @xmath113 be a measurable set in the range of @xmath9 and let @xmath114 and @xmath115 be sets in the ranges of @xmath116 , @xmath117 and @xmath100 respectively . then @xmath118 \label{bvcc13}\ ] ] is the impossible event and therefore has probability 0 . recall that @xmath0 signifies the sending out of a particular particle pair from the source . this result simply reflects the impossibility in the space - time of relativity to accomplish two different settings on both sides within the same short time interval and all for the same @xmath0 . hence for each time interval @xmath111 each of the sixteen probabilities @xmath119 = 0 \label{bvcc15}\ ] ] must vanish . here @xmath120 denotes the dependence on source and equipment parameters that in turn depend on @xmath0 and @xmath97 respectively just as in eq.([ccc2 ] ) . now let @xmath121 be a finite but arbitrarily long time interval . then @xmath121 can be split up into a large but finite number @xmath122 of intervals @xmath123 with length @xmath124 . then the probability in eq.([bvcc15 ] ) with @xmath111 replaced by @xmath121 also must vanish because of finite additivity and thus @xmath125 and @xmath106 can not be defined on a common probability space as claimed . in other words , not only must we have different probability spaces involved in the aspect - type experiment for mathematical reasons , we must have different probability spaces for physical reasons , the requirements of relativity . we emphasize that none of the assumptions in the above proof imply any synchronization of the measurement times with certain settings . both settings and measurement times can be chosen randomly , only the measurement times in @xmath14 and @xmath16 are correlated for any given photon pair . note that the essence of bohr s discussion is not violated by the above . we just need to view both spin and measurement equipment in the sense of information theory : the measurement outcome is really not the single consequence of the source information @xmath82 that characterizes particle properties but also that of the measurement equipment and the corresponding @xmath126 etc .. these equipment parameters correspond to the use of decoding machines in information theory @xcite . both the source information content together with that of the decoding machines or equipment parameters ( that involve different probability spaces ) determine the measurement outcomes i.e. the values @xmath26 that the functions @xmath127 etc . in a larger sense this fulfills the spirit of bohr . the spin does not really exist before the measurement , but only in the very moment of measurement is the outcome determined ( decoded ) and can not be separated from the equipment and act of measurement . the contextuality is implicitly contained in the dependence of the probability densities of the various variables on measurement time . for example , it is now incorrect to say that it makes no difference if one measures with setting @xmath15 or setting @xmath21 on the other side . it does make a difference because one necessarily makes these different measurements during different time intervals . the measurements in both wings are also performed at the same clock - time or at least at correlated clock - times which opens the possibility of correlations between the two wings even though the settings are randomly chosen . what is the meaning then of the aspect et al . @xcite experiment in view of the above discussions ? if one assumes that this experiment is free from any problems related to non - ideal experimental conditions and if one assumes that a space - time explanation must be possible then the aspect et al . experiment has proven the existence of setting and time dependent equipment parameters . we have shown that the inequalities of bell can be derived as special cases of a more general theorem found by bass ten years earlier . we have further shown that the bell inequalities are valid if and only if the three random variables involved can actually be defined on a common probability space . as a consequence the bell theorem is correct at least for the following systems of hidden variables , in the sense that these systems can be ruled out : 1 . source parameter @xmath9 only , 2 . source parameter @xmath9 and equipment parameters @xmath116 , @xmath117 and @xmath100 that depend only on the respective settings . on the other hand , equipment parameters that depend on the measurement times as well as on the respective instrument settings can not be ruled out . a space - time explanation of the aspect et al . experiment is therefore not ruled out by bell s inequalities . any such space - time explanation can not rely on source parameters only but must involve a certain type of time and setting dependent equipment parameter random variables . thus , the validity of the bell inequalities for objective local parameter spaces has not been proven by any of the proofs reported in the literature @xcite , @xcite , @xcite . the authors would like to thank m. aschwanden for creating the figures of the manuscript and helpful suggestions . support of the office of naval research ( n00014 - 98 - 1 - 0604 ) is gratefully acknowledged .

the theorem of bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables . we show that the inequalities of bell are special cases of theorems found ten years earlier by bass and stated in full generality by vorobev . this fact implies precise necessary and sufficient mathematical conditions for the validity of the bell inequalities . we show that these precise conditions differ significantly from the definition of objective local variable spaces and as an application that the bell inequalities may be violated even for objective local random variables .

<s>[INST]einstein - podolsky - rosen ( epr ) @xcite suggested that quantum mechanics was incomplete and that hidden variables may be needed for completion . this was the subject of an extensive debate with bohr @xcite who denied the existence of such hidden variables using his well known reasoning that is at the basis of the copenhagen interpretation of quantum mechanics . a mathematical non - existence proof for these hidden variables was presented by von neumann within the framework of quantum mechanics . bell @xcite , however , showed that von neumann s proof assumed the simultaneous measurability of certain quantities that could not possibly be simultaneously measured . subsequently bell himself presented a non - existence proof @xcite in form of inequalities that are derived by using more complex assumptions that did not necessarily include simultaneous measurability . the inequalities of bell @xcite are derived by the use of probability theory , in essence by the use of very elementary facts about random variables within the framework pioneered by kolmogorov . the derivation of the inequalities does not involve physics or quantum mechanics , yet the inequalities have assumed an important role for the foundations of quantum mechanics . this role is a consequence of the assumptions for the random variables ( and other possible variables ) that are used to derive the bell inequalities . it is commonly believed that these assumptions are needed and moreover are equivalent to the basic postulates of an objective local " parameter space @xcite . these postulates or conditions encompass einstein - locality and the existence of elements of reality in the sense of mach that co - determine the outcome of measurements . the fact that some results of quantum mechanics violate the bell inequalities has therefore led to the belief that no objective local parameter space can exist that explains all the results of quantum mechanics . subsequent to these discussions experiments were proposed @xcite , @xcite and later realized @xcite that confirmed the theoretical result of quantum mechanics . this seemed to leave only difficult options for theoretical physics such as ( i ) to deny that the microscopic entities of physics have objective reality ( non - existence of objective local parameters ) or ( ii ) to assert that an influence can be propagated faster than the speed of light @xcite . additional options involving the validity of counterfactual reasoning have also been suggested and will be discussed below . we show in this paper that because of the historical sequence of events , viz . the development of bell s theory before the performance of the actual experiments , some very important facts of probability theory have not been considered and/or misinterpreted . these facts are connected with the concept of a probability space that is important to link probability theory and mathematical statistics to the evaluation of actual experiments . we reconsider here these concepts and show that violations of the bell inequalities have a purely mathematical reason , in particular that the bell inequalities represent a special case of theorems given earlier by bass @xcite , vorobev @xcite , @xcite and schell @xcite . these theorems permit us to deduce that , for all the possible bell inequalities to be valid , it is a necessary and sufficient condition that the random variables involved in their proof are defined on one common probability space . beyond this we show that the requirement of the use of one common probability space does not follow from the requirements of objective local spaces and vice versa . in fact , we show that there exist objective local random variables that can not be defined on a common probability space and therefore do not need to obey the bell inequalities . as mentioned , bell has dismissed von neumann s proof that assumed from the start the simultaneous measurability of the observables that correspond to our random variables and that can not be measured simultaneously . our contribution here is that we also dismiss non - existence proofs of certain systems of random variables that need to be defined on one common probability space when it is clear from the outset that these systems of random variables can not be defined on any common probability space . we believe that our results give additional options of explanation for aspect - type experiments without violating relativity or denying objective reality . as outlined above , probability theory provides a probability space and random variables and the link to the statistical treatment of the data from an actual experiment . bell @xcite considered an experimental situation advocated by bohm and aharonov @xcite , and by bohm and hiley @xcite . this proposal was transformed into an actual experiment by aspect et al . @xcite including the suggestion of bell and others that a rapid change of the settings needed to be implemented to accomplish a delayed choice situation @xcite . we develop now an idealized experiment and a probability model for this actual experiment by aspect et al within the framework of kolmogorov . we note that our procedure also applies to other related experiments . we first recall the concepts of a ( discrete ) probability space and of a random variable defined on it . as feller states @xciteif we want to speak about experiments or observations in a theoretical way and without ambiguity , we first must agree on the simple events representing the thinkable outcomes ; _ they define the idealized experiment _ ...... by definition _ every indecomposable result of the ( idealized ) experiment is represented by one , and only one , sample point_. the aggregate of all sample points will be called the _ sample space_. " in our case of the idealized epr experiment , the simple event can be chosen , for example , as the event of sending out one ( and only one ) correlated pair . with this event we associate an element @xmath0 . in order to avoid mathematical technicalities that are not needed for the purpose of our paper we assume that the sample space @xmath1 is at most countable . each simple event @xmath2 is assigned the probability @xmath3 that @xmath0 occurs . @xmath4 is a set function , defined for all subsets of @xmath1 , that satisfies the usual axioms , such as countable additivity and it assigns to @xmath1 the value @xmath5 . the pair @xmath6 is called a probability space . a random variable is a real - valued function on @xmath1 , but if needed it also can assume values in high - dimensional space . we now turn to the specifics of an idealized epr - experiment . a correlated spin pair in the singlet state is sent out from a source in opposite directions toward measurement stations . these stations are characterized by certain randomly and rapidly switched settings which we denote by three dimensional unit vectors @xmath7 . the measurements in the stations are mathematically represented by random variables @xmath8 that may in turn be functions of other random variables e.g. a source parameter @xmath9 that characterizes all the properties of the particles sent out from the source . @xmath10 indicates that the measurements that correspond to the outcomes of random variable @xmath10 have been performed using the setting @xmath11 and similarly for @xmath12 and @xmath13 . we perform three categories of experiments , each with a different pair of setting vectors . the first category is characterized by the vectors @xmath11 in station @xmath14 and @xmath15 in station @xmath16 . according to our notational convention we denote the pair of measurements @xmath17 and the joint probability density of @xmath10 and @xmath12 by @xmath18 . thus @xmath18 is given by @xmath19 @xmath20 the second category of experiments will be characterized by the vectors @xmath11 in @xmath14 and @xmath21 in @xmath16 with the resulting pair of measurements @xmath22 having density @xmath23 , and the third category by the vectors @xmath15 in @xmath14 and @xmath21 in @xmath16 resulting in a pair of measurements @xmath24 with density @xmath25 . the measurement outcomes on both sides need to be completely random and @xmath26 with equal probability , i.e. all three distributions have identical marginals . this is dictated by the rules of quantum mechanics and verified by experiment . from this it follows that the @xmath27 have the center of gravity for their point masses at the origin @xmath28 and @xmath29 the idealized mathematical model with exactly the properties described above and used within the framework of kolmogorov is the basis for all our further considerations and we call it the ma - epr model . we start with an example that illustrates the theorems of bass @xcite and vorobev @xcite for the special case of the ma - epr model . the essential point of these theorems is that , in general , it is not possible to find three random variables @xmath30 and @xmath13 , defined on a common probability space such that the three pairs @xmath31 , @xmath32 , and @xmath33 of random variables have their joint densities equal to @xmath34 and @xmath25 , respectively . hence the notation that is commonly used and that we also introduced in section 2 above is misleading in the sense that it suggests there exist three random variables @xmath30 and @xmath13 that can reproduce the joint densities @xmath18 , @xmath23 and @xmath25 , when in fact they can not . here is a modification of an example of vorobev @xcite . .vorobev - type example @xcite . [ cols="<,>,>,>,>",options="header " , ] it is easy to show that under the assumption of eq([bv1 ] ) the joint pair densities can be expressed in terms of the covariances @xmath35 defined by these pair densities . the pair densities are then given by table [ ta : ob ] ( see also the lemma below ) . note that the covariances @xmath36 do not exceed @xmath37 in absolute value . suppose now that there exist three random variables @xmath38 defined on one common probability space that reproduce the densities @xmath39 in table [ ta : ob ] . then @xmath40 , @xmath41 , and @xmath42 where @xmath43 denotes the expectation value . expressing the entries of table [ ta : ob ] in terms of the eight unknown probabilities @xmath44 will result in a system of twelve linear equations in these eight unknowns that can be solved in an elementary way . in particular , solving this system shows that these eight probabilities can be expressed in terms of the three covariances @xmath45 . it turns out that five of these twelve linear equations are redundant . thus this system has infinitely many solutions . taking into account that the solutions of this system represent probabilities @xmath46 we obtain in a straightforward way that the following four inequalities are necessary and sufficient conditions for the solvability of the consistency problem for the three pair distributions given in table [ ta : ob ] : @xmath47 @xmath48 @xmath49 @xmath50 of course , the necessity part of this conclusion can be shown directly and trivially by modifying the standard proofs of the bell inequality along the lines shown in @xcite . replacing the covariances @xmath51 by the corresponding expectation values , one obtains from eqs.([bvcc2]-[bvcc3 ] ) : @xmath52 and @xmath53 eqs.([bv6 ] ) and ( [ bv7 ] ) give @xmath54 this is , of course , one of the celebrated bell inequalities . five more can be obtained in analogous fashion from eqs.([bvcc1]-[bvcc4 ] ) giving a total of 6 ( 4 choose 2 ) . these can also be obtained by cyclic permutation in eq.([bv8 ] ) and replacing both minus signs by plus signs . bass @xcite proved that for three general pair distributions the consistency problem can be solved if and only if the triple @xmath55 considered as a point in @xmath56 belongs to a certain domain . in the special case we have been considering this domain reduces to the tetrahedron defined by the inequalities of eqs.([bvcc1]-[bvcc4 ] ) . we shall call it the covariance tetrahedron . it is diplayed in fig . [ fig : tetrahedra ] . we formulate now our findings for the ma - epr experiment as a theorem . we first collect a few facts of section 3 above in form of a lemma . lemma : let @xmath57 be a density supported on the four vertices @xmath58 of a square . suppose that @xmath59 then @xmath60 where the sums are extended over the four points @xmath61 . conversely , if @xmath57 satisfies eq.([bvcc6 ] ) then @xmath57 also satisfies eq.([bvcc5 ] ) . set @xmath62 with the same proviso for the sum . then @xmath57 can be expressed in terms of @xmath51 by the equations @xmath63 @xmath64 theorem1 : let @xmath39 be three probability densities satisfying the hypotheses of the lemma with corresponding covariances @xmath65 . then the following statements are equivalent 1 . the point @xmath66 satisfies the system of inequalities eqs.([bvcc1]-[bvcc4 ] ) and therefore belongs to the covariance tetrahedron . the point @xmath55 satisfies the following six bell - type inequalities @xmath67 @xmath68 @xmath69 3 . there exist three random variables @xmath38 defined on a single common probability space with the following properties . the joint probability densities of @xmath70 and @xmath24 are @xmath34 and @xmath25 respectively . in particular , the expectation values equal @xmath71 the covariances equal @xmath72 using eqs.([bvcc10 ] ) and ( [ bvcc12 ] ) one obtains the six bell inequalities for the expectation values @xmath73 . proofs : the proof of the lemma is straightforward . the proof that conditions ( i ) and ( ii ) of theorem1 are equivalent can be done by inspection . the proof that ( iii ) implies ( ii ) or the six bell inequalities obtained from eq.([bvcc10 ] ) and eq.([bvcc12 ] ) can be carried out by a simple modification of the standard proof of the bell inequalities @xcite . finally , the proof that ( i ) implies ( iii ) was outlined at the end of section 3 . we have shown therefore the following . the inequalities of bell are a special case of the theorems of bass and vorobev for the ma - epr experiment . if the 6 bell inequalities are valid then it is possible to find three random variables @xmath30 and @xmath13 , defined on one common probability space that reproduce the three joint pair densities @xmath74 of table [ ta : ob ] and their covariances @xmath75 and @xmath42 . these covariances satisfy the bell inequalities . therefore , if quantum mechanics predicts that , for a given idealized experiment involving random variables @xmath30 and @xmath13 and @xmath76 , @xmath77 , and @xmath78 , one of the six bell inequalities in eq.([bvcc10 ] ) will be violated or equivalently if the point with coordinates @xmath79 does not belong to the covariance tetrahedron of fig . [ fig : tetrahedra ] , then the random variables @xmath30 and @xmath13 , that are supposed to form the basis for the model of this idealized experiment , can not be defined on one common probability space . we note that the work of fine @xcite has already shown the importance of a joint density and therefore of a common probability space in the derivations of bell - type inequalities . the importance of a common probability space was also stressed more recently in @xcite and other publications . in summary , we have shown that the definability of @xmath30 and @xmath13 on one common probability space ( ocps ) is a necessary and sufficient condition for the validity of bell s inequalities and that this condition is of a purely mathematical nature and has nothing to do with the questions of non - locality or counterfactual reasoning that usually surround discussions of the bell inequalities . the condition is , however , related to some of the physics of epr experiments in a variety of ways that will be discussed in section 6 . we add here that other inequalities of similar type such as the clauser - horne - holt - shimony ( chhs ) @xcite inequalities can be treated similarly , although with greater algebraic exertion ( 16 linear equations in 16 unknowns ) . their validity is again a necessary and sufficient reason that all involved random variables are defined on one common probability space . in fact , a theorem analogous to theorem1 above holds , with the covariance tetrahedron replaced by a four - dimensional polytope . this polytope equals the intersection of the four - dimensional parallelepiped , defined by the four chhs inequalities , and the four - dimensional cube with vertices @xmath80 . the details will be published elsewhere . in view of the ocps condition and the theorems of bass and vorobev , the proofs for the bell inequalities as given by bell and others become obvious and at the same time lacking physical justification . consider bell s original proof @xcite . here bell assumes that all random variables @xmath38 are in turn functions of a single random variable @xmath9 . then it is clear that @xmath38 are defined on one common probability space and therefore the inequalities can not be violated by the pair expectation values as explained above . it is clear that no @xmath9 can exist that leads to a violation of the inequalities for purely mathematical reasons as already found by bass much earlier . bell s physical justification is wanting because he attempts to show that the inequalities follow from the fact that @xmath9 does not depend on the settings @xmath81 . in fact , it does not matter on what @xmath9 depends as long as the resulting @xmath30 and @xmath13 are random variables defined on one probability space . we will discuss this in more detail below . other well known proofs @xcite invoke counterfactual " reasoning of the following kind : if , for example , @xmath10 is measured given a certain information that we denote by @xmath82 ( a value that @xmath9 assumes in a given experiment ) and that is carried by the correlated spin pair , then one could have measured with another setting , say @xmath15 and the same @xmath82 . as we have explained in more detail previously @xcite , it is permissible to ask the question of what would have been obtained if the measurement had been performed with a different setting . it is also permissible to hypothesize the existence of an element of reality related to that different setting if that different setting had been chosen . however , to assume then , as is always done in bell type proofs , that all these possible different measurement results are actually contained in the data set of actual outcomes of the idealized experiment is arbitrary and against all the rules of modelling and simulation especially for the particular case of the aspect - type experiment and all other known epr experiments @xcite . naturally , we do not have to pay for all items on a restaurant s menu just because we could have chosen them . we call this latter assumption the extended counterfactual assumption ( eca ) . eca is equivalent to the assumption that @xmath30 and @xmath13 only depend on one random variable @xmath9 and is therefore an assumption , not a proof . as a consequence , eca implies that @xmath30 and @xmath13 are defined on one common probability space . in view of the bass - vorobev theorem it leads to a contradiction from the outset irrespective and independent of any physical considerations a number of physical conditions have been given in the past that have been thought to be necessary and sufficient for the bell inequalities to be valid . most prominently among these conditions ranks the definition of an objective local parameter space @xcite , @xcite . this definition involves several conditions that are automatically fulfilled in our kolmogorovian model as has been outlined before @xcite ; it further implies the existence of elements of reality that contain information related to the spin ( represented by the random variable @xmath9 ) and , most importantly einstein locality . armed with the knowledge that the validity of the bell inequalities as described above is equivalent to the assumption that @xmath38 can be defined on one common probability space , we must now ask the question how this fact can be related to the condition of an objective local parameter space i.e. essentially to einstein locality and the existence of elements of reality . we first deal with the question of the relation between the elements of reality that are carried " by the correlated spin pair and the elements @xmath0 of a probability space . part of the work around the bell theorem concentrates on the question whether elements of reality that determine ( or at least co - determine ) the outcome of the spin measurement can exist . is not @xmath0 such an element of reality and do we not assume then its existence to start with ? the answer is that the @xmath0 s represent only a necessary tool to count and average all measurements correctly . whether or not the outcome of a single measurement is the causal consequence of an element of reality is , at this point , not discussed . the symbol @xmath0 represents just the choice of the goddess tyche ( fortuna ) for the given experiment . of course , if an element of reality exists , @xmath0 can just represent this element . the question of whether such elements of reality can exist in nature and do explain the epr experiments was , of course , a subject of the einstein - bohr debate and is also subject of our discussion here . to explore this question using the bell inequalities we need to explore whether there exist physical reasons that demand the definition of @xmath38 on one probability space . a very important and broadly applicable physical reason for the definition of @xmath38 on one common probability space arises for the case in which all random variables are characterized only by the information emanating from a common source . if in addition this information is stochastically independent of the settings ( delayed choice arguments ) , then in line with our notational convention @xmath38 are completely determined by one random variable @xmath9 corresponding to the elements of reality @xmath82 . these elements of reality can be viewed as the value the random variable @xmath9 assumes for the experiment that we denoted by @xmath0 i.e. we have the relation @xmath83 . the settings may , of course , also be treated as random variables and may be defined on a separate probability space . however , because @xmath9 and the settings are stochastically independent , all random variables can be defined on one common probability space namely the product space . we have discussed details of these facts in @xcite . under these conditions the bell inequalities will hold and the mathematical model obeying these conditions is in contradiction to quantum mechanics . we will show in the next section how this contradiction can be resolved by still using a classical space - time framework and just adding time and setting dependent equipment random variables in addition to the source random variable @xmath9 . we would like to emphasize , however , that even though the system consisting of source parameters only correctly can be ruled out , this fact does not necessarily have anything to do with einstein locality . for example , we can introduce a source parameter represented by a random variable @xmath84 that operates only if the settings @xmath85 and @xmath21 are employed and @xmath84 knows " of these settings by action at a distance . similarly we admit a completely different source parameter @xmath86 that operates and operates only if the three different settings @xmath87 and @xmath88 are going to be chosen . again @xmath86 knows " of these settings @xmath89 , @xmath88 by action at a distance . as long as @xmath84 is a random variable defined on some probability space and @xmath86 is a random variable defined on some possibly different probability space , the bell inequalities formed as before for the settings @xmath85 , @xmath21 respectively for @xmath89,@xmath88 are valid in spite of the assumption of action at a distance . thus a contradiction exists between the results of quantum mechanics and the physical assumptions that have just been described and that appear , on the surface , to be very general . this contradiction has therefore been explained by some authors invoking violations of einstein locality @xcite . others have given more reasonable , albeit noncommittal , explanations by postulating that ( i ) the elements of reality simply do not exist and/or ( ii ) there exists a contextuality " as discussed in @xcite . different contexts of measurements provide then different probability spaces . there were also other choices to explain the difficult situation such as ( iii ) counterfactual reasoning was held responsible for the difficulties @xcite . as we have shown , no counterfactual reasoning is necessary to derive the inequalities and the extended counterfactual reasoning ( eca ) described above is flawed from the viewpoint of mathematical modelling . we will show in the next section that explanations ( i ) and ( ii ) can , in principle , be reformulated in such a way as to have a natural explanation in the space - time of relativity . we note that ( i ) and ( ii ) contain in essence bohr s interpretation : the spin is determined in the moment of measurement and , with respect to measurements in any of the two wings of the experiment , there is essentially the question of an influence on the very conditions which define the possible types of prediction ... " @xcite . as the basis for our reasoning in this section , we will assume or postulate certain properties for the parameters and random variables of the probability theory that are in harmony with special relativity . we define with each basic experiment that corresponds to an element @xmath0 of the probability space a pair of light - cones corresponding to locations and time at which the experiments are performed as shown in fig [ fig : lightcones ] . the elements of reality and the corresponding random variables of the mathematical model are permitted to be functions of the space - time coordinates of the respective light - cones . as parameter random variables we admit not only source parameters but also equipment parameters for each measurement station . what we introduce below is a dependence of the equipment parameters of a given station on the setting vector in the light - cone of that station and an additional dependence on the time of measurement of a clock in the inertial frame of the equipment . all we need to achieve is to derive a model for ma - epr within the space - time of relativity that is not refuted by bell - type inequalities and agrees with ( i ) and ( ii ) in spirit ( if not the letter ) . for this it is only necessary to find an einstein local model with random variables @xmath38 that can not be defined on one common probability space . to show that this is possible we revert to the standard notation using the settings as subscripts and denoting the functions in the two experimental wings by @xmath90 on one side and @xmath91 on the other . we continue to permit all functions to be functions of a source parameter @xmath9 which may have a time dependence e.g. @xmath9 may depend on the time of emission of the correlated pair . however , we also add equipment random variables . of course , equipment parameters have been discussed before in many research articles . but none of them considered the role of time dependencies of these equipment parameters except our work ( see @xcite ) . we permit that the probability densities of these additional random variables depend on the time of measurement @xmath92 as shown by a local clock and also to depend on the local setting . we indicate this latter fact by denoting the additional random variable e.g. for setting @xmath11 by @xmath93 we then have @xmath94 and similar for the other settings and the @xmath12 s on the other side e.g. @xmath95 . notice that all light - cones for different measurement times may contain different @xmath93 even though the setting is the same . no matter how a probabilistic model is conceived , different light - cones can certainly support different probability distributions for the elements of reality . assume now that as in the aspect - type experiment the settings on each side are sequentially changed . because according to relativity this change of settings to take place requires a time interval of length bounded away from 0 by a positive constant @xmath96 , all light - cone pairs of a sequence of measurements are different and each such experiment may be on a different probability space with a different density of the involved random variables . furthermore , let @xmath97 be an element of a probability space that determines the random times of measurement i.e. @xmath98 is the actual measurement time of a given experiment . we now show that physical reasons , derived from the framework of relativity only , necessitate the involvement of different probability spaces if one postulates the existence of time and setting dependent einstein local equipment parameters . theorem2 : assume that there exist a source parameter @xmath9 and equipment parameters @xmath99 and @xmath100 such that @xmath99 and @xmath100 not only depend on the setting vectors @xmath101 and @xmath21 , respectively , but also on the time @xmath92 of a given measurement . here we consider @xmath92 to be a random variable @xmath102 . thus @xmath103 the source parameter @xmath104 is permitted to depend on emission time . we assume further that the random variables corresponding to the measurements of spin @xmath105 and @xmath106 all equal to @xmath26 are functions of the source parameter and of the equipment parameters @xmath99 and @xmath100 . then , under the assumption that the velocity of light in vacuo is an upper limit for the velocities by which the settings can be changed , there is no probability space on which all of @xmath107 @xmath108 @xmath109 @xmath110 can be consistently defined . proof : let @xmath111 be any time interval of length @xmath112 . let @xmath113 be a measurable set in the range of @xmath9 and let @xmath114 and @xmath115 be sets in the ranges of @xmath116 , @xmath117 and @xmath100 respectively . then @xmath118 \label{bvcc13}\ ] ] is the impossible event and therefore has probability 0 . recall that @xmath0 signifies the sending out of a particular particle pair from the source . this result simply reflects the impossibility in the space - time of relativity to accomplish two different settings on both sides within the same short time interval and all for the same @xmath0 . hence for each time interval @xmath111 each of the sixteen probabilities @xmath119 = 0 \label{bvcc15}\ ] ] must vanish . here @xmath120 denotes the dependence on source and equipment parameters that in turn depend on @xmath0 and @xmath97 respectively just as in eq.([ccc2 ] ) . now let @xmath121 be a finite but arbitrarily long time interval . then @xmath121 can be split up into a large but finite number @xmath122 of intervals @xmath123 with length @xmath124 . then the probability in eq.([bvcc15 ] ) with @xmath111 replaced by @xmath121 also must vanish because of finite additivity and thus @xmath125 and @xmath106 can not be defined on a common probability space as claimed . in other words , not only must we have different probability spaces involved in the aspect - type experiment for mathematical reasons , we must have different probability spaces for physical reasons , the requirements of relativity . we emphasize that none of the assumptions in the above proof imply any synchronization of the measurement times with certain settings . both settings and measurement times can be chosen randomly , only the measurement times in @xmath14 and @xmath16 are correlated for any given photon pair . note that the essence of bohr s discussion is not violated by the above . we just need to view both spin and measurement equipment in the sense of information theory : the measurement outcome is really not the single consequence of the source information @xmath82 that characterizes particle properties but also that of the measurement equipment and the corresponding @xmath126 etc .. these equipment parameters correspond to the use of decoding machines in information theory @xcite . both the source information content together with that of the decoding machines or equipment parameters ( that involve different probability spaces ) determine the measurement outcomes i.e. the values @xmath26 that the functions @xmath127 etc . in a larger sense this fulfills the spirit of bohr . the spin does not really exist before the measurement , but only in the very moment of measurement is the outcome determined ( decoded ) and can not be separated from the equipment and act of measurement . the contextuality is implicitly contained in the dependence of the probability densities of the various variables on measurement time . for example , it is now incorrect to say that it makes no difference if one measures with setting @xmath15 or setting @xmath21 on the other side . it does make a difference because one necessarily makes these different measurements during different time intervals . the measurements in both wings are also performed at the same clock - time or at least at correlated clock - times which opens the possibility of correlations between the two wings even though the settings are randomly chosen . what is the meaning then of the aspect et al . @xcite experiment in view of the above discussions ? if one assumes that this experiment is free from any problems related to non - ideal experimental conditions and if one assumes that a space - time explanation must be possible then the aspect et al . experiment has proven the existence of setting and time dependent equipment parameters . we have shown that the inequalities of bell can be derived as special cases of a more general theorem found by bass ten years earlier . we have further shown that the bell inequalities are valid if and only if the three random variables involved can actually be defined on a common probability space . as a consequence the bell theorem is correct at least for the following systems of hidden variables , in the sense that these systems can be ruled out : 1 . source parameter @xmath9 only , 2 . source parameter @xmath9 and equipment parameters @xmath116 , @xmath117 and @xmath100 that depend only on the respective settings . on the other hand , equipment parameters that depend on the measurement times as well as on the respective instrument settings can not be ruled out . a space - time explanation of the aspect et al . experiment is therefore not ruled out by bell s inequalities . any such space - time explanation can not rely on source parameters only but must involve a certain type of time and setting dependent equipment parameter random variables . thus , the validity of the bell inequalities for objective local parameter spaces has not been proven by any of the proofs reported in the literature @xcite , @xcite , @xcite . the authors would like to thank m. aschwanden for creating the figures of the manuscript and helpful suggestions . support of the office of naval research ( n00014 - 98 - 1 - 0604 ) is gratefully acknowledged .[/INST] the theorem of bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables . we show that the inequalities of bell are special cases of theorems found ten years earlier by bass and stated in full generality by vorobev . this fact implies precise necessary and sufficient mathematical conditions for the validity of the bell inequalities . we show that these precise conditions differ significantly from the definition of objective local variable spaces and as an application that the bell inequalities may be violated even for objective local random variables . </s>

let @xmath10 be a connected orientable surface of genus @xmath11 with @xmath3 punctures and negative euler characteristic @xmath12 in order that @xmath13 is uniformized by a fuchsian group @xmath14 . namely , let @xmath15 denote the upper half plane with its poincar metric @xmath16 and projective matrix group @xmath17 of oriented isometries , where @xmath18 denotes the identity matrix ; there is then an injective representation @xmath19 of the fundamental group @xmath20 , which is a free group of rank @xmath21 , onto a discrete subgroup @xmath22 so that non - trivial loops about punctures are represented by parabolic transformations , namely , those with absolute trace equal to two . see @xcite for example . the _ teichmller space _ of @xmath2 is @xmath23 where the prime indicates fuchsian representations as just defined and the action of @xmath6 on @xmath24 is by conjugation . the _ super - teichmller space _ of @xmath2 as already formulated in the context of representation theory and moduli spaces by bryant and hodgkin @xcite ( see also @xcite ) is @xmath25 where the corresponding super fuchsian representations comprising @xmath24 are defined to be those whose projection @xmath26 are fuchsian , where @xmath8 denotes the orthosymplectic group of @xmath27-by-@xmath27 dimensional super matrices with its canonical projection @xmath28 , cf . @xcite or appendix i , and the action on @xmath24 is again by conjugation . the similarities are evident . in particular , the _ mapping class group _ @xmath29 of homotopy classes of orientation - preserving homeomorphisms of @xmath2 acts on @xmath5 and @xmath1 in the natural way . consider a graph @xmath30 embedded in @xmath2 as a deformation retract also called a _ spine _ of @xmath2 . the _ valence _ of a vertex of @xmath31 is the number of half - edges incident upon it , where a half - edge is defined as a complementary component to an interior point of the edge , and @xmath31 is said to be _ trivalent _ if each vertex has valence exactly three . an orientation on @xmath2 induces the counter clockwise ordering on the half edges of @xmath31 incident on each fixed vertex thus giving the abstract graph @xmath31 the structure of a _ fatgraph _ sometimes also called a ribbon graph . there is a combinatorial move on trivalent fatgraph spines @xmath30 called a _ flip _ as illustrated in figure [ flip0 ] , where one contracts an edge of @xmath31 with distinct endpoints and then expands the resulting 4-valent vertex in the unique distinct manner in order to produce another trivalent fatgraph spine . this leads to the so - called _ ptolemy groupoid _ of @xmath2 whose objects are homotopy classes of trivalent fatgraph spines in @xmath2 and whose morphisms are compositions of flips . as we shall recall in the next introductory section dedicated to the bosonic case , finite compositions of flips act transitively on homotopy classes of trivalent fatgraph spines . it follows that flips generate @xmath29 in the sense that if @xmath30 is a trivalent fatgraph spine and @xmath32 , then there is a sequence @xmath33 of trivalent fatgraph spines of @xmath2 where any consecutive pair differ by a flip . in fact @xcite , the components of @xmath34 are naturally indexed by the set @xmath35 of spin structures on @xmath2 , and here is a basic difference from the bosonic case : the super - teichmller space is disconnected with the @xmath29-action permuting components . there are a number of equivalent formulations of spin structure , and we shall rely upon several of them at various junctures . milnor s elegant formulation of a spin structure on @xmath2 is a class in the mod two first cohomology of the unit tangent bundle of @xmath2 which is non - zero on the fiber class ; see @xcite . more combinatorial formulations from the literature which we shall require are as follows : .2 in @xmath36 the description @xcite due to johnson in terms of _ quadratic forms _ @xmath37 on @xmath38 , i.e. , functions @xmath39 which are quadratic for the intersection pairing @xmath40 in the sense that @xmath41 if @xmath42 . @xmath36 cimasoni and reshetikhin @xcite formulate spin structures using @xcite in terms of so - called kastelyn orientations and dimer configurations on the one - skeleton of a suitable cw decomposition of @xmath2 as we shall explain in detail later . @xmath36 a spin structure on a uniformized surface @xmath13 is determined by a lift @xmath43 of @xmath44 , and natanzon @xcite computes in terms of the quadratic form @xmath45 that @xmath46 if and only if @xmath47)\neq 0 $ ] , where @xmath48\in h_1 $ ] here and in the sequel is the image of @xmath49 under the mod two hurewicz map . = 0ex our first main result gives yet another combinatorial formulation of spin structures on @xmath2 in terms of the equivalence classes @xmath50 of all orientations on a trivalent fatgraph spine @xmath30 , where the equivalence relation is generated by reversing the orientation of each edge incident on some fixed vertex , with the added bonus of a computable evolution under flips . * theorem a. * _ fix any trivalent fatgraph spine @xmath51 . then @xmath52 and @xmath53 are isomorphic as affine @xmath54-spaces . moreover , the action of @xmath29 on @xmath37 or @xmath35 lifts to the action of the ptolemy groupoid on @xmath52 illustrated in figure [ flipper ] . _ + a spin structure on @xmath2 manifest for instance as a quadratic form @xmath55 distinguishes two types of punctures as follows . if @xmath56 is a simple loop about the puncture @xmath57 of @xmath2 , then @xmath57 is called a _ neveu - schwarz _ ( ns ) puncture if @xmath58)=0 $ ] and is otherwise called a _ ramond _ ( r ) puncture . the dimension of a component of @xmath1 depends on the types of punctures , and each component of @xmath59 is in fact @xcite a superball of dimension @xmath60 , where @xmath61 and @xmath62 are the respective numbers of @xmath63 and @xmath64 punctures . it is not hard to see that @xmath65 must be even since the sum of the @xmath66-monodromies about the punctures must agree with the trivial monodromy about a small inessential curve in the surface , and we furthermore evidently have @xmath67 . in the bosonic case @xcite , there is a principal @xmath68-bundle @xmath69 called the _ decorated teichmller space _ of @xmath10 recalled in some detail in the next introductory section . letting @xmath70 here and in the sequel denote the subspace of @xmath71 whose even coordinates have positive body , there is likewise a principal @xmath72-bundle over each component of @xmath1 with @xmath65 ramond punctures called the _ decorated super - teichmller space _ and written simply @xmath73 and the action of @xmath29 lifts to @xmath0 as we shall see . here we combine the main results from sections 8 and 9 into one result : * omnibus theorem b. * _ fix a surface @xmath10 of genus @xmath11 with @xmath3 punctures , where @xmath74 , let @xmath30 be some trivalent fatgraph spine and suppose that @xmath75 is an orientation on the edges of @xmath31 whose class in @xmath50 determines the component @xmath76 of @xmath0 . then there are global affine coordinates on @xmath76 , one even coordinate called a @xmath77-length for each edge and one odd coordinate called a @xmath78-invariant for each vertex of @xmath31 , the latter of which are taken modulo an overall change of sign denoted by @xmath66 ; that is , @xmath77-lengths and @xmath78-invariants establish a real - analytic homeomorphism @xmath79 these coordinates are natural in the sense that if @xmath32 has induced action @xmath80 on @xmath81 , then @xmath82 is determined by the orientation and coordinates on edges and vertices of @xmath83 induced by @xmath84 from the orientation @xmath75 , the @xmath77-lengths and @xmath78-invariants on @xmath31 . + orientations on fatgraph spines evolve under flips in accordance with the previous theorem , and the following super ptolemy transformation further describes the evolution of @xmath77-lengths and @xmath78-invariants in the notation of figure [ flip0 ] where nearby roman letters denote @xmath77-lengths , nearby greek letters denote @xmath78-invariants and @xmath85 denotes the cross - ratio @xmath86 + finally , there is an even 2-form on @xmath0 which is invariant under super ptolemy transformations , namely , @xmath87 where the sum is over all vertices @xmath88 of @xmath31 where the consecutive half edges incident on @xmath88 in clockwise order have induced @xmath77-lengths @xmath89 and @xmath90 is the @xmath78-invariant of @xmath88 . _ in order to further explain the coordinates and give an intrinsic meaning to the decorated spaces , we shall recall and extend the bosonic case in the next section . the super - teichmller space is of interest on its own as one of the higher teichmller theories associated with the simplest supergroup extension of @xmath91 , namely , the orthosymplectic group @xmath8 which is however special among supergroups in that its invariant bilinear form is non - degenerate . nevertheless , this should be the first step in a general approach to higher super teichmller theory as well as its quantization . notice that the symplectic or corresponding poisson structure of theorem b has constant coefficients opening the possibility of canonical quantization as in the bosonic case @xcite . furthermore just as for @xmath77-lengths in the bosonic case , our coordinates on decorated super - teichmller space provide a computationally effective description of super moduli geometry . another key reason for interest in the super - teichmller space is that it is a cornerstone of superstring perturbation theory , and the geometry of the supersymmetric moduli uncovered here is evidently more involved than its bosonic counterpart . moreover , the well - known relationship @xcite of teichmller theory with @xmath92-dimensional gravity may suggest that the super - teichmller theory as probed here may play an analogous role for @xmath92-dimensional supergravity . we finally mention that prior to our work , there was a phd thesis @xcite , presumably to be continued in @xcite , where the author provided other coordinates on a version of super - teichmller space via a different treatment of spin structures and based upon quite a different approach effectively using so - called shear coordinates instead of @xmath77-lengths without our deep connection to super minkowski geometry described in the next several sections . + * acknowledgements . * both authors are grateful to institut des hautes tudes scientifiques for hospitality at the initial phase of this work . is indebted to a.n . fedorova for careful reading of the manuscript . the decorated teichmller space @xmath93 is intimately connected to the geometry of minkowski space @xmath7 , namely , @xmath94 imbued with the quadratic form @xmath95 and its corresponding bilinear pairing @xmath96 or equivalently the quadratic form @xmath97 in the variables @xmath98 and @xmath99 . the upper sheet @xmath100 of the hyperboloid with the induced metric gives a model for the hyperbolic plane @xcite . furthermore @xcite , the positive light cone @xmath101 parametrizes horocycles ( that is , those curves with geodesic curvature unity ) in the sense that @xmath102 establishes a bijection is the more natural choice ; cf . @xcite . ] between all @xmath103 and the collection of all horocycles @xmath104 , and moreover , this identification is geometrically natural in the sense that @xmath105 is the signed hyperbolic distance between @xmath106 and @xmath107 . this invariant @xmath108 of a pair @xmath109 of horocycles is called the _ lambda length _ , and these are the basic coordinates on @xmath93 . it is convenient both here and in the sequel to consider not only trivalent fatgraph spines of @xmath10 but also their duals : an _ ideal triangulation _ @xmath110 of @xmath2 is a maximal family of arcs embedded in @xmath2 with endpoints at the punctures , which are here regarded as distinguished points of @xmath2 , where no two arcs in @xmath110 are properly homotopic or intersect except perhaps at their endpoints . by maximality , each complementary region to @xmath110 in @xmath2 is an ideal triangle , and these meet along their frontiers in @xmath2 . construct a trivalent fatgraph spine @xmath111 of @xmath2 with one vertex for each complementary region and one edge for each arc in @xmath110 required to connect the vertices corresponding to regions on either side of the arc this construction evidently establishes a bijection between homotopy classes of trivalent fatgraph spines and homotopy classes of ideal triangulations of @xmath2 together with a natural identification between their edges . the dual of a flip , also called a flip , is the removal of an edge from @xmath110 with distinct triangles on either side followed by its replacement by the other diagonal of the quadrilateral formed by their union . a key point of the decorated space in the bosonic case is that the fiber @xmath112 of @xmath113 is identified with all @xmath114-tuples of ( lengths of ) horocycles in @xmath2 with one horocycle about each puncture ; this is precisely the sense in which a usual hyperbolic structure in @xmath5 is _ decorated with a horocycle at each puncture _ in @xmath93 . the @xmath29-action on @xmath5 thus lifts to @xmath93 by permuting lengths . an arc connecting punctures in a decorated hyperbolic surface has a well - defined lambda length computable in the surface itself or equivalently in @xmath7 as just discussed . + * omnibus theorem c. * @xcite _ fix a surface @xmath10 of genus @xmath11 with @xmath3 punctures , where @xmath74 , and let @xmath110 be a homotopy class of ideal triangulation or equivalently of a trivalent fatgraph spine of @xmath2 . then the assignment of lambda lengths to the arcs in @xmath110 establishes a real - analytic homeomorphism @xmath115 . moreover , the lambda length @xmath116 of a ( homotopy class of ) arc @xmath117 in @xmath2 connecting punctures for @xmath118 is natural in the sense that if @xmath32 has induced action @xmath119 on @xmath93 , then @xmath120 . + the ptolemy transformation @xmath121 describes the evolution of lambda lengths under flips in the notation of figure [ flip0 ] . + the weil - petersson khler form on @xmath122 pulls back to the ptolemy - invariant form @xmath123 where the sum is over all complementary triangles to @xmath110 with consecutive half edges in clockwise order having induced lambda lengths @xmath89 . + a convex hull construction in @xmath124 gives rise to a real - analytic @xmath29-invariant ideal cell decomposition of @xmath125 itself where there is one open simplex together with certain of its faces for each homotopy class of decompositions of @xmath2 into ideal polygons and the face relation is generated by removal of arcs . _ + thus in the equivalent formalism of trivalent fatgraph spines as opposed to ideal triangulations , theorem b extends all but the last paragraph of theorem c from @xmath93 to @xmath0 , and the proof of the former provides a paradigm for the proof of the latter . notice that by this last paragraph of theorem c , we may connect interior points of simplices for any two ideal triangulations of @xmath2 by a path in @xmath125 , which can be perturbed to general position with respect to the codimension - one faces of the cell decomposition . since crossing these faces corresponds to flips , it follows that any two ( homotopy classes of ) ideal triangulations of @xmath2 are related by a finite sequence of flips , and dually we recover whitehead s result @xcite : * corollary d * _ for any surface @xmath10 with @xmath74 , finite sequences of flips act transitively on homotopy classes of trivalent fatgraph spines in @xmath2 . _ moreover , the codimension - two faces analogously give rise to a presentation of the ptolemy groupoid of @xmath2 , cf . @xcite . we next discuss the proof of the first part of theorem c , namely , the construction of lambda length coordinates on @xmath93 which brings us more deeply into minkowski space . the topological universal cover @xmath126 of @xmath2 may be identified with upper half space @xmath127 or equivalently via the cayley transform @xmath128 with the unit disk @xmath129 supporting its poincar metric and ideal boundary the circle @xmath130 at infinity . central projection of @xmath131 from @xmath132 to the disk at height zero establishes an isometry of @xmath131 and @xmath129 which continuously extends to the projection @xmath133 mapping @xmath103 to the center of the horocycle @xmath106 . an ideal triangulation @xmath110 of @xmath2 lifts to an ideal triangulation @xmath134 of @xmath126 , and the collection of ideal points of @xmath135 is invariant under homotopy of @xmath110 in @xmath2 . in order to define a point of @xmath93 , we must determine a fuchsian representation @xmath136 in the component @xmath137 of the identity of the minkowski isometry group @xmath138 , corresponding to the underlying point in @xmath5 , together with a lift @xmath139 , corresponding via affine duality to the decoration and realizing the lambda lengths in the obvious sense , which is @xmath140-equivariant with respect to our constructed representation @xmath141 , namely , we have @xmath142 , for all @xmath143 and @xmath49 . this construction of @xmath144 and @xmath145 from lambda lengths is performed recursively as we shall recall in proving theorem b. in our current case , there is an embedding of @xmath8 into the super lorentz group of the super minkowski space @xmath9 with pairing @xmath146 as described in the next section . there is again a positive light cone @xmath147 comprised of isotropic vectors so that the bodies of @xmath148 and @xmath149 are non negative . however , here is another fundamental distinction between the bosonic case and the general case treated here : whereas the action of @xmath137 on @xmath150 is transitive , an @xmath8-orbit of positive isotropic vectors is determined by a fermionic invariant @xmath151 up to sign . though most of the computations of this paper can be completed in the general setting , the super teichmller theory seems to require taking this fermion label @xmath152 . it is the special light cone @xmath153 consisting of those positive isotropic vectors with vanishing fermion label @xmath154 that provide the analogue of @xmath150 for us here . again , we define the @xmath77-length of a pair of points in @xmath155 to be the square root of their inner product and prove that this is the unique invariant of the @xmath8-orbit of a pair of linearly independent points in @xmath155 . we shall again recursively define a mapping @xmath156 which realizes @xmath77-lengths in the obvious sense and is @xmath140-equivariant with respect to the representation @xmath157 that we construct . here is yet another fundamental distinction between the bosonic case and the general case : whereas @xmath137 acts transitively on triples of rays in @xmath150 which are consistent with the positive orientation on @xmath7 , an @xmath8 orbit of a triple in @xmath155 whose underlying bosonic vectors in @xmath150 have this property is again determined by a fermion invariant @xmath158 up to sign . manin @xcite had already observed this basic phenomenon hence our term @xmath78-invariant for the odd invariants associated to vertices of a fatgraph spine in theorem b which come from consistent choices of signs and are , like @xmath77-lengths , realized by the mapping @xmath144 in the obvious sense . consistency here is given by an explicit relationship on signs of @xmath78-invariants for adjacent triangles in @xmath159 . there are thus three basic differences here from the bosonic case : the failure of transitivity of the @xmath8-action on points and on triples in @xmath155 already mentioned and the further fact that the identification of @xmath150 with the space of horocycles in @xmath131 has no known analogue in the general case . thus , the decorated super - teichmller space @xmath0 _ can only be defined here _ as the space of @xmath8 orbits of those maps @xmath156 that are @xmath140-equivariant for some super fuchsian representation with no intrinsic interpretation of _ super horocycle _ for the decoration beyond the analogous but un - illuminating affine dual in @xmath9 of a point in @xmath155 . indeed , in addition to the research frontiers discussed at the end of the previous section that the current work presumably illuminates , so also first glimpses of _ super hyperbolic geometry _ are hopefully to be gleaned here . the supergroup @xmath8 is defined as follows . the group elements are square @xmath160 supermatrices with superdeterminant equal to 1 which satisfy the relation @xmath161 where the superscript @xmath162 denotes the super transpose and @xmath163 . we refer the reader to appendix i for more information about @xmath8 including the definition of super transpose ( or see ( [ action ] ) below ) and our sign conventions for products of supermatrices . the useful property @xmath164 is of course a direct consequence of ( [ ospdef ] ) . we are interested in the adjoint action of @xmath8 and to this end consider its even element @xmath165 we claim that the adjoint action @xmath166 of @xmath167 on @xmath168 leaves invariant @xmath146 since it is proportional to the quadratic form arising from the killing form of @xmath8 applied to @xmath168 . we shall prove this differently as follows . observe that in the 3-dimensional representation of @xmath8 owing to the property ( [ ainv ] ) , the element @xmath169 , where @xmath170 for any fixed constant @xmath171 , transforms as @xmath172 under the adjoint action . in particular when @xmath171 is invertible , this implies that the superdeterminant of @xmath173 is preserved under the action of @xmath8 sending @xmath174 to @xmath175 . it is not hard to calculate that @xmath176 and so @xmath146 is invariant under the action of @xmath8 as was claimed . the following proposition therefore holds . the formula @xmath177 , for fixed but arbitrary @xmath171 , gives the action of the @xmath8 subgroup of the full lorentz supergroup of the superspace @xmath178 with the minkowski pairing defined by the quadratic form @xmath146 . to be entirely explicit , the pairing of two vectors @xmath179 and @xmath180 in @xmath178 is given by @xmath181 in keeping with @xcite , we shall henceforth refer to the square root of such an inner product as a _ @xmath77-length_. two surfaces of special importance for us in the following are the _ ( super ) hyperboloid _ @xmath182 consisting of points @xmath183 satisfying the condition @xmath184 corresponding to @xmath185 in equation ( [ goop ] ) , where the bodies of the @xmath148- and @xmath149-coordinates of @xmath186 are non - negative , and most especially the _ ( positive super ) light cone _ @xmath187 consisting of points @xmath188 satisfying @xmath189 and corresponding to @xmath190 , where again the bodies of @xmath148- and @xmath149-coordinates are non - negative . a standard superspace which however plays a subsidiary role for us , the complex _ superplane _ @xmath191 consists of pairs @xmath192 , and its subspace the _ super upper half - plane _ @xmath193 is comprised of those points @xmath192 such that the body of the real part of @xmath194 is non - negative . it is well known @xcite that @xmath8 acts on @xmath193 by means of superconformal transformations @xmath195 another direct analogue of the standard bosonic case , we have [ splane ] the expressions @xmath196 define an @xmath8-equivariant monomorphism from the hyperboloid @xmath197 onto the super half - plane @xmath193 . * proof . * the easiest way to prove this statement is to consider the infinitesimal actions of the corresponding generators described in appendix i. for example , the transformation @xmath198 amounts to the infinitesimal @xmath199 and therefore @xmath200 meanwhile , we have @xmath201 where we have used the relation @xmath202 in the last line . it follows that @xmath203 as required , and one can similarly show that @xmath204 . thus , this corresponds to the superconformal transformation . we leave it for the reader to complete the proof for the other four infinitesimal transformations corresponding to the generators discussed in appendix i. @xmath205 again just to be entirely explicit in the context of relevant subsequent calculations , the light cone is described by @xmath206 and the action of the supermatrix @xmath207 on @xmath208 is given by @xmath209 where these products of supermatrices have the signs ] explained in appendix i. this is entirely analogous to the bosonic action @xcite of @xmath210 on the light cone in @xmath7 given by the change of basis for binary symmetric bilinear forms . there is the particular element of @xmath8 given by @xmath211 that is of special significance . the supermatrix @xmath212 generates the center of @xmath8 , and its explicit action on any @xmath213 is given by @xmath214 . thus , @xmath212 simply changes the signs of the fermions and will henceforth be referred to as _ ( fermionic ) reflection_. we next show that @xmath8 does not act transitively on the light cone @xmath187 , and in fact , the moduli space of orbits is homeomorphic to the space @xmath215 , where @xmath66 acts by the change of sign of fermions . to begin , we normalize with respect to the subgroup @xmath216 . for each vector @xmath217 , there is some @xmath218 so that @xmath219 , where t has positive body . * proof . * consider an arbitrary vector @xmath220 . since one of @xmath148 or @xmath149 is invertible , we can apply an element of the @xmath221 subgroup to transform to a vector @xmath222 where both of @xmath223 are invertible and the body of @xmath224 is positive . we can subsequently apply a diagonal matrix from the @xmath221 subgroup in order that the resulting vector @xmath225 satisfies @xmath226 and hence has the required form . @xmath205 + the next result provides the classification of orbits , namely , we can reduce all degrees of freedom to a single fermion modulo sign via the action of @xmath8 . [ orb ] every vector in the light cone can be put into the form @xmath227 via an @xmath8 transformation . the only solutions to the equation @xmath228 , where @xmath167 , are given by @xmath229 . * according to the previous lemma , in order to prove the first part , we may assume that our specified vector is of the form @xmath230 , where @xmath231 has positive body . a direct computation then shows that the matrix @xmath232 achieves the required expression @xmath233 , where in fact @xmath234 and @xmath235 is likewise taken with positive body . the second part is proven by explicitly solving the equation @xmath228 as follows . consider an arbitrary element @xmath236 the vector @xmath237 is characterized by the identities @xmath238 thus , if @xmath239 , then using @xmath240 as well as the constraints on the entries of @xmath241 given in appendix i , we find that @xmath242 , @xmath243 imply @xmath244 and then @xmath245 , @xmath246 imply @xmath247 it follows that @xmath229 as was claimed.@xmath205 + the next result follows immediately . the moduli space of orbits of the @xmath8 action on the light cone is given by @xmath248 where @xmath66 reflects the sign of the fermion . the explicit solution to the equation @xmath249 given in proposition [ orb ] yields the following corollary which will be of utility in the sequel . [ stab ] for @xmath250 , an element @xmath251 of the stabilizer subgroup of @xmath252 in @xmath8 necessarily has the form @xmath253 where @xmath254 are free parameters with @xmath171 even and @xmath90 odd . moreover for @xmath255 , the stabilizer of @xmath256 has one component for ramond punctures given by the expression @xmath257 above as well as a second component for neveu - schwarz punctures given by its composition @xmath258 with the fermionic reflection @xmath212 . given a point @xmath208 , the fermion @xmath259 ( defined up to an overall sign ) so that @xmath186 and @xmath260 lie in the same @xmath8-orbit is called the _ fermion label _ of @xmath186 , and it admits the following simple expression . [ orbitform ] if @xmath261 , then the fermion label of @xmath186 is given by @xmath262 if @xmath148 is invertible and by @xmath263 if @xmath149 is invertible . here and throughout since @xmath148- and @xmath149-coordinates have non - negative body on the positive light cone , there are well - defined square roots @xmath264 and @xmath265 also with non - negative body . the fermionic reflection on @xmath266 thus changes the sign of @xmath90 here . + * proof . * the result follows from direct calculation starting from the formulas ( [ ga ] ) using the constraints on entries of @xmath8 in appendix i as we explicate in the case where @xmath148 is invertible . we have @xmath267 at the same time , we have @xmath268 and therefore @xmath269 it follows that @xmath270 where we again use the constraints on elements of @xmath8 from appendix i. @xmath205 + the @xmath8-orbit of @xmath271 will play a special role for us here . we shall denote it @xmath272 and refer to it as the _ special light cone_. the special light cone @xmath273 is isomorphic to superprojective space @xmath274 with the action of @xmath8 given by superconformal transformations . provided @xmath275 , the natural correspondence between @xmath276 and @xmath277 is given by : @xmath278 the proof follows along the lines of theorem [ splane ] . this section provides abstract identifications for the spaces of @xmath8-orbits of linearly independent ordered pairs and certain triples of points in the special light cone @xmath279 . specifically , we shall say that an ordered triple @xmath280 of points in @xmath279 is _ positive _ provided @xmath281 are linearly independent and the underlying triple of bosonic vectors in the usual light cone @xmath282 in this order provides a positively oriented basis for @xmath283 with its usual orientation . in fact , the latter moduli space of positive triples in the light cone plays a key role in the sequel , and several further parametrizations of it are derived in the next section . the moduli space of all ordered pairs of linearly independent vectors ( i.e. , with non - vanishing minkowski inner product or equivalently vectors lying in distinct rays ) in the special light cone is described by [ 2pts ] there is a unique @xmath8-invariant of two linearly independent vectors @xmath284 , and it is given by the pairing @xmath285 . * proof . * according to proposition [ orb ] , by applying an appropriate element of @xmath8 to both points , we may assume @xmath286 and @xmath287 . note that @xmath149 must be invertible , for otherwise the vectors are not linearly independent in the super - sense , namely , there exist @xmath288 with non - zero bodies so that @xmath289 has zero body . we may apply a transformation @xmath251 of the form ( [ stabil ] ) thus stabilizing @xmath186 and mapping @xmath290 to @xmath291 , where @xmath292 we wish to normalize so that this vector takes the form @xmath293 and thus impose the two further conditions @xmath294 and @xmath295 . this implies @xmath296 which gives @xmath297 as required . @xmath205 the moduli space of @xmath8-orbits of ordered pairs of vectors in the special light cone lying in distinct rays is given by @xmath298 . turning now to ordered triples of linearly independent vectors in @xmath279 , the underlying bosonic triple may provide either a positively or a negatively oriented basis of @xmath299 , and we have already christened the former case a positive triple . the well - known three - effectiveness of the action of @xmath6 on positively oriented ( i.e. , correctly cyclically ordered ) triples of points in the circle at infinity of hyperbolic space fails in our current context of @xmath178 because there is one additional odd degree of freedom which can not be fixed . we next compute the moduli space of orbits of positive triples to be @xmath300 modulo the fermionic reflection and postpone the further discussion of this interesting additional parameter to the next section . [ 3pts]let @xmath301 be a positive triple in the special light cone . then there is @xmath167 , which is unique up to composition with the fermionic reflection , and unique even @xmath302 , which have positive bodies , and odd @xmath303 so that @xmath304 * proof . * first , one can put @xmath305 into the form @xmath306 by means of @xmath8 according to lemma [ orb ] . second , @xmath307 can be put in the form @xmath308 using the stabilizer of @xmath309 as in the proof of lemma [ 2pts ] . finally by a diagonal matrix whose entries have positive bodies , one can put @xmath310 into the form where its @xmath148- and @xmath149-coordinates agree . since @xmath301 is a positive triple , the @xmath311-coordinate of @xmath310 after these transformations has positive body , and so @xmath310 indeed transforms to a vector with the required form @xmath312 while the other two transformed vectors evidently also have the desired forms @xmath313 , @xmath314 . the asserted uniqueness up to reflection of the transformation @xmath167 thus constructed follows from corollary [ stab].@xmath315 + just to be clear , let us note that there are thus precisely two lifts to @xmath155 of a positive triple @xmath316 with abstract coordinates @xmath317 given by @xmath318 ( where the @xmath311-coordinate of @xmath310 has positive body in the notation of the lemma ) and its image @xmath319 under the fermionic reflection @xmath212 . in any case , the invariants @xmath302 have positive body and only the signs of the fermions change . as a parenthetical point of notation , we mention that the labeling @xmath320 is used here rather than the more natural @xmath321 in order to accommodate later conventions . [ modsp3 ] the moduli space of @xmath8-orbits of positive triples in the light cone is given by @xmath322 , where @xmath66 acts by fermionic reflection . in fact , the even invariants @xmath302 of a triple , which we shall call _ normalization coefficients _ , are the direct analogues of the reciprocal @xmath323-lengths from @xcite , and they can be nicely computed in terms of the @xmath77-lengths @xmath324 [ evenones ] the normalization coefficients @xmath302 in lemma [ 3pts ] are given by @xmath325 we have found that a positive triple of points in the special light cone naturally determines three even and one odd invariant , namely , the @xmath77-lengths @xmath326 or the normalization coeffcients @xmath302 and the fermion label @xmath303 given in the previous lemma . it appears that the definition of the odd parameter @xmath303 depends on a choice of member of the positive triple , and we next discuss how to eliminate this dependence . in fact given a positive triple @xmath280 , there is a canonical cube root of unity in @xmath8 called the _ @xmath280 prime transformation _ which cyclically permutes its members @xmath327 , and we shall compute this transformation on the coordinates of lemma [ 3pts ] explicitly and denote it @xmath328 where the @xmath77-lengths are of course also cyclically permuted in the natural way . the choice - free way to express the additional odd degree of freedom is to average our ansatz @xmath303 over this prime transformation and define the _ manin invariant _ of a triple of points in @xmath329 capturing the basic non - transitivity of the @xmath8 action there , and by making choices ( of spin structure among other conventions ) one can @xcite lift this to a signed expression @xmath90 , namely , our manin invariant . ] or simply the _ @xmath78-invariant _ to be @xmath330 in practice , @xmath78-invariants and @xmath77-lengths give a parametrization of decorated super - teichmller space as we shall see . to complete our definition of the @xmath78-invariant , it therefore remains to compute the prime transformation . to this end , we alter notation slightly setting @xmath331 , @xmath332 , @xmath333 as illustrated in figure [ 3nota ] . -lengths @xmath326 on edges and one @xmath78-invariant @xmath90.,scaledwidth=30.0% ] given three points @xmath334 in the special light cone @xmath279 , where @xmath302 have positive body , we claim there exists a group element @xmath335 from @xmath8 respectively transforming the points @xmath281 into @xmath336 and in fact , there are two possible ways to construct such a transformation ( again unique up to fermionic reflection ) . however , there is a unique transformation whose third power @xmath337 is equal to identity , and it turns out that its action on @xmath303 is rather simple . [ prime ] the group element @xmath335 acts so that @xmath338 , and this is the unique group element @xmath339 satisfying the identity ( [ gid ] ) . * proof . * we first use the group element @xmath340 in ( [ gtpp ] ) in order to transform @xmath290 into @xmath309 . the effects of this transformation on the other points produces @xmath341 finally , acting by the diagonal matrix @xmath342 we obtain the desired result by composing with the fermionic reflection @xmath343 @xmath344 so that @xmath345 , @xmath346 , @xmath347 . @xmath205 + the @xmath78-invariant @xmath348 of a positive triple @xmath280 is invariant under the @xmath280 prime transformation . as follows directly from this plus the discussion of the previous section , we have the moduli space of @xmath8-orbits of positive triples in the light cone is given by equivalence classes under fermionic reflection of three even @xmath77-lengths @xmath326 with positive bodies plus the @xmath78-invariant @xmath90 defined up to fermionic reflection . this section is dedicated to a computation called the `` basic calculation '' giving a parametrization of the moduli space of @xmath8-orbits of four - tuples @xmath349 in the special light cone @xmath273 comprised of two positive triples @xmath350 and @xmath351 of points in terms of five @xmath77-lengths and two @xmath78-invariants . in effect , one positive triple @xmath350 is put into the canonical position of lemma [ 3pts ] using certain of the putative parameters , and the remaining ones are then used to completely and uniquely determine the fourth point @xmath352 , where @xmath311 has non - negative body ; it is precisely here that compatibility of signs of adjacent @xmath78-invariants arises . this basic calculation is the critical ingredient both for our global coordinates and for the ptolemy transformation just as in @xcite . in fact provided only that the triple @xmath350 is in standard position , the standard position of @xmath351 is easily calculated in terms of the coordinates of its vertices as follows . [ hats ] the triple @xmath353 can be transformed by an element of @xmath8 , which is itself uniquely determined up to fermionic reflection , into the triple @xmath354 where @xmath355{\frac{x_1}{x_2}}\frac{\lambda}{\sqrt{x_1x_2}}=\sqrt[4]{\frac{x_2}{x_1}}\frac{\rho}{\sqrt{x_1x_2}},\end{aligned}\ ] ] * proof . * act first by @xmath356 to interchange the roles of @xmath186 and @xmath76 while mapping @xmath357 to a point with non - negative @xmath311-coordinate and then act by @xmath358{{x_1}/ { x_2 } } & 0 & 0 \\ 0 & \sqrt[4]{{x_2}/ { x_1 } } & 0 \\ 0 & 0 & 1 \end{smallmatrix } \right)$ ] to realize equality of the first two coordinates . the composition of these two elements of @xmath8 achieves the desired result in accordance with lemma [ 3pts ] . @xmath205 + note that the normalization factors admit the uniform expressions @xmath359 this transformation in @xmath8 which maps @xmath351 to standard position if @xmath360 is in standard position is called the _ switch transformation _ of the quadruple @xmath349 though in fact it depends only upon @xmath351 according to the formula for it given above . -lengths and @xmath78-invariants near an edge before ( left ) and after ( right ) a flip , scaledwidth=60.0% ] now turning to the basic calculation itself , let @xmath361 be points in the light cone as in lemma [ 3pts ] with @xmath77-lengths @xmath326 and @xmath78-invariant @xmath90 . up to fermionic reflection , the @xmath8-orbit of the positive triple @xmath350 is then uniquely determined by these parameters according to lemma [ 3pts ] . the basic calculation aims to compute @xmath362 , where @xmath311 has non - negative body , from the data @xmath363{\frac{x_1}{x_2}}\frac{\lambda}{\sqrt{x_1x_2}}=\sqrt[4]{\frac{x_2}{x_1}}\frac{\rho}{\sqrt{x_1x_2 } } , \quad\langle a , d\rangle = d^2 , \quad \langle d , c\rangle = c^2\end{aligned}\ ] ] depicted in figure [ figint ] , and the following arises directly from equations ( [ rst ] ) and ( [ 4point ] ) . [ bascalc ] we have the expressions @xmath364 solving the basic calculation . introducing the cross - ratio @xmath365 , this expression of the basic calculation can be concisely written @xmath366 the utility of this version of the basic calculation for computing the ptolemy transformation is already evident from the following proposition . [ pt * ] in the notation above with @xmath367 , we have @xmath368 * proof . * simply expand the expression @xmath369 in @xmath77-lengths . this is equivalent to @xmath370 and the desired formula for @xmath371 follows upon taking square roots.@xmath205 + now let us reproduce the same four points @xmath372 using the parameters of adjacent positive triples @xmath373 and @xmath374 . to do so , let us move the positive triple @xmath373 to standard position @xmath375 to this end , we first apply the stabilizer of @xmath376 , namely , the matrix @xmath377 as in corollary [ stab ] , in order to transform @xmath378 , where the corresponding @xmath171 and @xmath379 are given by @xmath380 yielding @xmath381 . applying this transformation to @xmath382 , we obtain a new vector @xmath383 , where @xmath384 applying @xmath385 followed by the diagonal matrix @xmath386{\frac{\hat{x}_1}{\hat{x}_2}}&0&0\cr 0&\sqrt[4]{\frac{\hat{x}_2}{\hat{x}_1}}&0\cr 0&0&1\end{smallmatrix}\biggr)$ ] to each of @xmath387 yields : @xmath388{\frac{\hat{x}_1}{\hat{x}_2}}\big)=\frac{\hat{\rho}}{\sqrt{\hat{x}_1\hat{x}_2 } } \big(\sqrt[4]{\frac{\hat{x}_2}{\hat{x}_1}}\big)\end{aligned}\ ] ] for the parameters in equation ( [ tildas ] ) . thus , the @xmath78-invariant of the positive triple @xmath389 is given by @xmath390 as this is invariant under the @xmath389 prime transformation . [ fl1 ] the @xmath78-invariants for the positive triples @xmath389 and @xmath391 depend only on the @xmath78-invariants @xmath392 and the cross - ratio @xmath393 and are given by @xmath394 @xmath395 * proof . * equation ( [ one ] ) follows from the direct calculation @xmath396{\frac{\hat{x}_1}{\hat{x}_2}}\big)=\frac{\theta x_2-\lambda } { \chi^{\frac{3}{4}}(\sqrt{2}\frac{cd}{e})\sqrt{\sqrt{\chi}+\sqrt{\chi}^{-1}}}= \frac{\theta\sqrt{\chi}+\sigma}{\sqrt{1+\chi}}.\end{aligned}\ ] ] in order to write @xmath78 in terms of the same function @xmath397 , we must transform @xmath398 as follows @xmath399 and this can be achieved by first applying the matrices given in lemma [ hats ] so that @xmath400{\frac{x_1}{x_2}}\theta , \quad \check \lambda= t\sqrt[4]{\frac{x_2}{x_1}}\theta,\nonumber\\ & & \check\phi=-\sqrt[4]{\frac{x_1}{x_2}}\frac{\lambda}{\sqrt{x_1x_2}}=\sqrt[4]{\frac{x_2}{x_1}}\frac{\rho}{\sqrt{x_1x_2}}.\nonumber\end{aligned}\ ] ] it follows that @xmath401 where the checked arguments of @xmath78 are related to checked variables from ( [ tcheck ] ) as before and @xmath402 it follows that @xmath403 as required . @xmath205 as a direct corollary to the proof , we have [ switch ] consider the odd ptolemy transformation on ordered pairs @xmath404 together with the corresponding action on @xmath77-lengths and apply it twice to the quadrilateral @xmath349 , with @xmath360 in standard position . then the effect is the switch transformation of @xmath349 described in lemma [ hats ] . specifically after this transformation , @xmath351 is in standard position with @xmath405 while the image of @xmath290 is determined not by @xmath90 but rather by @xmath406 . in this section , we relate the collection of spin structures on a punctured surface to orientations on any trivalent fatgraph spine of the surface . to begin , we recall results of cimasoni - reshetikhin from @xcite . the _ boundary _ of a one - dimensional cw complex @xmath407 is its set @xmath408 of vertices of valence one . @xmath407 is a _ surface graph with boundary _ for some compact oriented surface @xmath409 with boundary @xmath410 if @xmath407 is embedded in @xmath409 with @xmath411 so that @xmath412 is the 1-skeleton of a cellular decomposition of @xmath409 . a _ dimer configuration _ on @xmath407 is a choice of certain of its edges called _ dimers _ such that each vertex not in @xmath413 has exactly one incident dimer while vertices in @xmath413 may or may not have an incident dimer , the specification of which is regarded as an _ a priori _ boundary condition on the dimer configuration . given an orientation @xmath414 on the edges of @xmath415 and a closed oriented edge curve @xmath76 in it , we denote by @xmath416 the number of edges counted with multiplicity where the orientation of @xmath76 disagrees with that of @xmath414 . a _ kasteleyn orientation _ on @xmath417 is an orientation @xmath414 on the edges of the 1-skeleton @xmath415 so that @xmath418 for each face @xmath371 of @xmath409 . define an equivalence relation @xmath419 between two kasteleyn orientations @xmath420 on @xmath421 generated by altering the orientation on every edge incident on some fixed vertex , which is called a _ kastelyn reflection _ , and let @xmath422 denote the set of equivalence classes . there is furthermore a cochain @xmath423 defined by setting @xmath424 if and only if @xmath425 and @xmath426 disagree on @xmath427 , for @xmath427 an edge of @xmath421 . [ corollary 1 of @xcite][theta ] in fact , @xmath428 is a cocycle which is a coboundary if and only if @xmath419 . furthermore , the set of equivalence classes of kasteleyn orientations is an affine @xmath429-space . seminal work of dennis johnson @xcite mentioned before identifies as affine @xmath430-spaces the collection @xmath35 of all spin structures on a surface @xmath409 with the collection @xmath431 of all quadratic forms @xmath432 satisfying @xmath41 with respect to the homology intersection pairing @xmath433 of @xmath434 . in fact , kasteleyn orientations on a surface graph for @xmath409 and quadratic functions on @xmath435 are also isomorphic as affine @xmath429-spaces , and the correspondence is given via an explicit construction relative to a fixed dimer @xmath357 as follows . [ cr ] fix a dimer configuration @xmath357 on a surface graph with boundary @xmath407 for the surface @xmath409 and let @xmath436 be represented by oriented closed curves @xmath437 . if @xmath414 is a kasteleyn orientation on @xmath407 , then the function @xmath438 given by @xmath439 is a well - defined quadratic form , where @xmath440 is the number of edges of @xmath357 sticking out to the left of @xmath76 , and @xmath416 as before is the number of edges counted with multiplicity where the orientation of @xmath76 disagrees with that of @xmath414 . moreover , for each fixed dimer @xmath357 , this establishes an isomorphism @xmath441 as affine @xmath429-spaces . together with @xcite , this establishes an isomorphism of affine @xmath429-spaces between the collection @xmath442 of spin structures on @xmath409 and @xmath422 for any surface graph @xmath421 with boundary for @xmath409 with respect to a fixed dimer configuration . now , given a trivalent fatgraph spine @xmath31 for @xmath10 , we shall build an appropriate surface graph with boundary for a surface embedded in @xmath2 as a deformation retract . construct a cw decomposition of this compact so - called skinny surface @xmath443 with boundary taking one hexagon @xmath444 for each vertex @xmath88 and one rectangle @xmath445 for each edge @xmath427 of @xmath31 glued together in the natural way in @xmath2 as in figure [ cell ] . there is a canonical surface graph @xmath446 for @xmath409 comprised of the common boundaries of these hexagonal and rectangular regions as also illustrated in the figure by bold line segments , two such segments for each edge of @xmath31 . there is also a canonical dimer @xmath447 given by exactly this same set of segments , so each vertex in @xmath413 has an incident dimer . a hexagon has the two special kastelyn orientations that are either outgoing or incoming at each vertex , and these are related by reversal of orientation of each edge . furthermore identifying @xmath444 with this abstract hexagon , for some vertex @xmath88 of @xmath31 , there is a unique such orientation which agrees with the one induced from the counter - clockwise orientation of @xmath421 with @xmath444 on the left as illustrated on the top of figure [ orient ] . thus , any kastelyn orientation on @xmath448 can be modified by kastelyn reflections to agree with this one on @xmath444 for each vertex @xmath88 of @xmath31 , i.e. , the special kastelyn orientations saturate the equivalence classes . on the top and orientation on fatgraph @xmath31 from special kasteleyn orientations on @xmath449 on the bottom , scaledwidth=80.0% ] suppose that @xmath414 is such a special kastelyn orientation on @xmath448 that thus agrees with the special hexagonal ones near each vertex of @xmath31 oriented as already discussed . there are exactly two methods that @xmath414 can extend as a kastelyn orientation to a rectangle @xmath445 as illustrated on the top in figure [ orient ] , and these are naturally in bijective correspondence with orientations on the edges of @xmath31 themselves insofar as they are parallel as illustrated on the bottom of figure [ orient ] . conversely , suppose that @xmath75 is an orientation on @xmath31 and let @xmath450 denote the associated special kastelyn orientation on @xmath448 defined to be parallel on each @xmath445 and special on each @xmath444 as before . in the same spirit as kastelyn reflection , we define a _ fatgraph reflection _ at a vertex @xmath88 of @xmath31 to reverse the orientations of @xmath75 on every edge of @xmath31 incident on @xmath88 , consider the equivalence relation @xmath451 thus generated on the set of all orientations on @xmath31 and let @xmath50 denote the set of all equivalence classes . one easily checks that the fatgraph reflection at @xmath88 is given precisely by the composition of kastelyn reflections at the six vertices of @xmath444 , so @xmath451 implies @xmath452 . conversely , in order that the orientation on an edge of some @xmath444 is invariant , we must perform kastelyn reflection either at both or neither of its endpoints , and it follows that @xmath452 also implies @xmath451 . furthermore , given orientations @xmath453 on @xmath31 , there is the analogous cochain @xmath454 taking a non - zero value on an edge of @xmath31 if and only if @xmath455 and @xmath456 disagree on the edge , and we clearly have @xmath457 . summarizing , we have : [ equiva ] for each orientation @xmath75 on the edges of a fatgraph @xmath31 , there exists a unique special kasteleyn orientation @xmath458 on @xmath459 , and this induces an isomorphism @xmath460 of equivalence classes under reflection as affine @xmath461-spaces . as follows directly from theorem [ cr ] and proposition [ equiva ] , we have [ qando ] let @xmath31 be a fatgraph spine in the surface @xmath10 with corresponding surface graph @xmath462 for @xmath463 . then the formula ( [ q ] ) with the canonical dimer configuration @xmath464 establishes an isomorphism @xmath465 as affine @xmath466-spaces , and indeed also @xmath467 since @xmath463 is a homotopy equivalence . it remains for us here only to compute the effect that flipping a fatgraph edge has on an orientation class : suppose that @xmath468 is a trivalent fatgraph spine for @xmath2 and that @xmath469 arises by flipping an edge of @xmath468 . there is a unique bijection @xmath470 covering the identity map of @xmath37 , and it is described by figure [ flipper ] . * proof . * consider a neighborhood of the edge of @xmath468 upon which the flip is performed depicted in figure [ curves ] where there are illustrated six distinct oriented paths in @xmath2 denoted @xmath471 , which may be completed to closed oriented curves in @xmath2 and contribute to the value of the quadratic form . a tedious computation given in appendix ii compares formula ( [ q ] ) before and after the flip for these six paths and determines that there is the unique evolution of orientation class from @xmath468 to @xmath469 illustrated in figure [ flipper ] that leaves invariant these contributions . @xmath205 on @xmath472 are indicated by bold lines , title="fig:",scaledwidth=40.0% ] on @xmath472 are indicated by bold lines , title="fig:",scaledwidth=40.0% ] + on @xmath472 are indicated by bold lines , title="fig:",scaledwidth=40.0% ] [ oops ] let @xmath31 be a trivalent fatgraph spine of @xmath473 . then @xmath474 is isomorphic to the set @xmath35 of spin structures on @xmath2 as affine @xmath475-spaces . moreover , the action of @xmath29 on @xmath35 lifts naturally to the action of the ptolemy groupoid on @xmath476 ) illustrated in figure [ flipper ] . by naturality here , we mean that if @xmath32 , then there is a finite sequence @xmath477 where @xmath478 arises from @xmath479 by a flip , for @xmath480 . suppose that @xmath75 is an orientation on @xmath31 inducing via the identification @xmath84 the orientation @xmath455 on @xmath468 and moreover that the evolution of orientation illustrated in figure [ flipper ] serially induces from @xmath455 the orientation @xmath481 on @xmath482 . the spin structure on @xmath2 associated to @xmath75 maps to that of @xmath483 under the action of @xmath84 on @xmath35 by construction . equivalent to the choice of trivalent fatgraph spine @xmath30 is the specification of its dual ideal triangulation @xmath110 of @xmath2 . an orientation @xmath75 on @xmath31 induces an orientation on @xmath110 by requiring that the oriented edge of @xmath110 occurs clockwise from its dual oriented edge in @xmath31 near their point of intersection here using an orientation of the surface @xmath2 . dual to the fatgraph reflection at a vertex is the change of orientation on each edge in the frontier of a triangle complementary to @xmath110 . we consider the lift of @xmath110 to an ideal triangulation @xmath134 of the universal cover @xmath484 . fixing a base point in @xmath2 , the fundamental group @xmath20 acts as deck transformations on @xmath126 leaving invariant @xmath134 . of course @xmath126 is _ topologically equivalent _ to @xmath129 , and a hyperbolic metric on @xmath2 further determines a _ metric equivalence_. in any case , we may consider the collection of ideal vertices @xmath135 of all the arcs in @xmath134 as an abstract set . _ fix a surface @xmath10 of genus @xmath11 with @xmath3 punctures , where @xmath74 , and let @xmath110 be some ideal triangulation of @xmath2 whose lift @xmath134 to the universal cover @xmath485 has ideal vertices @xmath486 . suppose that @xmath75 is an orientation class on the arcs in @xmath110 corresponding to a specified spin structure , and assign to each edge of @xmath110 an even coordinate and to each triangle complementary to @xmath110 an odd coordinate where the latter are taken modulo an overall sign . then there is a function @xmath487 uniquely determined up to post - composition with an element of @xmath8 so that _ .3 in i ) if @xmath488 span an edge in @xmath134 , then the coordinate on this edge is given by the @xmath77-length @xmath489 ; ii ) if @xmath490 span a triangle complementary to @xmath134 and occur in the positive order in @xmath130 , then up to a sign the coordinate of this triangle is given by the @xmath78-invariant of the positive triple @xmath491 ; moreover , if @xmath492 likewise occur in the positive order and span a triangle , then the coordinates of these respective triangles are given up to an overall sign by the @xmath78-invariants of the positive triples @xmath491 and @xmath493 as related by proposition [ bascalc ] . = 0ex furthermore , there is a representation @xmath494 with respect to which @xmath144 is @xmath140-equivariant in the sense that @xmath495 for each @xmath49 and @xmath496 so that @xmath497 is a fuchsian representation whose lift @xmath498 agrees with the specified spin structure . moreover @xmath499 is uniquely determined up to conjugacy by an element of @xmath8 . for any @xmath11 and @xmath3,scaledwidth=75.0% ] * proof . * the argument closely follows the bosonic case @xcite using the putative coordinates to recursively construct the mapping @xmath144 and finally the representation @xmath499 . let us first consider the case that the trivalent fatgraph spine @xmath30 dual to @xmath110 is bipartite , namely , there is a two - coloring of the vertices of @xmath31 so that the endpoints of any edge of @xmath31 have different colors . an example of a bipartite fatgraph spine is illustrated in figure [ hip ] for each topological type of punctured surface . dually letting @xmath500 denote the collection of triangles complementary to @xmath110 in @xmath2 , there is a function @xmath501 so that for any two triangles @xmath502 sharing an edge , we must have @xmath503 . notice that in this bipartite case there are exactly two distinct such functions differing by an overall sign . the coordinates on @xmath110 lift to coordinates on @xmath134 in the natural way assigning to each edge @xmath504 the even coordinate of @xmath505 and to each complementary triangle @xmath506 the odd coordinate @xmath507 of @xmath508 . the function @xmath509 likewise lifts to the eponymous function @xmath510 satisfying @xmath511 . choose a distinguished triangle - edge pair or equivalently a distinguished oriented edge of @xmath134 which determines the triangle @xmath512 lying to its left in the oriented surface @xmath126 . according to lemma [ 3pts ] , there is a positive triple @xmath280 in the special light cone realizing the putative @xmath77-lengths and @xmath78-invariant @xmath507 so that the point @xmath290 is opposite to the distinguished oriented edge , and @xmath280 is furthermore uniquely determined up to fermionic reflection @xmath212 . choosing a particular representative @xmath280 or @xmath513 at this stage gauge fixes the @xmath66-action and thus determines well - defined signs on all of the fermionic coordinates @xmath514 for @xmath515 . ( in the special case when the fermionic coordinate on @xmath231 vanishes , we have @xmath516 and can still gauge fix at this point to determine the signs on all of the non - vanishing fermionic coordinates . ) this lift to a positive triple in @xmath155 of the vertices of @xmath231 constitutes the basis step of our recursive construction of the mapping @xmath144 . in order to lift the triangle @xmath517 to the right of the distinguished oriented edge with its specified fermionic coordinate @xmath518 , we shall rely on the basic calculation formulated as proposition [ bascalc ] to lift the vertex of @xmath519 distinct from those of @xmath231 to a point @xmath520 , however , the coordinates employed to determine @xmath357 are the specified putative @xmath77-lengths and the _ @xmath509-modified @xmath78-invariant _ @xmath521 rather than @xmath518 itself . conjugating by the @xmath280 prime transformation and its square , we can likewise uniquely lift to @xmath279 the vertices of the other two triangles in @xmath522 adjacent to @xmath231 . continue recursively in this way moving each triangle in @xmath522 already lifted into standard position with its specified @xmath78-invariant using @xmath8 and then employing the putative @xmath77-lengths and @xmath509-modified @xmath78-invariants to lift the next adjacent triangle in @xmath522 using proposition [ bascalc ] in order to finally uniquely lift all of @xmath486 and completely define @xmath523 in keeping with requirements i ) and ii ) in the statement of the theorem . there are actually only finitely many values of coordinates employed in this construction since there are only finitely many arcs in @xmath110 and triangles in @xmath500 . in particular , the bodies of @xmath77-lengths are uniformly bounded above and below . as in the pure even case @xcite , it follows from this bounded geometry that the bosonic projection @xmath524 induces a mapping from the ideal triangulation of @xmath126 onto a tessellation of all of @xmath129 . we claim that changing the distinguished oriented edge of @xmath159 used to initiate this construction merely modifies the function @xmath144 by post - composition with a group element in @xmath8 . to see this , first notice that if we change orientation of the distinguished oriented edge , then @xmath519 will be in standard position with its @xmath78-invariant @xmath518 , and the triangle @xmath231 is then produced using the @xmath509-modified @xmath78-invariant @xmath525 . applying the switch transformation ( and possibly overall fermionic reflection for the @xmath66 gauge group ) , based on the fact that @xmath526 together with proposition [ switch ] , we recover the image of the previous construction under the switch transformation , which lies in @xmath8 , with the correct signs for fermionic parameters . moreover , any change in the distinguished oriented edge can be achieved by means of a finite composition of prime transformations and at most one reversal of orientation . since prime transformations are again group elements of @xmath8 , we conclude that our equivalence class of lifts under the action of @xmath8 is independent of the distinguished oriented edge as required . uniqueness of the mapping @xmath144 up to post - composition with an element of @xmath8 follows by construction from the uniqueness statements in lemma [ 3pts ] and proposition [ bascalc ] completing the proof of the first part under the bipartite assumption . from the lift @xmath527 , we shall presently construct the required representation @xmath528 . to this end , choose a connected fundamental domain @xmath529 for the action of @xmath140 comprised of a collection of triangles in @xmath522 which contains the base triangle @xmath231 specified earlier which began the recursive construction of @xmath144 . the frontier edges of @xmath357 in @xmath126 arise in pairs @xmath530 together with an abstract identification @xmath531 induced by some @xmath49 , and we let @xmath532 enumerate the collection of these edge pairings , for @xmath533 , where the @xmath534 thus freely generate @xmath140 . to determine the image @xmath535 of @xmath536 in order to define the representation @xmath499 , let us further enumerate two triangles for each edge pairing , namely , the unique triangles @xmath537 and @xmath538 in @xmath522 where @xmath539 and @xmath540 . notice as before that the coordinates for @xmath541 or @xmath542 have gauge - fixed signs from the basis step of the construction of @xmath144 , and the parameters on @xmath541 lifted from @xmath2 agree with those on @xmath542 since @xmath543 implies @xmath544 . let @xmath545 be the corresponding positive triple in @xmath155 . according to lemma [ 3pts ] again , there is a unique @xmath546 such that @xmath547 , where @xmath8 acts on the right and @xmath548 indicates the triple of points in standard position realizing the @xmath77-lengths and signed @xmath78-invariant of @xmath549 so that the fermion - dependent vertex is opposite to @xmath550 . let @xmath551 be the analogous group element for @xmath552 . we must furthermore take account of the spin structure in accordance with @xcite relating the sign of the trace of the bosonic reduction of @xmath553 with the value of the corresponding quadratic form on the underlying mod two homology class @xmath48\in h_1(f;{\mathbb z}_2)$ ] , for @xmath49 . in particular , notice that the fermionic reflection @xmath212 has the central element @xmath554 as its bosonic reduction . given the quadratic form @xmath55 corresponding via theorem [ qando ] to our specified orientation @xmath75 , we define @xmath555)=0 ~~ { \rm or}~~ { \rm trace}(h_i^{-1}\cdot h'_i)<0~\&~ q([\gamma_i])=1;\\ & \\ & h_i^{-1}\cdot h'_i , \\ & { \rm if}~~ { \rm trace}(h_i^{-1}\cdot h'_i)<0~\&~ q([\gamma_i])=0 ~~ { \rm or}~~ { \rm trace}(h_i^{-1}\cdot h'_i)>0~\&~ q([\gamma_i])=1 . \end{cases}\end{aligned}\ ] ] by construction , these group elements compose correctly so as to produce a representation , and since @xmath140 is a free group , there are no relations to confirm whence @xmath499 is indeed a representation of @xmath140 in @xmath8 onto a subgroup @xmath556 . also by construction , the projectivized bosonic reduction @xmath557 leaves invariant the tessellation of @xmath129 discussed before , and an argument in @xcite going back to poincar thus proves that @xmath14 is indeed a fuchsian group uniformizing the punctured surface . finally , the bosonic reduction @xmath558 itself as a lift of @xmath22 gives the correct spin structure on the underlying riemann surface in keeping with @xcite by construction since multiplication by @xmath212 alters the sign of the trace of the bosonic reduction . this completes the required construction of a representation from the asserted parameters including the spin structure . the procedure described is clearly equivariant for the fermionic reflection under the initial choice of sign on the @xmath78-invariant in the base triangle , and the distinction between pairs @xmath539 and @xmath540 amounts only to replacing a generator by its inverse . there are thus two essential choices : the choice of base triangle @xmath231 to begin the inductive construction as well as the fundamental domain @xmath357 containing it . we must show that these choices are resolved by the overall conjugacy in the definition of the decorated super - teichmller space . to this end , consider two such fundamental domains containing specified base triangles @xmath559 with corresponding mappings @xmath560 and representations @xmath561 , for @xmath562 . there is a unique triangle @xmath563 whose projection to @xmath2 agrees with that of @xmath564 since @xmath565 is a fundamental domain for the action of @xmath140 , whence @xmath564 and @xmath566 thus share the same invariants . by lemma [ 3pts ] again @xmath66 gauge - fixed as before , there is a unique @xmath167 so that @xmath567 . by uniqueness in lemma [ 3pts ] and proposition [ bascalc ] , we must then have @xmath568 , and so @xmath241 furthermore conjugates @xmath569 to @xmath570 as required . notice that the trace of the bosonic reduction of an element of @xmath8 is invariant under conjugacy , so the spin structure is left invariant by conjugation of representations . we must finally extend the construction from bipartite to general trivalent fatgraph spines @xmath30 . to this end according corollary d , there is a finite sequence of flips starting from @xmath31 and ending with a bipartite fatgraph spine @xmath571 such as the one depicted in figure [ hip ] to which we may apply the construction just described based upon the coordinates on @xmath572 induced from those on @xmath31 via super ptolemy transformations in proposition [ pt * ] and theorem [ fl1 ] as well as the orientation class on @xmath572 induced from that on @xmath31 in theorem [ oops ] determining the spin structure . since these super ptolemy transformations are computed relative to a fixed configuration of points in @xmath155 , this gives a well - defined lift @xmath523 for any trivalent fatgraph spine and hence a corresponding representation @xmath157 which is determined up to conjugacy since the mapping @xmath144 is determined up to post - composition with an element of @xmath8 . @xmath205 + fix a trivalent fatgraph spine @xmath30 for a surface @xmath10 of negative euler characteristic and specify an orientation on the edges of @xmath31 determining the component @xmath76 of @xmath0 . then @xmath77-lengths on the edges together with @xmath78-invariants on the vertices of @xmath31 , the latter taken modulo an overall sign , provide global coordinates on @xmath76 . moreover , these coordinates are natural in the sense that if @xmath32 and @xmath33 is a sequence of trivalent fatgraph spines of @xmath2 with consecutive ones related by a flip , then we identically induce coordinates and orientation class on @xmath83 from these data on @xmath31 using @xmath84 and perform the corresponding sequence of super ptolemy transformations in proposition [ pt * ] and theorem [ fl1 ] and evolution of orientation in theorem [ oops ] to induce new coordinates and orientation on @xmath31 itself . then these induced coordinates and orientation class on @xmath31 describe the action of @xmath84 on @xmath0 . * this follows directly from the previous result and theorem [ oops ] together with the observation that @xmath77-lengths and @xmath78-invariants are defined intrinsically in @xmath9 . @xmath205 first , let us recall in some detail the ptolemy transformations studied in section [ sec : bcpt ] . there were two aspects to the calculation corresponding to even and odd , namely , the even ptolemy transformation is a simple modification @xmath573 of the standard pure even case @xmath121 , and the odd ptolemy transformation again in the notation of section [ sec : bcpt ] is given by @xmath574 taken together ( [ ptle ] ) and ( [ 0opt ] ) give expression to the _ super ptolemy transformation_. these formulas in particular specialize to those of @xcite where shear coordinates on the super - teichmller space are introduced . namely as in the classical case , given an ideal triangulation @xmath110 of the surface @xmath2 , to each edge @xmath575 as in figure [ figint ] is associated its cross ratio @xmath576 , written again in terms of @xmath77-lengths . given the two positive triples @xmath350 and @xmath351 in the special light cone @xmath279 , denote by @xmath577 , @xmath578 , @xmath579 , @xmath580 these cross ratios associated to each respective edge @xmath581 also illustrated in figure [ figint ] identifying an edge with its @xmath77-length here for convenience ; of course , each of these depends in turn on the @xmath77-lengths of other nearby edges , for instance , @xmath582 , where @xmath241 , @xmath323 are @xmath77-lengths on the frontier edges of the other complementary triangle to @xmath110 than @xmath350 that contains @xmath583 . nevertheless , under the even ptolemy transformation , we find that @xmath582 transforms to @xmath584 and one similarly computes @xmath585 in fact , these transformations together with equation ( [ 0opt ] ) coincide with those in @xcite up to a conventional inversion of the cross ratio coordinate ( see figure 2 in @xcite ) . in the pure even case @xcite , the khler 2-form of the weil - petersson hermitian metric on the teichmller space @xmath5 or moduli space @xmath122 of a punctured surface @xmath2 was computed relative to the @xmath77-lengths on any convenient triangulation @xmath110 of @xmath2 . namely , it is given by @xmath586 where the sum is over all complementary triangles @xmath316 to @xmath110 in @xmath2 with frontier edges of @xmath316 occurring in the cyclic order @xmath587 compatibly with the clockwise orientation on @xmath588 . it is not difficult to check directly that this expression is invariant under the pure even ptolemy transformation @xmath121 , and indeed in the 1980 s before it was recognized as this particular 2-form , it was nevertheless already confirmed to be invariant under ptolemy transformations and hence arise from some 2-form on the quotient moduli space @xmath589 . much this same computation applies in the current case . if @xmath110 is an ideal triangulation of the punctured surface @xmath2 , then consider the even 2-form on @xmath590 given by @xmath591 where the sum is over all triangles whose consecutive edges in the clockwise ordering have @xmath77-lengths @xmath89 and @xmath78-invariant @xmath90 . then this 2-form is invariant under super ptolemy transformations . notice that @xmath592 is manifestly invariant under the fermionic reflection changing the signs of all fermions , and we have dropped the pre factor 2 here compared to the khler form so that if one converts the expression @xmath592 from @xmath77-lengths to shear coordinates as described before , then the resulting 2-form is associated with the poisson bracket given in @xcite . * * let us remind @xcite the reader that on supermanifolds the de rham operator anticommutes with odd constants , and in local coordiantes @xmath593 is given by @xmath594 , where the odd derivative acts from the left and the @xmath595 are even . adopt the notation @xmath596 for any invertible expression @xmath597 and compute as in the pure even case @xcite for a pair @xmath350 and @xmath598 of positive triples that the contribution to @xmath592 before the flip on @xmath575 in the notation of figure [ flip0 ] is given by @xmath599 and after the flip is given by @xmath600 we must show that these two expressions coincide . to this end , notice that if @xmath601 , then @xmath602 and we find @xmath603 where @xmath604 meanwhile , the super ptolemy transformation gives @xmath605 which coincides with equation ( [ du ] ) as required.@xmath205 in this appendix , we provide basic information concerning the lie supergroup @xmath8 and its lie superalgebra . our cursory treatment here is presumably sufficient for the purposes of the text , and we refer the interested reader to @xcite for further details about general lie superalgebras and supergroups . let us first introduce certain conventions ( which differ from those in @xcite ) . given a lie superalgebra @xmath606 , one can consider its grassmann envelope , namely , the lie superagebra @xmath607 for some grassmann algebra @xmath608 with decomposition @xmath609 into even and odd elements . it follows that @xmath610 is both a right and left @xmath608-module , i.e. , @xmath611 if @xmath612 and @xmath613 are homogeneous elements of respective degrees @xmath614 and @xmath615 . this rule allows one to construct a representation of the corresponding lie superalgebra @xmath610 in the space @xmath616 from a given representation of @xmath606 in @xmath617 . one can then produce a representation of the corresponding lie group @xmath618 by exponentiating pure even elements from @xmath610 in @xmath616 . when writing a super matrix @xmath619 representing the action of @xmath618 or @xmath610 as elements of @xmath620 on @xmath621 , notice that for pure even supermatrices , the composition rule is given by @xmath622 where the products on the right hand side are the usual products of ( super)matrices . the usual ( super)matrix multiplication ( without the minus signs above ) is recovered upon replacing @xmath290 with @xmath623 . this difference in sign is related to the fact that one typically considers the action of group elements on @xmath624 , which can be identified with the space of even elements in @xmath625 , and the extra minus sign in front of @xmath290 comes from that isomorphism . however , throughout this paper we keep the above convention for multiplication of superalgebras ( with the extra signs ) since it gives a cleaner relationship with the representation of the original lie superalgebra . another essential ingredient is the superdeterminant or berezinian of an even supermatrix @xmath626 with @xmath357 invertible which is defined as @xmath627 where the products of matrices are standard matrix products , and we have the nonstandard plus sign @xmath628 in the definition reflecting our conventions . now , the lie superalgebra @xmath8 has three even @xmath629 and two odd generators @xmath630 satisfying the commutation relations @xmath631=\pm v_{\pm } , \quad[v_{\pm},v_{\pm}]=\mp 2x_{\pm},\quad [ v_+,v_{-}]=h.\end{aligned}\ ] ] the corresponding realization via @xmath632 supermatrices is given by @xmath633 and the corresponding supergroup @xmath8 can be faithfully realized as @xmath632 supermatrices @xmath241 with @xmath634 equal to one obeying the relation @xmath635 where @xmath636 and where the supertranspose @xmath637 of @xmath241 is given by @xmath638 this leads to the following system of constraints on the entries of @xmath241 : @xmath639 in particular , @xmath640 describes the canonical inclusion @xmath216 , and the body of the upper - left @xmath641 block conversely gives the bosonic reduction in @xmath221 of a matrix in @xmath8 . and @xmath642 before and after the flip , title="fig:",scaledwidth=50.0% ] + and @xmath642 before and after the flip , title="fig:",scaledwidth=50.0% ] in this appendix , we prove the last part of theorem [ oops ] and compute the evolution of orientations under flips illustrated in figure [ flipper ] . we must verify that the contributions of the arcs @xmath643 illustrated in figure [ curves ] to a quadratic form via theorem [ cr ] with the canonical dimer @xmath464 for the specified orientations of edges is the same before and after the flip . to that end for the purpose of explicit computation , let us fix the representative arcs @xmath84 , @xmath642 as edge - paths before and after the flip as illustrated in figure [ curveflip ] . representatives edge - paths of the other arcs @xmath644 are taken to lie entirely in the boundary . now in the notation of theorem [ cr ] for the canonical dimer @xmath464 , we find @xmath645 both before and after the flip , @xmath646 before the flip and @xmath647 , @xmath648 after the flip . the numbers @xmath649 of theorem [ cr ] are tabulated in figure 10 in the eight cases where the interior edge runs from left to right with the northwest leaf pointing towards it as may always be arranged by fatgraph reflections on the two vertices . uniqueness of this solution for the orientations after the flip is obvious since changing orientation on anything other than all leaves simultaneously evidently changes certain of the numbers @xmath649 . moreover , changing the orientation on each leaf is a composition of the fatgraph reflections at the two interior vertices . finally , enumerating the eight cases in figure 10 in the manner @xmath650 , one finds by inspection that cases 1 , 3 , 4 , 8 are identical as are cases 2 , 5 , 6 , 7 thus leading to the two cases illustrated in figure [ flipper].@xmath205 99 a. beardon , the geometry of discrete groups , springer , 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we introduce coordinates for a principal bundle @xmath0 over the super teichmller space @xmath1 of a surface @xmath2 with @xmath3 punctures that extend the lambda length coordinates on the decorated bundle @xmath4 over the usual teichmller space @xmath5 . in effect , the action of a fuchsian subgroup of @xmath6 on minkowski space @xmath7 is replaced by the action of a super fuchsian subgroup of @xmath8 on the super minkowski space @xmath9 , where @xmath8 denotes the orthosymplectic lie supergroup , and the lambda lengths are extended by fermionic invariants of suitable triples of isotropic vectors in @xmath9 . as in the bosonic case , there is the analogue of the ptolemy transformation now on both even and odd coordinates as well as an invariant even two - form on @xmath0 generalizing the weil - petersson khler form . this finally solves a problem posed in yuri ivanovitch manin s moscow seminar some thirty years ago to find the super analogue of decorated teichmller theory and provides a natural geometric interpretation in @xmath9 for the super moduli of @xmath0 .

<s>[INST]let @xmath10 be a connected orientable surface of genus @xmath11 with @xmath3 punctures and negative euler characteristic @xmath12 in order that @xmath13 is uniformized by a fuchsian group @xmath14 . namely , let @xmath15 denote the upper half plane with its poincar metric @xmath16 and projective matrix group @xmath17 of oriented isometries , where @xmath18 denotes the identity matrix ; there is then an injective representation @xmath19 of the fundamental group @xmath20 , which is a free group of rank @xmath21 , onto a discrete subgroup @xmath22 so that non - trivial loops about punctures are represented by parabolic transformations , namely , those with absolute trace equal to two . see @xcite for example . the _ teichmller space _ of @xmath2 is @xmath23 where the prime indicates fuchsian representations as just defined and the action of @xmath6 on @xmath24 is by conjugation . the _ super - teichmller space _ of @xmath2 as already formulated in the context of representation theory and moduli spaces by bryant and hodgkin @xcite ( see also @xcite ) is @xmath25 where the corresponding super fuchsian representations comprising @xmath24 are defined to be those whose projection @xmath26 are fuchsian , where @xmath8 denotes the orthosymplectic group of @xmath27-by-@xmath27 dimensional super matrices with its canonical projection @xmath28 , cf . @xcite or appendix i , and the action on @xmath24 is again by conjugation . the similarities are evident . in particular , the _ mapping class group _ @xmath29 of homotopy classes of orientation - preserving homeomorphisms of @xmath2 acts on @xmath5 and @xmath1 in the natural way . consider a graph @xmath30 embedded in @xmath2 as a deformation retract also called a _ spine _ of @xmath2 . the _ valence _ of a vertex of @xmath31 is the number of half - edges incident upon it , where a half - edge is defined as a complementary component to an interior point of the edge , and @xmath31 is said to be _ trivalent _ if each vertex has valence exactly three . an orientation on @xmath2 induces the counter clockwise ordering on the half edges of @xmath31 incident on each fixed vertex thus giving the abstract graph @xmath31 the structure of a _ fatgraph _ sometimes also called a ribbon graph . there is a combinatorial move on trivalent fatgraph spines @xmath30 called a _ flip _ as illustrated in figure [ flip0 ] , where one contracts an edge of @xmath31 with distinct endpoints and then expands the resulting 4-valent vertex in the unique distinct manner in order to produce another trivalent fatgraph spine . this leads to the so - called _ ptolemy groupoid _ of @xmath2 whose objects are homotopy classes of trivalent fatgraph spines in @xmath2 and whose morphisms are compositions of flips . as we shall recall in the next introductory section dedicated to the bosonic case , finite compositions of flips act transitively on homotopy classes of trivalent fatgraph spines . it follows that flips generate @xmath29 in the sense that if @xmath30 is a trivalent fatgraph spine and @xmath32 , then there is a sequence @xmath33 of trivalent fatgraph spines of @xmath2 where any consecutive pair differ by a flip . in fact @xcite , the components of @xmath34 are naturally indexed by the set @xmath35 of spin structures on @xmath2 , and here is a basic difference from the bosonic case : the super - teichmller space is disconnected with the @xmath29-action permuting components . there are a number of equivalent formulations of spin structure , and we shall rely upon several of them at various junctures . milnor s elegant formulation of a spin structure on @xmath2 is a class in the mod two first cohomology of the unit tangent bundle of @xmath2 which is non - zero on the fiber class ; see @xcite . more combinatorial formulations from the literature which we shall require are as follows : .2 in @xmath36 the description @xcite due to johnson in terms of _ quadratic forms _ @xmath37 on @xmath38 , i.e. , functions @xmath39 which are quadratic for the intersection pairing @xmath40 in the sense that @xmath41 if @xmath42 . @xmath36 cimasoni and reshetikhin @xcite formulate spin structures using @xcite in terms of so - called kastelyn orientations and dimer configurations on the one - skeleton of a suitable cw decomposition of @xmath2 as we shall explain in detail later . @xmath36 a spin structure on a uniformized surface @xmath13 is determined by a lift @xmath43 of @xmath44 , and natanzon @xcite computes in terms of the quadratic form @xmath45 that @xmath46 if and only if @xmath47)\neq 0 $ ] , where @xmath48\in h_1 $ ] here and in the sequel is the image of @xmath49 under the mod two hurewicz map . = 0ex our first main result gives yet another combinatorial formulation of spin structures on @xmath2 in terms of the equivalence classes @xmath50 of all orientations on a trivalent fatgraph spine @xmath30 , where the equivalence relation is generated by reversing the orientation of each edge incident on some fixed vertex , with the added bonus of a computable evolution under flips . * theorem a. * _ fix any trivalent fatgraph spine @xmath51 . then @xmath52 and @xmath53 are isomorphic as affine @xmath54-spaces . moreover , the action of @xmath29 on @xmath37 or @xmath35 lifts to the action of the ptolemy groupoid on @xmath52 illustrated in figure [ flipper ] . _ + a spin structure on @xmath2 manifest for instance as a quadratic form @xmath55 distinguishes two types of punctures as follows . if @xmath56 is a simple loop about the puncture @xmath57 of @xmath2 , then @xmath57 is called a _ neveu - schwarz _ ( ns ) puncture if @xmath58)=0 $ ] and is otherwise called a _ ramond _ ( r ) puncture . the dimension of a component of @xmath1 depends on the types of punctures , and each component of @xmath59 is in fact @xcite a superball of dimension @xmath60 , where @xmath61 and @xmath62 are the respective numbers of @xmath63 and @xmath64 punctures . it is not hard to see that @xmath65 must be even since the sum of the @xmath66-monodromies about the punctures must agree with the trivial monodromy about a small inessential curve in the surface , and we furthermore evidently have @xmath67 . in the bosonic case @xcite , there is a principal @xmath68-bundle @xmath69 called the _ decorated teichmller space _ of @xmath10 recalled in some detail in the next introductory section . letting @xmath70 here and in the sequel denote the subspace of @xmath71 whose even coordinates have positive body , there is likewise a principal @xmath72-bundle over each component of @xmath1 with @xmath65 ramond punctures called the _ decorated super - teichmller space _ and written simply @xmath73 and the action of @xmath29 lifts to @xmath0 as we shall see . here we combine the main results from sections 8 and 9 into one result : * omnibus theorem b. * _ fix a surface @xmath10 of genus @xmath11 with @xmath3 punctures , where @xmath74 , let @xmath30 be some trivalent fatgraph spine and suppose that @xmath75 is an orientation on the edges of @xmath31 whose class in @xmath50 determines the component @xmath76 of @xmath0 . then there are global affine coordinates on @xmath76 , one even coordinate called a @xmath77-length for each edge and one odd coordinate called a @xmath78-invariant for each vertex of @xmath31 , the latter of which are taken modulo an overall change of sign denoted by @xmath66 ; that is , @xmath77-lengths and @xmath78-invariants establish a real - analytic homeomorphism @xmath79 these coordinates are natural in the sense that if @xmath32 has induced action @xmath80 on @xmath81 , then @xmath82 is determined by the orientation and coordinates on edges and vertices of @xmath83 induced by @xmath84 from the orientation @xmath75 , the @xmath77-lengths and @xmath78-invariants on @xmath31 . + orientations on fatgraph spines evolve under flips in accordance with the previous theorem , and the following super ptolemy transformation further describes the evolution of @xmath77-lengths and @xmath78-invariants in the notation of figure [ flip0 ] where nearby roman letters denote @xmath77-lengths , nearby greek letters denote @xmath78-invariants and @xmath85 denotes the cross - ratio @xmath86 + finally , there is an even 2-form on @xmath0 which is invariant under super ptolemy transformations , namely , @xmath87 where the sum is over all vertices @xmath88 of @xmath31 where the consecutive half edges incident on @xmath88 in clockwise order have induced @xmath77-lengths @xmath89 and @xmath90 is the @xmath78-invariant of @xmath88 . _ in order to further explain the coordinates and give an intrinsic meaning to the decorated spaces , we shall recall and extend the bosonic case in the next section . the super - teichmller space is of interest on its own as one of the higher teichmller theories associated with the simplest supergroup extension of @xmath91 , namely , the orthosymplectic group @xmath8 which is however special among supergroups in that its invariant bilinear form is non - degenerate . nevertheless , this should be the first step in a general approach to higher super teichmller theory as well as its quantization . notice that the symplectic or corresponding poisson structure of theorem b has constant coefficients opening the possibility of canonical quantization as in the bosonic case @xcite . furthermore just as for @xmath77-lengths in the bosonic case , our coordinates on decorated super - teichmller space provide a computationally effective description of super moduli geometry . another key reason for interest in the super - teichmller space is that it is a cornerstone of superstring perturbation theory , and the geometry of the supersymmetric moduli uncovered here is evidently more involved than its bosonic counterpart . moreover , the well - known relationship @xcite of teichmller theory with @xmath92-dimensional gravity may suggest that the super - teichmller theory as probed here may play an analogous role for @xmath92-dimensional supergravity . we finally mention that prior to our work , there was a phd thesis @xcite , presumably to be continued in @xcite , where the author provided other coordinates on a version of super - teichmller space via a different treatment of spin structures and based upon quite a different approach effectively using so - called shear coordinates instead of @xmath77-lengths without our deep connection to super minkowski geometry described in the next several sections . + * acknowledgements . * both authors are grateful to institut des hautes tudes scientifiques for hospitality at the initial phase of this work . is indebted to a.n . fedorova for careful reading of the manuscript . the decorated teichmller space @xmath93 is intimately connected to the geometry of minkowski space @xmath7 , namely , @xmath94 imbued with the quadratic form @xmath95 and its corresponding bilinear pairing @xmath96 or equivalently the quadratic form @xmath97 in the variables @xmath98 and @xmath99 . the upper sheet @xmath100 of the hyperboloid with the induced metric gives a model for the hyperbolic plane @xcite . furthermore @xcite , the positive light cone @xmath101 parametrizes horocycles ( that is , those curves with geodesic curvature unity ) in the sense that @xmath102 establishes a bijection is the more natural choice ; cf . @xcite . ] between all @xmath103 and the collection of all horocycles @xmath104 , and moreover , this identification is geometrically natural in the sense that @xmath105 is the signed hyperbolic distance between @xmath106 and @xmath107 . this invariant @xmath108 of a pair @xmath109 of horocycles is called the _ lambda length _ , and these are the basic coordinates on @xmath93 . it is convenient both here and in the sequel to consider not only trivalent fatgraph spines of @xmath10 but also their duals : an _ ideal triangulation _ @xmath110 of @xmath2 is a maximal family of arcs embedded in @xmath2 with endpoints at the punctures , which are here regarded as distinguished points of @xmath2 , where no two arcs in @xmath110 are properly homotopic or intersect except perhaps at their endpoints . by maximality , each complementary region to @xmath110 in @xmath2 is an ideal triangle , and these meet along their frontiers in @xmath2 . construct a trivalent fatgraph spine @xmath111 of @xmath2 with one vertex for each complementary region and one edge for each arc in @xmath110 required to connect the vertices corresponding to regions on either side of the arc this construction evidently establishes a bijection between homotopy classes of trivalent fatgraph spines and homotopy classes of ideal triangulations of @xmath2 together with a natural identification between their edges . the dual of a flip , also called a flip , is the removal of an edge from @xmath110 with distinct triangles on either side followed by its replacement by the other diagonal of the quadrilateral formed by their union . a key point of the decorated space in the bosonic case is that the fiber @xmath112 of @xmath113 is identified with all @xmath114-tuples of ( lengths of ) horocycles in @xmath2 with one horocycle about each puncture ; this is precisely the sense in which a usual hyperbolic structure in @xmath5 is _ decorated with a horocycle at each puncture _ in @xmath93 . the @xmath29-action on @xmath5 thus lifts to @xmath93 by permuting lengths . an arc connecting punctures in a decorated hyperbolic surface has a well - defined lambda length computable in the surface itself or equivalently in @xmath7 as just discussed . + * omnibus theorem c. * @xcite _ fix a surface @xmath10 of genus @xmath11 with @xmath3 punctures , where @xmath74 , and let @xmath110 be a homotopy class of ideal triangulation or equivalently of a trivalent fatgraph spine of @xmath2 . then the assignment of lambda lengths to the arcs in @xmath110 establishes a real - analytic homeomorphism @xmath115 . moreover , the lambda length @xmath116 of a ( homotopy class of ) arc @xmath117 in @xmath2 connecting punctures for @xmath118 is natural in the sense that if @xmath32 has induced action @xmath119 on @xmath93 , then @xmath120 . + the ptolemy transformation @xmath121 describes the evolution of lambda lengths under flips in the notation of figure [ flip0 ] . + the weil - petersson khler form on @xmath122 pulls back to the ptolemy - invariant form @xmath123 where the sum is over all complementary triangles to @xmath110 with consecutive half edges in clockwise order having induced lambda lengths @xmath89 . + a convex hull construction in @xmath124 gives rise to a real - analytic @xmath29-invariant ideal cell decomposition of @xmath125 itself where there is one open simplex together with certain of its faces for each homotopy class of decompositions of @xmath2 into ideal polygons and the face relation is generated by removal of arcs . _ + thus in the equivalent formalism of trivalent fatgraph spines as opposed to ideal triangulations , theorem b extends all but the last paragraph of theorem c from @xmath93 to @xmath0 , and the proof of the former provides a paradigm for the proof of the latter . notice that by this last paragraph of theorem c , we may connect interior points of simplices for any two ideal triangulations of @xmath2 by a path in @xmath125 , which can be perturbed to general position with respect to the codimension - one faces of the cell decomposition . since crossing these faces corresponds to flips , it follows that any two ( homotopy classes of ) ideal triangulations of @xmath2 are related by a finite sequence of flips , and dually we recover whitehead s result @xcite : * corollary d * _ for any surface @xmath10 with @xmath74 , finite sequences of flips act transitively on homotopy classes of trivalent fatgraph spines in @xmath2 . _ moreover , the codimension - two faces analogously give rise to a presentation of the ptolemy groupoid of @xmath2 , cf . @xcite . we next discuss the proof of the first part of theorem c , namely , the construction of lambda length coordinates on @xmath93 which brings us more deeply into minkowski space . the topological universal cover @xmath126 of @xmath2 may be identified with upper half space @xmath127 or equivalently via the cayley transform @xmath128 with the unit disk @xmath129 supporting its poincar metric and ideal boundary the circle @xmath130 at infinity . central projection of @xmath131 from @xmath132 to the disk at height zero establishes an isometry of @xmath131 and @xmath129 which continuously extends to the projection @xmath133 mapping @xmath103 to the center of the horocycle @xmath106 . an ideal triangulation @xmath110 of @xmath2 lifts to an ideal triangulation @xmath134 of @xmath126 , and the collection of ideal points of @xmath135 is invariant under homotopy of @xmath110 in @xmath2 . in order to define a point of @xmath93 , we must determine a fuchsian representation @xmath136 in the component @xmath137 of the identity of the minkowski isometry group @xmath138 , corresponding to the underlying point in @xmath5 , together with a lift @xmath139 , corresponding via affine duality to the decoration and realizing the lambda lengths in the obvious sense , which is @xmath140-equivariant with respect to our constructed representation @xmath141 , namely , we have @xmath142 , for all @xmath143 and @xmath49 . this construction of @xmath144 and @xmath145 from lambda lengths is performed recursively as we shall recall in proving theorem b. in our current case , there is an embedding of @xmath8 into the super lorentz group of the super minkowski space @xmath9 with pairing @xmath146 as described in the next section . there is again a positive light cone @xmath147 comprised of isotropic vectors so that the bodies of @xmath148 and @xmath149 are non negative . however , here is another fundamental distinction between the bosonic case and the general case treated here : whereas the action of @xmath137 on @xmath150 is transitive , an @xmath8-orbit of positive isotropic vectors is determined by a fermionic invariant @xmath151 up to sign . though most of the computations of this paper can be completed in the general setting , the super teichmller theory seems to require taking this fermion label @xmath152 . it is the special light cone @xmath153 consisting of those positive isotropic vectors with vanishing fermion label @xmath154 that provide the analogue of @xmath150 for us here . again , we define the @xmath77-length of a pair of points in @xmath155 to be the square root of their inner product and prove that this is the unique invariant of the @xmath8-orbit of a pair of linearly independent points in @xmath155 . we shall again recursively define a mapping @xmath156 which realizes @xmath77-lengths in the obvious sense and is @xmath140-equivariant with respect to the representation @xmath157 that we construct . here is yet another fundamental distinction between the bosonic case and the general case : whereas @xmath137 acts transitively on triples of rays in @xmath150 which are consistent with the positive orientation on @xmath7 , an @xmath8 orbit of a triple in @xmath155 whose underlying bosonic vectors in @xmath150 have this property is again determined by a fermion invariant @xmath158 up to sign . manin @xcite had already observed this basic phenomenon hence our term @xmath78-invariant for the odd invariants associated to vertices of a fatgraph spine in theorem b which come from consistent choices of signs and are , like @xmath77-lengths , realized by the mapping @xmath144 in the obvious sense . consistency here is given by an explicit relationship on signs of @xmath78-invariants for adjacent triangles in @xmath159 . there are thus three basic differences here from the bosonic case : the failure of transitivity of the @xmath8-action on points and on triples in @xmath155 already mentioned and the further fact that the identification of @xmath150 with the space of horocycles in @xmath131 has no known analogue in the general case . thus , the decorated super - teichmller space @xmath0 _ can only be defined here _ as the space of @xmath8 orbits of those maps @xmath156 that are @xmath140-equivariant for some super fuchsian representation with no intrinsic interpretation of _ super horocycle _ for the decoration beyond the analogous but un - illuminating affine dual in @xmath9 of a point in @xmath155 . indeed , in addition to the research frontiers discussed at the end of the previous section that the current work presumably illuminates , so also first glimpses of _ super hyperbolic geometry _ are hopefully to be gleaned here . the supergroup @xmath8 is defined as follows . the group elements are square @xmath160 supermatrices with superdeterminant equal to 1 which satisfy the relation @xmath161 where the superscript @xmath162 denotes the super transpose and @xmath163 . we refer the reader to appendix i for more information about @xmath8 including the definition of super transpose ( or see ( [ action ] ) below ) and our sign conventions for products of supermatrices . the useful property @xmath164 is of course a direct consequence of ( [ ospdef ] ) . we are interested in the adjoint action of @xmath8 and to this end consider its even element @xmath165 we claim that the adjoint action @xmath166 of @xmath167 on @xmath168 leaves invariant @xmath146 since it is proportional to the quadratic form arising from the killing form of @xmath8 applied to @xmath168 . we shall prove this differently as follows . observe that in the 3-dimensional representation of @xmath8 owing to the property ( [ ainv ] ) , the element @xmath169 , where @xmath170 for any fixed constant @xmath171 , transforms as @xmath172 under the adjoint action . in particular when @xmath171 is invertible , this implies that the superdeterminant of @xmath173 is preserved under the action of @xmath8 sending @xmath174 to @xmath175 . it is not hard to calculate that @xmath176 and so @xmath146 is invariant under the action of @xmath8 as was claimed . the following proposition therefore holds . the formula @xmath177 , for fixed but arbitrary @xmath171 , gives the action of the @xmath8 subgroup of the full lorentz supergroup of the superspace @xmath178 with the minkowski pairing defined by the quadratic form @xmath146 . to be entirely explicit , the pairing of two vectors @xmath179 and @xmath180 in @xmath178 is given by @xmath181 in keeping with @xcite , we shall henceforth refer to the square root of such an inner product as a _ @xmath77-length_. two surfaces of special importance for us in the following are the _ ( super ) hyperboloid _ @xmath182 consisting of points @xmath183 satisfying the condition @xmath184 corresponding to @xmath185 in equation ( [ goop ] ) , where the bodies of the @xmath148- and @xmath149-coordinates of @xmath186 are non - negative , and most especially the _ ( positive super ) light cone _ @xmath187 consisting of points @xmath188 satisfying @xmath189 and corresponding to @xmath190 , where again the bodies of @xmath148- and @xmath149-coordinates are non - negative . a standard superspace which however plays a subsidiary role for us , the complex _ superplane _ @xmath191 consists of pairs @xmath192 , and its subspace the _ super upper half - plane _ @xmath193 is comprised of those points @xmath192 such that the body of the real part of @xmath194 is non - negative . it is well known @xcite that @xmath8 acts on @xmath193 by means of superconformal transformations @xmath195 another direct analogue of the standard bosonic case , we have [ splane ] the expressions @xmath196 define an @xmath8-equivariant monomorphism from the hyperboloid @xmath197 onto the super half - plane @xmath193 . * proof . * the easiest way to prove this statement is to consider the infinitesimal actions of the corresponding generators described in appendix i. for example , the transformation @xmath198 amounts to the infinitesimal @xmath199 and therefore @xmath200 meanwhile , we have @xmath201 where we have used the relation @xmath202 in the last line . it follows that @xmath203 as required , and one can similarly show that @xmath204 . thus , this corresponds to the superconformal transformation . we leave it for the reader to complete the proof for the other four infinitesimal transformations corresponding to the generators discussed in appendix i. @xmath205 again just to be entirely explicit in the context of relevant subsequent calculations , the light cone is described by @xmath206 and the action of the supermatrix @xmath207 on @xmath208 is given by @xmath209 where these products of supermatrices have the signs ] explained in appendix i. this is entirely analogous to the bosonic action @xcite of @xmath210 on the light cone in @xmath7 given by the change of basis for binary symmetric bilinear forms . there is the particular element of @xmath8 given by @xmath211 that is of special significance . the supermatrix @xmath212 generates the center of @xmath8 , and its explicit action on any @xmath213 is given by @xmath214 . thus , @xmath212 simply changes the signs of the fermions and will henceforth be referred to as _ ( fermionic ) reflection_. we next show that @xmath8 does not act transitively on the light cone @xmath187 , and in fact , the moduli space of orbits is homeomorphic to the space @xmath215 , where @xmath66 acts by the change of sign of fermions . to begin , we normalize with respect to the subgroup @xmath216 . for each vector @xmath217 , there is some @xmath218 so that @xmath219 , where t has positive body . * proof . * consider an arbitrary vector @xmath220 . since one of @xmath148 or @xmath149 is invertible , we can apply an element of the @xmath221 subgroup to transform to a vector @xmath222 where both of @xmath223 are invertible and the body of @xmath224 is positive . we can subsequently apply a diagonal matrix from the @xmath221 subgroup in order that the resulting vector @xmath225 satisfies @xmath226 and hence has the required form . @xmath205 + the next result provides the classification of orbits , namely , we can reduce all degrees of freedom to a single fermion modulo sign via the action of @xmath8 . [ orb ] every vector in the light cone can be put into the form @xmath227 via an @xmath8 transformation . the only solutions to the equation @xmath228 , where @xmath167 , are given by @xmath229 . * according to the previous lemma , in order to prove the first part , we may assume that our specified vector is of the form @xmath230 , where @xmath231 has positive body . a direct computation then shows that the matrix @xmath232 achieves the required expression @xmath233 , where in fact @xmath234 and @xmath235 is likewise taken with positive body . the second part is proven by explicitly solving the equation @xmath228 as follows . consider an arbitrary element @xmath236 the vector @xmath237 is characterized by the identities @xmath238 thus , if @xmath239 , then using @xmath240 as well as the constraints on the entries of @xmath241 given in appendix i , we find that @xmath242 , @xmath243 imply @xmath244 and then @xmath245 , @xmath246 imply @xmath247 it follows that @xmath229 as was claimed.@xmath205 + the next result follows immediately . the moduli space of orbits of the @xmath8 action on the light cone is given by @xmath248 where @xmath66 reflects the sign of the fermion . the explicit solution to the equation @xmath249 given in proposition [ orb ] yields the following corollary which will be of utility in the sequel . [ stab ] for @xmath250 , an element @xmath251 of the stabilizer subgroup of @xmath252 in @xmath8 necessarily has the form @xmath253 where @xmath254 are free parameters with @xmath171 even and @xmath90 odd . moreover for @xmath255 , the stabilizer of @xmath256 has one component for ramond punctures given by the expression @xmath257 above as well as a second component for neveu - schwarz punctures given by its composition @xmath258 with the fermionic reflection @xmath212 . given a point @xmath208 , the fermion @xmath259 ( defined up to an overall sign ) so that @xmath186 and @xmath260 lie in the same @xmath8-orbit is called the _ fermion label _ of @xmath186 , and it admits the following simple expression . [ orbitform ] if @xmath261 , then the fermion label of @xmath186 is given by @xmath262 if @xmath148 is invertible and by @xmath263 if @xmath149 is invertible . here and throughout since @xmath148- and @xmath149-coordinates have non - negative body on the positive light cone , there are well - defined square roots @xmath264 and @xmath265 also with non - negative body . the fermionic reflection on @xmath266 thus changes the sign of @xmath90 here . + * proof . * the result follows from direct calculation starting from the formulas ( [ ga ] ) using the constraints on entries of @xmath8 in appendix i as we explicate in the case where @xmath148 is invertible . we have @xmath267 at the same time , we have @xmath268 and therefore @xmath269 it follows that @xmath270 where we again use the constraints on elements of @xmath8 from appendix i. @xmath205 + the @xmath8-orbit of @xmath271 will play a special role for us here . we shall denote it @xmath272 and refer to it as the _ special light cone_. the special light cone @xmath273 is isomorphic to superprojective space @xmath274 with the action of @xmath8 given by superconformal transformations . provided @xmath275 , the natural correspondence between @xmath276 and @xmath277 is given by : @xmath278 the proof follows along the lines of theorem [ splane ] . this section provides abstract identifications for the spaces of @xmath8-orbits of linearly independent ordered pairs and certain triples of points in the special light cone @xmath279 . specifically , we shall say that an ordered triple @xmath280 of points in @xmath279 is _ positive _ provided @xmath281 are linearly independent and the underlying triple of bosonic vectors in the usual light cone @xmath282 in this order provides a positively oriented basis for @xmath283 with its usual orientation . in fact , the latter moduli space of positive triples in the light cone plays a key role in the sequel , and several further parametrizations of it are derived in the next section . the moduli space of all ordered pairs of linearly independent vectors ( i.e. , with non - vanishing minkowski inner product or equivalently vectors lying in distinct rays ) in the special light cone is described by [ 2pts ] there is a unique @xmath8-invariant of two linearly independent vectors @xmath284 , and it is given by the pairing @xmath285 . * proof . * according to proposition [ orb ] , by applying an appropriate element of @xmath8 to both points , we may assume @xmath286 and @xmath287 . note that @xmath149 must be invertible , for otherwise the vectors are not linearly independent in the super - sense , namely , there exist @xmath288 with non - zero bodies so that @xmath289 has zero body . we may apply a transformation @xmath251 of the form ( [ stabil ] ) thus stabilizing @xmath186 and mapping @xmath290 to @xmath291 , where @xmath292 we wish to normalize so that this vector takes the form @xmath293 and thus impose the two further conditions @xmath294 and @xmath295 . this implies @xmath296 which gives @xmath297 as required . @xmath205 the moduli space of @xmath8-orbits of ordered pairs of vectors in the special light cone lying in distinct rays is given by @xmath298 . turning now to ordered triples of linearly independent vectors in @xmath279 , the underlying bosonic triple may provide either a positively or a negatively oriented basis of @xmath299 , and we have already christened the former case a positive triple . the well - known three - effectiveness of the action of @xmath6 on positively oriented ( i.e. , correctly cyclically ordered ) triples of points in the circle at infinity of hyperbolic space fails in our current context of @xmath178 because there is one additional odd degree of freedom which can not be fixed . we next compute the moduli space of orbits of positive triples to be @xmath300 modulo the fermionic reflection and postpone the further discussion of this interesting additional parameter to the next section . [ 3pts]let @xmath301 be a positive triple in the special light cone . then there is @xmath167 , which is unique up to composition with the fermionic reflection , and unique even @xmath302 , which have positive bodies , and odd @xmath303 so that @xmath304 * proof . * first , one can put @xmath305 into the form @xmath306 by means of @xmath8 according to lemma [ orb ] . second , @xmath307 can be put in the form @xmath308 using the stabilizer of @xmath309 as in the proof of lemma [ 2pts ] . finally by a diagonal matrix whose entries have positive bodies , one can put @xmath310 into the form where its @xmath148- and @xmath149-coordinates agree . since @xmath301 is a positive triple , the @xmath311-coordinate of @xmath310 after these transformations has positive body , and so @xmath310 indeed transforms to a vector with the required form @xmath312 while the other two transformed vectors evidently also have the desired forms @xmath313 , @xmath314 . the asserted uniqueness up to reflection of the transformation @xmath167 thus constructed follows from corollary [ stab].@xmath315 + just to be clear , let us note that there are thus precisely two lifts to @xmath155 of a positive triple @xmath316 with abstract coordinates @xmath317 given by @xmath318 ( where the @xmath311-coordinate of @xmath310 has positive body in the notation of the lemma ) and its image @xmath319 under the fermionic reflection @xmath212 . in any case , the invariants @xmath302 have positive body and only the signs of the fermions change . as a parenthetical point of notation , we mention that the labeling @xmath320 is used here rather than the more natural @xmath321 in order to accommodate later conventions . [ modsp3 ] the moduli space of @xmath8-orbits of positive triples in the light cone is given by @xmath322 , where @xmath66 acts by fermionic reflection . in fact , the even invariants @xmath302 of a triple , which we shall call _ normalization coefficients _ , are the direct analogues of the reciprocal @xmath323-lengths from @xcite , and they can be nicely computed in terms of the @xmath77-lengths @xmath324 [ evenones ] the normalization coefficients @xmath302 in lemma [ 3pts ] are given by @xmath325 we have found that a positive triple of points in the special light cone naturally determines three even and one odd invariant , namely , the @xmath77-lengths @xmath326 or the normalization coeffcients @xmath302 and the fermion label @xmath303 given in the previous lemma . it appears that the definition of the odd parameter @xmath303 depends on a choice of member of the positive triple , and we next discuss how to eliminate this dependence . in fact given a positive triple @xmath280 , there is a canonical cube root of unity in @xmath8 called the _ @xmath280 prime transformation _ which cyclically permutes its members @xmath327 , and we shall compute this transformation on the coordinates of lemma [ 3pts ] explicitly and denote it @xmath328 where the @xmath77-lengths are of course also cyclically permuted in the natural way . the choice - free way to express the additional odd degree of freedom is to average our ansatz @xmath303 over this prime transformation and define the _ manin invariant _ of a triple of points in @xmath329 capturing the basic non - transitivity of the @xmath8 action there , and by making choices ( of spin structure among other conventions ) one can @xcite lift this to a signed expression @xmath90 , namely , our manin invariant . ] or simply the _ @xmath78-invariant _ to be @xmath330 in practice , @xmath78-invariants and @xmath77-lengths give a parametrization of decorated super - teichmller space as we shall see . to complete our definition of the @xmath78-invariant , it therefore remains to compute the prime transformation . to this end , we alter notation slightly setting @xmath331 , @xmath332 , @xmath333 as illustrated in figure [ 3nota ] . -lengths @xmath326 on edges and one @xmath78-invariant @xmath90.,scaledwidth=30.0% ] given three points @xmath334 in the special light cone @xmath279 , where @xmath302 have positive body , we claim there exists a group element @xmath335 from @xmath8 respectively transforming the points @xmath281 into @xmath336 and in fact , there are two possible ways to construct such a transformation ( again unique up to fermionic reflection ) . however , there is a unique transformation whose third power @xmath337 is equal to identity , and it turns out that its action on @xmath303 is rather simple . [ prime ] the group element @xmath335 acts so that @xmath338 , and this is the unique group element @xmath339 satisfying the identity ( [ gid ] ) . * proof . * we first use the group element @xmath340 in ( [ gtpp ] ) in order to transform @xmath290 into @xmath309 . the effects of this transformation on the other points produces @xmath341 finally , acting by the diagonal matrix @xmath342 we obtain the desired result by composing with the fermionic reflection @xmath343 @xmath344 so that @xmath345 , @xmath346 , @xmath347 . @xmath205 + the @xmath78-invariant @xmath348 of a positive triple @xmath280 is invariant under the @xmath280 prime transformation . as follows directly from this plus the discussion of the previous section , we have the moduli space of @xmath8-orbits of positive triples in the light cone is given by equivalence classes under fermionic reflection of three even @xmath77-lengths @xmath326 with positive bodies plus the @xmath78-invariant @xmath90 defined up to fermionic reflection . this section is dedicated to a computation called the `` basic calculation '' giving a parametrization of the moduli space of @xmath8-orbits of four - tuples @xmath349 in the special light cone @xmath273 comprised of two positive triples @xmath350 and @xmath351 of points in terms of five @xmath77-lengths and two @xmath78-invariants . in effect , one positive triple @xmath350 is put into the canonical position of lemma [ 3pts ] using certain of the putative parameters , and the remaining ones are then used to completely and uniquely determine the fourth point @xmath352 , where @xmath311 has non - negative body ; it is precisely here that compatibility of signs of adjacent @xmath78-invariants arises . this basic calculation is the critical ingredient both for our global coordinates and for the ptolemy transformation just as in @xcite . in fact provided only that the triple @xmath350 is in standard position , the standard position of @xmath351 is easily calculated in terms of the coordinates of its vertices as follows . [ hats ] the triple @xmath353 can be transformed by an element of @xmath8 , which is itself uniquely determined up to fermionic reflection , into the triple @xmath354 where @xmath355{\frac{x_1}{x_2}}\frac{\lambda}{\sqrt{x_1x_2}}=\sqrt[4]{\frac{x_2}{x_1}}\frac{\rho}{\sqrt{x_1x_2}},\end{aligned}\ ] ] * proof . * act first by @xmath356 to interchange the roles of @xmath186 and @xmath76 while mapping @xmath357 to a point with non - negative @xmath311-coordinate and then act by @xmath358{{x_1}/ { x_2 } } & 0 & 0 \\ 0 & \sqrt[4]{{x_2}/ { x_1 } } & 0 \\ 0 & 0 & 1 \end{smallmatrix } \right)$ ] to realize equality of the first two coordinates . the composition of these two elements of @xmath8 achieves the desired result in accordance with lemma [ 3pts ] . @xmath205 + note that the normalization factors admit the uniform expressions @xmath359 this transformation in @xmath8 which maps @xmath351 to standard position if @xmath360 is in standard position is called the _ switch transformation _ of the quadruple @xmath349 though in fact it depends only upon @xmath351 according to the formula for it given above . -lengths and @xmath78-invariants near an edge before ( left ) and after ( right ) a flip , scaledwidth=60.0% ] now turning to the basic calculation itself , let @xmath361 be points in the light cone as in lemma [ 3pts ] with @xmath77-lengths @xmath326 and @xmath78-invariant @xmath90 . up to fermionic reflection , the @xmath8-orbit of the positive triple @xmath350 is then uniquely determined by these parameters according to lemma [ 3pts ] . the basic calculation aims to compute @xmath362 , where @xmath311 has non - negative body , from the data @xmath363{\frac{x_1}{x_2}}\frac{\lambda}{\sqrt{x_1x_2}}=\sqrt[4]{\frac{x_2}{x_1}}\frac{\rho}{\sqrt{x_1x_2 } } , \quad\langle a , d\rangle = d^2 , \quad \langle d , c\rangle = c^2\end{aligned}\ ] ] depicted in figure [ figint ] , and the following arises directly from equations ( [ rst ] ) and ( [ 4point ] ) . [ bascalc ] we have the expressions @xmath364 solving the basic calculation . introducing the cross - ratio @xmath365 , this expression of the basic calculation can be concisely written @xmath366 the utility of this version of the basic calculation for computing the ptolemy transformation is already evident from the following proposition . [ pt * ] in the notation above with @xmath367 , we have @xmath368 * proof . * simply expand the expression @xmath369 in @xmath77-lengths . this is equivalent to @xmath370 and the desired formula for @xmath371 follows upon taking square roots.@xmath205 + now let us reproduce the same four points @xmath372 using the parameters of adjacent positive triples @xmath373 and @xmath374 . to do so , let us move the positive triple @xmath373 to standard position @xmath375 to this end , we first apply the stabilizer of @xmath376 , namely , the matrix @xmath377 as in corollary [ stab ] , in order to transform @xmath378 , where the corresponding @xmath171 and @xmath379 are given by @xmath380 yielding @xmath381 . applying this transformation to @xmath382 , we obtain a new vector @xmath383 , where @xmath384 applying @xmath385 followed by the diagonal matrix @xmath386{\frac{\hat{x}_1}{\hat{x}_2}}&0&0\cr 0&\sqrt[4]{\frac{\hat{x}_2}{\hat{x}_1}}&0\cr 0&0&1\end{smallmatrix}\biggr)$ ] to each of @xmath387 yields : @xmath388{\frac{\hat{x}_1}{\hat{x}_2}}\big)=\frac{\hat{\rho}}{\sqrt{\hat{x}_1\hat{x}_2 } } \big(\sqrt[4]{\frac{\hat{x}_2}{\hat{x}_1}}\big)\end{aligned}\ ] ] for the parameters in equation ( [ tildas ] ) . thus , the @xmath78-invariant of the positive triple @xmath389 is given by @xmath390 as this is invariant under the @xmath389 prime transformation . [ fl1 ] the @xmath78-invariants for the positive triples @xmath389 and @xmath391 depend only on the @xmath78-invariants @xmath392 and the cross - ratio @xmath393 and are given by @xmath394 @xmath395 * proof . * equation ( [ one ] ) follows from the direct calculation @xmath396{\frac{\hat{x}_1}{\hat{x}_2}}\big)=\frac{\theta x_2-\lambda } { \chi^{\frac{3}{4}}(\sqrt{2}\frac{cd}{e})\sqrt{\sqrt{\chi}+\sqrt{\chi}^{-1}}}= \frac{\theta\sqrt{\chi}+\sigma}{\sqrt{1+\chi}}.\end{aligned}\ ] ] in order to write @xmath78 in terms of the same function @xmath397 , we must transform @xmath398 as follows @xmath399 and this can be achieved by first applying the matrices given in lemma [ hats ] so that @xmath400{\frac{x_1}{x_2}}\theta , \quad \check \lambda= t\sqrt[4]{\frac{x_2}{x_1}}\theta,\nonumber\\ & & \check\phi=-\sqrt[4]{\frac{x_1}{x_2}}\frac{\lambda}{\sqrt{x_1x_2}}=\sqrt[4]{\frac{x_2}{x_1}}\frac{\rho}{\sqrt{x_1x_2}}.\nonumber\end{aligned}\ ] ] it follows that @xmath401 where the checked arguments of @xmath78 are related to checked variables from ( [ tcheck ] ) as before and @xmath402 it follows that @xmath403 as required . @xmath205 as a direct corollary to the proof , we have [ switch ] consider the odd ptolemy transformation on ordered pairs @xmath404 together with the corresponding action on @xmath77-lengths and apply it twice to the quadrilateral @xmath349 , with @xmath360 in standard position . then the effect is the switch transformation of @xmath349 described in lemma [ hats ] . specifically after this transformation , @xmath351 is in standard position with @xmath405 while the image of @xmath290 is determined not by @xmath90 but rather by @xmath406 . in this section , we relate the collection of spin structures on a punctured surface to orientations on any trivalent fatgraph spine of the surface . to begin , we recall results of cimasoni - reshetikhin from @xcite . the _ boundary _ of a one - dimensional cw complex @xmath407 is its set @xmath408 of vertices of valence one . @xmath407 is a _ surface graph with boundary _ for some compact oriented surface @xmath409 with boundary @xmath410 if @xmath407 is embedded in @xmath409 with @xmath411 so that @xmath412 is the 1-skeleton of a cellular decomposition of @xmath409 . a _ dimer configuration _ on @xmath407 is a choice of certain of its edges called _ dimers _ such that each vertex not in @xmath413 has exactly one incident dimer while vertices in @xmath413 may or may not have an incident dimer , the specification of which is regarded as an _ a priori _ boundary condition on the dimer configuration . given an orientation @xmath414 on the edges of @xmath415 and a closed oriented edge curve @xmath76 in it , we denote by @xmath416 the number of edges counted with multiplicity where the orientation of @xmath76 disagrees with that of @xmath414 . a _ kasteleyn orientation _ on @xmath417 is an orientation @xmath414 on the edges of the 1-skeleton @xmath415 so that @xmath418 for each face @xmath371 of @xmath409 . define an equivalence relation @xmath419 between two kasteleyn orientations @xmath420 on @xmath421 generated by altering the orientation on every edge incident on some fixed vertex , which is called a _ kastelyn reflection _ , and let @xmath422 denote the set of equivalence classes . there is furthermore a cochain @xmath423 defined by setting @xmath424 if and only if @xmath425 and @xmath426 disagree on @xmath427 , for @xmath427 an edge of @xmath421 . [ corollary 1 of @xcite][theta ] in fact , @xmath428 is a cocycle which is a coboundary if and only if @xmath419 . furthermore , the set of equivalence classes of kasteleyn orientations is an affine @xmath429-space . seminal work of dennis johnson @xcite mentioned before identifies as affine @xmath430-spaces the collection @xmath35 of all spin structures on a surface @xmath409 with the collection @xmath431 of all quadratic forms @xmath432 satisfying @xmath41 with respect to the homology intersection pairing @xmath433 of @xmath434 . in fact , kasteleyn orientations on a surface graph for @xmath409 and quadratic functions on @xmath435 are also isomorphic as affine @xmath429-spaces , and the correspondence is given via an explicit construction relative to a fixed dimer @xmath357 as follows . [ cr ] fix a dimer configuration @xmath357 on a surface graph with boundary @xmath407 for the surface @xmath409 and let @xmath436 be represented by oriented closed curves @xmath437 . if @xmath414 is a kasteleyn orientation on @xmath407 , then the function @xmath438 given by @xmath439 is a well - defined quadratic form , where @xmath440 is the number of edges of @xmath357 sticking out to the left of @xmath76 , and @xmath416 as before is the number of edges counted with multiplicity where the orientation of @xmath76 disagrees with that of @xmath414 . moreover , for each fixed dimer @xmath357 , this establishes an isomorphism @xmath441 as affine @xmath429-spaces . together with @xcite , this establishes an isomorphism of affine @xmath429-spaces between the collection @xmath442 of spin structures on @xmath409 and @xmath422 for any surface graph @xmath421 with boundary for @xmath409 with respect to a fixed dimer configuration . now , given a trivalent fatgraph spine @xmath31 for @xmath10 , we shall build an appropriate surface graph with boundary for a surface embedded in @xmath2 as a deformation retract . construct a cw decomposition of this compact so - called skinny surface @xmath443 with boundary taking one hexagon @xmath444 for each vertex @xmath88 and one rectangle @xmath445 for each edge @xmath427 of @xmath31 glued together in the natural way in @xmath2 as in figure [ cell ] . there is a canonical surface graph @xmath446 for @xmath409 comprised of the common boundaries of these hexagonal and rectangular regions as also illustrated in the figure by bold line segments , two such segments for each edge of @xmath31 . there is also a canonical dimer @xmath447 given by exactly this same set of segments , so each vertex in @xmath413 has an incident dimer . a hexagon has the two special kastelyn orientations that are either outgoing or incoming at each vertex , and these are related by reversal of orientation of each edge . furthermore identifying @xmath444 with this abstract hexagon , for some vertex @xmath88 of @xmath31 , there is a unique such orientation which agrees with the one induced from the counter - clockwise orientation of @xmath421 with @xmath444 on the left as illustrated on the top of figure [ orient ] . thus , any kastelyn orientation on @xmath448 can be modified by kastelyn reflections to agree with this one on @xmath444 for each vertex @xmath88 of @xmath31 , i.e. , the special kastelyn orientations saturate the equivalence classes . on the top and orientation on fatgraph @xmath31 from special kasteleyn orientations on @xmath449 on the bottom , scaledwidth=80.0% ] suppose that @xmath414 is such a special kastelyn orientation on @xmath448 that thus agrees with the special hexagonal ones near each vertex of @xmath31 oriented as already discussed . there are exactly two methods that @xmath414 can extend as a kastelyn orientation to a rectangle @xmath445 as illustrated on the top in figure [ orient ] , and these are naturally in bijective correspondence with orientations on the edges of @xmath31 themselves insofar as they are parallel as illustrated on the bottom of figure [ orient ] . conversely , suppose that @xmath75 is an orientation on @xmath31 and let @xmath450 denote the associated special kastelyn orientation on @xmath448 defined to be parallel on each @xmath445 and special on each @xmath444 as before . in the same spirit as kastelyn reflection , we define a _ fatgraph reflection _ at a vertex @xmath88 of @xmath31 to reverse the orientations of @xmath75 on every edge of @xmath31 incident on @xmath88 , consider the equivalence relation @xmath451 thus generated on the set of all orientations on @xmath31 and let @xmath50 denote the set of all equivalence classes . one easily checks that the fatgraph reflection at @xmath88 is given precisely by the composition of kastelyn reflections at the six vertices of @xmath444 , so @xmath451 implies @xmath452 . conversely , in order that the orientation on an edge of some @xmath444 is invariant , we must perform kastelyn reflection either at both or neither of its endpoints , and it follows that @xmath452 also implies @xmath451 . furthermore , given orientations @xmath453 on @xmath31 , there is the analogous cochain @xmath454 taking a non - zero value on an edge of @xmath31 if and only if @xmath455 and @xmath456 disagree on the edge , and we clearly have @xmath457 . summarizing , we have : [ equiva ] for each orientation @xmath75 on the edges of a fatgraph @xmath31 , there exists a unique special kasteleyn orientation @xmath458 on @xmath459 , and this induces an isomorphism @xmath460 of equivalence classes under reflection as affine @xmath461-spaces . as follows directly from theorem [ cr ] and proposition [ equiva ] , we have [ qando ] let @xmath31 be a fatgraph spine in the surface @xmath10 with corresponding surface graph @xmath462 for @xmath463 . then the formula ( [ q ] ) with the canonical dimer configuration @xmath464 establishes an isomorphism @xmath465 as affine @xmath466-spaces , and indeed also @xmath467 since @xmath463 is a homotopy equivalence . it remains for us here only to compute the effect that flipping a fatgraph edge has on an orientation class : suppose that @xmath468 is a trivalent fatgraph spine for @xmath2 and that @xmath469 arises by flipping an edge of @xmath468 . there is a unique bijection @xmath470 covering the identity map of @xmath37 , and it is described by figure [ flipper ] . * proof . * consider a neighborhood of the edge of @xmath468 upon which the flip is performed depicted in figure [ curves ] where there are illustrated six distinct oriented paths in @xmath2 denoted @xmath471 , which may be completed to closed oriented curves in @xmath2 and contribute to the value of the quadratic form . a tedious computation given in appendix ii compares formula ( [ q ] ) before and after the flip for these six paths and determines that there is the unique evolution of orientation class from @xmath468 to @xmath469 illustrated in figure [ flipper ] that leaves invariant these contributions . @xmath205 on @xmath472 are indicated by bold lines , title="fig:",scaledwidth=40.0% ] on @xmath472 are indicated by bold lines , title="fig:",scaledwidth=40.0% ] + on @xmath472 are indicated by bold lines , title="fig:",scaledwidth=40.0% ] [ oops ] let @xmath31 be a trivalent fatgraph spine of @xmath473 . then @xmath474 is isomorphic to the set @xmath35 of spin structures on @xmath2 as affine @xmath475-spaces . moreover , the action of @xmath29 on @xmath35 lifts naturally to the action of the ptolemy groupoid on @xmath476 ) illustrated in figure [ flipper ] . by naturality here , we mean that if @xmath32 , then there is a finite sequence @xmath477 where @xmath478 arises from @xmath479 by a flip , for @xmath480 . suppose that @xmath75 is an orientation on @xmath31 inducing via the identification @xmath84 the orientation @xmath455 on @xmath468 and moreover that the evolution of orientation illustrated in figure [ flipper ] serially induces from @xmath455 the orientation @xmath481 on @xmath482 . the spin structure on @xmath2 associated to @xmath75 maps to that of @xmath483 under the action of @xmath84 on @xmath35 by construction . equivalent to the choice of trivalent fatgraph spine @xmath30 is the specification of its dual ideal triangulation @xmath110 of @xmath2 . an orientation @xmath75 on @xmath31 induces an orientation on @xmath110 by requiring that the oriented edge of @xmath110 occurs clockwise from its dual oriented edge in @xmath31 near their point of intersection here using an orientation of the surface @xmath2 . dual to the fatgraph reflection at a vertex is the change of orientation on each edge in the frontier of a triangle complementary to @xmath110 . we consider the lift of @xmath110 to an ideal triangulation @xmath134 of the universal cover @xmath484 . fixing a base point in @xmath2 , the fundamental group @xmath20 acts as deck transformations on @xmath126 leaving invariant @xmath134 . of course @xmath126 is _ topologically equivalent _ to @xmath129 , and a hyperbolic metric on @xmath2 further determines a _ metric equivalence_. in any case , we may consider the collection of ideal vertices @xmath135 of all the arcs in @xmath134 as an abstract set . _ fix a surface @xmath10 of genus @xmath11 with @xmath3 punctures , where @xmath74 , and let @xmath110 be some ideal triangulation of @xmath2 whose lift @xmath134 to the universal cover @xmath485 has ideal vertices @xmath486 . suppose that @xmath75 is an orientation class on the arcs in @xmath110 corresponding to a specified spin structure , and assign to each edge of @xmath110 an even coordinate and to each triangle complementary to @xmath110 an odd coordinate where the latter are taken modulo an overall sign . then there is a function @xmath487 uniquely determined up to post - composition with an element of @xmath8 so that _ .3 in i ) if @xmath488 span an edge in @xmath134 , then the coordinate on this edge is given by the @xmath77-length @xmath489 ; ii ) if @xmath490 span a triangle complementary to @xmath134 and occur in the positive order in @xmath130 , then up to a sign the coordinate of this triangle is given by the @xmath78-invariant of the positive triple @xmath491 ; moreover , if @xmath492 likewise occur in the positive order and span a triangle , then the coordinates of these respective triangles are given up to an overall sign by the @xmath78-invariants of the positive triples @xmath491 and @xmath493 as related by proposition [ bascalc ] . = 0ex furthermore , there is a representation @xmath494 with respect to which @xmath144 is @xmath140-equivariant in the sense that @xmath495 for each @xmath49 and @xmath496 so that @xmath497 is a fuchsian representation whose lift @xmath498 agrees with the specified spin structure . moreover @xmath499 is uniquely determined up to conjugacy by an element of @xmath8 . for any @xmath11 and @xmath3,scaledwidth=75.0% ] * proof . * the argument closely follows the bosonic case @xcite using the putative coordinates to recursively construct the mapping @xmath144 and finally the representation @xmath499 . let us first consider the case that the trivalent fatgraph spine @xmath30 dual to @xmath110 is bipartite , namely , there is a two - coloring of the vertices of @xmath31 so that the endpoints of any edge of @xmath31 have different colors . an example of a bipartite fatgraph spine is illustrated in figure [ hip ] for each topological type of punctured surface . dually letting @xmath500 denote the collection of triangles complementary to @xmath110 in @xmath2 , there is a function @xmath501 so that for any two triangles @xmath502 sharing an edge , we must have @xmath503 . notice that in this bipartite case there are exactly two distinct such functions differing by an overall sign . the coordinates on @xmath110 lift to coordinates on @xmath134 in the natural way assigning to each edge @xmath504 the even coordinate of @xmath505 and to each complementary triangle @xmath506 the odd coordinate @xmath507 of @xmath508 . the function @xmath509 likewise lifts to the eponymous function @xmath510 satisfying @xmath511 . choose a distinguished triangle - edge pair or equivalently a distinguished oriented edge of @xmath134 which determines the triangle @xmath512 lying to its left in the oriented surface @xmath126 . according to lemma [ 3pts ] , there is a positive triple @xmath280 in the special light cone realizing the putative @xmath77-lengths and @xmath78-invariant @xmath507 so that the point @xmath290 is opposite to the distinguished oriented edge , and @xmath280 is furthermore uniquely determined up to fermionic reflection @xmath212 . choosing a particular representative @xmath280 or @xmath513 at this stage gauge fixes the @xmath66-action and thus determines well - defined signs on all of the fermionic coordinates @xmath514 for @xmath515 . ( in the special case when the fermionic coordinate on @xmath231 vanishes , we have @xmath516 and can still gauge fix at this point to determine the signs on all of the non - vanishing fermionic coordinates . ) this lift to a positive triple in @xmath155 of the vertices of @xmath231 constitutes the basis step of our recursive construction of the mapping @xmath144 . in order to lift the triangle @xmath517 to the right of the distinguished oriented edge with its specified fermionic coordinate @xmath518 , we shall rely on the basic calculation formulated as proposition [ bascalc ] to lift the vertex of @xmath519 distinct from those of @xmath231 to a point @xmath520 , however , the coordinates employed to determine @xmath357 are the specified putative @xmath77-lengths and the _ @xmath509-modified @xmath78-invariant _ @xmath521 rather than @xmath518 itself . conjugating by the @xmath280 prime transformation and its square , we can likewise uniquely lift to @xmath279 the vertices of the other two triangles in @xmath522 adjacent to @xmath231 . continue recursively in this way moving each triangle in @xmath522 already lifted into standard position with its specified @xmath78-invariant using @xmath8 and then employing the putative @xmath77-lengths and @xmath509-modified @xmath78-invariants to lift the next adjacent triangle in @xmath522 using proposition [ bascalc ] in order to finally uniquely lift all of @xmath486 and completely define @xmath523 in keeping with requirements i ) and ii ) in the statement of the theorem . there are actually only finitely many values of coordinates employed in this construction since there are only finitely many arcs in @xmath110 and triangles in @xmath500 . in particular , the bodies of @xmath77-lengths are uniformly bounded above and below . as in the pure even case @xcite , it follows from this bounded geometry that the bosonic projection @xmath524 induces a mapping from the ideal triangulation of @xmath126 onto a tessellation of all of @xmath129 . we claim that changing the distinguished oriented edge of @xmath159 used to initiate this construction merely modifies the function @xmath144 by post - composition with a group element in @xmath8 . to see this , first notice that if we change orientation of the distinguished oriented edge , then @xmath519 will be in standard position with its @xmath78-invariant @xmath518 , and the triangle @xmath231 is then produced using the @xmath509-modified @xmath78-invariant @xmath525 . applying the switch transformation ( and possibly overall fermionic reflection for the @xmath66 gauge group ) , based on the fact that @xmath526 together with proposition [ switch ] , we recover the image of the previous construction under the switch transformation , which lies in @xmath8 , with the correct signs for fermionic parameters . moreover , any change in the distinguished oriented edge can be achieved by means of a finite composition of prime transformations and at most one reversal of orientation . since prime transformations are again group elements of @xmath8 , we conclude that our equivalence class of lifts under the action of @xmath8 is independent of the distinguished oriented edge as required . uniqueness of the mapping @xmath144 up to post - composition with an element of @xmath8 follows by construction from the uniqueness statements in lemma [ 3pts ] and proposition [ bascalc ] completing the proof of the first part under the bipartite assumption . from the lift @xmath527 , we shall presently construct the required representation @xmath528 . to this end , choose a connected fundamental domain @xmath529 for the action of @xmath140 comprised of a collection of triangles in @xmath522 which contains the base triangle @xmath231 specified earlier which began the recursive construction of @xmath144 . the frontier edges of @xmath357 in @xmath126 arise in pairs @xmath530 together with an abstract identification @xmath531 induced by some @xmath49 , and we let @xmath532 enumerate the collection of these edge pairings , for @xmath533 , where the @xmath534 thus freely generate @xmath140 . to determine the image @xmath535 of @xmath536 in order to define the representation @xmath499 , let us further enumerate two triangles for each edge pairing , namely , the unique triangles @xmath537 and @xmath538 in @xmath522 where @xmath539 and @xmath540 . notice as before that the coordinates for @xmath541 or @xmath542 have gauge - fixed signs from the basis step of the construction of @xmath144 , and the parameters on @xmath541 lifted from @xmath2 agree with those on @xmath542 since @xmath543 implies @xmath544 . let @xmath545 be the corresponding positive triple in @xmath155 . according to lemma [ 3pts ] again , there is a unique @xmath546 such that @xmath547 , where @xmath8 acts on the right and @xmath548 indicates the triple of points in standard position realizing the @xmath77-lengths and signed @xmath78-invariant of @xmath549 so that the fermion - dependent vertex is opposite to @xmath550 . let @xmath551 be the analogous group element for @xmath552 . we must furthermore take account of the spin structure in accordance with @xcite relating the sign of the trace of the bosonic reduction of @xmath553 with the value of the corresponding quadratic form on the underlying mod two homology class @xmath48\in h_1(f;{\mathbb z}_2)$ ] , for @xmath49 . in particular , notice that the fermionic reflection @xmath212 has the central element @xmath554 as its bosonic reduction . given the quadratic form @xmath55 corresponding via theorem [ qando ] to our specified orientation @xmath75 , we define @xmath555)=0 ~~ { \rm or}~~ { \rm trace}(h_i^{-1}\cdot h'_i)<0~\&~ q([\gamma_i])=1;\\ & \\ & h_i^{-1}\cdot h'_i , \\ & { \rm if}~~ { \rm trace}(h_i^{-1}\cdot h'_i)<0~\&~ q([\gamma_i])=0 ~~ { \rm or}~~ { \rm trace}(h_i^{-1}\cdot h'_i)>0~\&~ q([\gamma_i])=1 . \end{cases}\end{aligned}\ ] ] by construction , these group elements compose correctly so as to produce a representation , and since @xmath140 is a free group , there are no relations to confirm whence @xmath499 is indeed a representation of @xmath140 in @xmath8 onto a subgroup @xmath556 . also by construction , the projectivized bosonic reduction @xmath557 leaves invariant the tessellation of @xmath129 discussed before , and an argument in @xcite going back to poincar thus proves that @xmath14 is indeed a fuchsian group uniformizing the punctured surface . finally , the bosonic reduction @xmath558 itself as a lift of @xmath22 gives the correct spin structure on the underlying riemann surface in keeping with @xcite by construction since multiplication by @xmath212 alters the sign of the trace of the bosonic reduction . this completes the required construction of a representation from the asserted parameters including the spin structure . the procedure described is clearly equivariant for the fermionic reflection under the initial choice of sign on the @xmath78-invariant in the base triangle , and the distinction between pairs @xmath539 and @xmath540 amounts only to replacing a generator by its inverse . there are thus two essential choices : the choice of base triangle @xmath231 to begin the inductive construction as well as the fundamental domain @xmath357 containing it . we must show that these choices are resolved by the overall conjugacy in the definition of the decorated super - teichmller space . to this end , consider two such fundamental domains containing specified base triangles @xmath559 with corresponding mappings @xmath560 and representations @xmath561 , for @xmath562 . there is a unique triangle @xmath563 whose projection to @xmath2 agrees with that of @xmath564 since @xmath565 is a fundamental domain for the action of @xmath140 , whence @xmath564 and @xmath566 thus share the same invariants . by lemma [ 3pts ] again @xmath66 gauge - fixed as before , there is a unique @xmath167 so that @xmath567 . by uniqueness in lemma [ 3pts ] and proposition [ bascalc ] , we must then have @xmath568 , and so @xmath241 furthermore conjugates @xmath569 to @xmath570 as required . notice that the trace of the bosonic reduction of an element of @xmath8 is invariant under conjugacy , so the spin structure is left invariant by conjugation of representations . we must finally extend the construction from bipartite to general trivalent fatgraph spines @xmath30 . to this end according corollary d , there is a finite sequence of flips starting from @xmath31 and ending with a bipartite fatgraph spine @xmath571 such as the one depicted in figure [ hip ] to which we may apply the construction just described based upon the coordinates on @xmath572 induced from those on @xmath31 via super ptolemy transformations in proposition [ pt * ] and theorem [ fl1 ] as well as the orientation class on @xmath572 induced from that on @xmath31 in theorem [ oops ] determining the spin structure . since these super ptolemy transformations are computed relative to a fixed configuration of points in @xmath155 , this gives a well - defined lift @xmath523 for any trivalent fatgraph spine and hence a corresponding representation @xmath157 which is determined up to conjugacy since the mapping @xmath144 is determined up to post - composition with an element of @xmath8 . @xmath205 + fix a trivalent fatgraph spine @xmath30 for a surface @xmath10 of negative euler characteristic and specify an orientation on the edges of @xmath31 determining the component @xmath76 of @xmath0 . then @xmath77-lengths on the edges together with @xmath78-invariants on the vertices of @xmath31 , the latter taken modulo an overall sign , provide global coordinates on @xmath76 . moreover , these coordinates are natural in the sense that if @xmath32 and @xmath33 is a sequence of trivalent fatgraph spines of @xmath2 with consecutive ones related by a flip , then we identically induce coordinates and orientation class on @xmath83 from these data on @xmath31 using @xmath84 and perform the corresponding sequence of super ptolemy transformations in proposition [ pt * ] and theorem [ fl1 ] and evolution of orientation in theorem [ oops ] to induce new coordinates and orientation on @xmath31 itself . then these induced coordinates and orientation class on @xmath31 describe the action of @xmath84 on @xmath0 . * this follows directly from the previous result and theorem [ oops ] together with the observation that @xmath77-lengths and @xmath78-invariants are defined intrinsically in @xmath9 . @xmath205 first , let us recall in some detail the ptolemy transformations studied in section [ sec : bcpt ] . there were two aspects to the calculation corresponding to even and odd , namely , the even ptolemy transformation is a simple modification @xmath573 of the standard pure even case @xmath121 , and the odd ptolemy transformation again in the notation of section [ sec : bcpt ] is given by @xmath574 taken together ( [ ptle ] ) and ( [ 0opt ] ) give expression to the _ super ptolemy transformation_. these formulas in particular specialize to those of @xcite where shear coordinates on the super - teichmller space are introduced . namely as in the classical case , given an ideal triangulation @xmath110 of the surface @xmath2 , to each edge @xmath575 as in figure [ figint ] is associated its cross ratio @xmath576 , written again in terms of @xmath77-lengths . given the two positive triples @xmath350 and @xmath351 in the special light cone @xmath279 , denote by @xmath577 , @xmath578 , @xmath579 , @xmath580 these cross ratios associated to each respective edge @xmath581 also illustrated in figure [ figint ] identifying an edge with its @xmath77-length here for convenience ; of course , each of these depends in turn on the @xmath77-lengths of other nearby edges , for instance , @xmath582 , where @xmath241 , @xmath323 are @xmath77-lengths on the frontier edges of the other complementary triangle to @xmath110 than @xmath350 that contains @xmath583 . nevertheless , under the even ptolemy transformation , we find that @xmath582 transforms to @xmath584 and one similarly computes @xmath585 in fact , these transformations together with equation ( [ 0opt ] ) coincide with those in @xcite up to a conventional inversion of the cross ratio coordinate ( see figure 2 in @xcite ) . in the pure even case @xcite , the khler 2-form of the weil - petersson hermitian metric on the teichmller space @xmath5 or moduli space @xmath122 of a punctured surface @xmath2 was computed relative to the @xmath77-lengths on any convenient triangulation @xmath110 of @xmath2 . namely , it is given by @xmath586 where the sum is over all complementary triangles @xmath316 to @xmath110 in @xmath2 with frontier edges of @xmath316 occurring in the cyclic order @xmath587 compatibly with the clockwise orientation on @xmath588 . it is not difficult to check directly that this expression is invariant under the pure even ptolemy transformation @xmath121 , and indeed in the 1980 s before it was recognized as this particular 2-form , it was nevertheless already confirmed to be invariant under ptolemy transformations and hence arise from some 2-form on the quotient moduli space @xmath589 . much this same computation applies in the current case . if @xmath110 is an ideal triangulation of the punctured surface @xmath2 , then consider the even 2-form on @xmath590 given by @xmath591 where the sum is over all triangles whose consecutive edges in the clockwise ordering have @xmath77-lengths @xmath89 and @xmath78-invariant @xmath90 . then this 2-form is invariant under super ptolemy transformations . notice that @xmath592 is manifestly invariant under the fermionic reflection changing the signs of all fermions , and we have dropped the pre factor 2 here compared to the khler form so that if one converts the expression @xmath592 from @xmath77-lengths to shear coordinates as described before , then the resulting 2-form is associated with the poisson bracket given in @xcite . * * let us remind @xcite the reader that on supermanifolds the de rham operator anticommutes with odd constants , and in local coordiantes @xmath593 is given by @xmath594 , where the odd derivative acts from the left and the @xmath595 are even . adopt the notation @xmath596 for any invertible expression @xmath597 and compute as in the pure even case @xcite for a pair @xmath350 and @xmath598 of positive triples that the contribution to @xmath592 before the flip on @xmath575 in the notation of figure [ flip0 ] is given by @xmath599 and after the flip is given by @xmath600 we must show that these two expressions coincide . to this end , notice that if @xmath601 , then @xmath602 and we find @xmath603 where @xmath604 meanwhile , the super ptolemy transformation gives @xmath605 which coincides with equation ( [ du ] ) as required.@xmath205 in this appendix , we provide basic information concerning the lie supergroup @xmath8 and its lie superalgebra . our cursory treatment here is presumably sufficient for the purposes of the text , and we refer the interested reader to @xcite for further details about general lie superalgebras and supergroups . let us first introduce certain conventions ( which differ from those in @xcite ) . given a lie superalgebra @xmath606 , one can consider its grassmann envelope , namely , the lie superagebra @xmath607 for some grassmann algebra @xmath608 with decomposition @xmath609 into even and odd elements . it follows that @xmath610 is both a right and left @xmath608-module , i.e. , @xmath611 if @xmath612 and @xmath613 are homogeneous elements of respective degrees @xmath614 and @xmath615 . this rule allows one to construct a representation of the corresponding lie superalgebra @xmath610 in the space @xmath616 from a given representation of @xmath606 in @xmath617 . one can then produce a representation of the corresponding lie group @xmath618 by exponentiating pure even elements from @xmath610 in @xmath616 . when writing a super matrix @xmath619 representing the action of @xmath618 or @xmath610 as elements of @xmath620 on @xmath621 , notice that for pure even supermatrices , the composition rule is given by @xmath622 where the products on the right hand side are the usual products of ( super)matrices . the usual ( super)matrix multiplication ( without the minus signs above ) is recovered upon replacing @xmath290 with @xmath623 . this difference in sign is related to the fact that one typically considers the action of group elements on @xmath624 , which can be identified with the space of even elements in @xmath625 , and the extra minus sign in front of @xmath290 comes from that isomorphism . however , throughout this paper we keep the above convention for multiplication of superalgebras ( with the extra signs ) since it gives a cleaner relationship with the representation of the original lie superalgebra . another essential ingredient is the superdeterminant or berezinian of an even supermatrix @xmath626 with @xmath357 invertible which is defined as @xmath627 where the products of matrices are standard matrix products , and we have the nonstandard plus sign @xmath628 in the definition reflecting our conventions . now , the lie superalgebra @xmath8 has three even @xmath629 and two odd generators @xmath630 satisfying the commutation relations @xmath631=\pm v_{\pm } , \quad[v_{\pm},v_{\pm}]=\mp 2x_{\pm},\quad [ v_+,v_{-}]=h.\end{aligned}\ ] ] the corresponding realization via @xmath632 supermatrices is given by @xmath633 and the corresponding supergroup @xmath8 can be faithfully realized as @xmath632 supermatrices @xmath241 with @xmath634 equal to one obeying the relation @xmath635 where @xmath636 and where the supertranspose @xmath637 of @xmath241 is given by @xmath638 this leads to the following system of constraints on the entries of @xmath241 : @xmath639 in particular , @xmath640 describes the canonical inclusion @xmath216 , and the body of the upper - left @xmath641 block conversely gives the bosonic reduction in @xmath221 of a matrix in @xmath8 . and @xmath642 before and after the flip , title="fig:",scaledwidth=50.0% ] + and @xmath642 before and after the flip , title="fig:",scaledwidth=50.0% ] in this appendix , we prove the last part of theorem [ oops ] and compute the evolution of orientations under flips illustrated in figure [ flipper ] . we must verify that the contributions of the arcs @xmath643 illustrated in figure [ curves ] to a quadratic form via theorem [ cr ] with the canonical dimer @xmath464 for the specified orientations of edges is the same before and after the flip . to that end for the purpose of explicit computation , let us fix the representative arcs @xmath84 , @xmath642 as edge - paths before and after the flip as illustrated in figure [ curveflip ] . representatives edge - paths of the other arcs @xmath644 are taken to lie entirely in the boundary . now in the notation of theorem [ cr ] for the canonical dimer @xmath464 , we find @xmath645 both before and after the flip , @xmath646 before the flip and @xmath647 , @xmath648 after the flip . the numbers @xmath649 of theorem [ cr ] are tabulated in figure 10 in the eight cases where the interior edge runs from left to right with the northwest leaf pointing towards it as may always be arranged by fatgraph reflections on the two vertices . uniqueness of this solution for the orientations after the flip is obvious since changing orientation on anything other than all leaves simultaneously evidently changes certain of the numbers @xmath649 . moreover , changing the orientation on each leaf is a composition of the fatgraph reflections at the two interior vertices . finally , enumerating the eight cases in figure 10 in the manner @xmath650 , one finds by inspection that cases 1 , 3 , 4 , 8 are identical as are cases 2 , 5 , 6 , 7 thus leading to the two cases illustrated in figure [ flipper].@xmath205 99 a. beardon , the geometry of discrete groups , springer , 1983 . f. a. berezin , _ introduction to superanalysis _ , springer , 1987 . f. bouschbacher , _ shear coordinates on the super - teichmller space _ , phd thesis , strasbourg , 2014 , https://tel.archives-ouvertes.fr/tel-00835500v1/document f. bouschbacher , v. fock , f. constantino , _ shear coordinates on the super - teichmller space _ , to appear . p. bryant , l. hodgkin , _ nielsen s theorem and super - teichmllerspace _ , ann . . h. poincare phys . * 58 * ( 3 ) ( 1993 ) 247 - 265 . l. chekhov , v. v. fock , _ quantum teichmller space _ , theor.math.phys . * 120 * ( 1999 ) 1245 - 1259 ; teor . mat . * 120 * ( 1999 ) 511 - 528 , arxiv : math/9908165 . d. cimasoni , n. reshetikhin , _ dimers on surface graphs and spin structures . i _ , comm . * 275 * ( 2007 ) , 187 - 208 . d. cimasoni , n. reshetikhin , _ dimers on surface graphs and spin structures . ii _ , comm . * 281 * ( 2008 ) , 445 - 468 . l. crane , j. rabin , _ super riemann surfaces : uniformization and teichmller theory _ , * 113 * ( 1998 ) 601 - 623 . a. fathi , f. laudenbach , v. poenaru , travaux de thurston sur les surfaces , _ asterisque _ * 66 - 67 * ( 1979 ) l. ford , automorphic functions , american mathematical society ( 1951 ) . l. hodgkin,_super teichmller spaces : puctures and elliptic points _ , lett . math . phys . * 15 * ( 1988 ) 159 - 163 . d. johnson , _ spin structures and quadratic forms on surfaces _ , j. london math . * 22 * ( 1980 ) 365 - 373 . r. kashaev , _ quantization of teichmller spaces and the quantum dilogarithm _ , lett . math . phys . * 43 * ( 1998 ) 105 - 115 . i. manin , _ topics in noncommutative geometry _ , princeton university press , 1991 . j. milnor , remarks concerning spin manifolds in _ differential and combinatorial topology _ , princeton , 1965 . natanzon , _ moduli of riemann surfaces , hurwitz - type spaces , and their superanalogues _ , russian math . surveys * 54 * 1 ( 1999 ) 61 - 117 . natanzon , _ moduli of riemann surfaces , real algebraic curves , and their superanalogs _ , transl . math . monographs * 225 * , american mathematical society , 2004 . r. c. penner , _ the decorated teichmller space of punctured surfaces _ , comm . math . * 113 * ( 1987 ) , 299 - 339 . , _ weil - petersson volumes _ , j. diff . * 35 * ( 1992 ) , 559 - 608 . , _ decorated teichmller theory _ , european mathematical society , 2012 . k. strebel , _ quadratic differentials _ , ergebnisse der mathematik und ihrer grenzgebiete * 5 * springer - verlag , berlin , 1984 h. verlinde,_conformal field theory , two - dimensional quantum gravity and quantization of teichmller space _ b * 337 * ( 1990 ) 652 - 680 . e. witten , _ notes on super riemann surfaces and their moduli _ , arxiv:1209.2459 .[/INST] we introduce coordinates for a principal bundle @xmath0 over the super teichmller space @xmath1 of a surface @xmath2 with @xmath3 punctures that extend the lambda length coordinates on the decorated bundle @xmath4 over the usual teichmller space @xmath5 . in effect , the action of a fuchsian subgroup of @xmath6 on minkowski space @xmath7 is replaced by the action of a super fuchsian subgroup of @xmath8 on the super minkowski space @xmath9 , where @xmath8 denotes the orthosymplectic lie supergroup , and the lambda lengths are extended by fermionic invariants of suitable triples of isotropic vectors in @xmath9 . as in the bosonic case , there is the analogue of the ptolemy transformation now on both even and odd coordinates as well as an invariant even two - form on @xmath0 generalizing the weil - petersson khler form . this finally solves a problem posed in yuri ivanovitch manin s moscow seminar some thirty years ago to find the super analogue of decorated teichmller theory and provides a natural geometric interpretation in @xmath9 for the super moduli of @xmath0 . </s>

a trauma is an event that is not within the normal range of the common experience . it is perceived as overwhelming physically and/or emotionally and may involve a perceived threat to the individual or a loved one . highly traumatic and stressful events usually produce a range of cognitive , emotional , behavioral responses that influence the eventual outcome . the most commonly observed psyhiatric disorder after a natural disaster is posttraumatic stress disorder ( ptsd ) . however , depressive disorders , somotization , specific phobia , agoraphobia , social anxiety , and psychotic disorders are commonly observed among the survivors . in a study with elderly population , after a natural disaster , the estimated prevalence rates of probable ptsd , anxiety , and depression were found to be 26.3% , 42.9% and 35.2% , respectively . the prevalence of psychiatric disorders reported by earthquake survivors in western countries is as high as 85% for acute stress symptoms , 14 - 87% for ptsd , and 27 - 85% for psychiatric morbidity . most of the studies evaluating post - disaster psychiatric morbidity at the population level have not included measures of functional impairment . a survey of the general population has shown that impairment caused by ptsd is comparable to the impairment observed in major depression . occupational dysfunctioning , absenteeism , and reduced productivity and performance on the job is associated with depression and ptsd.[1416 ] moreover , ptsd symptom severity has been found to be associated with unemployment and work disability even after controlling for the effects of co - morbid disorders . the objectives of the present study are to investigate the prevalence of psychiatric disorders and work and social adjustment among those individuals who had witnessed 8 october 2005 earthquake and were extricated from under the rubble / debris . we expected that there would be high prevalence of psychiatric disorders among these highly traumatized survivors . higher the prevalence of psychiatric disorders , lower will be the work and social adjustment . the mini international neuropsychiatry interview , a short structured diagnostic interview developed by psychiatrists and clinicians in the united states and france for the major axis i psychiatric disorders in dsm - iv and icd-10 , was used to assess the psychiatric disorders . inclusion criteria of the sample included those individuals who had some rubble experience and were rescued from under the rubble in 8 october 2005 earthquake . participants ' age ranged from 17 to 55 years , with the average age being 37.7 years ( sd = 9.46 ) . among all participants , 52.5% of participants were self - employed or owners of small shops and restaurants and 47.5% were unemployed . participants were assured that the information they gave would be kept confidential and would be used only for the research purpose . a short interview was first conducted with individual participants to establish the initial rapport and to explain the purpose of the study . participants were assured of the confidentiality of their responses and were informed that they could withdraw from the study at any time . the mini international neuropsychiatry interview , a short structured diagnostic interview developed by psychiatrists and clinicians in the united states and france for the major axis i psychiatric disorders in dsm - iv and icd-10 , was used to assess the psychiatric disorders . inclusion criteria of the sample included those individuals who had some rubble experience and were rescued from under the rubble in 8 october 2005 earthquake . participants ' age ranged from 17 to 55 years , with the average age being 37.7 years ( sd = 9.46 ) . among all participants , 52.5% of participants were self - employed or owners of small shops and restaurants and 47.5% were unemployed . participants were assured that the information they gave would be kept confidential and would be used only for the research purpose . a short interview was first conducted with individual participants to establish the initial rapport and to explain the purpose of the study . participants were assured of the confidentiality of their responses and were informed that they could withdraw from the study at any time . prevalence of psychiatric co - morbidity and its relationship with work and social adjustment was investigated . about 91% of participants self - reported to have suffered from personal injuries as a result of the earthquake . about 89% of all participants reported personal or family property being damaged or destroyed , and 66% needed to relocate to temporary shelters following this disaster . about 67.4% of participants also reported family members or friends missing , injured , or killed . the results in table 1 show that the most prevalent disorders in the population were ptsd ( 32.5% ) , depressive disorders ( both major depression and dysthymia ) , panic anxiety , social phobia , and agoraphobia . frequencies and percentages of psychiatric disorders among the survivors extricated from under the rubble table 2 shows that 32.5% of population had no disorder , 30% had at least one disorder , 15% had at least two disorders , 17% had three , and 15% had the four psychiatric disorders . percentages of psychiatric co - morbidities among male and female survivors negative correlation was found between the psychiatric illness and work and social functioning . figure 1 show that there is an inverse relationship of work and social adjustment and the psychiatric co - morbidity . the figure also depicts that both the genders ( i.e. males and females ) had the same pattern . the present study aimed at exploring the different psychiatric disorders and work and social adjustment among survivors extricated from under the debris . ptsd , depression , and anxiety disorder were found to be quite prevalent irrespective of gender . . the reason could be that they are more predisposed to maintain negative attitudes toward life events than males , and gender differences are due to differences in expressed emotionality for the sexes , with women more likely than men to express feelings of fear . another reason may be that in collectivistic cultures , both the genders share almost equal responsibilities of life because of strong binding among family members . so , the sufferings due to any trauma are equally disturbing for both husband and wife . it was also observed that as the co - morbidity increases , the functionality decreases [ figure 1 ] . another finding of the present study was that higher the prevalence of psychiatric disorders , lower was the work and social adjustment of the individuals who were living in the affected areas and had rubble experience . results of the present study show that the experience of enormously traumatic events can lead to both short- and long - term psychological and physical risks . this risk is exacerbated when the stressor is external and uncontrollable , such as the case of a natural disaster and effective interventions and rehabilitation measures are missing . findings are in line with the past studies that were conducted on the subject of loss and trauma . though the present study provides experiential evidence to an otherwise well - understood phenomenon , it has important practical implications in a country where not many experiential studies have been conducted on traumatized or stressed persons exposed to natural disasters . the present study helps in raising awareness about the needs of traumatized persons who had rubble experience and may continue having problems 6 years after exposure to trauma . the studies like the present one may advocate a society think of polices and evolve strategies to improve their mental health services . the findings of the current study suggest the need for the specialized mental health services to the affected population , as the risk from disaster exposure continued to accumulate over time . there were no data on predisaster protective or vulnerability factors such as prior psychological adjustment , prior traumatic exposure , family history of psychopathology , and so on . it remained unclear to what extent post - disaster psychiatric morbidity or perceived positive changes were the results of the current event . it should be noted that the present sample approximated the population that resided and worked in the more affluent regions of muzaffarabad . it is also possible that more severely affected survivors were still in hospitals or shelters , and some might have been relocated to other places . thus , the present study might undermine the impact of the earthquake on post - disaster adjustment . the present study relied solely on self - reports of survivors , which were often subject to recall and social desirability biases . snowball sampling technique was applied to carry out the research , which can not yield much appropriate results as it is not a systematic way of sampling . we evaluated 12 axis i dsm - iv disorders that are common in the general population , but we can not rule out the presence of other psychiatric disorders or conditions that may influence the course of psychiatric morbidity post - disaster . future research should be conducted on a large sample so as to assure the high probability of the generalizability . the present study may be very helpful in raising awareness among the lay persons about the effects of trauma and may prove to be a baseline for future researches . the study thus helps improve mental health services and broaden our information on the psychological impact of traumatic events . though the present study provides experiential evidence to an otherwise well - understood phenomenon , it has important practical implications in a country where not many experiential studies have been conducted on traumatized or stressed persons exposed to natural disasters . the present study helps in raising awareness about the needs of traumatized persons who had rubble experience and may continue having problems 6 years after exposure to trauma . the studies like the present one may advocate a society think of polices and evolve strategies to improve their mental health services . the findings of the current study suggest the need for the specialized mental health services to the affected population , as the risk from disaster exposure continued to accumulate over time . there were no data on predisaster protective or vulnerability factors such as prior psychological adjustment , prior traumatic exposure , family history of psychopathology , and so on . it remained unclear to what extent post - disaster psychiatric morbidity or perceived positive changes were the results of the current event . it should be noted that the present sample approximated the population that resided and worked in the more affluent regions of muzaffarabad . it is also possible that more severely affected survivors were still in hospitals or shelters , and some might have been relocated to other places . thus , the present study might undermine the impact of the earthquake on post - disaster adjustment . the present study relied solely on self - reports of survivors , which were often subject to recall and social desirability biases . snowball sampling technique was applied to carry out the research , which can not yield much appropriate results as it is not a systematic way of sampling . we evaluated 12 axis i dsm - iv disorders that are common in the general population , but we can not rule out the presence of other psychiatric disorders or conditions that may influence the course of psychiatric morbidity post - disaster . future research should be conducted on a large sample so as to assure the high probability of the generalizability . the present study may be very helpful in raising awareness among the lay persons about the effects of trauma and may prove to be a baseline for future researches . the study thus helps improve mental health services and broaden our information on the psychological impact of traumatic events . the mental health professional must take psychiatric disorders other than ptsd , especially depressive and anxiety disorders , into account when assessing the long - term effects of disaster . interventions designed to diminish distress and endorse psychological adjustment can greatly reduce the psychological and physical costs associated with a natural disaster . therefore , there is a need , particularly in a developing country like pakistan , for a broader understanding of the adaptive processes that may facilitate renovation and rehabilitation of busted and traumatized human beings in the aftermath of natural disasters .

objectives : this cross - sectional study examined psychiatric co - morbidity and work and social adjustment after a natural disaster among survivors who were extricated from under the rubble.materials and methods : individuals ( n=40 ) belonging to district muzaffarabad , a severely earthquake affected area on 8th october 2005 , were interviewed . the examination included the mini international neuropsychiatric interview for dsm - iv axis i disorders , work and social adjustment scale , and questions covering background characteristics and disaster exposure.results:the most prevalent disorders were posttaumatic stress disorder ( 32.5% ) , major depressive disorder ( 17.5% ) , dysthymia ( 15.0% ) , agoraphobia ( 25.0% ) , and panic disorder ( 20.0% ) . moreover , 77% of the respondents have been diagnosed with at least one psychiatric disorder . work and soical adjustment was found to have an inverse relationship with the psychiatric co-morbidity.conclusion:small sample size and lack of comparison group from non - earthquake struck areas may limit the generalizability of the psychatric disorders . psychiatric disorders other than ptsd , especially depressive and anxiety disorders , are of clinical importance when considering long - term mental health effect of disasters .

<s>[INST]a trauma is an event that is not within the normal range of the common experience . it is perceived as overwhelming physically and/or emotionally and may involve a perceived threat to the individual or a loved one . highly traumatic and stressful events usually produce a range of cognitive , emotional , behavioral responses that influence the eventual outcome . the most commonly observed psyhiatric disorder after a natural disaster is posttraumatic stress disorder ( ptsd ) . however , depressive disorders , somotization , specific phobia , agoraphobia , social anxiety , and psychotic disorders are commonly observed among the survivors . in a study with elderly population , after a natural disaster , the estimated prevalence rates of probable ptsd , anxiety , and depression were found to be 26.3% , 42.9% and 35.2% , respectively . the prevalence of psychiatric disorders reported by earthquake survivors in western countries is as high as 85% for acute stress symptoms , 14 - 87% for ptsd , and 27 - 85% for psychiatric morbidity . most of the studies evaluating post - disaster psychiatric morbidity at the population level have not included measures of functional impairment . a survey of the general population has shown that impairment caused by ptsd is comparable to the impairment observed in major depression . occupational dysfunctioning , absenteeism , and reduced productivity and performance on the job is associated with depression and ptsd.[1416 ] moreover , ptsd symptom severity has been found to be associated with unemployment and work disability even after controlling for the effects of co - morbid disorders . the objectives of the present study are to investigate the prevalence of psychiatric disorders and work and social adjustment among those individuals who had witnessed 8 october 2005 earthquake and were extricated from under the rubble / debris . we expected that there would be high prevalence of psychiatric disorders among these highly traumatized survivors . higher the prevalence of psychiatric disorders , lower will be the work and social adjustment . the mini international neuropsychiatry interview , a short structured diagnostic interview developed by psychiatrists and clinicians in the united states and france for the major axis i psychiatric disorders in dsm - iv and icd-10 , was used to assess the psychiatric disorders . inclusion criteria of the sample included those individuals who had some rubble experience and were rescued from under the rubble in 8 october 2005 earthquake . participants ' age ranged from 17 to 55 years , with the average age being 37.7 years ( sd = 9.46 ) . among all participants , 52.5% of participants were self - employed or owners of small shops and restaurants and 47.5% were unemployed . participants were assured that the information they gave would be kept confidential and would be used only for the research purpose . a short interview was first conducted with individual participants to establish the initial rapport and to explain the purpose of the study . participants were assured of the confidentiality of their responses and were informed that they could withdraw from the study at any time . the mini international neuropsychiatry interview , a short structured diagnostic interview developed by psychiatrists and clinicians in the united states and france for the major axis i psychiatric disorders in dsm - iv and icd-10 , was used to assess the psychiatric disorders . inclusion criteria of the sample included those individuals who had some rubble experience and were rescued from under the rubble in 8 october 2005 earthquake . participants ' age ranged from 17 to 55 years , with the average age being 37.7 years ( sd = 9.46 ) . among all participants , 52.5% of participants were self - employed or owners of small shops and restaurants and 47.5% were unemployed . participants were assured that the information they gave would be kept confidential and would be used only for the research purpose . a short interview was first conducted with individual participants to establish the initial rapport and to explain the purpose of the study . participants were assured of the confidentiality of their responses and were informed that they could withdraw from the study at any time . prevalence of psychiatric co - morbidity and its relationship with work and social adjustment was investigated . about 91% of participants self - reported to have suffered from personal injuries as a result of the earthquake . about 89% of all participants reported personal or family property being damaged or destroyed , and 66% needed to relocate to temporary shelters following this disaster . about 67.4% of participants also reported family members or friends missing , injured , or killed . the results in table 1 show that the most prevalent disorders in the population were ptsd ( 32.5% ) , depressive disorders ( both major depression and dysthymia ) , panic anxiety , social phobia , and agoraphobia . frequencies and percentages of psychiatric disorders among the survivors extricated from under the rubble table 2 shows that 32.5% of population had no disorder , 30% had at least one disorder , 15% had at least two disorders , 17% had three , and 15% had the four psychiatric disorders . percentages of psychiatric co - morbidities among male and female survivors negative correlation was found between the psychiatric illness and work and social functioning . figure 1 show that there is an inverse relationship of work and social adjustment and the psychiatric co - morbidity . the figure also depicts that both the genders ( i.e. males and females ) had the same pattern . the present study aimed at exploring the different psychiatric disorders and work and social adjustment among survivors extricated from under the debris . ptsd , depression , and anxiety disorder were found to be quite prevalent irrespective of gender . . the reason could be that they are more predisposed to maintain negative attitudes toward life events than males , and gender differences are due to differences in expressed emotionality for the sexes , with women more likely than men to express feelings of fear . another reason may be that in collectivistic cultures , both the genders share almost equal responsibilities of life because of strong binding among family members . so , the sufferings due to any trauma are equally disturbing for both husband and wife . it was also observed that as the co - morbidity increases , the functionality decreases [ figure 1 ] . another finding of the present study was that higher the prevalence of psychiatric disorders , lower was the work and social adjustment of the individuals who were living in the affected areas and had rubble experience . results of the present study show that the experience of enormously traumatic events can lead to both short- and long - term psychological and physical risks . this risk is exacerbated when the stressor is external and uncontrollable , such as the case of a natural disaster and effective interventions and rehabilitation measures are missing . findings are in line with the past studies that were conducted on the subject of loss and trauma . though the present study provides experiential evidence to an otherwise well - understood phenomenon , it has important practical implications in a country where not many experiential studies have been conducted on traumatized or stressed persons exposed to natural disasters . the present study helps in raising awareness about the needs of traumatized persons who had rubble experience and may continue having problems 6 years after exposure to trauma . the studies like the present one may advocate a society think of polices and evolve strategies to improve their mental health services . the findings of the current study suggest the need for the specialized mental health services to the affected population , as the risk from disaster exposure continued to accumulate over time . there were no data on predisaster protective or vulnerability factors such as prior psychological adjustment , prior traumatic exposure , family history of psychopathology , and so on . it remained unclear to what extent post - disaster psychiatric morbidity or perceived positive changes were the results of the current event . it should be noted that the present sample approximated the population that resided and worked in the more affluent regions of muzaffarabad . it is also possible that more severely affected survivors were still in hospitals or shelters , and some might have been relocated to other places . thus , the present study might undermine the impact of the earthquake on post - disaster adjustment . the present study relied solely on self - reports of survivors , which were often subject to recall and social desirability biases . snowball sampling technique was applied to carry out the research , which can not yield much appropriate results as it is not a systematic way of sampling . we evaluated 12 axis i dsm - iv disorders that are common in the general population , but we can not rule out the presence of other psychiatric disorders or conditions that may influence the course of psychiatric morbidity post - disaster . future research should be conducted on a large sample so as to assure the high probability of the generalizability . the present study may be very helpful in raising awareness among the lay persons about the effects of trauma and may prove to be a baseline for future researches . the study thus helps improve mental health services and broaden our information on the psychological impact of traumatic events . though the present study provides experiential evidence to an otherwise well - understood phenomenon , it has important practical implications in a country where not many experiential studies have been conducted on traumatized or stressed persons exposed to natural disasters . the present study helps in raising awareness about the needs of traumatized persons who had rubble experience and may continue having problems 6 years after exposure to trauma . the studies like the present one may advocate a society think of polices and evolve strategies to improve their mental health services . the findings of the current study suggest the need for the specialized mental health services to the affected population , as the risk from disaster exposure continued to accumulate over time . there were no data on predisaster protective or vulnerability factors such as prior psychological adjustment , prior traumatic exposure , family history of psychopathology , and so on . it remained unclear to what extent post - disaster psychiatric morbidity or perceived positive changes were the results of the current event . it should be noted that the present sample approximated the population that resided and worked in the more affluent regions of muzaffarabad . it is also possible that more severely affected survivors were still in hospitals or shelters , and some might have been relocated to other places . thus , the present study might undermine the impact of the earthquake on post - disaster adjustment . the present study relied solely on self - reports of survivors , which were often subject to recall and social desirability biases . snowball sampling technique was applied to carry out the research , which can not yield much appropriate results as it is not a systematic way of sampling . we evaluated 12 axis i dsm - iv disorders that are common in the general population , but we can not rule out the presence of other psychiatric disorders or conditions that may influence the course of psychiatric morbidity post - disaster . future research should be conducted on a large sample so as to assure the high probability of the generalizability . the present study may be very helpful in raising awareness among the lay persons about the effects of trauma and may prove to be a baseline for future researches . the study thus helps improve mental health services and broaden our information on the psychological impact of traumatic events . the mental health professional must take psychiatric disorders other than ptsd , especially depressive and anxiety disorders , into account when assessing the long - term effects of disaster . interventions designed to diminish distress and endorse psychological adjustment can greatly reduce the psychological and physical costs associated with a natural disaster . therefore , there is a need , particularly in a developing country like pakistan , for a broader understanding of the adaptive processes that may facilitate renovation and rehabilitation of busted and traumatized human beings in the aftermath of natural disasters .[/INST]objectives : this cross - sectional study examined psychiatric co - morbidity and work and social adjustment after a natural disaster among survivors who were extricated from under the rubble.materials and methods : individuals ( n=40 ) belonging to district muzaffarabad , a severely earthquake affected area on 8th october 2005 , were interviewed . the examination included the mini international neuropsychiatric interview for dsm - iv axis i disorders , work and social adjustment scale , and questions covering background characteristics and disaster exposure.results:the most prevalent disorders were posttaumatic stress disorder ( 32.5% ) , major depressive disorder ( 17.5% ) , dysthymia ( 15.0% ) , agoraphobia ( 25.0% ) , and panic disorder ( 20.0% ) . moreover , 77% of the respondents have been diagnosed with at least one psychiatric disorder . work and soical adjustment was found to have an inverse relationship with the psychiatric co-morbidity.conclusion:small sample size and lack of comparison group from non - earthquake struck areas may limit the generalizability of the psychatric disorders . psychiatric disorders other than ptsd , especially depressive and anxiety disorders , are of clinical importance when considering long - term mental health effect of disasters .</s>

Tweet with a location You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more ||||| Supporters of President Donald Trump, background left, intermingle with others protesting the President near Trump Tower, Tuesday, Aug. 15, 2017, in New York. (AP Photo/Craig Ruttle) (Associated Press) Supporters of President Donald Trump, background left, intermingle with others protesting the President near Trump Tower, Tuesday, Aug. 15, 2017, in New York. (AP Photo/Craig Ruttle) (Associated Press) NEW YORK (AP) — Michael Moore has led the audience of his Broadway play to Trump Tower to protest President Donald Trump's comments about the deadly violence in Charlottesville, Virginia. On Facebook, Moore urged people to join him at the tower following Tuesday night's performance of his one-man show "The Terms of My Surrender" to "nonviolently express our rage." After the play, the 63-year-old Oscar-winning filmmaker, commentator and liberal activist is seen on a Facebook Live video leading a group of people on buses to the tower, where the president is currently staying for the first time since his inauguration. Moore was joined by actor Mark Ruffalo. During the bus ride, Ruffalo, using a bullhorn, led the group in chants including "No Trump, no KKK, no fascist USA" and encouraged people on the street to join them at the tower. Hundreds of demonstrators have been gathering there since Trump arrived Monday night. Earlier Tuesday, during an impromptu news conference in the building's lobby, Trump declared that "there is blame on both sides" for the violence in Virginia, appearing to once again equate the actions of white supremacist groups and those protesting them. Moore described the president's comments as "just awful, disgusting." White nationalists, neo-Nazis and other far-right extremists assembled last Saturday to protest a decision by the city of Charlottesville to remove a statue of Confederate Gen. Robert E. Lee. Heather Heyer, 32, was killed when a man plowed his car into a crowd of counter-protesters. Outside Trump Tower Tuesday night, Moore and Ruffalo held a candlelight vigil and urged the crowd to never forget Heyer and make sure she didn't "die in vain." ___ This story has been corrected to show that Trump made the comments earlier Tuesday, not Monday.

– Michael Moore led the audience of his Broadway play to Trump Tower on Tuesday to protest President Trump's comments about the deadly violence in Charlottesville. On Facebook, Moore urged people to join him at the tower following Tuesday night's performance of his one-man show The Terms of My Surrender to "nonviolently express our rage," per the AP. After the play, the 63-year-old liberal activist led a group of people on buses to the tower, where the president is staying for the first time since his inauguration. Moore was joined by actor Mark Ruffalo, who led a chant of "Heather Heyer," the name of the woman killed in Charlottesville. (See video of Ruffalo's speech.) Moore and Ruffalo held a candlelight vigil and urged the crowd to never forget Heyer and make sure she didn't "die in vain."

<s>[INST]Tweet with a location You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more ||||| Supporters of President Donald Trump, background left, intermingle with others protesting the President near Trump Tower, Tuesday, Aug. 15, 2017, in New York. (AP Photo/Craig Ruttle) (Associated Press) Supporters of President Donald Trump, background left, intermingle with others protesting the President near Trump Tower, Tuesday, Aug. 15, 2017, in New York. (AP Photo/Craig Ruttle) (Associated Press) NEW YORK (AP) — Michael Moore has led the audience of his Broadway play to Trump Tower to protest President Donald Trump's comments about the deadly violence in Charlottesville, Virginia. On Facebook, Moore urged people to join him at the tower following Tuesday night's performance of his one-man show "The Terms of My Surrender" to "nonviolently express our rage." After the play, the 63-year-old Oscar-winning filmmaker, commentator and liberal activist is seen on a Facebook Live video leading a group of people on buses to the tower, where the president is currently staying for the first time since his inauguration. Moore was joined by actor Mark Ruffalo. During the bus ride, Ruffalo, using a bullhorn, led the group in chants including "No Trump, no KKK, no fascist USA" and encouraged people on the street to join them at the tower. Hundreds of demonstrators have been gathering there since Trump arrived Monday night. Earlier Tuesday, during an impromptu news conference in the building's lobby, Trump declared that "there is blame on both sides" for the violence in Virginia, appearing to once again equate the actions of white supremacist groups and those protesting them. Moore described the president's comments as "just awful, disgusting." White nationalists, neo-Nazis and other far-right extremists assembled last Saturday to protest a decision by the city of Charlottesville to remove a statue of Confederate Gen. Robert E. Lee. Heather Heyer, 32, was killed when a man plowed his car into a crowd of counter-protesters. Outside Trump Tower Tuesday night, Moore and Ruffalo held a candlelight vigil and urged the crowd to never forget Heyer and make sure she didn't "die in vain." ___ This story has been corrected to show that Trump made the comments earlier Tuesday, not Monday.[/INST]– Michael Moore led the audience of his Broadway play to Trump Tower on Tuesday to protest President Trump's comments about the deadly violence in Charlottesville. On Facebook, Moore urged people to join him at the tower following Tuesday night's performance of his one-man show The Terms of My Surrender to "nonviolently express our rage," per the AP. After the play, the 63-year-old liberal activist led a group of people on buses to the tower, where the president is staying for the first time since his inauguration. Moore was joined by actor Mark Ruffalo, who led a chant of "Heather Heyer," the name of the woman killed in Charlottesville. (See video of Ruffalo's speech.) Moore and Ruffalo held a candlelight vigil and urged the crowd to never forget Heyer and make sure she didn't "die in vain."</s>

rare meson decays are expected to serve as harbinger for new physics ( np ) in experiments at the intensity frontier @xcite . better measurements or upper limits on a plethora of rare ( semi)leptonic and radiative @xmath6 and @xmath7 meson decays in forthcoming experiments , compared to precise standard model ( sm ) predictions , eventually will provide indirect indications of heavier particles with new interactions . particularly sensitive for np searches are those decays dominated by short - distance ( sd ) dynamics where the hadronic uncertainties are well under control . conversely , precise measurements of these rare decays , combined with non - observation of np effects , will furnish a better determination of flavor mixing parameters . very recently , the lhcb collaboration has reported a deficit in the ratio of muon to electron pairs produced in @xmath8 decays , in the @xmath9 gev@xmath5 region for the squared invariant - mass of the lepton pair @xcite . this energy region is cleverly chosen as it excludes long - distance ( ld ) contributions associated to charmonium and light vector resonance production in @xmath10 decays followed by their conversion to lepton pairs ( for definiteness , hereafter we will focus on decays of negatively charged @xmath7 mesons , unless otherwise indicated ) . the measured ratio @xmath11 @xcite , if confirmed in more refined measurements , would call for lepton universality violating interactions since in the sm @xmath12 @xcite for the energy region reported by lhcb @xcite . possible explanations involving np interactions have been suggested as the source of non - universal leptonic interactions @xcite . interestingly , other anomalies have been reported in angular observables of related @xmath13 decays @xcite which have been widely discussed in the literature @xcite . in the sm , the semileptonic @xmath14 ( @xmath15 ) decays are dominated by the sd @xmath16 transition @xcite . this elementary process is induced by the electromagnetic and weak penguin ( figure 1a ) , as well as @xmath17 boson box ( figure 1b ) diagram contributions , which are dominated by loops involving the top quark . in these exclusive processes , ld chiral corrections to the hadronic matrix element have been computed for soft momenta of light pseudoscalars ( i.e. high - momentum @xmath18 of dilepton pairs ) , where they amount to rather large @xmath19 corrections @xcite . our point here is that , although this kind of corrections will be much smaller on the other energy end ( large recoil region for the heavy - to - light b - meson form factors @xcite ) , the high precision of measurements as well as the sharp predictions of the dominating sd contributions suggests ld effects associated to resonance dynamics at the gev scale be taken into account as well for these more energetic @xmath20 mesons . contributions of four - quark operators giving rise to tree - level wa amplitudes with virtual photon emission are also possible for exclusive @xmath14 processes and are the main concern of this paper . as far as we know , the one - photon exchange feynman diagrams ( arising from wa operators ) shown in figures 1c-1d provide a so far neglected ld contribution that must be included in the calculation of these exclusive semileptonic rare decays . neutrino - exchange amplitude . this one was checked to give a highly suppressed effect in @xmath21 decays @xcite . ] these additional ld contributions could in principle modify the @xmath22 value due to kinematical effects @xcite . according to chiral effective theories of qcd @xcite , for photon four - momenta below @xmath23 gev , photon - hadron interactions are best formulated in terms of the relevant ( pseudo-)scalar and ( axial-)vector hadronic degrees of freedom . as it was shown long ago @xcite , the @xmath21 rare semileptonic decays are dominated by the one - photon exchange contributions analogous to the ones of figure 1c and 1d ; the sd top - quark loop penguin and w - box contributions in that case are negligible small @xcite . owing to gauge - invariance , this ld contribution vanishes at lowest order in chiral perturbation theory but this is not the case at higher orders @xcite . according to the respective ckm mixing factors in the sd and ld amplitudes of @xmath14 decays , one can envisage a correction at the percent level for @xmath24 but a slightly higher effect could be expected for @xmath25 depending on the limits of the integrated observables . it is worth noticing that wa contributions were previously considered for @xmath26 @xcite and @xmath27 @xcite decays in the framework of the qcd factorization ( qcdf ) scheme @xcite . recently , non - local effects in @xmath28 decays have been computed in ref . @xcite using the method developed in ref . @xcite and previously used in ref . @xcite for @xmath29 decays for low dilepton invariant masses . at large hadronic recoil ( corresponding to low values of the squared virtual photon momentum @xmath30 ) , the light - meson energy ( @xmath31 ) is much larger than the energy scale of hadronic binding : @xmath32 . then , the virtual photon exchange between the hadrons and the dilepton pair and hard gluon scattering can be systematically expanded in powers of @xmath33 using qcdf . however , the @xmath34 amplitude suffers from nonperturbative corrections due to @xmath35 and @xmath36 intermediate states , which form the @xmath37 , @xmath38 , @xmath39 , ... resonances @xcite ( similarly , in @xmath40 processes @xmath41 and @xmath42 can be excited and the @xmath43 meson plays a prominent role @xcite ) . therefore , a clean qcdf prediction shall be limited to an energy range which excludes these resonant contributions , conservatively @xmath44 gev@xmath5 . on the contrary , the extension of these limits requires the inclusion of near - threshold @xmath35 and @xmath36 ( @xmath41 and @xmath42 ) resonances . let us recall ref . @xcite where these are accounted for studying the @xmath45 processes leading to a relevant effect of the charmonium resonances in the inclusive decay width . also , ref . @xcite considered resonance effects from @xmath46 excitations in @xmath47 processes , where @xmath43 exchange basically saturates the decay width . in the analyzed @xmath48 decays , cutting at a maximum @xmath49 value well below the charmonium region kills the effects of the @xmath36 resonances and we have checked that the remaining contributions of @xmath35 resonances are negligible . there are , however , other resonance contributions that may be relevant in our case : the ones where the photon is attached to the initial and final state mesons in wa contributions ( fig . 1c-1d ) . in the spirit of the phenomenological lagrangians , we would like to focus in the @xmath50 gev@xmath5 region by adding the effect of the lowest - lying light - flavoured resonances and pseudoscalar mesons as active degrees of freedom as it is done in the ( resonance ) chiral lagrangians . this is the approach that we follow to ensure the applicability of the qcdf analysis of the @xmath51 decays down to threshold . here we treat the photon - meson interaction by considering the exchange of resonances in the framework of two different models which have shown to give a very accurate description of experimental data for @xmath49 values up to @xmath52 gev@xmath5 . this agreement shows that up to those energies , the photon does not resolve the quark structure of mesons and only probes their electromagnetic structure . in order to avoid potential double counting of effects from wa contributions ( in the qcdf approach and ours ) , we will consider our ld wa contribution only for photons with @xmath53 gev@xmath5 and match it to the qcdf contribution for @xmath54 gev@xmath5 as discussed in section [ matching ] . the purpose of this paper is to quantify these expectations and evaluate the contributions given by diagrams in figures 1(c , d ) for the @xmath14 decays for low and intermediate values of the invariant mass of di - lepton pair ( other diagrams present in figure 2 vanish due to gauge invariance , see below ) . we use two different approaches for the @xmath55 and @xmath56 electromagnetic form factors in order to estimate the systematic error of our computation . for these rare @xmath7 decays , it is found that the one - photon exchange diagrams do not modify lepton universality for the energy range measured by lhcb @xcite and that they turn out to be very small in the @xmath24 case , although their effects in the @xmath25 rates are more significant . the wa contribution that we study has a different dependence on ckm mixing elements than the dominant sd one and also carries a sizable strong phase , leading to possible cp violating effects . the dominant source of cp violation , both in our paper and in the qcdf approach , arises from the interference between the sd top - mediated loop and the wa diagrams . however , the strong phase in our case is provided by the imaginary parts of the light resonance shapes , while in the qcdf approach it arises from the on - shell spectator @xmath57 quark in the @xmath7 meson after having emitted the photon . we find measurable effects both for @xmath58 on the integrated cp asymmetry and encourage the lhcb and belle - ii collaborations to measure such asymmetries which could be useful to validate the models employed in the description of exclusive @xmath59 decays at low photon virtualities . decays are shown in @xmath60 ( penguin ) and @xmath61 ( @xmath17 box ) diagrams . the one - photon , ld , wa contributions are shown in @xmath62 and @xmath63 . the full circle denotes the electromagnetic form factor of the charged pseudoscalar mesons . other long - distance structure - dependent vector and axial - vector terms ( shown in fig . 2 ) do not contribute due to gauge invariance @xcite . ] in the standard model , observables like direct cp asymmetry in @xmath64 have shown to be particularly sensitive to the interference of top dominated loops and wa amplitudes , which carry different weak and strong phases . both amplitudes have been evaluated within the framework of qcdf where the strong phase in the wa amplitude , at relatively low photon virtualities , arises mainly from the on - shell @xmath57 spectator quark in the @xmath7 meson after having emitted the photon . in this section we provide an alternative evaluation of this wa amplitude using the resonance chiral theory within a factorization approximation , which we expect to be valid for @xmath65 gev@xmath5 . in a later section we will show how to match this contribution to the corresponding wa amplitude calculated within qcdf , which will be used for larger @xmath49 values . since the strong phase in our calculation stems from the pseudoscalar electromagnetic form factors , our approach provides an independent evaluation of the cp asymmetry for low and intermediate values of the lepton - pair invariant masses . for completeness and later use , we will consider first the description of these decays within qcdf as given in ref . let us choose the following convention for the particle s momenta : @xmath66 the contributions of the diagrams in figures ( 1a , b ) , including higher order qcd corrections , to the decay amplitude can be written , to a very good approximation as @xcite : @xmath67\ , \ ] ] where @xmath68 is the total momentum of the lepton pair , the subindex in the ckm matrix element stands for @xmath69 in the case of @xmath70 transitions . the factors @xmath71 and @xmath72 denote the vector and axial wilson coefficients at nnlo @xcite corresponding to the @xmath73 and @xmath74 operators in the effective weak hamiltonian for the @xmath75 transition . the wa contributions induced by four quark operators are conventionally absorbed into the effective @xmath76 coefficient , by replacing its numerical value given above by @xmath77 . for the @xmath25 case , the product of ckm matrix elements for loops involving all up - type quarks ( @xmath78 ) scale as @xmath79 . however , the loop function favors the top quark as the dominant contribution ) , see ref . @xcite . ] owing to the hierarchy of up - type quarks . although we are aware that more refined heavy - to - light meson form factors have been developed @xcite , we will use the classical ball and zwicky form factors @xcite for our estimates and include the corresponding uncertainty in the errors , as discussed below . the expressions for the @xmath49-dependent form factors are @xmath80 ^ 2 } + { \cal p}_k(q^2)\nonumber , \end{aligned}\ ] ] where the polynomials @xmath81 as well as the needed gegenbauer moments at the required energy scale can be found in refs . @xcite . in this section , we would like to consider specifically light - resonance effects in the wa contribution to @xmath83 for the @xmath84 gev@xmath5 region . we assume that in this energy range the relevant degrees of freedom are these light mesons and resonances ( and not the quark and gluon fields ) , according to the methodology of phenomenological lagrangians . low - energy phenomenology supports widely this hypothesis @xcite . applying this method to the process under consideration requires further hypothesis about the strong and electromagnetic interactions of @xmath7 mesons which , we argue , play a subleading role in our description . the decay amplitude corresponding to wa is given by @xmath85 where @xmath86 denotes the effective hadronic electromagnetic current coupled to the leptonic current . conservation of the electromagnetic current demands @xmath87f(q^2 ) \ , \ ] ] where only the first term within square brackets gives a non - vanishing contribution owing to the condition @xmath88 ( for the same reason , we can also replace @xmath89 ) . the factor @xmath90 encodes the information about the dynamics of weak and electromagnetic interactions in the hadronic blob . owing to gauge - invariance , most of the diagrams ( shown in figure [ newfig ] ) contributing to wa , vanish . to illustrate this , we insert a complete set of intermediate states in the relevant hadron matrix element and take into account the t - ordering of the electromagnetic and weak interactions , which gives rise to the leading order factorizable contributions @xmath91 where the sum over virtual intermediate states @xmath92 and @xmath93 that are allowed by the quantum numbers of the weak and electromagnetic interactions , should be understood . some of the feynman diagrams that contribute to @xmath94 are depicted in fig . [ newfig ] . non - factorizable contributions , like the ones shown in figure [ newfig]k , are sub - leading in the @xmath95 expansion and will not be considered in our calculationt is an expansion in @xmath95 ] . at lower photon virtualities , where resonance degrees of freedom may be neglected , it was shown that non - factorizable ( local ) contributions partially cancel among themselves@xcite , leaving the form factors of @xmath6 and @xmath97 as the dominant contributions in @xmath98 . single lines stand for pseudoscalar mesons , double lines for ( axial-)vector resonances and wavy lines for the virtual photon ( due to the spin - one nature of the weak current , spin - zero resonance contributions are suppressed ) . filled squares denote the weak / electromagnetic vertex , while the empty rectangles denote the wa hamiltonian . all contributions to the @xmath99 decays ( including the pointlike interactions in the first line ) vanish due to gauge invariance @xcite or are suppressed , except diagrams ( i ) and ( j ) which contribute to the electromagnetic form factors of pseudoscalar mesons . odd - intrinsic parity violating vertices are also considered in the calculation . ] under the above approximations , which justify the naive factorization of the hadronic matrix element of the weak hamiltonian , the leading order one - photon exchange ( wa ) amplitude corresponding to figure [ newfig](i , j ) can be computed taking into account that @xmath100[derivativecouplings ] and is given by ( neglecting the contribution of diagram 1c which is of order @xmath101 with respect to 1d is , however , a good approximation ) . ] ) @xmath102 p_b^{\mu}\bar{\ell}\gamma_{\mu}\ell\,,\end{aligned}\ ] ] where @xmath103 denotes the decay constant of the pseudoscalar meson @xmath92 according to the pdg @xcite conventions for @xmath104 and @xmath105 is the electromagnetic form factor of the corresponding meson . note that the pure scalar qed ( point meson approximation ) , as well as the structure - dependent vector and axial - vector terms , do not contribute to the amplitude as required by gauge invariance @xcite . or @xmath106 vertices for the @xmath107 transition ( and analogous vertices for the @xmath6 case ) . ] thus , the one - photon exchange contribution is sensitive to the intermediate @xmath49 region of the pseudoscalar form factor , and eventually to their resonance structure . due to the vector nature of the one - photon exchange contribution , its amplitude can be absorbed into the contribution of the @xmath108 operator in the qcdf amplitude under the replacement @xmath109,\ ] ] where @xmath110 note that @xmath111 so that its influence is governed by the ratio of ckm factors which is @xmath112 for @xmath25 and @xmath113 for @xmath24 . this suggests a larger effect for @xmath114 transitions but a detailed analysis of the electromagnetic meson form factors is needed to confirm these expectations . for the electromagnetic form factors of the light pseudoscalar mesons ( @xmath58 ) we have considered two approaches . on the one hand we have used form factors that are obtained within the frame of resonance chiral theory ( r@xmath82 t ) @xcite and , on the other hand , the phenomenological form factors used by the babar collaboration which employs the gounaris - sakurai ( gs ) parametrization @xcite . the first approach has the advantage of providing a low - energy behaviour complying with the chiral limit of qcd @xcite , which is a must if we want to get close to thresholds in some of our evaluations . alternatively , the gs parametrizations include more excited resonances and , for this reason , are expected to give a closer description of data at higher energies . in the cases at hand , the bulk of the contribution ( even for integrated observables starting at @xmath115 gev@xmath5 ) will be given by the @xmath116 ( @xmath117 ) meson exchange in the k ( @xmath97 ) cases . therefore , we should expect very similar results for the two approaches , @xmath118 being more reliable for observables starting near thresholds and the gs for the much less important higher energy range ( up to @xmath119 or @xmath120 gev@xmath5 depending on the channel ) . the minimal lagrangian of @xmath118 was derived in ref . @xcite upon the requirement of chiral symmetry for the pseudogoldstone fields and flavor symmetry for the light - flavored resonances . @xcite supplements the @xmath121 lagrangian at lowest order ( @xmath122 ) in the chiral counting @xcite @xmath123 with the following interaction terms between a light spin - one resonance and the pseudogoldstone fields @xcite @xmath124 the real couplings @xmath76 , @xmath125 and @xmath126 are unrestricted by symmetries and encode the dynamics . one can proceed similarly for the spin - zero resonances @xcite and include terms with more resonance fields and excited resonances , extending also to the odd - intrinsic parity sector @xcite . within the single resonance approximation , the evaluation of the @xmath20-vector form factor using the @xmath118 lagrangian yields @xmath127 by demanding a brodsky - lepage behaviour @xcite to @xmath128 one gets the relation @xmath129 , which gives a parameter - free expression . this naive result can be improved by including the next - to - leading order effect in the @xmath95 counting , _ i. e. _ the meson ( off - shell ) width according to chiral constraints ( the corresponding real part of the chiral loops is also included ) , and adding the effect of higher excitations and ( in the @xmath97 case ) including the dominant isospin - breaking effect given by the @xmath130 mixing . specifically for @xmath131 , we have used the parametrizations in the last two refs . in @xcite , which include three isovector resonances ( @xmath117 , @xmath132 and @xmath133 ) and the resummation of final state interactions encoded in the chiral loop functions . these representations provide good quality fits to belle data @xcite for @xmath134 decays . additionally , we have included the characteristic @xmath135 interference appearing in the neutral channel by multiplying the @xmath117 term by the factor @xmath136 with @xmath137 gev@xmath5 @xcite . other isospin breaking corrections are neglected . this parametrization is compared to babar data @xcite in figure 2 , which are available for the energy region @xmath138 gev . there , the phenomenological gs parametrization includes an additional @xmath37-like excitation . tiny differences between both parametrizations are seen in the region where the destructive interference between the @xmath132 and the @xmath133 resonances is stronger . the comparison also shows the effect of the @xmath118 parametrization lacking of the @xmath139 meson , which is clearly visible in the @xmath140 gev region . these minor differences are taken into account in the final quoted errors . analogously , we have employed two parametrizations of @xmath141 form factor . since this form factor is completely dominated by the extremely narrow @xmath116 meson , we have considered the @xmath118 prediction with only one multiplet of resonances @xcite . on the other hand , the babar collaboration @xcite has reported measurements of the kaon form factor from threshold up to @xmath142 gev . since @xmath143 drops by 6 orders of magnitude in going from the peak to @xmath142 gev ( see figure 3 ) , it should be sufficient to include only the @xmath116 resonance in its parametrization . as it can be observed in figure 3 , experimental data for @xmath143 are reasonably well described from threshold up to approximately @xmath144 gev . deviations at higher energies have a negligible impact in the integrated observables of rare @xmath7 decays . above this energy , other resonance structures with very small ( and alternating ) peaks and dips around the single resonance queue can be observed . these , in turn , are well described using the parameterization quoted in the babar paper @xcite ( which we fitted to the babar data ) , which includes two @xmath43 , three @xmath37 and three @xmath38 excitations in addition to the single lightest vector meson multiplet included in the @xmath118 form factor . mixing the former state does not contribute to @xmath141 and only @xmath117 and @xmath116 remain , with a prominent role of the latter . ] because of its relevance in the study of cp violating observables , we plot in fig . [ reimparts ] the real and imaginary parts of the light - meson electromagnetic form factors according to the two different descriptions that we used . while models agree nicely for the @xmath97 case , they do not in the @xmath6 case around the @xmath117 peak . since the corresponding phase shift has been validated by data in the case of the @xmath118 description , we attribute this to an incorrect phase of the @xmath145 kaon form factor . finally , the @xmath7-meson electromagnetic form factor contribution is suppressed by a factor @xmath146 in eq . ( [ eqld ] ) with respect to the ones of lighter mesons . in addition , a dynamical suppression of the form factor itself is expected according to the reduced charged radius of heavy mesons . just in order to confirm this , meson form factor at small values of the momentum transfer , would be by means of elastic electron-@xmath7 meson scattering . given the difficulty to produce a @xmath7 meson target / beam , it becomes rather complicated to test this low energy behavior of the @xmath7 meson form factor . ] we consider the effective lagrangian coupling @xmath147-mesons to lighter mesons and external sources in ref . @xcite generalized to include @xmath7 mesons . it can be seen that , upon requiring a brodsky - lepage behaviour @xcite of this form factor at infinite momentum transfer , the shape of @xmath148 is given just by flavour symmetry , yielding @xmath149 where @xmath150 can be found in refs . our numerical evaluations confirm that the effect of this form factor will be completely negligible in rates of rare @xmath10 mesons . the spectra of the lepton pair , normalized to the @xmath10 meson decay width are plotted in figure [ fig : leptonpair ] for low values of the lepton - pair invariant mass . we observe that above the muon - pair threshold both spectra are identical . clearly , the integrated rates in the whole kinematical range would exhibit a trivial breaking of leptonic universality owing to the lower electronic threshold and its enhancement due to the @xmath151 dependence in the ld wa amplitude . however , this will happen both in the well - known qcdf as well as in the new ld wa contributions ; thus only the numerical evaluation will tell if there is any additional measurable breaking of universality due to ld wa effects in the considered processes . the ld ( one - photon exchange ) contribution to the @xmath14 decays that we have discussed in previous sections and the one evaluated in the qcdf approach originate from the wa four - quark operator of the effective hamiltonian . then it naturally arises the question whether there is some double - counting between both contributions or not . for low enough values of @xmath49 ( @xmath30 ) , the qcdf expansion in 1/@xmath31 is the best way to organize the perturbative series . however , when approaching the @xmath35 threshold ( @xmath152 ) light - resonance effects need to be included explicitely as active degrees of freedom in the action as done in the resonance chiral lagrangians . within the interval from threshold to @xmath153 , we expect that chiral lagrangians give an adequate description for low @xmath49 values , while qcdf be more appropriate for the higher @xmath49 region . we thus assume there is an intermediate energy scale where both descriptions are good approximations and search for this matching scale where the ( complex ) effective wilson coefficient @xmath154 smoothly matches both descriptions for the @xmath97 and @xmath6 meson channels . we have found such matching scale at @xmath155 gev@xmath5 , as it can be seen in figs . [ fig : matching ] . then we have consider our ld one - photon exchange diagrams as the wa contribution for @xmath50 gev@xmath5 and the sd qcdf counterpart ( where the photon is radiated by the valence quarks in the @xmath7 and @xmath20 mesons ) for @xmath156 gev@xmath5 . we have used this separation scale between the ld and sd ( qcdf ) descriptions of wa contributions in the following and a slight variation of the matching scale has been taken into account in the error estimates . in the following , whenever we use qcdf it is understood that the corresponding result for wa is only used above @xmath52 gev@xmath5 . searches for new physics at large hadronic recoil in the @xmath157 decays are restricted to the @xmath158 gev@xmath5 range of @xmath49 @xcite . thus we will stick to this region for this channel . the @xmath107 decays have just been observed @xcite and such studies have not taken place yet . we therefore include our results both for a range starting at @xmath159 gev@xmath5 ( basically the muon threshold ) and at @xmath160 gev@xmath5 . in either case we cut the phase - space integration at @xmath120 gev@xmath5 to avoid the charmonium region . in table [ table1 ] we show the corresponding branching ratios of ld wa , qcdf and their interference contributions by considering these different kinematical integration domains . values for required input parameters are taken from the pdg @xcite except for the ckm matrix elements which come from ref . @xcite . .integrated branching ratios of @xmath48 decays for @xmath25 ( left hand side ) and @xmath24 ( right hand side ) for different @xmath49 ranges . we tabulate separately the qcdf , long - distance wa ( ld ) and their interference contributions for the kinematical ranges of interest . [ cols="<,<,<,<",options="header " , ] [ table2 ] this @xmath161 cp violating figures shall enhance the case for their measurements . current values at the pdg are well compatible with zero @xcite in @xmath162 ( and also in @xmath163 ) decays , while this observable is not yet reported in the @xmath164 case . the most recent measurement reported by the lhcb collaboration for the integrated cp asymmetry , namely @xmath165 @xcite , is still consistent with the different theoretical predictions . therefore , despite the fact that the tree - level one - photon exchange diagrams give a small contribution to the decay rates ( specially for the @xmath6 case ) , they can generate a non - negligible cp asymmetry within the standard model . this cp asymmetry altogether with measurements of the decay rates can be used as a test of new physics in the rare @xmath166 decays . this makes us emphasize the need of a dedicated measurement of these observables in the next lhc run at lhcb and in the forthcoming belle - ii experiment . in this paper we have considered the one - photon exchange contribution to the rare @xmath167 decays , with @xmath25 or @xmath6 . its effects in the decay rates of the @xmath24 case turn out to be of order 1@xmath168 with respect to the ( top quark loop dominated ) sd contribution for the range @xmath169 gev@xmath5 of the squared lepton pair invariant mass . we do not foresee forthcoming measurements being sensitive to this contribution in the near future . on the contrary , this fact confirms the suitability of this range for new physics searches . in the case of a @xmath170 meson in the final state , the corresponding effect turns out to be significant in integrated observables starting close to threshold . this suggests to take in analogy to the case of a final state with @xmath6 the range @xmath171 gev@xmath5 for precision measurements , since the ld wa contribution is reduced to less than 10@xmath168 with a negligible uncertainty in that interval . on the other hand , more refined measurements of the fully integrated branching fraction for this decay could be sensitive to our contribution once the error is reduced below a half of the current uncertainty interestingly , the different weak and strong phases of the qcdf and ld wa ( one - photon exchange ) contributions are capable to generate a cp asymmetry . again , this cp asymmetry is large in the case of a pion in the final state for @xmath172 gev@xmath5 values of the lepton - pair invariant mass , but also sizable and worth to measure in the @xmath173 gev@xmath5 interval . for the kaon case , the range @xmath174 gev@xmath5 is optimal for such a search . our cp violation results are smaller than those obtained within qcdf because of the different description of the wa amplitudes at low energies . future measurements shall be sensitive to this kind of contribution and shed light on its appropriate description . more refined measurements of this cp asymmetry and of the magnitudes of the decay rates at lhcb and future @xmath7-superfactories can provide another non - trivial test of the standard model or may furnish indications of new physics . * acknowledgements * : the authors would like to thank conacyt ( mxico ) for financial support . we appreciate very much helpful correspondence with bogdan malaescu concerning the babar parametrization of the kaon electromagnetic form factor . we thank javier virto for useful discussions on the topic of this article . g. buchalla , a. j. buras and m. e. lautenbacher , rev . * 68 * , 1125 ( 1996 ) . v. cirigliano , g. ecker , h. neufeld , a. pich , and j. portols , rev . phys . * 84 * , 399 ( 2012 ) . t. hurth and m. nakao , ann . nucl . part . * 60 * , 645 ( 2010 ) . r. aaij _ et al . _ [ lhcb collaboration ] , phys . rev . lett . * 113 * , 151601 ( 2014 ) . c. bobeth , g. hiller and g. piranishvili , j. high energy phys . * 12 * , 040 ( 2007 ) . c. bobeth , g. hiller , d. van dyk and ch . wacker , j. high energy phys . * 01 * , 107 ( 2012 ) . g. hiller and f. krger , phys . rev . d**69 * * , 074020 ( 2004 ) . g. hiller and m. schmaltz , phys . d**90 * * , 054014 ( 2014 ) . r. alonso , b. grinstein and j. martn camalich , phys . * 113 * ( 2014 ) 24 , 241802 ; 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we propose an alternative evaluation of the long - distance weak annihilation ( wa , also called one - photon exchange in this paper ) contribution to the rare semileptonic @xmath0 ( @xmath1 ) decays . this hadronic description at low energies is matched at intermediate energies to its short - distance counterpart in terms of quark and gluon degrees of freedom . although the wa contribution does not contribute to solve the possible breaking of lepton - universality observed by lhcb in the @xmath2 ratio , nor provides an important hadronic contamination to their decay rates , its contribution to the branching ratios ( and direct cp asymmetry ) of the @xmath3 transitions turns out to be significant . this hadronic pollution should be taken into account when looking for new physics effects in decays into pions , which suggests to restrict these searches to squared lepton - pair invariant mass in the @xmath4 gev@xmath5 range . the interference of the one - photon exchange contribution with the dominant short - distance one - loop amplitude induces a sizable cp asymmetry in these rare decays , which calls for dedicated measurements .

<s>[INST]rare meson decays are expected to serve as harbinger for new physics ( np ) in experiments at the intensity frontier @xcite . better measurements or upper limits on a plethora of rare ( semi)leptonic and radiative @xmath6 and @xmath7 meson decays in forthcoming experiments , compared to precise standard model ( sm ) predictions , eventually will provide indirect indications of heavier particles with new interactions . particularly sensitive for np searches are those decays dominated by short - distance ( sd ) dynamics where the hadronic uncertainties are well under control . conversely , precise measurements of these rare decays , combined with non - observation of np effects , will furnish a better determination of flavor mixing parameters . very recently , the lhcb collaboration has reported a deficit in the ratio of muon to electron pairs produced in @xmath8 decays , in the @xmath9 gev@xmath5 region for the squared invariant - mass of the lepton pair @xcite . this energy region is cleverly chosen as it excludes long - distance ( ld ) contributions associated to charmonium and light vector resonance production in @xmath10 decays followed by their conversion to lepton pairs ( for definiteness , hereafter we will focus on decays of negatively charged @xmath7 mesons , unless otherwise indicated ) . the measured ratio @xmath11 @xcite , if confirmed in more refined measurements , would call for lepton universality violating interactions since in the sm @xmath12 @xcite for the energy region reported by lhcb @xcite . possible explanations involving np interactions have been suggested as the source of non - universal leptonic interactions @xcite . interestingly , other anomalies have been reported in angular observables of related @xmath13 decays @xcite which have been widely discussed in the literature @xcite . in the sm , the semileptonic @xmath14 ( @xmath15 ) decays are dominated by the sd @xmath16 transition @xcite . this elementary process is induced by the electromagnetic and weak penguin ( figure 1a ) , as well as @xmath17 boson box ( figure 1b ) diagram contributions , which are dominated by loops involving the top quark . in these exclusive processes , ld chiral corrections to the hadronic matrix element have been computed for soft momenta of light pseudoscalars ( i.e. high - momentum @xmath18 of dilepton pairs ) , where they amount to rather large @xmath19 corrections @xcite . our point here is that , although this kind of corrections will be much smaller on the other energy end ( large recoil region for the heavy - to - light b - meson form factors @xcite ) , the high precision of measurements as well as the sharp predictions of the dominating sd contributions suggests ld effects associated to resonance dynamics at the gev scale be taken into account as well for these more energetic @xmath20 mesons . contributions of four - quark operators giving rise to tree - level wa amplitudes with virtual photon emission are also possible for exclusive @xmath14 processes and are the main concern of this paper . as far as we know , the one - photon exchange feynman diagrams ( arising from wa operators ) shown in figures 1c-1d provide a so far neglected ld contribution that must be included in the calculation of these exclusive semileptonic rare decays . neutrino - exchange amplitude . this one was checked to give a highly suppressed effect in @xmath21 decays @xcite . ] these additional ld contributions could in principle modify the @xmath22 value due to kinematical effects @xcite . according to chiral effective theories of qcd @xcite , for photon four - momenta below @xmath23 gev , photon - hadron interactions are best formulated in terms of the relevant ( pseudo-)scalar and ( axial-)vector hadronic degrees of freedom . as it was shown long ago @xcite , the @xmath21 rare semileptonic decays are dominated by the one - photon exchange contributions analogous to the ones of figure 1c and 1d ; the sd top - quark loop penguin and w - box contributions in that case are negligible small @xcite . owing to gauge - invariance , this ld contribution vanishes at lowest order in chiral perturbation theory but this is not the case at higher orders @xcite . according to the respective ckm mixing factors in the sd and ld amplitudes of @xmath14 decays , one can envisage a correction at the percent level for @xmath24 but a slightly higher effect could be expected for @xmath25 depending on the limits of the integrated observables . it is worth noticing that wa contributions were previously considered for @xmath26 @xcite and @xmath27 @xcite decays in the framework of the qcd factorization ( qcdf ) scheme @xcite . recently , non - local effects in @xmath28 decays have been computed in ref . @xcite using the method developed in ref . @xcite and previously used in ref . @xcite for @xmath29 decays for low dilepton invariant masses . at large hadronic recoil ( corresponding to low values of the squared virtual photon momentum @xmath30 ) , the light - meson energy ( @xmath31 ) is much larger than the energy scale of hadronic binding : @xmath32 . then , the virtual photon exchange between the hadrons and the dilepton pair and hard gluon scattering can be systematically expanded in powers of @xmath33 using qcdf . however , the @xmath34 amplitude suffers from nonperturbative corrections due to @xmath35 and @xmath36 intermediate states , which form the @xmath37 , @xmath38 , @xmath39 , ... resonances @xcite ( similarly , in @xmath40 processes @xmath41 and @xmath42 can be excited and the @xmath43 meson plays a prominent role @xcite ) . therefore , a clean qcdf prediction shall be limited to an energy range which excludes these resonant contributions , conservatively @xmath44 gev@xmath5 . on the contrary , the extension of these limits requires the inclusion of near - threshold @xmath35 and @xmath36 ( @xmath41 and @xmath42 ) resonances . let us recall ref . @xcite where these are accounted for studying the @xmath45 processes leading to a relevant effect of the charmonium resonances in the inclusive decay width . also , ref . @xcite considered resonance effects from @xmath46 excitations in @xmath47 processes , where @xmath43 exchange basically saturates the decay width . in the analyzed @xmath48 decays , cutting at a maximum @xmath49 value well below the charmonium region kills the effects of the @xmath36 resonances and we have checked that the remaining contributions of @xmath35 resonances are negligible . there are , however , other resonance contributions that may be relevant in our case : the ones where the photon is attached to the initial and final state mesons in wa contributions ( fig . 1c-1d ) . in the spirit of the phenomenological lagrangians , we would like to focus in the @xmath50 gev@xmath5 region by adding the effect of the lowest - lying light - flavoured resonances and pseudoscalar mesons as active degrees of freedom as it is done in the ( resonance ) chiral lagrangians . this is the approach that we follow to ensure the applicability of the qcdf analysis of the @xmath51 decays down to threshold . here we treat the photon - meson interaction by considering the exchange of resonances in the framework of two different models which have shown to give a very accurate description of experimental data for @xmath49 values up to @xmath52 gev@xmath5 . this agreement shows that up to those energies , the photon does not resolve the quark structure of mesons and only probes their electromagnetic structure . in order to avoid potential double counting of effects from wa contributions ( in the qcdf approach and ours ) , we will consider our ld wa contribution only for photons with @xmath53 gev@xmath5 and match it to the qcdf contribution for @xmath54 gev@xmath5 as discussed in section [ matching ] . the purpose of this paper is to quantify these expectations and evaluate the contributions given by diagrams in figures 1(c , d ) for the @xmath14 decays for low and intermediate values of the invariant mass of di - lepton pair ( other diagrams present in figure 2 vanish due to gauge invariance , see below ) . we use two different approaches for the @xmath55 and @xmath56 electromagnetic form factors in order to estimate the systematic error of our computation . for these rare @xmath7 decays , it is found that the one - photon exchange diagrams do not modify lepton universality for the energy range measured by lhcb @xcite and that they turn out to be very small in the @xmath24 case , although their effects in the @xmath25 rates are more significant . the wa contribution that we study has a different dependence on ckm mixing elements than the dominant sd one and also carries a sizable strong phase , leading to possible cp violating effects . the dominant source of cp violation , both in our paper and in the qcdf approach , arises from the interference between the sd top - mediated loop and the wa diagrams . however , the strong phase in our case is provided by the imaginary parts of the light resonance shapes , while in the qcdf approach it arises from the on - shell spectator @xmath57 quark in the @xmath7 meson after having emitted the photon . we find measurable effects both for @xmath58 on the integrated cp asymmetry and encourage the lhcb and belle - ii collaborations to measure such asymmetries which could be useful to validate the models employed in the description of exclusive @xmath59 decays at low photon virtualities . decays are shown in @xmath60 ( penguin ) and @xmath61 ( @xmath17 box ) diagrams . the one - photon , ld , wa contributions are shown in @xmath62 and @xmath63 . the full circle denotes the electromagnetic form factor of the charged pseudoscalar mesons . other long - distance structure - dependent vector and axial - vector terms ( shown in fig . 2 ) do not contribute due to gauge invariance @xcite . ] in the standard model , observables like direct cp asymmetry in @xmath64 have shown to be particularly sensitive to the interference of top dominated loops and wa amplitudes , which carry different weak and strong phases . both amplitudes have been evaluated within the framework of qcdf where the strong phase in the wa amplitude , at relatively low photon virtualities , arises mainly from the on - shell @xmath57 spectator quark in the @xmath7 meson after having emitted the photon . in this section we provide an alternative evaluation of this wa amplitude using the resonance chiral theory within a factorization approximation , which we expect to be valid for @xmath65 gev@xmath5 . in a later section we will show how to match this contribution to the corresponding wa amplitude calculated within qcdf , which will be used for larger @xmath49 values . since the strong phase in our calculation stems from the pseudoscalar electromagnetic form factors , our approach provides an independent evaluation of the cp asymmetry for low and intermediate values of the lepton - pair invariant masses . for completeness and later use , we will consider first the description of these decays within qcdf as given in ref . let us choose the following convention for the particle s momenta : @xmath66 the contributions of the diagrams in figures ( 1a , b ) , including higher order qcd corrections , to the decay amplitude can be written , to a very good approximation as @xcite : @xmath67\ , \ ] ] where @xmath68 is the total momentum of the lepton pair , the subindex in the ckm matrix element stands for @xmath69 in the case of @xmath70 transitions . the factors @xmath71 and @xmath72 denote the vector and axial wilson coefficients at nnlo @xcite corresponding to the @xmath73 and @xmath74 operators in the effective weak hamiltonian for the @xmath75 transition . the wa contributions induced by four quark operators are conventionally absorbed into the effective @xmath76 coefficient , by replacing its numerical value given above by @xmath77 . for the @xmath25 case , the product of ckm matrix elements for loops involving all up - type quarks ( @xmath78 ) scale as @xmath79 . however , the loop function favors the top quark as the dominant contribution ) , see ref . @xcite . ] owing to the hierarchy of up - type quarks . although we are aware that more refined heavy - to - light meson form factors have been developed @xcite , we will use the classical ball and zwicky form factors @xcite for our estimates and include the corresponding uncertainty in the errors , as discussed below . the expressions for the @xmath49-dependent form factors are @xmath80 ^ 2 } + { \cal p}_k(q^2)\nonumber , \end{aligned}\ ] ] where the polynomials @xmath81 as well as the needed gegenbauer moments at the required energy scale can be found in refs . @xcite . in this section , we would like to consider specifically light - resonance effects in the wa contribution to @xmath83 for the @xmath84 gev@xmath5 region . we assume that in this energy range the relevant degrees of freedom are these light mesons and resonances ( and not the quark and gluon fields ) , according to the methodology of phenomenological lagrangians . low - energy phenomenology supports widely this hypothesis @xcite . applying this method to the process under consideration requires further hypothesis about the strong and electromagnetic interactions of @xmath7 mesons which , we argue , play a subleading role in our description . the decay amplitude corresponding to wa is given by @xmath85 where @xmath86 denotes the effective hadronic electromagnetic current coupled to the leptonic current . conservation of the electromagnetic current demands @xmath87f(q^2 ) \ , \ ] ] where only the first term within square brackets gives a non - vanishing contribution owing to the condition @xmath88 ( for the same reason , we can also replace @xmath89 ) . the factor @xmath90 encodes the information about the dynamics of weak and electromagnetic interactions in the hadronic blob . owing to gauge - invariance , most of the diagrams ( shown in figure [ newfig ] ) contributing to wa , vanish . to illustrate this , we insert a complete set of intermediate states in the relevant hadron matrix element and take into account the t - ordering of the electromagnetic and weak interactions , which gives rise to the leading order factorizable contributions @xmath91 where the sum over virtual intermediate states @xmath92 and @xmath93 that are allowed by the quantum numbers of the weak and electromagnetic interactions , should be understood . some of the feynman diagrams that contribute to @xmath94 are depicted in fig . [ newfig ] . non - factorizable contributions , like the ones shown in figure [ newfig]k , are sub - leading in the @xmath95 expansion and will not be considered in our calculationt is an expansion in @xmath95 ] . at lower photon virtualities , where resonance degrees of freedom may be neglected , it was shown that non - factorizable ( local ) contributions partially cancel among themselves@xcite , leaving the form factors of @xmath6 and @xmath97 as the dominant contributions in @xmath98 . single lines stand for pseudoscalar mesons , double lines for ( axial-)vector resonances and wavy lines for the virtual photon ( due to the spin - one nature of the weak current , spin - zero resonance contributions are suppressed ) . filled squares denote the weak / electromagnetic vertex , while the empty rectangles denote the wa hamiltonian . all contributions to the @xmath99 decays ( including the pointlike interactions in the first line ) vanish due to gauge invariance @xcite or are suppressed , except diagrams ( i ) and ( j ) which contribute to the electromagnetic form factors of pseudoscalar mesons . odd - intrinsic parity violating vertices are also considered in the calculation . ] under the above approximations , which justify the naive factorization of the hadronic matrix element of the weak hamiltonian , the leading order one - photon exchange ( wa ) amplitude corresponding to figure [ newfig](i , j ) can be computed taking into account that @xmath100[derivativecouplings ] and is given by ( neglecting the contribution of diagram 1c which is of order @xmath101 with respect to 1d is , however , a good approximation ) . ] ) @xmath102 p_b^{\mu}\bar{\ell}\gamma_{\mu}\ell\,,\end{aligned}\ ] ] where @xmath103 denotes the decay constant of the pseudoscalar meson @xmath92 according to the pdg @xcite conventions for @xmath104 and @xmath105 is the electromagnetic form factor of the corresponding meson . note that the pure scalar qed ( point meson approximation ) , as well as the structure - dependent vector and axial - vector terms , do not contribute to the amplitude as required by gauge invariance @xcite . or @xmath106 vertices for the @xmath107 transition ( and analogous vertices for the @xmath6 case ) . ] thus , the one - photon exchange contribution is sensitive to the intermediate @xmath49 region of the pseudoscalar form factor , and eventually to their resonance structure . due to the vector nature of the one - photon exchange contribution , its amplitude can be absorbed into the contribution of the @xmath108 operator in the qcdf amplitude under the replacement @xmath109,\ ] ] where @xmath110 note that @xmath111 so that its influence is governed by the ratio of ckm factors which is @xmath112 for @xmath25 and @xmath113 for @xmath24 . this suggests a larger effect for @xmath114 transitions but a detailed analysis of the electromagnetic meson form factors is needed to confirm these expectations . for the electromagnetic form factors of the light pseudoscalar mesons ( @xmath58 ) we have considered two approaches . on the one hand we have used form factors that are obtained within the frame of resonance chiral theory ( r@xmath82 t ) @xcite and , on the other hand , the phenomenological form factors used by the babar collaboration which employs the gounaris - sakurai ( gs ) parametrization @xcite . the first approach has the advantage of providing a low - energy behaviour complying with the chiral limit of qcd @xcite , which is a must if we want to get close to thresholds in some of our evaluations . alternatively , the gs parametrizations include more excited resonances and , for this reason , are expected to give a closer description of data at higher energies . in the cases at hand , the bulk of the contribution ( even for integrated observables starting at @xmath115 gev@xmath5 ) will be given by the @xmath116 ( @xmath117 ) meson exchange in the k ( @xmath97 ) cases . therefore , we should expect very similar results for the two approaches , @xmath118 being more reliable for observables starting near thresholds and the gs for the much less important higher energy range ( up to @xmath119 or @xmath120 gev@xmath5 depending on the channel ) . the minimal lagrangian of @xmath118 was derived in ref . @xcite upon the requirement of chiral symmetry for the pseudogoldstone fields and flavor symmetry for the light - flavored resonances . @xcite supplements the @xmath121 lagrangian at lowest order ( @xmath122 ) in the chiral counting @xcite @xmath123 with the following interaction terms between a light spin - one resonance and the pseudogoldstone fields @xcite @xmath124 the real couplings @xmath76 , @xmath125 and @xmath126 are unrestricted by symmetries and encode the dynamics . one can proceed similarly for the spin - zero resonances @xcite and include terms with more resonance fields and excited resonances , extending also to the odd - intrinsic parity sector @xcite . within the single resonance approximation , the evaluation of the @xmath20-vector form factor using the @xmath118 lagrangian yields @xmath127 by demanding a brodsky - lepage behaviour @xcite to @xmath128 one gets the relation @xmath129 , which gives a parameter - free expression . this naive result can be improved by including the next - to - leading order effect in the @xmath95 counting , _ i. e. _ the meson ( off - shell ) width according to chiral constraints ( the corresponding real part of the chiral loops is also included ) , and adding the effect of higher excitations and ( in the @xmath97 case ) including the dominant isospin - breaking effect given by the @xmath130 mixing . specifically for @xmath131 , we have used the parametrizations in the last two refs . in @xcite , which include three isovector resonances ( @xmath117 , @xmath132 and @xmath133 ) and the resummation of final state interactions encoded in the chiral loop functions . these representations provide good quality fits to belle data @xcite for @xmath134 decays . additionally , we have included the characteristic @xmath135 interference appearing in the neutral channel by multiplying the @xmath117 term by the factor @xmath136 with @xmath137 gev@xmath5 @xcite . other isospin breaking corrections are neglected . this parametrization is compared to babar data @xcite in figure 2 , which are available for the energy region @xmath138 gev . there , the phenomenological gs parametrization includes an additional @xmath37-like excitation . tiny differences between both parametrizations are seen in the region where the destructive interference between the @xmath132 and the @xmath133 resonances is stronger . the comparison also shows the effect of the @xmath118 parametrization lacking of the @xmath139 meson , which is clearly visible in the @xmath140 gev region . these minor differences are taken into account in the final quoted errors . analogously , we have employed two parametrizations of @xmath141 form factor . since this form factor is completely dominated by the extremely narrow @xmath116 meson , we have considered the @xmath118 prediction with only one multiplet of resonances @xcite . on the other hand , the babar collaboration @xcite has reported measurements of the kaon form factor from threshold up to @xmath142 gev . since @xmath143 drops by 6 orders of magnitude in going from the peak to @xmath142 gev ( see figure 3 ) , it should be sufficient to include only the @xmath116 resonance in its parametrization . as it can be observed in figure 3 , experimental data for @xmath143 are reasonably well described from threshold up to approximately @xmath144 gev . deviations at higher energies have a negligible impact in the integrated observables of rare @xmath7 decays . above this energy , other resonance structures with very small ( and alternating ) peaks and dips around the single resonance queue can be observed . these , in turn , are well described using the parameterization quoted in the babar paper @xcite ( which we fitted to the babar data ) , which includes two @xmath43 , three @xmath37 and three @xmath38 excitations in addition to the single lightest vector meson multiplet included in the @xmath118 form factor . mixing the former state does not contribute to @xmath141 and only @xmath117 and @xmath116 remain , with a prominent role of the latter . ] because of its relevance in the study of cp violating observables , we plot in fig . [ reimparts ] the real and imaginary parts of the light - meson electromagnetic form factors according to the two different descriptions that we used . while models agree nicely for the @xmath97 case , they do not in the @xmath6 case around the @xmath117 peak . since the corresponding phase shift has been validated by data in the case of the @xmath118 description , we attribute this to an incorrect phase of the @xmath145 kaon form factor . finally , the @xmath7-meson electromagnetic form factor contribution is suppressed by a factor @xmath146 in eq . ( [ eqld ] ) with respect to the ones of lighter mesons . in addition , a dynamical suppression of the form factor itself is expected according to the reduced charged radius of heavy mesons . just in order to confirm this , meson form factor at small values of the momentum transfer , would be by means of elastic electron-@xmath7 meson scattering . given the difficulty to produce a @xmath7 meson target / beam , it becomes rather complicated to test this low energy behavior of the @xmath7 meson form factor . ] we consider the effective lagrangian coupling @xmath147-mesons to lighter mesons and external sources in ref . @xcite generalized to include @xmath7 mesons . it can be seen that , upon requiring a brodsky - lepage behaviour @xcite of this form factor at infinite momentum transfer , the shape of @xmath148 is given just by flavour symmetry , yielding @xmath149 where @xmath150 can be found in refs . our numerical evaluations confirm that the effect of this form factor will be completely negligible in rates of rare @xmath10 mesons . the spectra of the lepton pair , normalized to the @xmath10 meson decay width are plotted in figure [ fig : leptonpair ] for low values of the lepton - pair invariant mass . we observe that above the muon - pair threshold both spectra are identical . clearly , the integrated rates in the whole kinematical range would exhibit a trivial breaking of leptonic universality owing to the lower electronic threshold and its enhancement due to the @xmath151 dependence in the ld wa amplitude . however , this will happen both in the well - known qcdf as well as in the new ld wa contributions ; thus only the numerical evaluation will tell if there is any additional measurable breaking of universality due to ld wa effects in the considered processes . the ld ( one - photon exchange ) contribution to the @xmath14 decays that we have discussed in previous sections and the one evaluated in the qcdf approach originate from the wa four - quark operator of the effective hamiltonian . then it naturally arises the question whether there is some double - counting between both contributions or not . for low enough values of @xmath49 ( @xmath30 ) , the qcdf expansion in 1/@xmath31 is the best way to organize the perturbative series . however , when approaching the @xmath35 threshold ( @xmath152 ) light - resonance effects need to be included explicitely as active degrees of freedom in the action as done in the resonance chiral lagrangians . within the interval from threshold to @xmath153 , we expect that chiral lagrangians give an adequate description for low @xmath49 values , while qcdf be more appropriate for the higher @xmath49 region . we thus assume there is an intermediate energy scale where both descriptions are good approximations and search for this matching scale where the ( complex ) effective wilson coefficient @xmath154 smoothly matches both descriptions for the @xmath97 and @xmath6 meson channels . we have found such matching scale at @xmath155 gev@xmath5 , as it can be seen in figs . [ fig : matching ] . then we have consider our ld one - photon exchange diagrams as the wa contribution for @xmath50 gev@xmath5 and the sd qcdf counterpart ( where the photon is radiated by the valence quarks in the @xmath7 and @xmath20 mesons ) for @xmath156 gev@xmath5 . we have used this separation scale between the ld and sd ( qcdf ) descriptions of wa contributions in the following and a slight variation of the matching scale has been taken into account in the error estimates . in the following , whenever we use qcdf it is understood that the corresponding result for wa is only used above @xmath52 gev@xmath5 . searches for new physics at large hadronic recoil in the @xmath157 decays are restricted to the @xmath158 gev@xmath5 range of @xmath49 @xcite . thus we will stick to this region for this channel . the @xmath107 decays have just been observed @xcite and such studies have not taken place yet . we therefore include our results both for a range starting at @xmath159 gev@xmath5 ( basically the muon threshold ) and at @xmath160 gev@xmath5 . in either case we cut the phase - space integration at @xmath120 gev@xmath5 to avoid the charmonium region . in table [ table1 ] we show the corresponding branching ratios of ld wa , qcdf and their interference contributions by considering these different kinematical integration domains . values for required input parameters are taken from the pdg @xcite except for the ckm matrix elements which come from ref . @xcite . .integrated branching ratios of @xmath48 decays for @xmath25 ( left hand side ) and @xmath24 ( right hand side ) for different @xmath49 ranges . we tabulate separately the qcdf , long - distance wa ( ld ) and their interference contributions for the kinematical ranges of interest . [ cols="<,<,<,<",options="header " , ] [ table2 ] this @xmath161 cp violating figures shall enhance the case for their measurements . current values at the pdg are well compatible with zero @xcite in @xmath162 ( and also in @xmath163 ) decays , while this observable is not yet reported in the @xmath164 case . the most recent measurement reported by the lhcb collaboration for the integrated cp asymmetry , namely @xmath165 @xcite , is still consistent with the different theoretical predictions . therefore , despite the fact that the tree - level one - photon exchange diagrams give a small contribution to the decay rates ( specially for the @xmath6 case ) , they can generate a non - negligible cp asymmetry within the standard model . this cp asymmetry altogether with measurements of the decay rates can be used as a test of new physics in the rare @xmath166 decays . this makes us emphasize the need of a dedicated measurement of these observables in the next lhc run at lhcb and in the forthcoming belle - ii experiment . in this paper we have considered the one - photon exchange contribution to the rare @xmath167 decays , with @xmath25 or @xmath6 . its effects in the decay rates of the @xmath24 case turn out to be of order 1@xmath168 with respect to the ( top quark loop dominated ) sd contribution for the range @xmath169 gev@xmath5 of the squared lepton pair invariant mass . we do not foresee forthcoming measurements being sensitive to this contribution in the near future . on the contrary , this fact confirms the suitability of this range for new physics searches . in the case of a @xmath170 meson in the final state , the corresponding effect turns out to be significant in integrated observables starting close to threshold . this suggests to take in analogy to the case of a final state with @xmath6 the range @xmath171 gev@xmath5 for precision measurements , since the ld wa contribution is reduced to less than 10@xmath168 with a negligible uncertainty in that interval . on the other hand , more refined measurements of the fully integrated branching fraction for this decay could be sensitive to our contribution once the error is reduced below a half of the current uncertainty interestingly , the different weak and strong phases of the qcdf and ld wa ( one - photon exchange ) contributions are capable to generate a cp asymmetry . again , this cp asymmetry is large in the case of a pion in the final state for @xmath172 gev@xmath5 values of the lepton - pair invariant mass , but also sizable and worth to measure in the @xmath173 gev@xmath5 interval . for the kaon case , the range @xmath174 gev@xmath5 is optimal for such a search . our cp violation results are smaller than those obtained within qcdf because of the different description of the wa amplitudes at low energies . future measurements shall be sensitive to this kind of contribution and shed light on its appropriate description . more refined measurements of this cp asymmetry and of the magnitudes of the decay rates at lhcb and future @xmath7-superfactories can provide another non - trivial test of the standard model or may furnish indications of new physics . * acknowledgements * : the authors would like to thank conacyt ( mxico ) for financial support . we appreciate very much helpful correspondence with bogdan malaescu concerning the babar parametrization of the kaon electromagnetic form factor . we thank javier virto for useful discussions on the topic of this article . g. buchalla , a. j. buras and m. e. lautenbacher , rev . * 68 * , 1125 ( 1996 ) . v. cirigliano , g. ecker , h. neufeld , a. pich , and j. portols , rev . phys . * 84 * , 399 ( 2012 ) . t. hurth and m. nakao , ann . nucl . part . * 60 * , 645 ( 2010 ) . r. aaij _ et al . _ [ lhcb collaboration ] , phys . rev . lett . * 113 * , 151601 ( 2014 ) . c. bobeth , g. hiller and g. piranishvili , j. high energy phys . * 12 * , 040 ( 2007 ) . c. bobeth , g. hiller , d. van dyk and ch . wacker , j. high energy phys . * 01 * , 107 ( 2012 ) . g. hiller and f. krger , phys . rev . d**69 * * , 074020 ( 2004 ) . g. hiller and m. schmaltz , phys . d**90 * * , 054014 ( 2014 ) . r. alonso , b. grinstein and j. martn camalich , phys . * 113 * ( 2014 ) 24 , 241802 ; 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cardia is a multicenter community - based longitudinal cohort study of the development and determinants of cardiovascular disease over time in 5,115 young adults initially aged 1830 years in 1985 to 1986 . black and white adults were recruited from four cities in the united states ( birmingham , al ; chicago , il ; minneapolis , mn ; and oakland , ca ) with population - based samples approximately balanced within center by sex , age ( 1824 years and 2530 years ) , race ( white and black ) , and education ( high school graduate or less , greater than high school graduate ) . to date , participants have been re - examined 2 , 5 , 7 , 10 , 15 , 20 , and 25 years after baseline , and retention rates across examinations were 91 , 86 , 81 , 79 , 74 , 72 , and 72% , respectively . all participants provided written informed consent at each examination , and institutional review boards from each field center and the coordinating center approved the study annually . of the 5,115 participants , we excluded those who had diabetes or an unknown diabetes status at baseline ( n = 240 ) , were abdominally obese [ > 102 cm in men and > 88 cm in women ( 20 ) ] or missing wc at baseline ( n = 387 ) , were pregnant during any examination ( n = 206 ) , had bariatric surgery during follow - up ( n = 33 ) , were transgender ( n = 2 ) , or were missing the measurement of wc during follow - up ( n = 155 ) . participants were asked to fast for at least 12 h before each examination and to avoid smoking or engaging in heavy physical activity for at least 2 h. wc was measured with a tape in duplicate to the nearest 0.5 cm around the minimal abdominal girth identified laterally midway between the iliac crest and the lowest portion of the rib cage and anteriorly midway between the xiphoid process and the umbilicus . body weight was measured to the nearest 0.2 kg with a calibrated balance - beam scale . the sum of years spent abdominally obese during the 25-year follow - up was calculated for participants without abdominal obesity at baseline . onset of abdominal obesity was considered to be the time between the examination first measured as abdominally obese and the prior examination year . the algorithm accounted for fluctuations in wc above and below the threshold of abdominal obesity during follow - up . for participants who developed diabetes , the number of years spent abdominally obese were determined up until the examination when incident diabetes was identified . for those who did not develop diabetes , years of abdominal obesity the age at first appearance of abdominal obesity was defined as the age at the examination year prior to the examination at which abdominal obesity was identified . blood was drawn by venipuncture and processed at the central laboratory according to a standard protocol . glucose was assayed at baseline ( i.e. , year 0 ) using the hexokinase ultraviolet method by american bio - science laboratories ( van nuys , ca ) and at years 7 , 10 , 15 , 20 , and 25 using hexokinase coupled to glucose-6-phosphate dehydrogenase by linco research ( st . glycated hemoglobin a1c was measured using the tosoh g7 high - performance liquid chromatography method ( tosoh bioscience ) at years 20 and 25 . diabetes was determined based on a combination of measured fasting glucose levels ( 7.0 mmol / l , 126 mg / dl ) at examination years 7 , 10 , 15 , 20 , or 25 ; self - report of oral hypoglycemic medications or insulin ( all examinations ) ; a 2-h postload glucose 11.1 mmol / l ( 200 mg / dl ) at examination years 10 , 20 , and 25 ; or a glycated hemoglobin a1c 6.5% at years 20 and 25 ( 21 ) . the incidence of diabetes over 25 years was determined among participants who did not have diabetes at baseline based on fasting glucose levels and report of medications . standard questionnaires were used to maintain consistency in the assessment of demographic ( age , sex , race , and education ) and behavioral ( physical activity , cigarette smoking , and alcohol use ) information across all cardia examination visits . the cardia physical activity history questionnaire was used to query the amount of time per week spent in 13 categories of leisure , occupational , and household physical activities over the past 12 months ( 22 ) . activity was expressed in exercise units ; a total activity score of 300 exercise units approximates department of health and human services recommendations of 150 min of moderate - intensity activity per week . cigarette smoking status was classified as ever or never based upon information collected at each examination . energy intake was measured with the interviewer - administered , validated cardia dietary history at years 0 , 7 , and 20 ( 23 ) . extreme values of energy intake ( high : > 8,000 kcal / day in men and > 6,000 kcal / day in women ; low : < 800 kcal / day in men and < 600 kcal / day in women ) were excluded as unreliable . diabetes diagnosed in an immediate family member ( mother , father , sister , or brother ) was also queried at years 0 , 5 , 10 , and 25 . among women , we calculated the incidence rate of diabetes ( number of incident cases per person time at risk ) per 1,000 person - years according to the duration of abdominal obesity . follow - up time at risk was calculated as the difference between baseline and the examination when incident diabetes was identified . for participants who did not develop diabetes , follow - up time was censored at the last known follow - up examination . multivariable cox proportional hazards regression models were used to estimate the hazard ratio ( hr ) and 95% ci for incident diabetes according to the duration of abdominal obesity . duration of abdominal obesity was included as a time - dependent variable in analyses in one of two exposure forms : first as a continuous variable assuming a linear dose - response association and second as a six - level categorical variable ( i.e. , 0 , 15 , 610 , 1115 , 1620 , and > 20 years ) . analyses were adjusted for baseline age , maximum years of education , family history of diabetes ( yes / no ) , cardia field center , and the following time - dependent covariates : wc ( cm ) , energy intake ( average kcal ) , smoking status ( never / ever ) , alcohol use ( average ml / day ) , physical activity ( average exercise units ) , and , among women in models stratified by race , number of pregnancies and postmenopausal status ( yes / no ) . to test for the presence of a quadratic trend , we added a squared duration of abdominal obesity term to the multivariable models that also included a linear term . potential effect modification by race in sex - stratified models was evaluated by testing the statistical significance of a multiplicative interaction term including race and duration of abdominal obesity as a categorical variable in models that also included lower - order terms . we also performed a sensitivity analysis to determine the influence of missing wc values ( 18.8% of all measurements ) on the association between the duration of abdominal obesity and incident diabetes . multiple imputation was used to impute missing wc using the sequential regression imputation approach that is implemented in the software package iveware ( 24 ) . five datasets were generated using all available wc data on the sample of 4,092 participants . each data set was analyzed separately , and results from the five analyses were combined using rubin 's rules ( 25 ) . tests of statistical significance were two - tailed , with an level of 0.05 . a type 1 error rate of 0.10 was set for tests of multiplicative interaction . sas version 9.2 ( sas institute , cary , nc ) was used to perform all analyses . cardia is a multicenter community - based longitudinal cohort study of the development and determinants of cardiovascular disease over time in 5,115 young adults initially aged 1830 years in 1985 to 1986 . black and white adults were recruited from four cities in the united states ( birmingham , al ; chicago , il ; minneapolis , mn ; and oakland , ca ) with population - based samples approximately balanced within center by sex , age ( 1824 years and 2530 years ) , race ( white and black ) , and education ( high school graduate or less , greater than high school graduate ) . to date , participants have been re - examined 2 , 5 , 7 , 10 , 15 , 20 , and 25 years after baseline , and retention rates across examinations were 91 , 86 , 81 , 79 , 74 , 72 , and 72% , respectively . all participants provided written informed consent at each examination , and institutional review boards from each field center and the coordinating center approved the study annually . of the 5,115 participants , we excluded those who had diabetes or an unknown diabetes status at baseline ( n = 240 ) , were abdominally obese [ > 102 cm in men and > 88 cm in women ( 20 ) ] or missing wc at baseline ( n = 387 ) , were pregnant during any examination ( n = 206 ) , had bariatric surgery during follow - up ( n = 33 ) , were transgender ( n = 2 ) , or were missing the measurement of wc during follow - up ( n = 155 ) . participants were asked to fast for at least 12 h before each examination and to avoid smoking or engaging in heavy physical activity for at least 2 h. wc was measured with a tape in duplicate to the nearest 0.5 cm around the minimal abdominal girth identified laterally midway between the iliac crest and the lowest portion of the rib cage and anteriorly midway between the xiphoid process and the umbilicus . body weight was measured to the nearest 0.2 kg with a calibrated balance - beam scale . the sum of years spent abdominally obese during the 25-year follow - up was calculated for participants without abdominal obesity at baseline . onset of abdominal obesity was considered to be the time between the examination first measured as abdominally obese and the prior examination year . the algorithm accounted for fluctuations in wc above and below the threshold of abdominal obesity during follow - up . for participants who developed diabetes , the number of years spent abdominally obese were determined up until the examination when incident diabetes was identified . for those who did not develop diabetes , years of abdominal obesity the age at first appearance of abdominal obesity was defined as the age at the examination year prior to the examination at which abdominal obesity was identified . blood was drawn by venipuncture and processed at the central laboratory according to a standard protocol . glucose was assayed at baseline ( i.e. , year 0 ) using the hexokinase ultraviolet method by american bio - science laboratories ( van nuys , ca ) and at years 7 , 10 , 15 , 20 , and 25 using hexokinase coupled to glucose-6-phosphate dehydrogenase by linco research ( st . glycated hemoglobin a1c was measured using the tosoh g7 high - performance liquid chromatography method ( tosoh bioscience ) at years 20 and 25 . diabetes was determined based on a combination of measured fasting glucose levels ( 7.0 mmol / l , 126 mg / dl ) at examination years 7 , 10 , 15 , 20 , or 25 ; self - report of oral hypoglycemic medications or insulin ( all examinations ) ; a 2-h postload glucose 11.1 mmol / l ( 200 mg / dl ) at examination years 10 , 20 , and 25 ; or a glycated hemoglobin a1c 6.5% at years 20 and 25 ( 21 ) . the incidence of diabetes over 25 years was determined among participants who did not have diabetes at baseline based on fasting glucose levels and report of medications . standard questionnaires were used to maintain consistency in the assessment of demographic ( age , sex , race , and education ) and behavioral ( physical activity , cigarette smoking , and alcohol use ) information across all cardia examination visits . the cardia physical activity history questionnaire was used to query the amount of time per week spent in 13 categories of leisure , occupational , and household physical activities over the past 12 months ( 22 ) . activity was expressed in exercise units ; a total activity score of 300 exercise units approximates department of health and human services recommendations of 150 min of moderate - intensity activity per week . cigarette smoking status was classified as ever or never based upon information collected at each examination . energy intake was measured with the interviewer - administered , validated cardia dietary history at years 0 , 7 , and 20 ( 23 ) . extreme values of energy intake ( high : > 8,000 kcal / day in men and > 6,000 kcal / day in women ; low : < 800 kcal / day in men and < 600 kcal / day in women ) were excluded as unreliable . diabetes diagnosed in an immediate family member ( mother , father , sister , or brother ) was also queried at years 0 , 5 , 10 , and 25 . among women , number of pregnancies and menopausal status were obtained by self - report . we calculated the incidence rate of diabetes ( number of incident cases per person time at risk ) per 1,000 person - years according to the duration of abdominal obesity . follow - up time at risk was calculated as the difference between baseline and the examination when incident diabetes was identified . for participants who did not develop diabetes , follow - up time was censored at the last known follow - up examination . multivariable cox proportional hazards regression models were used to estimate the hazard ratio ( hr ) and 95% ci for incident diabetes according to the duration of abdominal obesity . duration of abdominal obesity was included as a time - dependent variable in analyses in one of two exposure forms : first as a continuous variable assuming a linear dose - response association and second as a six - level categorical variable ( i.e. , 0 , 15 , 610 , 1115 , 1620 , and > 20 years ) . analyses were adjusted for baseline age , maximum years of education , family history of diabetes ( yes / no ) , cardia field center , and the following time - dependent covariates : wc ( cm ) , energy intake ( average kcal ) , smoking status ( never / ever ) , alcohol use ( average ml / day ) , physical activity ( average exercise units ) , and , among women in models stratified by race , number of pregnancies and postmenopausal status ( yes / no ) . to test for the presence of a quadratic trend , we added a squared duration of abdominal obesity term to the multivariable models that also included a linear term . potential effect modification by race in sex - stratified models was evaluated by testing the statistical significance of a multiplicative interaction term including race and duration of abdominal obesity as a categorical variable in models that also included lower - order terms . we also performed a sensitivity analysis to determine the influence of missing wc values ( 18.8% of all measurements ) on the association between the duration of abdominal obesity and incident diabetes . multiple imputation was used to impute missing wc using the sequential regression imputation approach that is implemented in the software package iveware ( 24 ) . five datasets were generated using all available wc data on the sample of 4,092 participants . each data set was analyzed separately , and results from the five analyses were combined using rubin 's rules ( 25 ) . tests of statistical significance were two - tailed , with an level of 0.05 . a type 1 error rate of 0.10 was set for tests of multiplicative interaction . sas version 9.2 ( sas institute , cary , nc ) was used to perform all analyses . of the 4,092 eligible participants without abdominal obesity or diabetes at baseline , 48.8% were black , and 50.0% were women . the characteristics of participants overall and according to race and sex group are shown in table 1 . at baseline , mean values of glucose were well below the therapeutic threshold across all race - sex groups . about one - third of participants had a family history of diabetes with a slightly higher proportion observed among black as compared with white adults . characteristics of 4,092 participants included in the current study overall and according to race and sex : the cardia study the percentage of participants who developed abdominal obesity , mean age at onset , mean duration , and the proportion of participants in each 5-year category of abdominal obesity overall and according to race and sex are shown in table 2 . the occurrence of abdominal obesity during follow - up was significantly higher among black women ( 57.5% ) than all other race - sex groups ( p < 0.001 ) . compared with all other groups , black women also developed abdominal obesity at a younger age ( mean 34.5 years ) , resulting in a longer duration of exposure ( mean 7.6 years ) ( p < 0.001 for both ) . additional comparisons showed the proportion ( 34.7 vs. 28.4% ) and duration ( 4.4 vs. 3.3 years ) of abdominal obesity were higher among white women as compared with black men ( p < 0.01 for both ) . on average , black men developed abdominal obesity at a younger age than white men ( 36.1 vs. 38.4 years ; p < 0.001 ) . descriptive characteristics on the occurrence of abdominal obesity * during follow - up overall and according to race and sex : the cardia study during 85,096 person - years of follow - up , 392 participants developed incident diabetes , a rate of 4.6/1,000 person - years ( table 3 ) . 1 displays the incidence of diabetes per 1,000 person - years according to the duration of abdominal obesity in 5-year increments overall and according to race and sex . the incidence of diabetes was higher with a longer duration of abdominal obesity peaking at 1115 years for black men and women , 1620 years for white men , and > 20 years for white women . adjusted hrs and 95% ci for incident diabetes * according to duration of abdominal obesity during follow - up overall and according to race and sex : the cardia study incidence of diabetes ( per 1,000 person - years ) according to duration of abdominal obesity in 5-year increments through year 25 ( 2010 to 2011 ) overall and according to race and sex : the cardia study . . a longer duration of exposure to abdominal obesity was associated with incident diabetes ( table 3 ) . overall , with each additional year of abdominal obesity , the multivariable adjusted hr for diabetes was 4% higher [ hr 1.04 ( 95% ci : 1.021.07 ) ] and was similar when a lower cut point was used to define abdominal obesity ( 94 cm for men and 80 cm for women ) [ 1.04 ( 1.011.06 ) ] . similar results were also observed in a sensitivity analysis that imputed missing values using all available measures of wc during follow - up on the sample of 4,092 participants [ 1.03 ( 1.011.06 ) ] . however , we found that a quadratic model best represented the risk for diabetes associated with the duration of abdominal obesity . compared with those who did not develop abdominal obesity ( zero years of abdominal obesity ) , each 5-year higher category of abdominal obesity was associated with a substantially higher risk for diabetes that peaked at 1115 years of abdominal obesity ( table 3 ) . wc was also associated with diabetes risk [ 1.04 ( 1.031.05/cm ) ] . in general , a quadratic trend in the risk for diabetes associated with the duration of abdominal obesity that peaked at 1115 years was observed in all race - sex groups except white women , in whom a significant linear trend was noted ( table 3 ) . with each additional year of abdominal obesity , an 8% higher risk for diabetes was observed in white women [ hr 1.08 ( 95% ci 1.021.15 ) ] . these associations did not vary significantly between white and black men or women ( p - interaction > 0.2 and 0.1 , respectively ) . in this multicenter , community - based , longitudinal cohort study of adults recruited and followed largely during the obesity epidemic over the last three decades in the united states , we found the duration of abdominal obesity starting in young adulthood and into middle age to be an important predictor of new - onset diabetes independent of the degree of abdominal adiposity , physical activity , energy intake , family history of diabetes , and a number of other potential confounding factors . overall , each additional year of abdominal obesity was associated with a 4% higher risk of developing diabetes later in life . however , we found this risk appeared to peak with 1115 years of abdominal obesity , but remained elevated for > 20 years . this finding suggests that the longer duration of exposure to excess abdominal adiposity as a result of the obesity epidemic and an earlier age at onset will have important implications on diabetes incidence rates in the united states . to the best of our knowledge , the current study is the first to determine whether the duration of abdominal obesity is associated with the development of diabetes . previous studies examining the influence of the duration of excess adiposity on diabetes risk have measured only overall obesity ( 815 ) . in order to quantify the duration of obesity , most of these studies have relied upon the recall of body weight at previous ages or the self - reported duration of obesity , methods that may be susceptible to a considerable amount of measurement error ( 9,10,1315 ) . however , in the current study , we used repeated assessments of wc collected every 25 years for a maximum of 25 years beginning early in adulthood to objectively determine the duration of abdominal obesity during follow - up . we found the duration of abdominal obesity was associated with the development of diabetes independent of the degree of abdominal adiposity . thus , we suggest that future studies interested in estimating the cumulative exposure to excess abdominal adiposity over the life course measure not only the degree of abdominal adiposity , but also its duration . in the present long - term study , we found the frequency of developing abdominal obesity was highest among black women . in addition , on average , black women developed abdominal obesity 2 years earlier than black men and 3 to 4 years earlier than white men and women . as a result , black women experienced the longest duration of exposure to abdominal obesity of all race - sex groups . in contrast , men , either black or white , generally tended to have the lowest rates of abdominal obesity . these findings are consistent with recent data from the national health and nutrition examination survey showing a substantially higher prevalence of abdominal obesity among black women in the united states ( 5 ) . despite a longer duration of abdominal obesity and a higher incidence of diabetes among black women , we found little to no difference in the association between the duration of abdominal obesity and risk for diabetes between white and black men and women . future studies are needed to confirm that black men and women do not have a smaller relative risk for diabetes associated with abdominal obesity than their white counterparts . overall , we found the risk for diabetes appeared to peak during the first 1115 years of abdominal obesity , but remained elevated for > 20 years . in general , this quadratic trend was confirmed in all race - sex groups except white women , among whom the risk for diabetes peaked with > 20 years of abdominal obesity . this finding suggests that the adverse metabolic effects of excess abdominal adiposity on diabetes risk , although elevated over the course of two decades , may begin to plateau after 1115 years . although the suspected mechanism to support this finding remains elusive , it may be possible that the number of individuals susceptible to the metabolic derangements of prolonged abdominal obesity decreases after approximately the first decade . a portion of the remaining abdominally obese individuals may be able to avoid hyperglycemia in the face of prolonged obesity by being either less responsive to the secretions of excess adipose tissue or their adipose tissue may not possess the same secretory properties of those abdominally obese individuals who develop diabetes . it is generally well - accepted that excess adiposity , particularly abdominal adiposity , can have deleterious metabolic effects , thereby increasing the risk of developing diabetes . expanded fat stores , a hallmark of obesity , results in enhanced lipolysis , leading to increased circulating free fatty acids , and promotes peripheral and hepatic insulin resistance ( 26 ) . the normal pancreatic -cell response to obesity - associated insulin resistance is compensatory insulin hypersecretion in order to maintain normoglycemia ( 27 ) . over time with prolonged obesity , -cell dysfunction results in low insulin response and an inability to maintain glycemia near normal ( 28 ) . thus , the early stages of abdominal obesity may be largely characterized by the development of insulin resistance , whereas a prolonged duration of abdominal obesity may promote progressive deterioration in -cell function , leading to the development of overt diabetes . additional mechanisms that may explain , at least in part , the association between a longer duration of abdominal obesity and the development of diabetes , include sustained expression and secretion of hormones , cytokines , and adipokines from intra - abdominal fat located in close proximity to the portal circulation ( 29 ) . strengths of our study include a community - based sampling method ; a biracial cohort ; extensive data on potential confounders ; a large sample size well balanced with respect to age , sex , race , and education that increased precision and permitted simultaneous adjustment and stratification by multiple variables ; repeat assessments of wc , glycemia , and potential confounding factors over a long follow - up period ; a high retention rate ; and the standardized data collection protocols and rigorous quality control of the cardia study . first , wc was used as an estimate of central obesity even though it does not distinguish between subcutaneous and visceral fat . nevertheless , wc has been shown to be strongly correlated with visceral fat and offers widespread appeal due to its relative ease of measurement ( 30 ) . second , our estimation of the duration of abdominal obesity during follow - up was based on the measurement of wc every 25 years . it is likely that a more frequent number of assessments would have led to a more accurate estimation of the duration of abdominal obesity during follow - up ; however , to the extent that there was random misclassification due to this assessment schedule , we may have underestimated the true association between the duration of abdominal obesity and diabetes risk in our cohort . third , since our study collected data over a 25-year period , some participants were missing at least one eligible measurement of wc . however , we noted similar results between our multiple imputed datasets and our primary dataset that did not account for missing wc values . in conclusion , our findings indicate that a longer duration of abdominal obesity is associated with a substantially higher risk for diabetes in adults independent of the degree of abdominal adiposity . this information is critical to understanding the consequences of a greater prevalence and cumulative exposure to excess adiposity over the life course . our findings suggest that preventing or at least delaying the onset of abdominal obesity in young adulthood may substantially reduce the risk of developing diabetes into middle age .

objectiveto examine whether the duration of abdominal obesity determined prospectively using measured waist circumference ( wc ) is associated with the development of new - onset diabetes independent of the degree of abdominal adiposity.research design and methodsthe coronary artery risk development in young adults study is a multicenter , community - based , longitudinal cohort study of 5,115 white and black adults aged 1830 years in 1985 to 1986 . years spent abdominally obese were calculated for participants without abdominal obesity ( wc > 102 cm in men and > 88 cm in women ) or diabetes at baseline ( n = 4,092 ) and was based upon repeat measurements conducted 2 , 5 , 7 , 10 , 15 , 20 , and 25 years later.resultsover 25 years , 392 participants developed incident diabetes . overall , following adjustment for demographics , family history of diabetes , study center , and time varying wc , energy intake , physical activity , smoking , and alcohol , each additional year of abdominal obesity was associated with a 4% higher risk of developing diabetes [ hazard ratio ( hr ) 1.04 ( 95% ci 1.021.07 ) ] . however , a quadratic model best represented the data . hrs for 0 , 15 , 610 , 1115 , 1620 , and > 20 years of abdominal obesity were 1.00 ( referent ) , 2.06 ( 1.432.98 ) , 3.45 ( 2.285.22 ) , 3.43 ( 2.285.22 ) , 2.80 ( 1.734.54 ) , and 2.91 ( 1.605.29 ) , respectively ; p - quadratic < 0.001.conclusionslonger duration of abdominal obesity was associated with substantially higher risk for diabetes independent of the degree of abdominal adiposity . preventing or at least delaying the onset of abdominal obesity in young adulthood may lower the risk of developing diabetes through middle age .

<s>[INST]cardia is a multicenter community - based longitudinal cohort study of the development and determinants of cardiovascular disease over time in 5,115 young adults initially aged 1830 years in 1985 to 1986 . black and white adults were recruited from four cities in the united states ( birmingham , al ; chicago , il ; minneapolis , mn ; and oakland , ca ) with population - based samples approximately balanced within center by sex , age ( 1824 years and 2530 years ) , race ( white and black ) , and education ( high school graduate or less , greater than high school graduate ) . to date , participants have been re - examined 2 , 5 , 7 , 10 , 15 , 20 , and 25 years after baseline , and retention rates across examinations were 91 , 86 , 81 , 79 , 74 , 72 , and 72% , respectively . all participants provided written informed consent at each examination , and institutional review boards from each field center and the coordinating center approved the study annually . of the 5,115 participants , we excluded those who had diabetes or an unknown diabetes status at baseline ( n = 240 ) , were abdominally obese [ > 102 cm in men and > 88 cm in women ( 20 ) ] or missing wc at baseline ( n = 387 ) , were pregnant during any examination ( n = 206 ) , had bariatric surgery during follow - up ( n = 33 ) , were transgender ( n = 2 ) , or were missing the measurement of wc during follow - up ( n = 155 ) . participants were asked to fast for at least 12 h before each examination and to avoid smoking or engaging in heavy physical activity for at least 2 h. wc was measured with a tape in duplicate to the nearest 0.5 cm around the minimal abdominal girth identified laterally midway between the iliac crest and the lowest portion of the rib cage and anteriorly midway between the xiphoid process and the umbilicus . body weight was measured to the nearest 0.2 kg with a calibrated balance - beam scale . the sum of years spent abdominally obese during the 25-year follow - up was calculated for participants without abdominal obesity at baseline . onset of abdominal obesity was considered to be the time between the examination first measured as abdominally obese and the prior examination year . the algorithm accounted for fluctuations in wc above and below the threshold of abdominal obesity during follow - up . for participants who developed diabetes , the number of years spent abdominally obese were determined up until the examination when incident diabetes was identified . for those who did not develop diabetes , years of abdominal obesity the age at first appearance of abdominal obesity was defined as the age at the examination year prior to the examination at which abdominal obesity was identified . blood was drawn by venipuncture and processed at the central laboratory according to a standard protocol . glucose was assayed at baseline ( i.e. , year 0 ) using the hexokinase ultraviolet method by american bio - science laboratories ( van nuys , ca ) and at years 7 , 10 , 15 , 20 , and 25 using hexokinase coupled to glucose-6-phosphate dehydrogenase by linco research ( st . glycated hemoglobin a1c was measured using the tosoh g7 high - performance liquid chromatography method ( tosoh bioscience ) at years 20 and 25 . diabetes was determined based on a combination of measured fasting glucose levels ( 7.0 mmol / l , 126 mg / dl ) at examination years 7 , 10 , 15 , 20 , or 25 ; self - report of oral hypoglycemic medications or insulin ( all examinations ) ; a 2-h postload glucose 11.1 mmol / l ( 200 mg / dl ) at examination years 10 , 20 , and 25 ; or a glycated hemoglobin a1c 6.5% at years 20 and 25 ( 21 ) . the incidence of diabetes over 25 years was determined among participants who did not have diabetes at baseline based on fasting glucose levels and report of medications . standard questionnaires were used to maintain consistency in the assessment of demographic ( age , sex , race , and education ) and behavioral ( physical activity , cigarette smoking , and alcohol use ) information across all cardia examination visits . the cardia physical activity history questionnaire was used to query the amount of time per week spent in 13 categories of leisure , occupational , and household physical activities over the past 12 months ( 22 ) . activity was expressed in exercise units ; a total activity score of 300 exercise units approximates department of health and human services recommendations of 150 min of moderate - intensity activity per week . cigarette smoking status was classified as ever or never based upon information collected at each examination . energy intake was measured with the interviewer - administered , validated cardia dietary history at years 0 , 7 , and 20 ( 23 ) . extreme values of energy intake ( high : > 8,000 kcal / day in men and > 6,000 kcal / day in women ; low : < 800 kcal / day in men and < 600 kcal / day in women ) were excluded as unreliable . diabetes diagnosed in an immediate family member ( mother , father , sister , or brother ) was also queried at years 0 , 5 , 10 , and 25 . among women , we calculated the incidence rate of diabetes ( number of incident cases per person time at risk ) per 1,000 person - years according to the duration of abdominal obesity . follow - up time at risk was calculated as the difference between baseline and the examination when incident diabetes was identified . for participants who did not develop diabetes , follow - up time was censored at the last known follow - up examination . multivariable cox proportional hazards regression models were used to estimate the hazard ratio ( hr ) and 95% ci for incident diabetes according to the duration of abdominal obesity . duration of abdominal obesity was included as a time - dependent variable in analyses in one of two exposure forms : first as a continuous variable assuming a linear dose - response association and second as a six - level categorical variable ( i.e. , 0 , 15 , 610 , 1115 , 1620 , and > 20 years ) . analyses were adjusted for baseline age , maximum years of education , family history of diabetes ( yes / no ) , cardia field center , and the following time - dependent covariates : wc ( cm ) , energy intake ( average kcal ) , smoking status ( never / ever ) , alcohol use ( average ml / day ) , physical activity ( average exercise units ) , and , among women in models stratified by race , number of pregnancies and postmenopausal status ( yes / no ) . to test for the presence of a quadratic trend , we added a squared duration of abdominal obesity term to the multivariable models that also included a linear term . potential effect modification by race in sex - stratified models was evaluated by testing the statistical significance of a multiplicative interaction term including race and duration of abdominal obesity as a categorical variable in models that also included lower - order terms . we also performed a sensitivity analysis to determine the influence of missing wc values ( 18.8% of all measurements ) on the association between the duration of abdominal obesity and incident diabetes . multiple imputation was used to impute missing wc using the sequential regression imputation approach that is implemented in the software package iveware ( 24 ) . five datasets were generated using all available wc data on the sample of 4,092 participants . each data set was analyzed separately , and results from the five analyses were combined using rubin 's rules ( 25 ) . tests of statistical significance were two - tailed , with an level of 0.05 . a type 1 error rate of 0.10 was set for tests of multiplicative interaction . sas version 9.2 ( sas institute , cary , nc ) was used to perform all analyses . cardia is a multicenter community - based longitudinal cohort study of the development and determinants of cardiovascular disease over time in 5,115 young adults initially aged 1830 years in 1985 to 1986 . black and white adults were recruited from four cities in the united states ( birmingham , al ; chicago , il ; minneapolis , mn ; and oakland , ca ) with population - based samples approximately balanced within center by sex , age ( 1824 years and 2530 years ) , race ( white and black ) , and education ( high school graduate or less , greater than high school graduate ) . to date , participants have been re - examined 2 , 5 , 7 , 10 , 15 , 20 , and 25 years after baseline , and retention rates across examinations were 91 , 86 , 81 , 79 , 74 , 72 , and 72% , respectively . all participants provided written informed consent at each examination , and institutional review boards from each field center and the coordinating center approved the study annually . of the 5,115 participants , we excluded those who had diabetes or an unknown diabetes status at baseline ( n = 240 ) , were abdominally obese [ > 102 cm in men and > 88 cm in women ( 20 ) ] or missing wc at baseline ( n = 387 ) , were pregnant during any examination ( n = 206 ) , had bariatric surgery during follow - up ( n = 33 ) , were transgender ( n = 2 ) , or were missing the measurement of wc during follow - up ( n = 155 ) . participants were asked to fast for at least 12 h before each examination and to avoid smoking or engaging in heavy physical activity for at least 2 h. wc was measured with a tape in duplicate to the nearest 0.5 cm around the minimal abdominal girth identified laterally midway between the iliac crest and the lowest portion of the rib cage and anteriorly midway between the xiphoid process and the umbilicus . body weight was measured to the nearest 0.2 kg with a calibrated balance - beam scale . the sum of years spent abdominally obese during the 25-year follow - up was calculated for participants without abdominal obesity at baseline . onset of abdominal obesity was considered to be the time between the examination first measured as abdominally obese and the prior examination year . the algorithm accounted for fluctuations in wc above and below the threshold of abdominal obesity during follow - up . for participants who developed diabetes , the number of years spent abdominally obese were determined up until the examination when incident diabetes was identified . for those who did not develop diabetes , years of abdominal obesity the age at first appearance of abdominal obesity was defined as the age at the examination year prior to the examination at which abdominal obesity was identified . blood was drawn by venipuncture and processed at the central laboratory according to a standard protocol . glucose was assayed at baseline ( i.e. , year 0 ) using the hexokinase ultraviolet method by american bio - science laboratories ( van nuys , ca ) and at years 7 , 10 , 15 , 20 , and 25 using hexokinase coupled to glucose-6-phosphate dehydrogenase by linco research ( st . glycated hemoglobin a1c was measured using the tosoh g7 high - performance liquid chromatography method ( tosoh bioscience ) at years 20 and 25 . diabetes was determined based on a combination of measured fasting glucose levels ( 7.0 mmol / l , 126 mg / dl ) at examination years 7 , 10 , 15 , 20 , or 25 ; self - report of oral hypoglycemic medications or insulin ( all examinations ) ; a 2-h postload glucose 11.1 mmol / l ( 200 mg / dl ) at examination years 10 , 20 , and 25 ; or a glycated hemoglobin a1c 6.5% at years 20 and 25 ( 21 ) . the incidence of diabetes over 25 years was determined among participants who did not have diabetes at baseline based on fasting glucose levels and report of medications . standard questionnaires were used to maintain consistency in the assessment of demographic ( age , sex , race , and education ) and behavioral ( physical activity , cigarette smoking , and alcohol use ) information across all cardia examination visits . the cardia physical activity history questionnaire was used to query the amount of time per week spent in 13 categories of leisure , occupational , and household physical activities over the past 12 months ( 22 ) . activity was expressed in exercise units ; a total activity score of 300 exercise units approximates department of health and human services recommendations of 150 min of moderate - intensity activity per week . cigarette smoking status was classified as ever or never based upon information collected at each examination . energy intake was measured with the interviewer - administered , validated cardia dietary history at years 0 , 7 , and 20 ( 23 ) . extreme values of energy intake ( high : > 8,000 kcal / day in men and > 6,000 kcal / day in women ; low : < 800 kcal / day in men and < 600 kcal / day in women ) were excluded as unreliable . diabetes diagnosed in an immediate family member ( mother , father , sister , or brother ) was also queried at years 0 , 5 , 10 , and 25 . among women , number of pregnancies and menopausal status were obtained by self - report . we calculated the incidence rate of diabetes ( number of incident cases per person time at risk ) per 1,000 person - years according to the duration of abdominal obesity . follow - up time at risk was calculated as the difference between baseline and the examination when incident diabetes was identified . for participants who did not develop diabetes , follow - up time was censored at the last known follow - up examination . multivariable cox proportional hazards regression models were used to estimate the hazard ratio ( hr ) and 95% ci for incident diabetes according to the duration of abdominal obesity . duration of abdominal obesity was included as a time - dependent variable in analyses in one of two exposure forms : first as a continuous variable assuming a linear dose - response association and second as a six - level categorical variable ( i.e. , 0 , 15 , 610 , 1115 , 1620 , and > 20 years ) . analyses were adjusted for baseline age , maximum years of education , family history of diabetes ( yes / no ) , cardia field center , and the following time - dependent covariates : wc ( cm ) , energy intake ( average kcal ) , smoking status ( never / ever ) , alcohol use ( average ml / day ) , physical activity ( average exercise units ) , and , among women in models stratified by race , number of pregnancies and postmenopausal status ( yes / no ) . to test for the presence of a quadratic trend , we added a squared duration of abdominal obesity term to the multivariable models that also included a linear term . potential effect modification by race in sex - stratified models was evaluated by testing the statistical significance of a multiplicative interaction term including race and duration of abdominal obesity as a categorical variable in models that also included lower - order terms . we also performed a sensitivity analysis to determine the influence of missing wc values ( 18.8% of all measurements ) on the association between the duration of abdominal obesity and incident diabetes . multiple imputation was used to impute missing wc using the sequential regression imputation approach that is implemented in the software package iveware ( 24 ) . five datasets were generated using all available wc data on the sample of 4,092 participants . each data set was analyzed separately , and results from the five analyses were combined using rubin 's rules ( 25 ) . tests of statistical significance were two - tailed , with an level of 0.05 . a type 1 error rate of 0.10 was set for tests of multiplicative interaction . sas version 9.2 ( sas institute , cary , nc ) was used to perform all analyses . of the 4,092 eligible participants without abdominal obesity or diabetes at baseline , 48.8% were black , and 50.0% were women . the characteristics of participants overall and according to race and sex group are shown in table 1 . at baseline , mean values of glucose were well below the therapeutic threshold across all race - sex groups . about one - third of participants had a family history of diabetes with a slightly higher proportion observed among black as compared with white adults . characteristics of 4,092 participants included in the current study overall and according to race and sex : the cardia study the percentage of participants who developed abdominal obesity , mean age at onset , mean duration , and the proportion of participants in each 5-year category of abdominal obesity overall and according to race and sex are shown in table 2 . the occurrence of abdominal obesity during follow - up was significantly higher among black women ( 57.5% ) than all other race - sex groups ( p < 0.001 ) . compared with all other groups , black women also developed abdominal obesity at a younger age ( mean 34.5 years ) , resulting in a longer duration of exposure ( mean 7.6 years ) ( p < 0.001 for both ) . additional comparisons showed the proportion ( 34.7 vs. 28.4% ) and duration ( 4.4 vs. 3.3 years ) of abdominal obesity were higher among white women as compared with black men ( p < 0.01 for both ) . on average , black men developed abdominal obesity at a younger age than white men ( 36.1 vs. 38.4 years ; p < 0.001 ) . descriptive characteristics on the occurrence of abdominal obesity * during follow - up overall and according to race and sex : the cardia study during 85,096 person - years of follow - up , 392 participants developed incident diabetes , a rate of 4.6/1,000 person - years ( table 3 ) . 1 displays the incidence of diabetes per 1,000 person - years according to the duration of abdominal obesity in 5-year increments overall and according to race and sex . the incidence of diabetes was higher with a longer duration of abdominal obesity peaking at 1115 years for black men and women , 1620 years for white men , and > 20 years for white women . adjusted hrs and 95% ci for incident diabetes * according to duration of abdominal obesity during follow - up overall and according to race and sex : the cardia study incidence of diabetes ( per 1,000 person - years ) according to duration of abdominal obesity in 5-year increments through year 25 ( 2010 to 2011 ) overall and according to race and sex : the cardia study . . a longer duration of exposure to abdominal obesity was associated with incident diabetes ( table 3 ) . overall , with each additional year of abdominal obesity , the multivariable adjusted hr for diabetes was 4% higher [ hr 1.04 ( 95% ci : 1.021.07 ) ] and was similar when a lower cut point was used to define abdominal obesity ( 94 cm for men and 80 cm for women ) [ 1.04 ( 1.011.06 ) ] . similar results were also observed in a sensitivity analysis that imputed missing values using all available measures of wc during follow - up on the sample of 4,092 participants [ 1.03 ( 1.011.06 ) ] . however , we found that a quadratic model best represented the risk for diabetes associated with the duration of abdominal obesity . compared with those who did not develop abdominal obesity ( zero years of abdominal obesity ) , each 5-year higher category of abdominal obesity was associated with a substantially higher risk for diabetes that peaked at 1115 years of abdominal obesity ( table 3 ) . wc was also associated with diabetes risk [ 1.04 ( 1.031.05/cm ) ] . in general , a quadratic trend in the risk for diabetes associated with the duration of abdominal obesity that peaked at 1115 years was observed in all race - sex groups except white women , in whom a significant linear trend was noted ( table 3 ) . with each additional year of abdominal obesity , an 8% higher risk for diabetes was observed in white women [ hr 1.08 ( 95% ci 1.021.15 ) ] . these associations did not vary significantly between white and black men or women ( p - interaction > 0.2 and 0.1 , respectively ) . in this multicenter , community - based , longitudinal cohort study of adults recruited and followed largely during the obesity epidemic over the last three decades in the united states , we found the duration of abdominal obesity starting in young adulthood and into middle age to be an important predictor of new - onset diabetes independent of the degree of abdominal adiposity , physical activity , energy intake , family history of diabetes , and a number of other potential confounding factors . overall , each additional year of abdominal obesity was associated with a 4% higher risk of developing diabetes later in life . however , we found this risk appeared to peak with 1115 years of abdominal obesity , but remained elevated for > 20 years . this finding suggests that the longer duration of exposure to excess abdominal adiposity as a result of the obesity epidemic and an earlier age at onset will have important implications on diabetes incidence rates in the united states . to the best of our knowledge , the current study is the first to determine whether the duration of abdominal obesity is associated with the development of diabetes . previous studies examining the influence of the duration of excess adiposity on diabetes risk have measured only overall obesity ( 815 ) . in order to quantify the duration of obesity , most of these studies have relied upon the recall of body weight at previous ages or the self - reported duration of obesity , methods that may be susceptible to a considerable amount of measurement error ( 9,10,1315 ) . however , in the current study , we used repeated assessments of wc collected every 25 years for a maximum of 25 years beginning early in adulthood to objectively determine the duration of abdominal obesity during follow - up . we found the duration of abdominal obesity was associated with the development of diabetes independent of the degree of abdominal adiposity . thus , we suggest that future studies interested in estimating the cumulative exposure to excess abdominal adiposity over the life course measure not only the degree of abdominal adiposity , but also its duration . in the present long - term study , we found the frequency of developing abdominal obesity was highest among black women . in addition , on average , black women developed abdominal obesity 2 years earlier than black men and 3 to 4 years earlier than white men and women . as a result , black women experienced the longest duration of exposure to abdominal obesity of all race - sex groups . in contrast , men , either black or white , generally tended to have the lowest rates of abdominal obesity . these findings are consistent with recent data from the national health and nutrition examination survey showing a substantially higher prevalence of abdominal obesity among black women in the united states ( 5 ) . despite a longer duration of abdominal obesity and a higher incidence of diabetes among black women , we found little to no difference in the association between the duration of abdominal obesity and risk for diabetes between white and black men and women . future studies are needed to confirm that black men and women do not have a smaller relative risk for diabetes associated with abdominal obesity than their white counterparts . overall , we found the risk for diabetes appeared to peak during the first 1115 years of abdominal obesity , but remained elevated for > 20 years . in general , this quadratic trend was confirmed in all race - sex groups except white women , among whom the risk for diabetes peaked with > 20 years of abdominal obesity . this finding suggests that the adverse metabolic effects of excess abdominal adiposity on diabetes risk , although elevated over the course of two decades , may begin to plateau after 1115 years . although the suspected mechanism to support this finding remains elusive , it may be possible that the number of individuals susceptible to the metabolic derangements of prolonged abdominal obesity decreases after approximately the first decade . a portion of the remaining abdominally obese individuals may be able to avoid hyperglycemia in the face of prolonged obesity by being either less responsive to the secretions of excess adipose tissue or their adipose tissue may not possess the same secretory properties of those abdominally obese individuals who develop diabetes . it is generally well - accepted that excess adiposity , particularly abdominal adiposity , can have deleterious metabolic effects , thereby increasing the risk of developing diabetes . expanded fat stores , a hallmark of obesity , results in enhanced lipolysis , leading to increased circulating free fatty acids , and promotes peripheral and hepatic insulin resistance ( 26 ) . the normal pancreatic -cell response to obesity - associated insulin resistance is compensatory insulin hypersecretion in order to maintain normoglycemia ( 27 ) . over time with prolonged obesity , -cell dysfunction results in low insulin response and an inability to maintain glycemia near normal ( 28 ) . thus , the early stages of abdominal obesity may be largely characterized by the development of insulin resistance , whereas a prolonged duration of abdominal obesity may promote progressive deterioration in -cell function , leading to the development of overt diabetes . additional mechanisms that may explain , at least in part , the association between a longer duration of abdominal obesity and the development of diabetes , include sustained expression and secretion of hormones , cytokines , and adipokines from intra - abdominal fat located in close proximity to the portal circulation ( 29 ) . strengths of our study include a community - based sampling method ; a biracial cohort ; extensive data on potential confounders ; a large sample size well balanced with respect to age , sex , race , and education that increased precision and permitted simultaneous adjustment and stratification by multiple variables ; repeat assessments of wc , glycemia , and potential confounding factors over a long follow - up period ; a high retention rate ; and the standardized data collection protocols and rigorous quality control of the cardia study . first , wc was used as an estimate of central obesity even though it does not distinguish between subcutaneous and visceral fat . nevertheless , wc has been shown to be strongly correlated with visceral fat and offers widespread appeal due to its relative ease of measurement ( 30 ) . second , our estimation of the duration of abdominal obesity during follow - up was based on the measurement of wc every 25 years . it is likely that a more frequent number of assessments would have led to a more accurate estimation of the duration of abdominal obesity during follow - up ; however , to the extent that there was random misclassification due to this assessment schedule , we may have underestimated the true association between the duration of abdominal obesity and diabetes risk in our cohort . third , since our study collected data over a 25-year period , some participants were missing at least one eligible measurement of wc . however , we noted similar results between our multiple imputed datasets and our primary dataset that did not account for missing wc values . in conclusion , our findings indicate that a longer duration of abdominal obesity is associated with a substantially higher risk for diabetes in adults independent of the degree of abdominal adiposity . this information is critical to understanding the consequences of a greater prevalence and cumulative exposure to excess adiposity over the life course . our findings suggest that preventing or at least delaying the onset of abdominal obesity in young adulthood may substantially reduce the risk of developing diabetes into middle age .[/INST]objectiveto examine whether the duration of abdominal obesity determined prospectively using measured waist circumference ( wc ) is associated with the development of new - onset diabetes independent of the degree of abdominal adiposity.research design and methodsthe coronary artery risk development in young adults study is a multicenter , community - based , longitudinal cohort study of 5,115 white and black adults aged 1830 years in 1985 to 1986 . years spent abdominally obese were calculated for participants without abdominal obesity ( wc > 102 cm in men and > 88 cm in women ) or diabetes at baseline ( n = 4,092 ) and was based upon repeat measurements conducted 2 , 5 , 7 , 10 , 15 , 20 , and 25 years later.resultsover 25 years , 392 participants developed incident diabetes . overall , following adjustment for demographics , family history of diabetes , study center , and time varying wc , energy intake , physical activity , smoking , and alcohol , each additional year of abdominal obesity was associated with a 4% higher risk of developing diabetes [ hazard ratio ( hr ) 1.04 ( 95% ci 1.021.07 ) ] . however , a quadratic model best represented the data . hrs for 0 , 15 , 610 , 1115 , 1620 , and > 20 years of abdominal obesity were 1.00 ( referent ) , 2.06 ( 1.432.98 ) , 3.45 ( 2.285.22 ) , 3.43 ( 2.285.22 ) , 2.80 ( 1.734.54 ) , and 2.91 ( 1.605.29 ) , respectively ; p - quadratic < 0.001.conclusionslonger duration of abdominal obesity was associated with substantially higher risk for diabetes independent of the degree of abdominal adiposity . preventing or at least delaying the onset of abdominal obesity in young adulthood may lower the risk of developing diabetes through middle age .</s>

one of the issues which received much emphasis and consideration in recent decades is the learners styles and learning strategies . considering all the researches , it is evident that the witkin s theory of field dependent - independent cognitive styles due to their increasing applications were extensively used in many researches . learning styles are the beliefs , preferences and behaviors that people employ in order to learn in a certain situation ( 1 ) . in cognitive style , they are inclined to overall field learning and tend to get the whole idea whereas the field independent learners conduct an analytical procedure and are more likely to break a model into different sections and details and tend to depend on their inner knowledge and analyze problems all by themselves without reference to the frame or the environment ( 2 - 4 ) . considering field dependent - independent cognitive styles effects on teaching and learning , and especially on the students course selection , studies show that field independent student had better academic achievement than field - dependent students ( 5 ) . the research by al - saai & dwyer ( 1993 ) also showed that if the educational subjects and materials conform to students cognitive styles , it will lead to a better achievement ( 6 ) . also , the studies revealed that if the field dependents and field independents are placed in homogeneous groups compared with being in the heterogeneous groups , they would show a better improvement the research by al - saai & dwyer ( 1993 ) also showed that if the educational subjects and materials conform to students cognitive styles , it will lead to a better achievement ( 7 ) . studies have shown that field independent learners performed better than field dependent in learning english language ( 8) . pointing to the gender differences on learning styles , hickson & baltimore ( 1996 ) have shown that men and women have different learning styles ( 9 ) . the researches on the relationship between cognitive styles and courses selection also revealed that there is a positive relationship between field independent cognitive styles and science courses selection and also field dependent and social sciences and human resources major selection ( 10 ) . therefore , regarding the researches conducted on this issue , this study seeks to examine the following research questions : is there any relationship between field dependent independent cognitive style and reading comprehension skill and english learning ? is there any relationship between the cognitive field dependent independent styles and academic achievement ? is there a difference between the average scores of witkin s theory of cognitive style in different high school majors ? the study samples consisted of all students studying at junior level of high school in sari , in the academic year of 2010 - 2011 . the numbers of students comprised to 1476 from those 305 were selected for the study . to determine the sample size , multistage cluster sampling was conducted to randomly select the sample . to measure the field dependency this test was used by witkin ( 2 ) in 1971 to measure the youngsters and adults field dependence - independence cognitive style . the reliability of the test was calculated by oltman and colleagues for men and for women as 0.82 & 0.79 , respectively . the criterion - related validity for men was 0.82 and for women 0.63 ( 11 ) . in addition , in this study , each subject s score in english for the first semester in the academic year of 2010 - 2011 was regarded as a criterion for his progress in learning english . in order to evaluate the different skills in students learning english at high school , we used the standard expert revised test which are used at national level and have objective scores . each student s score in reading comprehension was used as a criterion for students reading comprehension ability . then , the average score of all the lessons at the end of the semester was set as a criterion for assessing the student s achievement . the first research question : a ) is there any relationship between field dependent independent cognitive style and reading comprehension skill and english learning ? linear correlation between fdi cognitive style and reading comprehension skill and english learning regarding the table above , the correlation is about 0.296 and the determination coefficient is 0.088 which shows that 8.8% of the changes in the reading comprehension can be evaluated by the fdi ( field dependence / independence ) cognitive style . the regression analysis results showed that the correlation is significant at 0.05 and the null hypothesis is rejected and the research hypothesis is confirmed ( p<05 ) . therefore , it can be concluded that there is a significant linear relationship between fdi cognitive styles and reading comprehension . it can also be seen from the above table that the values associated with this style and learning english is equal to 0.304 and the determination coefficient equals to 0.092 , which shows that 9.2% of the changes in learning english can be explained by fdi cognitive style . the regression analysis results showed that the correlation is significant at 0/05 and the null hypothesis is rejected and the research hypothesis is confirmed ( p<05 ) . therefore , it can be concluded that there is a significant linear relationship between fdi cognitive styles and learning english . the second research question is there any relationship between the cognitive field dependent independent styles and academic achievement ? linear relationship between fdi cognitive style and academic achievement it can be witnessed that the correlation value equals to .341 and determination coefficient was equal to 0.116 which indicates that 11.6 of changes in academic achievement can be explained by fdi cognitive style . the regression analysis results showed that the correlation is significant at 0.05 and the null hypothesis is rejected and the research hypothesis is confirmed ( p<05 ) . therefore , it can be concluded that there is a significant linear relationship between fdi cognitive styles and academic achievement . the third research question is there a difference between the average scores of witkin s cognitive style in different high school majors ? the comparison of students cognitive styles averages based on their academic majors it can be seen from the given table that at the significant level of 0/05 , the differences between the students cognitive styles in various high school majors is significant because the achieved p - value is less than 0.05 , therefore , the null hypothesis is rejected and the research hypothesis is confirmed . so it can be stated that the students cognitive styles in different majors at high school are different . in order to determine the difference between the means , the tukey follow up test was used . by comparing the scores in table 4 , it can be inferred that the cognitive style scores in math students was higher than that of the students in the empirical sciences , and the empirical sciences students score was higher than the scores of students at human sciences and art students . comparison of the theoretical basis of cognitive styles multiple means using tukey follow - up test the general objective of this study was to examine the relationship between field dependent / independent cognitive styles of the students at the third year of secondary school for their reading comprehension skills . the results showed that there is a significant correlation between fdi cognitive styles and reading comprehension skill , english language learning and academic achievement at ( p < 0/.5 ) so that the fdi cognitive styles would explain 8/8% , 9/2% and 11/6% of students reading comprehension skills , learning english and academic achievement , respectively , which is congruent with the studies conducted by such ( 12 - 14 ) quoted by tinajero&paramo ( 1997 ) ( 12 ) . regarding such results we can say that fdi cognitive styles have important roles in learning and academic achievement . field independent students will perform better in formal educational environment such as schools which can be related to the effect of their cognitive style . tinajero & paramo ( 1998 ) stated that the studies in this field show that the field independent students have been performing better in formal educational environment in learning official languages . they argue that the advantage gives students a higher ability in learning official languages which helps him increase his knowledge of second language learning skills and various other skills . the results also showed a significant correlation between the scores of the fdi cognitive styles and course selection ( p < 0.05 ) which is consistent with researches by witkin & goodenough ( 1977 ) . also , applying the tukey s test for this study showed that cognitive styles scores in math and physics students was higher than those of empirical sciences and the cognitive style scores of empirical sciences students were higher than those of the human sciences and art students . witkin & goodenough ( 1977 ) reported that in academic environments , field independent students are inclined to study in mathematics , science , architecture and engineering related fields and field dependent students prefer studying in elementary education , social sciences and psychology . according to research conducted previously and also the findings of this research we can conclude that fdi cognitive styles can play an important role in second language text comprehension skills , academic achievement and second language learning and also the witkin s theory of cognitive styles can play a major role in students major selection . in this study , data analysis showed that field independent cognitive styles of students in formal settings give them the ability to enjoy the academic achievement and also second language text comprehension skills and thus providing educational assistance to field independent students with informal environments will have impact in their different language skills and as a result their academic achievement . besides , the result of the study showed that students with field independent cognitive styles are more inclined to math and physics and empirical sciences majors and the filed dependent students were more willing toward the human sciences and art majors with which students can be directed toward the majors which suits their cognitive styles . individual differences and cognitive styles should be considered in foreign language teaching and learning acquisition theories . although the cognitive process of acquiring a second language is not easily discovered and defined , understanding the cognitive styles helps clarify our understanding of language learning .

background : the learning styles are the distinctive learners strategies for information processing and discovering new concepts . one of the most important kinds of learning styles is the witkin s theory of field dependence - independence cognitive style.objective:this study seeks to find the relationship between field dependence independence cognitive style and english text reading comprehension , learning english as a foreign language , academic achievement and the choice of academic courses.methods:in this study , 305 students ( both girls and boys ) studying at the junior level at high school in sari were randomly selected through multistage selection who responded to group embedded figures test ( geft).results : the data analysis was conducted by using regression analysis which showed that fdi cognitive styles determined the changes in dependant variables of reading comprehension score , learning english and the total average with the respective values of % 8.8 , % 9.2 and % 11.6 ( p < 0.05).conclusion : regarding the findings , it can be concluded that the more field independent , the higher the reading comprehension skills and learning english and the more academic achievement will result . the results of this study can help in selecting students courses and also better directing the learners to improve their learning .

<s>[INST]one of the issues which received much emphasis and consideration in recent decades is the learners styles and learning strategies . considering all the researches , it is evident that the witkin s theory of field dependent - independent cognitive styles due to their increasing applications were extensively used in many researches . learning styles are the beliefs , preferences and behaviors that people employ in order to learn in a certain situation ( 1 ) . in cognitive style , they are inclined to overall field learning and tend to get the whole idea whereas the field independent learners conduct an analytical procedure and are more likely to break a model into different sections and details and tend to depend on their inner knowledge and analyze problems all by themselves without reference to the frame or the environment ( 2 - 4 ) . considering field dependent - independent cognitive styles effects on teaching and learning , and especially on the students course selection , studies show that field independent student had better academic achievement than field - dependent students ( 5 ) . the research by al - saai & dwyer ( 1993 ) also showed that if the educational subjects and materials conform to students cognitive styles , it will lead to a better achievement ( 6 ) . also , the studies revealed that if the field dependents and field independents are placed in homogeneous groups compared with being in the heterogeneous groups , they would show a better improvement the research by al - saai & dwyer ( 1993 ) also showed that if the educational subjects and materials conform to students cognitive styles , it will lead to a better achievement ( 7 ) . studies have shown that field independent learners performed better than field dependent in learning english language ( 8) . pointing to the gender differences on learning styles , hickson & baltimore ( 1996 ) have shown that men and women have different learning styles ( 9 ) . the researches on the relationship between cognitive styles and courses selection also revealed that there is a positive relationship between field independent cognitive styles and science courses selection and also field dependent and social sciences and human resources major selection ( 10 ) . therefore , regarding the researches conducted on this issue , this study seeks to examine the following research questions : is there any relationship between field dependent independent cognitive style and reading comprehension skill and english learning ? is there any relationship between the cognitive field dependent independent styles and academic achievement ? is there a difference between the average scores of witkin s theory of cognitive style in different high school majors ? the study samples consisted of all students studying at junior level of high school in sari , in the academic year of 2010 - 2011 . the numbers of students comprised to 1476 from those 305 were selected for the study . to determine the sample size , multistage cluster sampling was conducted to randomly select the sample . to measure the field dependency this test was used by witkin ( 2 ) in 1971 to measure the youngsters and adults field dependence - independence cognitive style . the reliability of the test was calculated by oltman and colleagues for men and for women as 0.82 & 0.79 , respectively . the criterion - related validity for men was 0.82 and for women 0.63 ( 11 ) . in addition , in this study , each subject s score in english for the first semester in the academic year of 2010 - 2011 was regarded as a criterion for his progress in learning english . in order to evaluate the different skills in students learning english at high school , we used the standard expert revised test which are used at national level and have objective scores . each student s score in reading comprehension was used as a criterion for students reading comprehension ability . then , the average score of all the lessons at the end of the semester was set as a criterion for assessing the student s achievement . the first research question : a ) is there any relationship between field dependent independent cognitive style and reading comprehension skill and english learning ? linear correlation between fdi cognitive style and reading comprehension skill and english learning regarding the table above , the correlation is about 0.296 and the determination coefficient is 0.088 which shows that 8.8% of the changes in the reading comprehension can be evaluated by the fdi ( field dependence / independence ) cognitive style . the regression analysis results showed that the correlation is significant at 0.05 and the null hypothesis is rejected and the research hypothesis is confirmed ( p<05 ) . therefore , it can be concluded that there is a significant linear relationship between fdi cognitive styles and reading comprehension . it can also be seen from the above table that the values associated with this style and learning english is equal to 0.304 and the determination coefficient equals to 0.092 , which shows that 9.2% of the changes in learning english can be explained by fdi cognitive style . the regression analysis results showed that the correlation is significant at 0/05 and the null hypothesis is rejected and the research hypothesis is confirmed ( p<05 ) . therefore , it can be concluded that there is a significant linear relationship between fdi cognitive styles and learning english . the second research question is there any relationship between the cognitive field dependent independent styles and academic achievement ? linear relationship between fdi cognitive style and academic achievement it can be witnessed that the correlation value equals to .341 and determination coefficient was equal to 0.116 which indicates that 11.6 of changes in academic achievement can be explained by fdi cognitive style . the regression analysis results showed that the correlation is significant at 0.05 and the null hypothesis is rejected and the research hypothesis is confirmed ( p<05 ) . therefore , it can be concluded that there is a significant linear relationship between fdi cognitive styles and academic achievement . the third research question is there a difference between the average scores of witkin s cognitive style in different high school majors ? the comparison of students cognitive styles averages based on their academic majors it can be seen from the given table that at the significant level of 0/05 , the differences between the students cognitive styles in various high school majors is significant because the achieved p - value is less than 0.05 , therefore , the null hypothesis is rejected and the research hypothesis is confirmed . so it can be stated that the students cognitive styles in different majors at high school are different . in order to determine the difference between the means , the tukey follow up test was used . by comparing the scores in table 4 , it can be inferred that the cognitive style scores in math students was higher than that of the students in the empirical sciences , and the empirical sciences students score was higher than the scores of students at human sciences and art students . comparison of the theoretical basis of cognitive styles multiple means using tukey follow - up test the general objective of this study was to examine the relationship between field dependent / independent cognitive styles of the students at the third year of secondary school for their reading comprehension skills . the results showed that there is a significant correlation between fdi cognitive styles and reading comprehension skill , english language learning and academic achievement at ( p < 0/.5 ) so that the fdi cognitive styles would explain 8/8% , 9/2% and 11/6% of students reading comprehension skills , learning english and academic achievement , respectively , which is congruent with the studies conducted by such ( 12 - 14 ) quoted by tinajero&paramo ( 1997 ) ( 12 ) . regarding such results we can say that fdi cognitive styles have important roles in learning and academic achievement . field independent students will perform better in formal educational environment such as schools which can be related to the effect of their cognitive style . tinajero & paramo ( 1998 ) stated that the studies in this field show that the field independent students have been performing better in formal educational environment in learning official languages . they argue that the advantage gives students a higher ability in learning official languages which helps him increase his knowledge of second language learning skills and various other skills . the results also showed a significant correlation between the scores of the fdi cognitive styles and course selection ( p < 0.05 ) which is consistent with researches by witkin & goodenough ( 1977 ) . also , applying the tukey s test for this study showed that cognitive styles scores in math and physics students was higher than those of empirical sciences and the cognitive style scores of empirical sciences students were higher than those of the human sciences and art students . witkin & goodenough ( 1977 ) reported that in academic environments , field independent students are inclined to study in mathematics , science , architecture and engineering related fields and field dependent students prefer studying in elementary education , social sciences and psychology . according to research conducted previously and also the findings of this research we can conclude that fdi cognitive styles can play an important role in second language text comprehension skills , academic achievement and second language learning and also the witkin s theory of cognitive styles can play a major role in students major selection . in this study , data analysis showed that field independent cognitive styles of students in formal settings give them the ability to enjoy the academic achievement and also second language text comprehension skills and thus providing educational assistance to field independent students with informal environments will have impact in their different language skills and as a result their academic achievement . besides , the result of the study showed that students with field independent cognitive styles are more inclined to math and physics and empirical sciences majors and the filed dependent students were more willing toward the human sciences and art majors with which students can be directed toward the majors which suits their cognitive styles . individual differences and cognitive styles should be considered in foreign language teaching and learning acquisition theories . although the cognitive process of acquiring a second language is not easily discovered and defined , understanding the cognitive styles helps clarify our understanding of language learning .[/INST]background : the learning styles are the distinctive learners strategies for information processing and discovering new concepts . one of the most important kinds of learning styles is the witkin s theory of field dependence - independence cognitive style.objective:this study seeks to find the relationship between field dependence independence cognitive style and english text reading comprehension , learning english as a foreign language , academic achievement and the choice of academic courses.methods:in this study , 305 students ( both girls and boys ) studying at the junior level at high school in sari were randomly selected through multistage selection who responded to group embedded figures test ( geft).results : the data analysis was conducted by using regression analysis which showed that fdi cognitive styles determined the changes in dependant variables of reading comprehension score , learning english and the total average with the respective values of % 8.8 , % 9.2 and % 11.6 ( p < 0.05).conclusion : regarding the findings , it can be concluded that the more field independent , the higher the reading comprehension skills and learning english and the more academic achievement will result . the results of this study can help in selecting students courses and also better directing the learners to improve their learning .</s>

SECTION 1. SHORT TITLE. This Act shall be cited as the ``Denver Federal Center Redevelopment Act''. SEC. 2. DENVER FEDERAL CENTER DEVELOPMENT AUTHORITY. Part C of subtitle II of title 40, United States Code, is amended by adding at the end thereof the following new chapter: ``CHAPTER 71--DENVER FEDERAL CENTER DEVELOPMENT ``Sec. 7101. Master lease development authority ``(a) In General.--The Administrator of General Services may enter into leases of Federal real property, including improvements thereon, with totally non-Federal entities to provide for the construction, rehabilitation, operation, maintenance, or use of all, or portions of, the Denver Federal Center as described in section 7106, or such other activities related to the Denver Federal Center as the Administrator considers appropriate. For purposes of this chapter, a lease of Federal real property, including improvements thereon, shall be referred to as a master lease. ``(b) Terms and Conditions.--A master lease entered into under this section-- ``(1) shall have as its primary purpose enhancing the value of the Denver Federal Center to the United States; ``(2) shall be negotiated pursuant to such procedures as the Administrator considers necessary to ensure the integrity of the selection process and to protect the interests of the United States; ``(3) may provide a lease option to the United States, to be exercised at the discretion of the Administrator, to occupy any general purpose office, storage or other usable space in a facility covered under the master lease; ``(4) shall be for a term not to exceed 50 years; ``(5) shall describe the consideration, duties and responsibilities for which the United States and the non- Federal entity are responsible; ``(6) shall provide-- ``(A) that all development risk shall remain with the non-Federal entity; ``(B) that the United States will not be liable for any action, debt or liability of any non-Federal entity; and ``(C) that such non-Federal entity may not execute any instrument or document creating or evidencing any indebtedness unless such instrument or document specifically disclaims any liability of the United States under the instrument or document; and ``(7) shall include such other terms and conditions as the Administrator considers appropriate. ``(c) Consideration.--A master lease entered into under this section shall be for fair consideration, as determined by the Administrator. Consideration under a master lease may be provided in whole or in part through in-kind consideration, including provision of other real and related property, goods or services of benefit to the United States, construction, repair, remodeling, or other physical improvements of Federal property, environmental remediation or maintenance of Federal property, or the provision of office, storage or other usable space. ``Sec. 7102. Additional authorities ``(a) Authority To Convey Remaining Interests.--In carrying out a master lease entered into under this chapter, the Administrator is authorized to convey the interest of the United States in the property covered by the master lease to the non-Federal entity by sale or exchange, if the Administrator first determines in writing that such conveyance is in the interests of the United States; ``(b) Other Authorities Not Affected.--The authority to enter into a master lease under this chapter shall be in addition to, and not in lieu of, any other authorities of the Administrator to convey interests in real property by lease, sale, or exchange. ``(c) Obligations To Make Payments.-- Any obligation to make payments by the Administrator for the use of space, goods or services by the General Services Administration on property that is subject to a master lease under this chapter may only be made to the extent that necessary funds have been made available to the Administrator, in advance, in an annual appropriations Act. ``Sec. 7103. Relationship to other laws ``(a) In General.--The authority of the Administrator under this chapter shall not be subject to-- ``(1) sections 521 through 529 and sections 541 through 559; ``(2) section 1302; ``(3) section 3307; or ``(4) any other provision of law (other than Federal laws relating to environmental and historic preservation) inconsistent with this chapter. ``(b) Unutilized or Underutilized Property.--Any property covered under a master lease entered into under this section shall be deemed to be property for which there is a continuing Federal need and may not be considered to be unutilized or underutilized for purposes of section 501 of the McKinney-Vento Homeless Assistance Act (42 U.S.C. 11411). ``Sec. 7104. Use of proceeds ``(a) In General.--Net proceeds from a master lease entered into under section 7101 shall be deposited into, administered, and expended, subject to appropriations Acts, as part of the Federal Building Fund established under section 592. In this section, the term `net proceeds from a master lease entered into under section 7101' means the rental proceeds from the master lease minus the expenses incurred by the Administrator with respect to the master lease. ``(b) Recovery of Expenses.--The Administrator may retain from the proceeds of a master lease entered into under section 7101 amounts necessary to recover the expenses incurred by the Administrator with respect to the master lease. Such amounts shall be deposited in the account in the Treasury from which the Administrator incurs such expenses. ``Sec. 7105. Reporting requirements ``(a) In General.--Before entering into a master lease under section 7101, the Administrator of General Services shall transmit to the appropriate Committees of Congress a report on the proposed development and master lease of the Denver Federal Center not less than 30 days before the award of a master lease; ``(b) Contents.--A report transmitted under this section shall include a summary of a cost-benefit analysis of the proposed development and a description of the provisions of the proposed master lease. ``Sec. 7106. Description of the Denver Federal Center ``As used in this chapter, the term `Denver Federal Center' means a parcel of land, located in section 9 and in the East half of the East half of the East half Section 8, Township 4 South, Range 69 West of the Sixth Principal Meridian, being more particularly described as follows: ``Commencing at the northeast corner of said section 9; ``thence S76 deg.38'34"W a distance of 779.20 feet to a point on the southerly right-of-way line of West 6th Avenue being also the true point of beginning; ``thence S45 deg.23'16"E a distance of 932.42 feet to a point on the westerly right-of-way line of Kipling Street; ``thence along the westerly right-of-way line of said Kipling Street the following three courses: ``thence S00 deg.23'16"E, a distance of 1806.59 feet; ``thence S00 deg.23'04"E, a distance of 2341.02 feet; ``thence S44 deg.37'45"W, a distance of 355.19 feet to a point on the northerly right-of-way line of West Alameda Avenue; ``thence along the northerly right-of-way line of said West Alameda Avenue the following three courses: ``thence S89 deg.23'50"W, a distance of 2298.81 feet; ``thence S89 deg.24'08"W, a distance of 2544.90 feet to a point of tangent curve; ``thence along said curve to the left an arc distance of 475.81 feet, having a central angle of 11 deg.38'25", a radius of 2342.00 feet and a chord bearing of S83 deg.31'57"W, a chord distance of 474.99 feet to a point on the south line of the southeast quarter of said section 8; ``thence S89 deg.37'30"W, along the said south line, a distance of 296.29 feet to a point on the westerly line of the east half of the east half of the east half of said section 8; ``thence along the westerly line of the east half of the east half of the east half of said section 8 the following two courses: ``thence N00 deg.00'10"W, a distance of 2634.40 feet; thence N00 deg.00'33"W, a distance of 2344.86 feet to a point on the southerly right-of-way line of West 6th Avenue; ``thence along said southerly right-of-way line the following five courses: ``thence N89 deg.44'33"E, a distance of 655.37 feet to a point on the westerly line of the northwest quarter of said section 9; ``thence N89 deg.44'33"E, a distance of 50.00 feet; ``thence N81 deg.11'33"E, a distance of 856.70 feet; ``thence N89 deg.14'41"E, a distance of 1741.83 feet; ``thence N89 deg.14'40"E, a distance of 1876.55 feet to the point of beginning. ``Said parcel contains 29,182,824 square feet or 669.95 acres, more or less. ``Note: For the purpose of this description the bearings are based on the east line of the northeast quarter of said section 9 bearing S00 deg.23'16"E, a distance of 2640.79 feet and monumented by a found 3\1/4\" aluminum cap marked `l.p.i. pls 34986' on the north end and by a found 3\1/4\" aluminum cap marked `vigil land consultants ls 20699' on the south end.''. SEC. 3. CONFORMING AMENDMENT. The index for part C of subtitle II of title 40, United States Code, is amended by inserting the following at the end thereof: ``Chapter 71--Denver Federal Center Development''.

Denver Federal Center Redevelopment Act - Authorizes the Administrator of General Services to enter into leases of Federal real property, including improvements thereon, with totally nonfederal entities to provide for the construction, rehabilitation, operation, maintenance, or use of all, or portions of, the Denver Federal Center. Lists terms and conditions for such a lease (master lease), including that it: (1) have as its primary purpose enhancing the value of the Center; (2) be negotiated pursuant to such procedures as the Administrator considers necessary to ensure the integrity of the selection process and to protect U.S. interests; (3) be for a term not to exceed 50 years; and (4) provide that all development risk remain with the nonfederal entity. Directs that a master lease be for fair consideration. Requires that net proceeds from a master lease be deposited into, administered, and expended, subject to appropriations Acts, as part of the Federal Building Fund. Authorizes the Administrator to retain from the proceeds of a master lease amounts necessary to recover the expenses incurred by the Administrator with respect to such lease.

<s>[INST]SECTION 1. SHORT TITLE. This Act shall be cited as the ``Denver Federal Center Redevelopment Act''. SEC. 2. DENVER FEDERAL CENTER DEVELOPMENT AUTHORITY. Part C of subtitle II of title 40, United States Code, is amended by adding at the end thereof the following new chapter: ``CHAPTER 71--DENVER FEDERAL CENTER DEVELOPMENT ``Sec. 7101. Master lease development authority ``(a) In General.--The Administrator of General Services may enter into leases of Federal real property, including improvements thereon, with totally non-Federal entities to provide for the construction, rehabilitation, operation, maintenance, or use of all, or portions of, the Denver Federal Center as described in section 7106, or such other activities related to the Denver Federal Center as the Administrator considers appropriate. For purposes of this chapter, a lease of Federal real property, including improvements thereon, shall be referred to as a master lease. ``(b) Terms and Conditions.--A master lease entered into under this section-- ``(1) shall have as its primary purpose enhancing the value of the Denver Federal Center to the United States; ``(2) shall be negotiated pursuant to such procedures as the Administrator considers necessary to ensure the integrity of the selection process and to protect the interests of the United States; ``(3) may provide a lease option to the United States, to be exercised at the discretion of the Administrator, to occupy any general purpose office, storage or other usable space in a facility covered under the master lease; ``(4) shall be for a term not to exceed 50 years; ``(5) shall describe the consideration, duties and responsibilities for which the United States and the non- Federal entity are responsible; ``(6) shall provide-- ``(A) that all development risk shall remain with the non-Federal entity; ``(B) that the United States will not be liable for any action, debt or liability of any non-Federal entity; and ``(C) that such non-Federal entity may not execute any instrument or document creating or evidencing any indebtedness unless such instrument or document specifically disclaims any liability of the United States under the instrument or document; and ``(7) shall include such other terms and conditions as the Administrator considers appropriate. ``(c) Consideration.--A master lease entered into under this section shall be for fair consideration, as determined by the Administrator. Consideration under a master lease may be provided in whole or in part through in-kind consideration, including provision of other real and related property, goods or services of benefit to the United States, construction, repair, remodeling, or other physical improvements of Federal property, environmental remediation or maintenance of Federal property, or the provision of office, storage or other usable space. ``Sec. 7102. Additional authorities ``(a) Authority To Convey Remaining Interests.--In carrying out a master lease entered into under this chapter, the Administrator is authorized to convey the interest of the United States in the property covered by the master lease to the non-Federal entity by sale or exchange, if the Administrator first determines in writing that such conveyance is in the interests of the United States; ``(b) Other Authorities Not Affected.--The authority to enter into a master lease under this chapter shall be in addition to, and not in lieu of, any other authorities of the Administrator to convey interests in real property by lease, sale, or exchange. ``(c) Obligations To Make Payments.-- Any obligation to make payments by the Administrator for the use of space, goods or services by the General Services Administration on property that is subject to a master lease under this chapter may only be made to the extent that necessary funds have been made available to the Administrator, in advance, in an annual appropriations Act. ``Sec. 7103. Relationship to other laws ``(a) In General.--The authority of the Administrator under this chapter shall not be subject to-- ``(1) sections 521 through 529 and sections 541 through 559; ``(2) section 1302; ``(3) section 3307; or ``(4) any other provision of law (other than Federal laws relating to environmental and historic preservation) inconsistent with this chapter. ``(b) Unutilized or Underutilized Property.--Any property covered under a master lease entered into under this section shall be deemed to be property for which there is a continuing Federal need and may not be considered to be unutilized or underutilized for purposes of section 501 of the McKinney-Vento Homeless Assistance Act (42 U.S.C. 11411). ``Sec. 7104. Use of proceeds ``(a) In General.--Net proceeds from a master lease entered into under section 7101 shall be deposited into, administered, and expended, subject to appropriations Acts, as part of the Federal Building Fund established under section 592. In this section, the term `net proceeds from a master lease entered into under section 7101' means the rental proceeds from the master lease minus the expenses incurred by the Administrator with respect to the master lease. ``(b) Recovery of Expenses.--The Administrator may retain from the proceeds of a master lease entered into under section 7101 amounts necessary to recover the expenses incurred by the Administrator with respect to the master lease. Such amounts shall be deposited in the account in the Treasury from which the Administrator incurs such expenses. ``Sec. 7105. Reporting requirements ``(a) In General.--Before entering into a master lease under section 7101, the Administrator of General Services shall transmit to the appropriate Committees of Congress a report on the proposed development and master lease of the Denver Federal Center not less than 30 days before the award of a master lease; ``(b) Contents.--A report transmitted under this section shall include a summary of a cost-benefit analysis of the proposed development and a description of the provisions of the proposed master lease. ``Sec. 7106. Description of the Denver Federal Center ``As used in this chapter, the term `Denver Federal Center' means a parcel of land, located in section 9 and in the East half of the East half of the East half Section 8, Township 4 South, Range 69 West of the Sixth Principal Meridian, being more particularly described as follows: ``Commencing at the northeast corner of said section 9; ``thence S76 deg.38'34"W a distance of 779.20 feet to a point on the southerly right-of-way line of West 6th Avenue being also the true point of beginning; ``thence S45 deg.23'16"E a distance of 932.42 feet to a point on the westerly right-of-way line of Kipling Street; ``thence along the westerly right-of-way line of said Kipling Street the following three courses: ``thence S00 deg.23'16"E, a distance of 1806.59 feet; ``thence S00 deg.23'04"E, a distance of 2341.02 feet; ``thence S44 deg.37'45"W, a distance of 355.19 feet to a point on the northerly right-of-way line of West Alameda Avenue; ``thence along the northerly right-of-way line of said West Alameda Avenue the following three courses: ``thence S89 deg.23'50"W, a distance of 2298.81 feet; ``thence S89 deg.24'08"W, a distance of 2544.90 feet to a point of tangent curve; ``thence along said curve to the left an arc distance of 475.81 feet, having a central angle of 11 deg.38'25", a radius of 2342.00 feet and a chord bearing of S83 deg.31'57"W, a chord distance of 474.99 feet to a point on the south line of the southeast quarter of said section 8; ``thence S89 deg.37'30"W, along the said south line, a distance of 296.29 feet to a point on the westerly line of the east half of the east half of the east half of said section 8; ``thence along the westerly line of the east half of the east half of the east half of said section 8 the following two courses: ``thence N00 deg.00'10"W, a distance of 2634.40 feet; thence N00 deg.00'33"W, a distance of 2344.86 feet to a point on the southerly right-of-way line of West 6th Avenue; ``thence along said southerly right-of-way line the following five courses: ``thence N89 deg.44'33"E, a distance of 655.37 feet to a point on the westerly line of the northwest quarter of said section 9; ``thence N89 deg.44'33"E, a distance of 50.00 feet; ``thence N81 deg.11'33"E, a distance of 856.70 feet; ``thence N89 deg.14'41"E, a distance of 1741.83 feet; ``thence N89 deg.14'40"E, a distance of 1876.55 feet to the point of beginning. ``Said parcel contains 29,182,824 square feet or 669.95 acres, more or less. ``Note: For the purpose of this description the bearings are based on the east line of the northeast quarter of said section 9 bearing S00 deg.23'16"E, a distance of 2640.79 feet and monumented by a found 3\1/4\" aluminum cap marked `l.p.i. pls 34986' on the north end and by a found 3\1/4\" aluminum cap marked `vigil land consultants ls 20699' on the south end.''. SEC. 3. CONFORMING AMENDMENT. The index for part C of subtitle II of title 40, United States Code, is amended by inserting the following at the end thereof: ``Chapter 71--Denver Federal Center Development''.[/INST]Denver Federal Center Redevelopment Act - Authorizes the Administrator of General Services to enter into leases of Federal real property, including improvements thereon, with totally nonfederal entities to provide for the construction, rehabilitation, operation, maintenance, or use of all, or portions of, the Denver Federal Center. Lists terms and conditions for such a lease (master lease), including that it: (1) have as its primary purpose enhancing the value of the Center; (2) be negotiated pursuant to such procedures as the Administrator considers necessary to ensure the integrity of the selection process and to protect U.S. interests; (3) be for a term not to exceed 50 years; and (4) provide that all development risk remain with the nonfederal entity. Directs that a master lease be for fair consideration. Requires that net proceeds from a master lease be deposited into, administered, and expended, subject to appropriations Acts, as part of the Federal Building Fund. Authorizes the Administrator to retain from the proceeds of a master lease amounts necessary to recover the expenses incurred by the Administrator with respect to such lease.</s>

n - methyl - d - aspartate ( nmda ) receptors are members of the family of ionotropic glutamate receptors that mediate excitatory neurotransmission . nmda receptors are tetrameric assemblies of two glun1 subunits , which bind the coagonist glycine , and two glun2 subunits , which bind glutamate . both glun1 and glun2 subunits share a similar architecture , comprised of an extracellular amino - terminal domain ( atd ) , an extracellular ligand - binding domain ( lbd ) , a transmembrane domain ( tmd ) , and an intracellular carboxyl - terminal domain ( ctd ) . the glun2 subunit is encoded by four distinct gene products ( glun2a - d ) , which have temporally and spatially distinct expression patterns in the brain . the glun2 subunit controls pharmacological characteristics such as agonist sensitivity , deactivation time course , mean open time , and open probability . the distinct anatomical locations of the glun2 subunits could allow subunit - selective modulators ( either potentiators or inhibitors ) to target specific brain regions for therapeutic gain . nmda receptors are thought to play a role in neuronal development , learning , and memory formation , as well as being implicated in ischemia , dementia , schizophrenia , treatment resistant depression , and parkinson s disease . recently discovered modulators have demonstrated selectivity for glun2a , 3-chloro-4-fluoro - n-[4-[[2-(phenylcarbonyl)hydrazino]carbonyl]benzyl]benzenesulfonamide ( tcn201 ) ; glun2a / glun2b , 9-cyclopropylphenanthrene-3-carboxylic acid ( ubp710 ) ; and glun2c / glun2d , ( 3-chlorophenyl ) [ 3,4-dihydro-6,7-dimethoxy-1-[(4-methoxyphenoxy)methyl]-2(1h)-isoquinolinyl]methanone ( ciq ) , 4-[6-methoxy-2-[(1e)-2-(3-nitrophen yl)ethenyl]-4-oxo-3(4h)quinazolinyl]benzoic acid ( qnz46 ) , 5-(4-bromophenyl)-3-(1,2-dihydro-6- methyl-2-oxo-4-phenyl-3-quinolinyl)-4,5-dihydro - g - oxo-1h - pyrazole-1-butanoic acid ( dqp1105 ) , and ( 2r,3s)-1-(phenanthrenyl-3-carbonyl)piperazine-2,3-dicarboxylic acid ( ubp141 ) . here , we describe the development of the first class of positive allosteric modulators that are selective for glun2c - containing nmda receptors over glun2a- , glun2b- , and glun2d - containing receptors . to identify this class of ligands , a glun1/glun2c cell line and multiwell fluorescence - based assay were developed to enable screening of compound libraries for nmda receptor modulators . we screened two commercial diversity libraries to identify several compounds that modulate glun2c - containing nmda receptors . one of these screening hits established a novel class of subunit - selective potentiators for recombinant glun1/glun2c nmda receptors , exemplified by compound 1 ( figure 1 ) . optimization of the initial lead pyrrolidinone scaffold involved the development of a structure activity relationship , which led to the identification of a novel series of compounds with potency in the low micromolar range and high selectivity for recombinant glun2c - containing receptors over glun2a / b / d - containing nmda receptors . in addition , no detectable potentiation was observed at recombinant ampa , kainate , gaba , glycine , serotonin , nicotinic , or purinergic receptors ( data not shown ) . these analogues represent a novel class of nmda receptor modulators that are highly selective for diheteromeric glun1/glun2c receptor subtypes and provide a useful tool with which to evaluate the physiological role of glun2c in normal and neuropathological conditions . chemical structure of methyl 4-(1-(2-(1h - indol-3-yl)ethyl)-3-acetyl-4-hydroxy-5-oxo-2,5-dihydro-1h - pyrrol-2-yl)benzoate ( compound 1 ) that was identified as a positive modulator using a fluorescence - based screen of compound libraries in a cell line expressing diheteromeric glun1/glun2c nmda receptors . we used bioinformatic searches and medicinal chemistry to obtain analogues for our initial screening hit , compound 1 ( see below ) . both commercially available analogues and compounds synthesized via a mi - component biginelli - like reaction ( scheme 1 ) were assessed at 30 m . we determined the ec50 and maximal potentiation from concentration effect curves for compounds that showed potentiation of more than 120% of control at 30 m . no compounds in this class potentiated glun2a- , glun2b- , or glun2d - containing receptors , suggesting remarkable selectivity for this class ( see below ) . modifications were made at either r , the a - ring , or the b - ring using alternative methodologies to access the appropriate precursor . reaction conditions : ppts , rt , 124 h , 2% to > 99% ( procedure i ) . final compounds 161180 , in which either the a or b ring is replaced , were also prepared using these conditions . addition of diethyl oxalate and sodium ethoxide to a methyl ketone generated a series of pyruvate analogues ( 320 ) containing modifications at r ( scheme 2 ) . only when r was a phenol was it necessary to first protect the hydroxyl group with triisopropyl chloride ( tipscl ) before the addition of diethyl oxalate . reaction conditions : ( a ) diethyl oxalate , naoet , etoh , 0 c to rt , 4 h , 15% to > 99% ( procedure ii ) ; ( b ) tipscl , imidazole , rt , 6 h , > 99% ; ( c ) diethyl oxalate , naoet , etoh , 0 c to rt , 4 h , 28% ( procedure ii ) ; ( d ) tbaf , 0 c to rt , 1 h , 43% . analogues containing disubstituted a - rings were synthesized using several procedures based on the commercially available precursors ( scheme 3 ) . suzuki coupling between dibutyl vinylboronate and the appropriately substituted methyl 4-iodobenzoate , followed by ozonolysis , gave phenols 34 and 35 . alternatively , addition of a grignard reagent and n , n - dimethylformamide ( dmf ) led to isolation of benzaldehyde 36 . finally , anisole 41 was prepared via a dialkylation of both the hydroxyl and carboxylic acid functional groups . reaction conditions : ( a ) 2.0 equiv nbs , ( phcoo)2 , reflux , 4 h , then agno3 , rt , 3 h , 3863% ; ( b ) dibutyl vinylboronate , 5 mol % ( pph3)2pdcl2 , naco3 , reflux , 2 h , 6880% ; ( c ) o3 ; then ( ch3)2s , 78 c to rt , 12 h , 6087% ; ( d ) i - prmgcl , dmf , 15 c to rt , 3 h , 70% ; ( e ) co(g ) , ( pph3)2pdcl2 , naco3 , 110 c , 824% ( procedure iv ) ; ( f ) ch3i , k2co3 , rt , 3 h , 58% . benzaldehydes containing a para - amide ( 4244 ) or para - ester ( 4547 ) substituent were synthesized as illustrated in scheme 4 . primary amide 42 was synthesized from carboxylic acid 155 by generating the acid chloride in situ . standard amide coupling conditions were employed for the preparation of amides 43 and 44 . alkylation of carboxylic acid 155 with the appropriate alkyl iodide afforded esters 45 and 46 , while t - butyl ester 47 was prepared using a method previously described . reaction conditions : ( a ) vilsmeier reagent , aq nh3 , 0 c , 16 h , 30% ; ( b ) rrn where r = h and r = me or where r = r = me , dmap , edci , 0 c to rt , 24 h , 1451% ; ( c ) ri where r = et or r = i - pr , k2co3 , rt , 4 h , 2487% ; ( d ) ( ch3)2nch(ot - bu)2 , reflux , 1/2 h , 81% . an alternative strategy was used to synthesize analogues containing a modification at r starting from pyrrolidinones 1 and 106 ( scheme 5 ) . alternatively , esters 159 and 160 were synthesized from enol 106 using the appropriate acyl chloride and triethylamine . reaction conditions : ( a ) tmsch2n2 , rt , 5 h , 46% ; ( b ) nh4hco2 , reflux , 3 h , 14% ; ( c ) ac2o , pyridine , rt , 6/2 h , 7% ; ( d ) rc(o)cl where r = ch2ch2ch3 or r = ch = ch2 , tea , 30 c , 2 h , 2035% . a fluorescence - based screen of 57504 compounds obtained from asinex and chemdiv libraries was performed in bhk cells with inducible expression of glun1/glun2c receptors . hits were defined as compounds that produced changes that were 2.5 standard deviations away from the average response to maximally effective agonist ( i.e. , glutamate and glycine ) application . in this primary screen , 1% of the compounds met these criteria . compounds that showed potentiation were further evaluated for their ability to produce responses in cells with no nmda receptor expression ( in uninduced cells ) in order to identify false positive hits . false positive results can occur when the compounds directly release ca from intracellular stores , enhance ca channel function , possess fluorescent properties in the excitation / emission range of fluo-4 , or otherwise produce an increase in intracellular ca signal independent of nmda receptor activation . compounds that showed potentiation of glutamate responses in induced cells and did not produce responses in uninduced cells were subsequently studied by two - electrode voltage - clamp recording of nmda receptor responses . a single compound was found to selectively potentiate the glun1/glun2c receptors and did not show any activity at glun2a / b / d - containing nmda receptors expressed in xenopus laevis oocytes ( figure 2a ) . compound 1 , which contains a pyrrolidinone core motif , potentiated glun1/glun2c responses to 238 8.2% of control at 100 m with an ec50 of 24 2.4 m ( n = 12 ) ( figure 2b ) . compound 1 had no agonist activity on its own in that it did not induce current responses in oocytes expressing glun1/glun2c in the absence of glutamate and glycine ( n = 4 ) . in addition , 30 m of compound 1 did not potentiate homomeric recombinant glua1 ampa receptor responses ( 97 1.1% control , n = 16 ) . in addition , 120 m of compound 1 did not potentiate homomeric gluk2 recombinant kainate receptors ( 95 2.3% of control , n = 5 ) . ( a ) current traces for 1 at the glun1/glun2a , glun1/glun2b , glun1/glun2c , and the glun1/glun2d receptors . ( b ) compound 1 selectively potentiates the glun1/glun2c receptor to a fitted maximum of 275 10% with an ec50 of 24 2.4 , n = 12 . ( c ) the ec50 for glycine in the absence and presence of 1 is 0.20 0.01 m ( n = 6 ) and 0.16 0.02 m ( n = 4 ) , respectively . the ec50 for glutamate in the absence and presence of 1 is 0.8 0.07 m ( n = 8) and 1.2 0.04 m ( n = 6 ) , respectively . the presence of 1 did not shift the glycine or glutamate ec50 values significantly . ( d ) the reversal potential is 5.1 0.8 mv when activated by coagonists ( 100 m glutamate and 30 m glycine ) and is 5.0 1.2 mv ( n = 6 ) when the glun1/glun2c receptor is potentiated by 1 . the reversal potential was not significantly shifted in the presence of 1 , suggesting that potentiation is independent of membrane potential . compound 1 ( 68 m ) did not detectably alter the ec50 of glycine or glutamate ( n = 46 ; figure 2c ) . additionally , the reversal potential of glutamate and glycine induced current responses was unchanged in the presence ( 5.0 + 1.2 mv , n = 6 ) or absence ( 5.1 + 0.8 mv , n = 6 ) of compound 1 . potentiation was not significantly different at 40 mv ( 202 11% ) compared to + 30 mv ( 180 12% ; p = 0.2679 ; paired t test ) , indicating that potentiation of glun2c - containing receptors by compound 1 at 20 m was voltage - independent ( n = 6 ; figure 2d ) . we subsequently evaluated the response to 30 m of all pyrrolidinone analogues at glun1/glun2a , glun1/glun2b , glun1/glun2c , and glun1/glun2d and proceeded to determine the concentration exploration of the effects of keto - linked r ( scheme 1 ; see chemistry section ) substitutions on potentiation of glun2c - containing receptors in oocytes revealed that additional steric bulk was tolerated , with only minimal improvements in potency ( table 1 , 6265 ) . for example , replacement of r with a phenyl group , as in 65 , produced a small increase in potency ( ec50 = 17 2.3 ) accompanied by a modest decrease in maximal potentiation compared to compound 1 ( table 1 ) . analogues containing m - substituted phenyl rings ( 6670 ) offered variable potentiation , while analogues with o- and p - substituted phenyl rings were inactive ( data not shown ) . notably , 66 , with a meta - hydroxyl group , displayed a considerably higher potency at glun2c - containing receptors ( 7.0 0.9 m ) but caused significant inhibition of glun2a- , glun2b- , and glun2d - containing receptors at 100 m ( responses were 76 2.0% , 42 1.6% , and 48 2.4% of control , respectively , normalized to agonist activated current ) . such mixed - action modulators that potentiate one subunit while inhibiting another are intriguing but of little utility as pharmacological probes . two compounds containing a pyridine ring at r potentiated responses up to 200% with ec50 values of 12 1.9 m ( 72 ) and 8.9 1.3 m ( 73 ) . interestingly , 71 , which contains a 2-substituted pyridine ring , was inactive at all receptor subunits . these initial experiments confirmed the ability of derivatives within this class to selectively potentiate glun2c - containing receptors compared to other nmda receptor subtypes . fitted ec50 values are shown for glun1/glun2c to two significant figures when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 6 and 12 oocytes from 23 frogs for each compound . when no effect was found ( n = 315 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 3 oocytes all compounds ) . for all tables , glun2 subunits were coexpressed with glun1 in xenopus oocytes and evaluated using two - electrode voltage - clamp recordings . the response to 100 m of test compound was greater than 140% of control . next , we evaluated the effects of various a - ring substituents ( table 2 ) utilizing r substitutions shown to offer the desired activity . one compound , 84 , which contains an ethyl ester at ring position r , displayed comparable potency compared to screening hit 1 . analogues containing bulkier ester substituents ( e.g. , 85 with an iso - propyl ester and 86 with a tert - butyl ester ) led to inactivity . a series of compounds containing ester isosteres including a nitrile ( 87 ) , nitro ( 88 ) , amide ( 8991 ) , and sulfonamide ( 92 and 93 ) were also evaluated for their ability to potentiate glun2c - containing nmda receptors . fitted ec50 values are shown for glun1/glun2c to two significant figures when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 8 and 12 oocytes from 23 frogs for each compound . when no effect was found ( n = 311 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 3 oocytes all compounds ) . a variety of substituents at a - ring positions r and r were systematically tested while holding the para - methyl ester constant at r ( table 3 ) . substitution at the meta position ( r ) revealed either a reduction in potency ( 95 ) or complete inactivity ( 9699 ) . evaluation of a series of ortho ( r ) ring substituents demonstrated a preference for electron donating groups . for example , analogues containing an ortho - hydroxyl ( 100 ) exhibited potentiation with a modest increase in potency , whereas ortho - chloro ( 103 ) or -fluoro ( 104 ) substituents were slightly less active . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response ; hill slopes ranged between 1.3 and 1.8 . data for active compounds at glun1/glun2c are from between 3 and 12 oocytes from 23 frogs for each compound . when no effect was found ( n = 315 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 5 oocytes for all compounds ) . replacement of the b - ring with an assortment of acyclic , cyclic , and heterocyclic systems generated a series of compounds that were evaluated for potency and subunit selectivity while retaining optimal r and a - ring substitutions ( table 4 ) . interestingly , substitution with a napthyl derivative , as in 162 , led to strong inhibition at all four subunits . replacement of the indole nh with an oxygen atom led only to weak activity ( 163 ) , suggesting the presence of a hydrogen bond in the binding pocket . in all other instances , removal of the indole led to complete inactivity ( i.e. , 164 and 165 ) . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . when no effect was found , the lack of effect was confirmed by testing at 100 m ( data not shown , n 3 oocytes for all compounds ) . inhibited at glun1/glun2a with an ic50 of 18 m , at glun1/glun2b with an ic50 of 7.2 m , at glun1/glun2c with an ic50 of 11 m , and glun1/glun2d with an ic50 of 5.7 m . this led us to examine b - ring substituents as an alternative strategy to access increased potency . methylation of the indole nitrogen led to inactivity ( 105 ) , further suggesting the importance of a hydrogen atom at this position in the binding pocket . the best potency was obtained for analogues with substitutions at b - ring position r. compound 111 demonstrated an ability to selectively potentiate glun2c - containing nmda receptors up to 218% with an ec50 value of 4.3 0.3 m . it is unclear whether the increase in potency observed for 111 can be ascribed to a steric effect or , alternatively , to a mildly electropositive effect . consistent with a steric effect , analogues which contain larger r substituents such as r = ome ( 112 ) revealed a loss of potency compared to 111 . analogues containing strongly electron withdrawing r substituents such as r = f ( 109 ) also decreased the observed activity . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 6 and 27 oocytes from 23 frogs for each compound . when no effect was found ( n = 411 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 4 oocytes for all compounds ) . we subsequently evaluated the effect of combining modifications at r , the a - ring and the b - ring that had previously demonstrated an improvement in potency ( table 6 ) . substitution with either a meta- or para - substituted pyridine ring at r and a para - ethyl ester at r revealed potentiation of glun1/glun2c responses with ec50 values of 8.2 0.9 m ( 116 ) and 9.7 0.6 m ( 117 ) , respectively . modification of the b - ring and either r ( r = m - pyridine ) or r ( r = p - co2et ) exhibited a similar increase in on - target potency . for example , substitution with a methyl group at r and a para - ethyl ester at r , as in analogue 119 , resulted in a 2-fold potency enhancement . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 8 and 14 oocytes from 2 frogs for each compound ; the hill slope varied between 1.2 and 1.5 . when no effect was found at 30 m ( n = 36 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 7 oocytes for all compounds ) . the original screening hit , 1 , contains a two carbon region linking the b - ring with the core pyrrolidinone . the linker modifications explored are illustrated in table 7 . both shortening ( 121 ) and extending ( 122 ) the linker eliminated all activity , suggesting that the potency of pyrrolidinone analogues is highly dependent on the length of the carbon linkage . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 7 and 8 oocytes from 2 frogs for each compound tested ; the hill slope varied between 1.3 and 1.4 . when no effect was found at 30 m ( n = 311 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 4 oocytes for all compounds ) . several modifications were made at r to determine the significance of the enol in controlling potency and selectivity ( table 8) . replacement with an amine , as in 157 , led to a complete loss of potentiation at concentrations up to 100 m . in most instances , compounds containing in contrast , propyl ester 159 maintained activity comparable to lead analogue 1 , with an ec50 of 17 1.8 m . these data suggest that enhancements in potency can not be gained though modifications of the enol . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 5 and 9 oocytes from 23 frogs for each compound . the hill slope varied between 1.2 and 1.8 and was fixed to be 1.5 for less potent analogues ( 157 , 159 ) . when no effect was found ( n = 39 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 4 oocytes for all compounds ) . to enable evaluation of potential stereoselectivity for pyrrolidinone analogues at glun1/glun2c , we separated the enantiomers of 106 using a semipreparatory od - rh chiral hplc column ( see chemistry experimentals ) . each enantiomer was subjected to two - electrode voltage clamp analysis in xenopus laevis oocytes . the results , illustrated in figure 3 , indicate that only one enantiomer ( 106a ) is active and may account for the activity of 106 . compound 106a potentiated glun2c response by 259 7.8% with an estimated ec50 value of 18 0.6 m ( n = 6 ) . in contrast , no activity was observed for the other enantiomer ( 106b ) ( n = 6 ) . the active analogue demonstrated weak inhibition at glun2d - containing receptors and had no effect at glun2a- or glun2b - containing receptors . these data suggest that the activity of pyrrolidinone analogues may rely on a single enantiomer and that the binding pocket can distinguish between the enantiomers . effect curves for the enantiomers of 106 demonstrate that only one enantiomer , 106a , is active , potentiating the glun1/glun2c receptor to a fitted maximum of 259 8% of control with an ec50 of 18 0.6 m ( n = 6 ) . the incorporation of a methyl group at the c-7 position of the indole of initial screening hit 1 afforded 111 , which selectively potentiates glun2c - containing nmda receptors with a potency of 4.3 0.3 m . in addition , the activity of this series appears to originate from one enantiomer . these compounds represent the first class of allosteric potentiators selective for diheteromeric glun1/glun2c receptors over receptors containing glun2a- , glun2b- , and glun2d subunits . future studies will address the activity of this series of modulators on triheteromeric glun2c - containing nmda receptors containing two different glun2 subunits ( e.g. , glun1/glun2a this series of molecules may serve as a pharmacological tool to evaluate the role of the glun2c subunit in normal and neuropathological function . all protocols involving xenopus laevis were approved by the emory university institutional animal care and use committee . two - electrode voltage - clamp recordings were made from xenopus laevis oocytes expressing recombinant glun1/glun2a , glun1/glun2b , glun1/glun2c , glun1/glun2d , glua1 , or gluk2 receptors following injection of crna . cdnas for rat glun11a ( genbank accession numbers u11418 and u08261 ; hereafter glun1 ) , glun2a ( d13211 ) , glun2b ( u11419 ) , glun2c ( m91563 ) , glun2d ( l31611 ) , glua1 ( x17184 ) , and gluk2 ( z11548 ) were provided by drs . s. heinemann ( salk institute ) , s. nakanishi ( kyoto university ) , and p. seeburg ( university of heidelberg ) . oocyte isolation , crna synthesis , and crna injection have been previously described ; some experiments were performed with oocytes obtained from ecocyte ( austin , tx ) . voltage - clamp recordings from oocytes were made during perfusion with recording solution containing 90 mm nacl , 1.0 mm kcl , 0.5 mm bacl2 , 0.005 mm edta , and 10 mm hepes at ph 7.4 ( 23 c ) . glass microelectrodes had resistances of 0.31.0 m and were filled with 0.33.0 m kcl ; the membrane potential was held at 40 mv for all recordings . compounds were made as 20 mm stock solutions in dmso and diluted to the final concentration in recording solution ; final dmso content was 0.050.5% ( v / v ) . oocytes expressing gluk2 receptors were pretreated with 10 m concanavalin a for 10 min . nmda receptors were activated by 100 m glutamate plus 30 m glycine ; glua1 and gluk2 receptors were activated by 100 m glutamate . to prevent a gradual increase in current response over the course of the experiment of glun1/glun2a receptor responses in oocytes , some oocytes expressing glun1/glun2a were injected with 2050 nl of 2 mm k - bapta ( potassium 1,2-bis(o - aminophenoxy)ethane - n , n , n,n-tetraacetic acid ) . when the response to agonist in the presence of 30 m of a test compound exceeded 120% of control , the response to glutamate and glycine in the absence and presence of 57 concentrations of active analogues were recorded in multiple oocytes obtained from two or more different frogs for all experiments . the ec50 ( half - maximally effective concentration of potentiator ) was determined by fitting the equation1to the concentration response data normalized to the current in the absence of potentiator ( 100% ) for each oocyte , and the mean ( sem ) presented . n is the hill slope , which ranged between 1 and 2 and is not reported ; maximum is the fitted maximal response expressed as a percent of control to a saturating concentration of potentiator . when responses were inhibited by test compound at 30 m to less than 60% of control , the ic50 value was determined by fitting the equation2to the concentration for some compounds , visual detection of precipitation led to inclusion of 110 mm 2-hydroxypropyl--cyclodextrin in the recording solution to enhance solubility and enable generation of the full concentration response data . to generate a cell line with inducible nmda receptor expression , we used a previously described tet - on ( tetracycline - inducible promoter ; clontech , mountain view , ca ) baby hamster kidney ( bhk-21 , atcc ccl-10 ) cell line . the bhk-21 tet - on cell line was maintained at 37 c , 5% co2 , and 95% relative humidity in culture medium composed of dulbecco s modified eagle medium ( dmem ) containing glutamax - i , 4500 mg / l glucose , and 110 mg / l sodium pyruvate ( invitrogen , carlsbad , ca ) supplemented with penicillin ( 100 units / ml ) , streptomycin ( 100 g / ml ) , ( invitrogen , carlsbad , ca ) , 10% dialyzed fetal bovine serum ( invitrogen , carlsbad , ca ) , and 1 mg / ml g418 ( invitrogen , carlsbad , ca ) . the selection marker g418 was always included to provide continuous selection of tet - on - compatible bhk-21 cells . u11418 ) in the inducible ptre2 vector and rat glun2c ( genbank accession no . d13212 ) in the pci - ires - bla vector ( see ref ( 16 ) for details on this vector ) using fugene 6 transfection reagent ( promega , madison , wi ) . the nmda receptor antagonists dl-2-amino-5-phosphonopentanoate ( ap5 ) ( 200 m ; abcam , cambridge , ma ) and 7-chloro - kynurenate ( 7-cka ) ( 200 m ; abcam , cambridge , ma ) were added to the culture medium to prevent nmda receptor - mediated cell death . the following day , the cells were diluted 1:1000 and 1:10,000 and seeded in 144 mm dishes . the next day ( e.g. , two days after transfection ) , 10 g / ml blasticidin s ( invivogen , san diego , ca ) was added to the culture medium to select for transfected cells . unless otherwise stated , the culture medium for the cell lines always contained 1 mg / ml g418 and 10 g / ml blasticidin s for selection as well as 200 m ap5 and 200 m dcka to prevent nmda receptor - mediated cell death . the media was changed every 23 days , and blasticidin s - resistant clones were isolated 1020 days after transfection and evaluated for their response properties . fluorescence - based assays were conducted as previously described , and test compounds were screened at 10 m . purity of purchased compounds was greater than 90% , as determined by the suppliers , via hplc or nmr . precoated glass plates ( silica gel 60 f254 , 0.25 mm ) were used to monitor the progress of reactions by thin layer chromatography ( tlc ) . purification by flash column chromatography was performed on a teledyne isco combiflash companion using prepackaged teledyne redisep disposable normal phase silica columns . h and c nmr experiments were each carried out on an inova-400 ( 400 mhz ) , vnmr 400 ( 400 mhz ) , inova-600 ( 600 mhz ) , unity-600 ( 600 mhz ) , or mercury 300 vx ( 300 mhz ) . all chemical shifts are reported in parts per million and referenced to the residual solvent peak . mass spectra were performed by the emory university mass spectrometry center on a vg 70-s nier johnson or jeol instrument . purity of all final compounds was found to be 95% by lc / ms analysis unless otherwise noted . the separation of the enantiomers of 106 was obtained using a chiralpak od - rh 30 mm 250 mm , 5 m column with the following conditions : flow rate 10 ml / min , injection volume 12 ml ( 5 mg / ml ) , 44% acn/66% water with 0.1% formic acid ; 106atr = 121.3 min ; 106btr = 129.3 min . enantiomeric excess ( ee ) of both enantiomers 106a and 106b was determined using a chiralpak od - rh 4.6 mm 150 mm , 5 m column with the following conditions : flow rate 0.5 ml / min , injection volume 10 l , 44% acn/66% water with 0.1% formic acid ; 106a [ ]d20 18 ( c = 0.10 , methanol ) , tr = 26.1 min , 98% ee ; 106b [ ]d20 + 9 ( c = 0.10 , methanol ) , tr = 29.1 min , 96% ee . a perkin - elmer 314 instrument was used to obtain optical rotation data . to a stirred solution of aldehyde ( 1.0 mmol ) in dioxane ( 1.0 m ) was added tryptamine ( 1.0 equiv ) and 10 mol % pyridinium 4-methylbenzenesulfonate . upon the formation of a slurry , methyl acetopyruvate ( 1.0 equiv ) was added . the resulting mixture was allowed to stir at rt for up to 12 h. in most instances , a precipitate was visible , which was collected via filtration and washed with et2o . the solid was dissolved in an appropriate solvent and washed with saturated ammonium chloride and brine before being dried over mgso4 , filtered , and concentrated in vacuo . if a precipitate did not form , the mixture was concentrated in vacuo before being subjected to the workup as described above . purification was achieved via flash column chromatography on sio2 ( meoh / dcm ) to afford the desired pyrrolidinone . additional purification was obtained by hplc ( 85% acn/15% water with 0.1% formic acid ) as needed . to a solution of sodium ethanolate ( 1.0 equiv ) in etoh ( 0.72 m ) at 0 c was added a mixture of diethyl oxalate ( 1.0 equiv ) and ethanone ( 1.0 mmol ) over 20 min . the mixture was allowed to stir at rt for 4 h. in most instances , a precipitate had formed which was collected via filtration and washed with absolute etoh . if no precipitate was evident , a minimal amount of water was added and the mixture was concentrated in vacuo . the residue was dissolved in water , neutralized with acetic acid , and extracted with et2o ( 3 ) . the combined organic layers were dried over mgso4 , filtered , and concentrated in vacuo . purification was achieved as needed via flash column chromatography on sio2 ( hexanes / etoac : 4/1 ) to obtain the product . to a solution of 4-bromobenzoic acid ( 1.0 mmol ) in thf : meoh ( 4:1 , 0.3 m ) at 0 c was added ( diazomethyl)trimethylsilane ( 2.4 equiv ) . the reaction was allowed to warm to rt over the period of 1 h. at this time , the mixture was concentrated in vacuo and 1.0 m hcl was added . the mixture was extracted with etoac ( 2 ) , dried over mgso4 , filtered , and concentrated in vacuo to afford the product . to a solution of methyl 4-bromobenzoate ( 1.0 mmol ) in dmf ( 0.6 m ) was added 17 mol % bis(triphenylphosphine)palladium(ii ) dichloride and sodium formate ( 1.5 equiv ) . the reaction mixture was stirred at 110 c under a steady stream of co(g ) for 2 h. at this time , the mixture was cooled to rt , diluted with saturated sodium carbonate , and extracted with etoac ( 2 ) . the combined organic layers were washed with brine , dried over mgso4 , filtered , and concentrated in vacuo . purification was achieved via flash column chromatography on sio2 ( hexanes / etoac : 3/1 ) to yield the desired product , which was taken on without further purification . compound 1 was prepared via procedure i from methyl 4-formylbenzoate ( 3.0 g , 18 mmol ) , tryptamine ( 2.9 g , 18 mmol ) , and methyl acetopyruvate ( 2.6 g , 18 mmol ) to yield a cream - colored solid ( 5.5 g , 72% ) . h nmr ( 400 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.88 ( d , j = 8.0 hz , 2h ) , 7.337.24 ( m , 4h ) , 7.127.03 ( m , 2h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.17 ( s , 1h ) , 3.83 ( s , 3h ) , 3.833.77 ( m , 1h ) , 3.002.90 ( m , 1h ) , 2.872.80 ( m , 1h ) , 2.742.67 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 165.6 , 165.1 , 142.5 , 136.3 , 129.3 , 128.1 , 126.9 , 125.5 , 122.9 , 121.2 , 121.1 , 118.4 , 118.3 , 118.1 , 111.6 , 111.5 , 110.8 , 66.4 , 59.8 , 52.2 , 40.8 , 23.6 ; mp 99105 c . hms ( apci ) calcd for c24h22n2o5 419.1607 ; found 419.1606 [ m + h ] . compound 62 was prepared via procedure i from methyl 4-formylbenzoate ( 0.095 g , 0.58 mmol ) , tryptamine ( 0.93 g , 0.58 mmol ) , and 3 ( 0.10 g , 0.58 mmol ) to yield a cream - colored solid ( 0.16 g , 64% ) . h nmr ( 400 mhz , dmso - d6 ) 10.84 ( s , 1h ) , 7.87 ( d , j = 8.4 hz , 2h ) , 7.337.23 ( m , 4h ) , 7.09 ( d , j = 2.4 hz , 1h ) , 7.05 ( t , j = 8.0 hz , 1h ) , 6.91 ( t , j = 6.8 hz , 1h ) , 5.17 ( s , 1h ) , 3.833.76 ( m , 4h ) , 2.962.89 ( m , 1h ) , 2.862.79 ( m , 1h ) , 2.752.57 ( m , 3h ) , 0.85 ( t , j = 7.6 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 165.9 , 165.1 , 142.5 , 136.2 , 129.7 , 129.3 , 128.1 , 126.9 , 125.5 , 122.9 , 121.0 , 118.2 , 118.1 , 111.5 , 110.7 , 59.8 , 54.9 , 52.2 , 40.8 , 40.0 , 23.6 ( note : carbons 1 and 2 are absent ) ; mp 175180 c . hms ( apci ) calcd c25h24n2o5 433.1758 ; found 433.1756 [ m + h ] . compound 63 was prepared via procedure i from methyl 4-formylbenzoate ( 0.088 g , 0.54 mmol ) , tryptamine ( 0.086 g , 0.54 mmol ) , and 4 ( 0.10 g , 0.54 mmol ) to yield a light - brown , amorphous solid ( 0.067 g , 28% ) . h nmr ( 600 mhz , dmso - d6 , 70 c ) 10.65 ( s , 1h ) , 7.84 ( d , j = 7.8 hz , 2h ) , 7.32 ( d , j = 7.8 hz , 2h ) , 7.28 ( d , j = 7.8 hz , 2h ) , 7.067.03 ( m , 2h ) , 6.92 ( t , j = 8.4 hz , 1h ) , 5.18 ( s , 1h ) , 3.83 ( s , 3h ) , 3.793.75 ( m , 1h ) , 3.403.20 ( m , 2h ) , 2.982.93 ( m , 1h ) , 2.912.86 ( m , 1h ) , 2.722.67 ( m , 1h ) , 0.86 ( d , j = 4.8 hz , 6h ) . c nmr ( 150 mhz , dmso - d6 ) 182.1 , 166.0 , 136.2 , 129.2 , 128.1 , 128.0 , 126.9 , 125.5 , 123.4 , 122.8 , 121.1 , 121.0 , 118.5 , 118.2 , 118.1 , 111.6 , 111.5 , 110.9 , 109.5 , 60.0 , 52.1 , 40.9 , 23.7 , 23.2 , 18.5 , 17.7 . hms ( apci ) calcd for c26h26n2o5 447.1915 ; found 447.1916 [ m + h ] . compound 64 was prepared via procedure i from methyl 4-formylbenzoate ( 0.082 g , 0.50 mmol ) , tryptamine ( 0.080 g , 0.50 mmol ) , and 5 ( 0.10 g , 0.50 mmol ) to yield an orange oil ( 0.092 g , 40% ) . h nmr ( 600 mhz , cdcl3 ) 8.17 ( br s , 1h ) , 7.93 ( d , j = 7.8 hz , 2h ) , 7.407.35 ( m , 2h ) , 7.20 ( t , j = 7.2 hz , 1h ) , 7.09 ( t , j = 7.2 hz , 1h ) , 7.04 ( dd , j = 1.2 hz , j = 7.8 hz , 2h ) , 6.96 ( s , 1h ) , 5.04 ( s , 1h ) , 4.023.99 ( m , 1h ) , 3.91 ( s , 3h ) , 3.093.00 ( m , 2h ) , 2.952.91 ( m , 1h ) , 1.06 ( s , 9h ) . c nmr ( 150 mhz , cdcl3 ) 202.2 , 181.2 , 166.7 , 141.2 , 136.5 , 130.6 , 130.2 , 128.0 , 127.2 , 122.5 , 122.2 , 119.8 , 118.8 , 118.7 , 111.6 , 111.4 , 63.0 , 52.4 , 41.7 , 27.7 , 25.3 , 24.5 ( note : either carbon 1 or 2 is absent ) . hms ( apci ) calcd for c27h28n2o5 461.2071 ; found 461.2077 [ m + h ] . compound 65 was prepared via procedure i from 6 ( 0.15 g , 0.68 mmol ) , tryptamine ( 0.11 g , 0.68 mmol ) , and methyl 4-formylbenzoate ( 0.11 g , 0.68 mmol ) to yield a cream - colored solid ( 0.031 g , 9% ) . h nmr ( 400 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.79 ( d , j = 7.2 hz , 2h ) , 7.597.48 ( m , 2h ) , 7.407.28 ( m , 3h ) , 7.247.21 ( m , 3h ) , 7.117.04 ( m , 2h ) , 6.92 ( t , j = 7.6 hz , 1h ) , 6.74 ( s , 1h ) , 5.25 ( s , 1h ) , 3.803.74 ( m , 4h ) , 3.002.90 ( m , 1h ) , 2.822.67 ( m , 2h ) . c nmr ( 150 mhz , dmso - d6 ) 190.1 , 188.9 , 165.9 , 165.4 , 142.1 , 138.2 , 136.4 , 132.4 , 129.6 , 129.5 , 128.7 , 128.3 , 128.1 , 127.0 , 123.0 , 121.1 , 118.9 , 118.4 , 118.2 , 111.6 , 110.9 , 60.8 , 52.1 , 41.2 , 23.8 ; mp 200205 c . hms ( apci ) calcd for c29h24n2o5 481.1771 ; found 481.1765 [ m + h ] . compound 66 was prepared via procedure i from methyl 4-formylbenzoate ( 0.35 g , 2.1 mmol ) , tryptamine ( 0.34 g , 2.1 mmol ) , and 21 ( 0.50 g , 2.1 mmol ) to yield a cream - colored solid ( 1.0 g , 96% ) . h nmr ( 600 mhz , dmso - d6 ) 10.77 ( s , 1h ) , 7.83 ( d , j = 7.8 hz , 2h ) , 7.377.29 ( m , 6h ) , 7.137.12 ( m , 1h ) , 7.077.03 ( m , 3h ) , 6.91 ( t , j = 7.8 hz , 1h ) , 5.36 ( s , 1h ) , 3.873.81 ( m , 4h ) , 3.002.93 ( m , 2h ) , 2.782.73 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 198.0 , 166.0 , 157.1 , 136.40 , 136.3 , 129.4 , 128.4 , 128.2 , 125.6 , 123.4 , 122.9 , 121.2 , 121.1 , 119.5 , 118.6 , 118.4 , 118.25 , 118.19 , 115.2 , 111.7 , 111.6 , 110.9 , 109.7 , 66.5 , 52.2 , 41.2 , 23.8 ; mp 7880 c . hms ( apci ) calcd for c29h24n2o6 497.1707 ; found 497.1707 [ m + h ] . compound 67 was prepared via procedure i from methyl 4-formylbenzoate ( 0.066 g , 0.40 mmol ) , tryptamine ( 0.064 g , 0.40 mmol ) , and 7 ( 0.10 g , 0.40 mmol ) to yield a pale - yellow , amorphous solid ( 0.046 g , 23% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.64 ( s , 1h ) , 7.897.82 ( m , 3h ) , 7.357.22 ( m , 6h ) , 7.077.05 ( m , 2h ) , 6.986.91 ( m , 2h ) , 5.34 ( s , 1h ) , 4.26 ( m , 1h ) , 3.82 ( s , 3h ) , 3.74 ( s , 3h ) , 3.012.90 ( m , 2h ) , 2.782.75 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 188.6 , 165.9 , 165.1 , 158.9 , 141.9 , 139.3 , 136.3 , 129.6 , 129.4 , 129.3 , 128.3 , 128.1 , 126.9 , 125.5 , 122.9 , 121.2 , 121.1 , 119.0 , 118.3 , 118.1 , 113.5 , 111.5 , 110.8 , 60.7 , 55.3 , 52.2 , 41.1 , 23.8 . hms ( apci ) calcd for c30h26n2o6 511.1877 ; found 511.1871 [ m + h ] . compound 68 was prepared via procedure i from methyl 4-formylbenzoate ( 0.17 g , 1.0 mmol ) , tryptamine ( 0.17 g , 1.0 mmol ) , and 8 ( 0.24 g , 1.0 mmol ) to yield a pale - yellow , amorphous solid ( 0.029 g , 6% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.67 ( s , 1h ) , 7.72 ( m , 2h ) , 7.367.33 ( m , 2h ) , 7.287.21 ( m , 2h ) , 7.117.04 ( m , 6h ) , 6.93 ( t , j = 7.2 hz , 1h ) , 5.29 ( s , 1h ) , 3.863.78 ( m , 4h ) , 3.012.96 ( m , 1h ) , 2.912.86 ( m , 1h ) , 2.762.72 ( m , 1h ) , 2.23 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 190.2 , 190.0 , 182.1 , 182.0 , 166.0 , 145.4 , 144.7 , 136.2 , 128.8 , 127.9 , 126.9 , 122.9 , 122.8 , 121.0 , 118.3 , 118.1 , 111.5 , 111.1 , 109.2 , 52.0 , 48.6 , 41.1 , 23.6 , 20.9 ( note : carbons 1 , 2 , 3 , and 4 are absent ) . hms ( apci ) calcd for c30h26n2o5 493.1769 ; found 493.1768 [ m h ] . compound 69 was prepared via procedure i from methyl 4-formylbenzoate ( 0.064 g , 0.39 mmol ) , tryptamine ( 0.063 g , 0.39 mmol ) , and 9 ( 0.10 g , 0.39 mmol ) to yield a pale - yellow , amorphous solid ( 0.045 g , 22% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.69 ( s , 1h ) , 7.82 ( d , j = 8.4 hz , 2h ) , 7.69 ( s , 1h ) , 7.58 ( d , j = 6.0 hz , 1h ) , 7.357.32 ( m , 3h ) , 7.297.26 ( m , 3h ) , 7.077.05 ( m , 2h ) , 6.93 ( t , j = 7.2 hz , 1h ) , 5.28 ( s , 1h ) , 3.823.79 ( m , 4h ) , 2.982.94 ( m , 1h ) , 2.882.84 ( m , 1h ) , 2.742.68 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 182.1 , 166.1 , 145.4 , 137.9 , 136.4 , 136.3 , 129.2 , 128.2 , 127.0 , 126.8 , 125.5 , 123.44 , 123.43 , 122.8 , 121.2 , 121.0 , 118.5 , 118.3 , 118.1 , 111.6 , 111.5 , 111.0 , 109.5 , 60.5 , 52.1 , 23.2 , 20.8 . hms ( apci ) calcd for c29h23cln2o5 513.1223 ; found 513.1219 [ m h ] . compound 70 was prepared via procedure i from methyl 4-formylbenzoate ( 0.069 g , 0.42 mmol ) , tryptamine ( 0.067 g , 0.42 mmol ) , and 10 ( 0.10 g , 0.42 mmol ) to yield a yellow , amorphous solid ( 0.028 g , 14% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.66 ( s , 1h ) , 7.79 ( d , j = 8.4 hz , 2h ) , 7.537.45 ( m , 2h ) , 7.34 ( dd , j = 3.0 hz , j = 8.4 hz , 2h ) , 7.297.26 ( m , 1h ) , 7.22 ( d , j = 7.8 hz , 2h ) , 7.137.10 ( m , 1h ) , 7.077.04 ( m , 2h ) , 6.93 ( t , j = 7.8 hz , 1h ) , 5.32 ( s , 1h ) , 3.843.79 ( m , 4h ) , 3.012.96 ( m , 1h ) , 2.922.88 ( m , 1h ) , 2.762.71 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 191.7 , 167.0 , 161.5 ( d , j = 241.7 hz ) , 143.0 , 137.6 , 136.2 , 129.3 , 128.9 , 128.6 , 128.1 , 127.9 , 126.9 , 125.5 , 124.1 , 122.8 , 121.0 , 118.3 , 118.1 , 116.6 , 116.5 , 111.5 , 110.9 , 61.0 , 52.0 , 41.2 , 23.5 ( note : carbon 3 is absent ) . hms ( apci ) calcd for c29h23fn2o5 497.1510 ; found 497.1513 [ m h ] . compound 71 was prepared via procedure i from methyl 4-formylbenzoate ( 0.074 g , 0.45 mmol ) , tryptamine ( 0.072 g , 0.45 mmol ) , and 18 ( 0.10 g , 0.45 mmol ) to yield a yellow , amorphous solid ( 0.037 g , 17% ) . h nmr ( 600 mhz , cdcl3 ) 8.66 ( d , j = 4.2 hz , 1h ) , 8.21 ( s , 1h ) , 8.14 ( d , j = 7.8 hz , 1h ) , 8.07 ( dt , j = 1.2 hz , j = 7.8 hz , 1h ) , 7.94 ( d , j = 8.4 hz , 2h ) , 7.71 ( dt , j = 0.6 hz , j = 6.0 hz , 1h ) , 7.39 ( d , j = 7.2 hz , 1h ) , 7.36 ( d , j = 7.8 hz , 1h ) , 7.217.17 ( m , 3h ) , 7.07 ( t , j = 8.4 hz , 1h ) , 7.01 ( d , j = 1.8 hz , 1h ) , 5.14 ( s , 1h ) , 4.154.10 ( m , 1h ) , 3.89 ( s , 3h ) , 3.112.95 ( m , 3h ) . c nmr ( 150 mhz , cdcl3 ) 181.8 , 173.2 , 166.8 , 165.7 , 151.7 , 145.3 , 142.5 , 140.6 , 136.5 , 130.3 , 130.0 , 128.3 , 128.1 , 127.3 , 125.2 , 122.3 , 119.6 , 118.7 , 112.5 , 111.5 , 109.6 , 61.6 , 41.4 , 29.9 , 24.3 ( note : carbon 3 is absent ) . hms ( apci ) calcd for c28h23n3o5 482.1710 ; found 482.1708 [ m + h ] . compound 72 was prepared via procedure i from methyl 4-formylbenzoate ( 0.079 g , 0.48 mmol ) , tryptamine ( 0.077 g , 0.45 mmol ) , and 19 ( 0.10 g , 0.48 mmol ) to yield a yellow solid ( 0.11 g , 49% ) . h nmr ( 400 mhz , dmso - d6 ) 10.89 ( s , 1h ) , 8.80 ( s , 1h ) , 8.69 ( d , j = 4.4 hz , 1h ) , 8.00 ( d , j = 7.6 hz , 1h ) , 7.88 ( d , j = 7.2 hz , 2h ) , 7.437.42 ( m , 2h ) , 7.347.29 ( m , 2h ) , 7.14 ( d , j = 8.0 hz , 2h ) , 7.06 ( t , j = 6.8 hz , 1h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.42 ( s , 1h ) , 3.873.82 ( m , 4h ) , 3.022.89 ( m , 2h ) , 2.792.74 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.8 , 165.9 , 165.0 , 152.1 , 149.1 , 142.1 , 136.3 , 133.9 , 129.5 , 129.4 , 128.3 , 128.1 , 126.9 , 125.5 , 123.5 , 122.9 , 121.0 , 118.3 , 118.1 , 111.5 , 110.7 , 109.5 , 60.4 , 52.2 , 41.1 , 23.7 ; mp 199205 c . hms ( apci ) calcd for c28h23n3o5 482.1711 ; found 482.1707 [ m + h ] . compound 73 was prepared via procedure i from methyl 4-formylbenzoate ( 0.15 g , 0.9 mmol ) , tryptamine ( 0.15 g , 0.9 mmol ) , and 20 ( 0.20 g , 0.9 mmol ) to yield a yellow solid ( 0.13 g , 30% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.63 ( s , 1h ) , 8.47 ( d , j = 2.8 hz , 1h ) , 7.766.92 ( m , 12h ) , 5.27 ( s , 1h ) , 3.823.78 ( m , 4h ) , 3.002.95 ( m , 1h ) , 2.912.86 ( m , 1h ) , 2.742.72 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 191.3 , 166.0 , 149.5 , 149.0 , 146.6 , 136.3 , 128.9 , 128.5 , 128.0 , 127.0 , 122.8 , 122.3 , 121.1 , 120.7 , 118.3 , 118.1 , 111.5 , 111.0 , 52.0 , 48.6 , 41.1 , 23.5 ( note : carbons 1 and 2 are absent ) ; mp > 250 c . hms ( apci ) calcd for c28h23n3o5 480.1570 ; found 480.1568 [ m h ] . compound 74 was prepared via procedure i from methyl 4-formylbenzoate ( 0.13 g , 0.80 mmol ) , tryptamine ( 0.13 g , 0.80 mmol ) , and 11 ( 0.20 g , 0.80 mmol ) to yield a pink , amorphous solid ( 0.028 g , 7% ) . h nmr ( 600 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.89 ( s , 1h ) , 7.50 ( d , j = 6.0 hz , 1h ) , 7.347.18 ( m , 5h ) , 7.097.04 ( m , 3h ) , 6.966.88 ( m , 3h ) , 5.27 ( s , 1h ) , 3.833.74 ( m , 6h ) , 2.992.87 ( m , 2h ) , 2.732.65 ( m , 2h ) . c nmr ( 150 mhz , dmso - d6 ) 190.1 , 182.1 , 166.2 , 156.0 , 146.1 , 137.3 , 132.7 , 129.1 , 128.8 , 128.4 , 128.1 , 128.0 , 127.7 , 127.0 , 125.6 , 122.8 , 121.0 , 119.7 , 118.2 , 118.1 , 111.5 , 111.1 , 111.0 , 60.3 , 56.1 , 55.2 , 52.1 , 40.9 , 23.6 , 18.6 . hms ( apci ) calcd for c30h26n2o6 509.1710 ; found 509.1711 [ m h ] . compound 75 was prepared via procedure i from methyl 4-formylbenzoate ( 0.14 g , 0.85 mmol ) , tryptamine ( 0.14 g , 0.85 mmol ) , and 12 ( 0.20 g , 0.85 mmol ) to yield a pale - yellow , amorphous solid ( 0.040 g , 9% ) . h nmr ( 600 mhz , dmso - d6 , 70 c ) 10.71 ( br s , 1h ) , 7.67 ( d , j = 7.2 hz , 2h ) , 7.37 ( d , j = 9.0 hz , 1h ) , 7.30 ( d , j = 7.8 hz , 1h ) , 7.136.99 ( m , 4h ) , 6.946.91 ( m , 2h ) , 6.846.74 ( m , 3h ) , 4.96 ( s , 1h ) , 3.823.76 ( m , 4h ) , 2.972.92 ( m , 1h ) , 2.822.71 ( m , 2h ) , 1.78 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 190.1 , 182.1 , 182.03 , 182.01 , 165.9 , 144.4 , 139.4 , 136.3 , 134.2 , 129.3 , 128.8 , 128.3 , 127.9 , 127.0 , 124.7 , 123.0 , 122.7 , 121.1 , 118.3 , 118.1 , 111.6 , 111.2 , 108.9 , 60.3 , 52.0 , 48.6 , 41.1 , 23.6 . hms ( apci ) calcd for c30h26n2o5 493.1761 ; found 493.1763 [ m h ] . compound 76 was prepared via procedure i from methyl 4-formylbenzoate ( 0.13 g , 0.79 mmol ) , tryptamine ( 0.13 g , 0.79 mmol ) , and 13 ( 0.20 g , 0.79 mmol ) to yield a cream - colored solid ( 0.27 g , 66% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.64 ( s,1h ) , 7.67 ( m , 2h ) , 7.35 ( d , j = 8.4 hz , 1h ) , 7.30 ( d , j = 7.8 hz , 1h ) , 7.247.18 ( m , 2h ) , 7.107.03 ( m , 4h ) , 6.92 ( t , j = 7.2 hz , 2h ) , 6.78 ( m , 1h ) , 5.04 ( s , 1h ) , 3.863.75 ( m , 4h ) , 2.972.92 ( m , 1h ) , 2.852.83 ( m , 1h ) , 2.732.68 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 185.2 , 165.9 , 144.1 , 136.3 , 130.0 , 129.5 , 129.1 , 128.8 , 128.7 , 128.6 , 128.1 , 128.0 , 126.9 , 126.5 , 123.0 , 121.0 , 118.3 , 118.1 , 111.5 , 111.0 , 67.1 , 52.1 , 40.0 , 25.2 ( note : carbons 1 , 2 , and 3 are absent ) ; mp 248253 c . hms ( apci ) calcd for c29h23cln2o5 513.1214 ; found 513.1215 [ m h ] . compound 77 was prepared via procedure i from methyl 4-formylbenzoate ( 0.19 g , 0.84 mmol ) , tryptamine ( 0.14 g , 0.84 mmol ) , and 14 ( 0.20 g , 0.84 mmol ) to yield a brown , amorphous solid ( 0.070 g , 17% ) . h nmr ( 600 mhz , dmso - d6 , 70 c ) 10.68 ( s , 1h ) , 7.807.54 ( m , 2h ) , 7.357.30 ( m , 4h ) , 7.116.78 ( m , 7h ) , 5.07 ( s , 1h ) , 3.813.74 ( m , 4h ) , 2.972.92 ( m , 1h ) , 2.872.82 ( m , 1h ) , 2.722.67 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 172.6 , 165.9 , 161.2 , 156.0 , 155.1 , 139.5 , 136.3 , 135.0 , 130.0 , 129.6 , 128.6 , 126.8 , 126.7 , 126.3 , 125.3 , 124.8 , 123.1 , 121.1 , 119.3 , 118.3 , 118.0 , 111.5 , 110.6 , 59.1 , 52.3 , 41.2 , 23.8 . hms ( apci ) calcd for c29h23fn2o5 497.1510 ; found 497.1513 [ m h ] . compound 78 was prepared via procedure i from methyl 4-formylbenzoate ( 0.42 g , 2.6 mmol ) , tryptamine ( 0.41 g , 2.6 mmol ) , and 15 ( 0.50 g , 2.6 mmol ) to yield an orange solid ( 0.079 g , 7% ) . h nmr ( 600 mhz , cdcl3 ) 8.32 ( s , 1h ) , 8.05 ( s , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.437.41 ( m , 2h ) , 7.32 ( d , j = 8.4 hz , 1h ) , 7.25 ( d , j = 8.4 hz , 2h ) , 7.16 ( t , j = 7.2 hz , 1h ) , 7.06 ( t , j = 7.2 hz , 1h ) , 6.94 ( s , 1h ) , 6.39 ( dd , j = 1.8 hz , j = 3.6 hz , 1h ) , 5.39 ( s , 1h ) , 4.043.99 ( m , 1h ) , 3.88 ( s , 3h ) , 3.072.96 ( m , 2h ) , 2.932.89 ( m , 1h ) . c nmr ( 150 mhz , cdcl3 ) 173.9 , 167.1 , 153.1 , 145.1 , 136.5 , 129.8 , 129.7 , 129.2 , 128.4 , 128.2 , 127.4 , 122.3 , 122.2 , 119.5 , 118.9 , 117.1 , 114.2 , 112.7 , 111.7 , 111.4 , 111.3 , 61.3 , 52.2 , 41.3 , 24.3 ; mp 6065 c . hms ( apci ) calcd for c27h22n2o6 471.1551 ; found 471.1547 [ m + h ] . compound 79 was prepared via procedure i from methyl 4-formylbenzoate ( 0.073 g , 0.44 mmol ) , tryptamine ( 0.071 g , 0.44 mmol ) , and 16 ( 0.10 g , 0.44 mmol ) to yield a yellow , amorphous solid ( 0.043 g , 20% ) . h nmr ( 400 mhz , dmso - d6 ) 10.80 ( s , 1h ) , 7.83 ( d , j = 8.4 hz , 2h ) , 7.55 ( d , j = 4.0 hz , 1h ) , 7.347.29 ( m , 4h ) , 7.067.02 ( m , 3h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.805.70 ( m , 1h ) , 5.28 ( s , 1h ) , 3.863.74 ( m , 4h ) , 3.002.89 ( m , 1h ) , 2.852.78 ( m , 1h ) , 2.732.67 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 165.8 , 144.7 , 136.2 , 129.0 , 128.2 , 126.9 , 126.8 , 123.4 , 122.9 , 121.2 , 121.0 , 118.5 , 118.3 , 118.1 , 111.6 , 111.5 , 111.1 , 109.5 , 52.0 , 48.6 , 40.0 , 23.5 ( note : carbons 1 , 2 , and 4 are absent ) ; mp 190195 c . hms ( apci ) calcd for c27h22n2o5s 485.1177 ; found 485.1173 [ m h ] . compound 80 was prepared via procedure i from methyl 4-formylbenzoate ( 0.36 g , 2.2 mmol ) , tryptamine ( 0.35 g , 2.2 mmol ) , and 17 ( 0.50 g , 2.2 mmol ) to yield a cream - colored solid ( 0.70 g , 65% ) . h nmr ( 400 mhz , dmso - d6 ) 10.86 ( s , 1h ) , 8.38 ( d , j = 2.8 hz , 1h ) , 7.85 ( d , j = 7.6 hz , 2h ) , 7.49 ( t , j = 4.0 hz , 1h ) , 7.377.31 ( m , 4h ) , 7.13 ( s , 1h ) , 7.07 ( t , j = 7.6 hz , 1h ) , 6.93 ( t , j = 6.8 hz , 1h ) , 5.76 ( d , j = 1.2 hz , 1h ) , 5.44 ( s , 1h ) , 3.893.81 ( m , 4h ) , 3.022.90 ( m , 2h ) , 2.802.74 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.8 , 165.9 , 142.1 , 141.6 , 136.3 , 134.2 , 129.5 , 129.4 , 128.3 , 128.1 , 127.3 , 126.9 , 126.3 , 125.5 , 122.9 , 121.1 , 118.3 , 118.1 , 111.5 , 110.8 , 60.7 , 52.1 , 41.1 , 23.8 ; mp 189192 c . hms ( apci ) calcd for c27h22n2o5s 487.1336 ; found 487.1335 [ m + h ] . compound 81 was prepared via procedure i from methyl 3-formylbenzoate ( 0.50 g , 3.1 mmol ) , tryptamine ( 0.49 g , 3.1 mmol ) , and methyl acetopyruvate ( 0.44 g , 3.1 mmol ) to yield a pale - pink solid ( 0.77 g , 60% ) . h nmr ( 400 mhz , dmso - d6 ) 10.82 ( s , 1h ) , 7.87 ( d , j = 7.6 hz , 1h ) , 7.73 ( s , 1h ) , 7.45 ( t , j = 7.2 hz , 1h ) , 7.397.26 ( m , 3h ) , 7.10 ( d , j = 2.0 hz , 1h ) , 7.05 ( t , j = 7.2 hz , 1h ) , 6.89 ( t , j = 8.0 hz , 1h ) , 5.24 ( s , 1h ) , 3.853.76 ( m , 4h ) , 2.982.91 ( m , 1h ) , 2.872.80 ( m , 1h ) , 2.722.65 ( m , 1h ) , 2.72 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 191.5 , 166.0 , 165.1 , 154.8 , 137.8 , 136.3 , 132.5 , 129.9 , 129.1 , 129.0 , 128.4 , 126.9 , 122.9 , 121.1 , 119.8 , 118.3 , 118.1 , 111.5 , 110.8 , 59.8 , 52.3 , 40.8 , 29.8 , 23.7 ; mp 218220 c . hms ( apci ) calcd for c24h22n2o5 419.1593 ; found 419.1596 [ m + h ] . compound 82 was prepared via procedure i from methyl 2-formylbenzoate ( 0.10 g , 0.61 mmol ) , tryptamine ( 0.098 g , 0.61 mmol ) , and methyl acetopyruvate ( 0.088 g , 0.61 mmol ) to yield a white solid ( 0.18 g , 72% ) . h nmr ( 400 mhz , dmso - d6 ) 10.82 ( s , 1h ) , 7.87 ( d , j = 7.6 hz , 1h ) , 7.72 ( s , 1h ) , 7.46 ( t , j = 7.6 hz , 1h ) , 7.38 ( d , j = 7.6 hz , 1h ) , 7.327.25 ( m , 2h ) , 7.10 ( d , j = 1.6 hz , 1h ) , 7.02 ( t , j = 7.6 hz , 1h ) , 6.89 ( t , j = 7.6 hz , 1h ) , 5.24 ( s , 1h ) , 3.86 ( s , 3h ) , 3.823.75 ( m , 1h ) , 2.972.90 ( m , 1h ) , 2.862.79 ( m , 1h ) , 2.712.66 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.6 , 166.0 , 165.0 , 154.5 , 137.8 , 136.2 , 132.5 , 129.8 , 129.0 , 128.9 , 128.3 , 126.8 , 122.9 , 121.0 , 119.9 , 118.2 , 118.0 , 111.4 , 110.7 , 59.7 , 52.2 , 40.8 , 29.8 , 23.6 ; mp 210218 c . hms ( apci ) calcd for c24h22n2o5 419.1602 ; found 419.1599 [ m + h ] . to a suspension of 1 ( 0.10 g , 0.24 mmol ) in etoh ( 3.5 ml ) was added a 2n aq sodium hydroxide solution ( 0.8 ml ) . the reaction was heated at reflux for 2 h. the solution was then cooled to 0 c , and concentrated hcl was added carefully . the precipitate was filtered off , rinsed with cold water , and dried under vacuum for 12 h to afford a white powder ( 0.090 g , 93% ) . h nmr ( 400 mhz , dmso - d6 ) 10.89 ( br s , 1h ) , 10.79 ( br s , 1h ) , 8.09 ( d , j = 8.0 hz , 2h ) , 7.307.28 ( m , 2h ) , 7.23 ( d , j = 8.0 hz , 2h ) , 7.037.01 ( m , 2h ) , 6.90 ( app t , j = 8.0 hz , 1h ) , 5.56 ( s , 1h ) , 3.773.74 ( m , 1h ) , 2.892.71 ( m , 1h ) , 2.712.61 ( m , 2h ) , 2.10 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 196.5 , 179.9 , 169.3 , 164.3 , 146.9 , 136.5 , 130.1 ( 2 ) , 128.5 , 127.8 ( 2 ) , 127.4 , 123.0 , 119.1 , 121.7 , 119.8 , 118.8 , 113.0 , 111.1 , 54.7 , 49.1 , 26.6 , 24.3 ; mp > 250 c . hms ( esi ) calcd for c23h20n2nao5 427.1270 ; found 427.1263 [ m + na ] . compound 84 was prepared via procedure i from 45 ( 0.20 g , 1.1 mmol ) , tryptamine ( 0.18 g , 1.1 mmol ) , and methyl acetopyruvate ( 0.16 g , 1.1 mmol ) to yield a pale - pink solid ( 0.20 g , 42% ) . h nmr ( 400 mhz , dmso - d6 ) 12.48 ( br s , 1h ) , 10.82 ( s , 1h ) , 7.87 ( d , j = 8.4 hz , 2h ) , 7.337.24 ( m , 4h ) , 7.09 ( d , j = 2.4 hz , 1h ) , 7.05 ( t , j = 7.2 hz , 1h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.18 ( s , 1h ) , 4.30 ( q , j = 7.2 hz , 2h ) , 3.833.76 ( m , 1h ) , 2.972.89 ( m , 1h ) , 2.872.80 ( m , 1h ) , 2.742.67 ( m , 1h ) , 2.26 ( s , 3h ) , 1.30 ( t , j = 7.2 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.6 , 165.4 , 165.1 , 142.4 , 136.2 , 129.6 , 129.3 , 128.1 , 126.9 , 122.9 , 121.0 , 118.3 , 118.1 , 111.5 , 110.7 , 60.7 , 59.8 , 40.8 , 39.9 , 23.6 , 14.2 ( note : carbon 3 and either carbon 1 or 2 are absent ) ; mp 180183 c . hms ( apci ) calcd for c25h24n2o5 433.1771 ; found 433.1765 [ m + h ] . compound 85 was prepared via procedure i from 46 ( 0.20 g , 1.0 mmol ) , tryptamine ( 0.17 g , 1.0 mmol ) , and methyl acetopyruvate ( 0.15 g , 1.0 mmol ) to yield an orange , amorphous solid ( 0.028 g , 6% ) . h nmr ( 400 mhz , dmso - d6 ) 10.70 ( s , 1h ) , 7.86 ( d , j = 8.4 hz , 2h ) , 7.337.23 ( m , 3h ) , 7.117.00 ( m , 3h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.165.11 ( m , 2h ) , 3.823.77 ( m , 1h ) , 3.022.85 ( m , 2h ) , 2.762.71 ( m , 1h ) , 2.26 ( s , 3h ) , 1.32 ( s , 3h ) , 1.31 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 190.0 , 164.9 , 136.2 , 129.2 , 128.1 , 126.8 , 125.5 , 123.5 , 122.8 , 121.2 , 121.0 , 118.5 , 118.3 , 118.1 , 111.5 , 110.8 , 68.1 , 59.8 , 40.9 , 39.9 , 23.6 , 21.6 ( note : carbons 1 and 2 are absent ) . hms ( apci ) calcd for c26h26n2o5 447.1928 ; found 447.1922 [ m + h ] . compound 86 was prepared via procedure i from 47 ( 0.50 g , 2.4 mmol ) , tryptamine ( 0.39 g , 2.4 mmol ) , and methyl acetopyruvate ( 0.35 g , 2.4 mmol ) to yield a pale - yellow solid ( 0.92 g , 83% ) . h nmr ( 400 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.81 ( d , j = 8.4 hz , 2h ) , 7.337.22 ( m , 4h ) , 7.10 ( d , j = 2.0 hz , 1h ) , 7.05 ( t , j = 7.2 hz , 1h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.17 ( s , 1h ) , 3.833.76 ( m , 1h ) , 2.962.89 ( m , 1h ) , 2.862.81 ( m , 1h ) , 2.792.67 ( m , 1h ) , 2.26 ( s , 3h ) , 1.53 ( s , 9h ) . c nmr ( 150 mhz , dmso - d6 ) 191.5 , 165.1 , 164.6 , 154.4 , 142.0 , 131.1 , 129.1 , 127.9 , 126.9 , 126.2 , 122.8 , 121.0 , 119.8 , 118.2 , 118.1 , 111.4 , 110.7 , 80.7 , 59.8 , 40.8 , 29.7 , 27.8 , 23.6 ; mp 145150 c . hms ( apci ) calcd for c27h28n2o5 461.2063 ; found 461.2065 [ m + h ] . compound 87 was prepared via procedure i from 4-formylbenzonitrile ( 0.15 g , 1.1 mmol ) , tryptamine ( 0.18 g , 1.1 mmol ) , and 19 ( 0.25 g , 1.1 mmol ) to yield a yellow solid ( 0.084 g , 17% ) . h nmr ( 600 mhz , dmso - d6 ) 10.84 ( s , 1h ) , 8.81 ( s , 1h ) , 8.69 ( d , j = 3.6 hz , 1h ) , 8.01 ( d , j = 7.8 hz , 1h ) , 7.75 ( d , j = 7.8 hz , 2h ) , 7.507.47 ( m , 3h ) , 7.33 ( d , j = 8.4 hz , 1h ) , 7.31 ( d , j = 7.8 hz , 1h ) , 7.13 ( s , 1h ) , 7.07 ( t , j = 7.8 hz , 1h ) , 6.94 ( t , j = 7.2 hz , 1h ) , 5.44 ( s , 1h ) , 3.883.83 ( m , 1h ) , 3.012.90 ( m , 2h ) , 2.792.75 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 189.3 , 165.1 , 152.1 , 150.2 , 149.2 , 142.5 , 136.3 , 133.9 , 132.4 , 129.0 , 126.9 , 123.9 , 123.4 , 122.9 , 121.1 , 118.6 , 118.3 , 118.1 , 117.7 , 111.5 , 111.0 , 110.7 , 60.3 , 41.2 , 23.7 ; mp > 250 c . hms ( apci ) calcd for c27h20n4o3 449.1608 ; found 449.1607 [ m + h ] . compound 88 was prepared via procedure i from 4-nitrobenzaldehyde ( 0.50 g , 3.3 mmol ) , tryptamine ( 0.53 g , 3.3 mmol ) , and methyl acetopyruvate ( 0.48 g , 3.3 mmol ) to yield a pale - yellow solid ( 1.0 g , 75% ) . h nmr ( 400 mhz , dmso - d6 ) 12.62 ( br s , 1h ) , 10.82 ( s , 1h ) , 8.10 ( d , j = 8.8 hz , 2h ) , 7.37 ( d , j = 8.8 hz , 2h ) , 7.31 ( d , j = 8.4 hz , 2h ) , 7.09 ( d , j = 1.6 hz , 1h ) , 7.04 ( t , j = 8.0 hz , 1h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.26 ( s , 1h ) , 3.853.78 ( m , 1h ) , 2.972.84 ( m , 2h ) , 2.802.77 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.6 , 165.2 , 154.7 , 147.1 , 144.9 , 136.2 , 129.0 , 126.8 , 123.5 , 122.9 , 121.0 , 118.2 , 118.0 , 111.4 , 110.7 , 59.4 , 41.0 , 29.8 , 23.5 ( note : carbon 3 is absent ) ; mp 142150 c . hms ( apci ) calcd for c22h19n3o5 406.1398 ; found 406.1395 [ m + h ] . compound 89 was prepared via procedure i from 42 ( 0.29 g , 2.0 mmol ) , tryptamine ( 0.32 g , 2.0 mmol ) , and 19 ( 0.44 g , 2.0 mmol ) to yield a yellow solid ( 0.70 g , 76% ) . h nmr ( 600 mhz , dmso - d6 ) 10.65 ( s , 1h ) , 8.81 ( s , 1h ) , 8.66 ( s , 1h ) , 7.99 ( d , j = 7.8 hz , 1h ) , 7.81 ( d , j = 8.4 hz , 2h ) , 7.457.32 ( m , 6h ) , 7.127.06 ( m , 3h ) , 6.95 ( t , j = 7.2 hz , 1h ) , 5.39 ( s , 1h ) , 3.913.86 ( m , 1h ) , 3.042.98 ( m , 2h ) , 2.832.79 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.1 , 175.4 , 167.3 , 165.0 , 148.7 , 139.8 , 136.1 , 135.7 , 135.3 , 134.0 , 133.9 , 127.4 , 127.2 , 126.7 , 122.8 , 122.7 , 122.4 , 120.6 , 117.7 , 111.1 , 110.7 , 108.5 , 60.2 , 39.9 , 13.7 ; mp 175180 c . hms ( apci ) calcd for c27h22n4o4 467.17138 ; found 467.17160 [ m + h ] . compound 90 was prepared via procedure i from 43 ( 0.15 g , 0.93 mmol ) , tryptamine ( 0.15 g , 0.93 mmol ) , and 19 ( 0.21 g , 0.93 mmol ) to yield a yellow solid ( 0.33 g , 73% ) . h nmr ( 600 mhz , dmso - d6 ) 10.72 ( s , 1h ) , 8.79 ( s , 1h ) , 8.67 ( d , j = 4.8 hz , 1h ) , 8.24 ( d , j = 3.6 hz , 1h ) , 7.99 ( d , j = 7.8 hz , 1h ) , 7.75 ( d , j = 7.8 hz , 2h ) , 7.45 ( t , j = 5.4 hz , 1h ) , 7.397.34 ( m , 4h ) , 7.117.05 ( m , 2h ) , 6.94 ( t , j = 7.2 hz , 1h ) , 5.38 ( s , 1h ) , 3.883.84 ( m , 1h ) , 3.113.09 ( m , 1h ) , 3.022.94 ( m , 2h ) , 2.76 ( d , j = 4.8 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 166.3 , 165.0 , 152.3 , 149.3 , 136.3 , 136.1 , 134.5 , 128.1 , 127.9 , 127.3 , 125.5 , 123.4 , 122.4 , 122.9 , 121.0 , 118.5 , 118.3 , 118.14 , 118.1 , 111.6 , 110.8 , 60.4 , 41.0 , 26.2 , 23.7 ( note : carbon 4 is absent ) ; mp 240245 c . hms ( apci ) calcd for c28h24n4o4 481.1876 ; found 481.1879 [ m + h ] . compound 91 was prepared via procedure i from 19 ( 0.38 g , 1.7 mmol ) , tryptamine ( 0.27 g , 1.7 mmol ) , and 44 ( 0.30 g , 1.7 mmol ) to yield a yellow solid ( 0.33 g , 39% ) . h nmr ( 600 mhz , dmso - d6 ) 10.85 ( s , 1h ) , 8.81 ( s , 1h ) , 8.69 ( d , j = 4.8 hz , 1h ) , 8.01 ( d , j = 7.8 hz , 1h ) , 7.497.47 ( m , 2h ) , 7.367.29 ( m , 4h ) , 7.147.10 ( m , 2h ) , 7.06 ( t , j = 7.8 hz , 1h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.42 ( s , 1h ) , 3.883.82 ( m , 1h ) , 3.022.95 ( m , 5h ) , 2.84 ( s , 3h ) , 2.772.71 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 169.71 , 164.9 , 152.3 , 149.3 , 136.4 , 136.3 , 136.2 , 128.1 , 127.8 , 127.2 , 125.5 , 123.4 , 122.9 , 121.2 , 121.0 , 118.5 , 118.3 , 118.1 , 111.6 , 111.5 , 110.8 , 60.5 , 41.0 , 40.0 , 23.8 , 23.2 ( note : carbon 4 is absent ) ; mp 210212 c . hms ( apci ) calcd for c29h26n4o4 495.2040 ; found 495.2036 [ m + h ] . compound 92 was prepared via procedure i from 4-formylbenzenesulfonamide ( 0.19 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a pale - orange solid ( 0.024 g , 5% ) . h nmr ( 600 mhz , dmso - d6 ) 10.86 ( s , 1h ) , 8.81 ( s , 1h ) , 8.69 ( d , j = 4.2 hz , 1h ) , 8.01 ( d , j = 7.8 hz , 1h ) , 7.76 ( d , j = 9.0 hz , 2h ) , 7.507.47 ( m , 3h ) , 7.34 ( d , j = 7.8 hz , 2h ) , 7.32 ( s , 2h ) , 7.14 ( d , j = 1.8 hz , 1h ) , 7.07 ( t , j = 8.4 hz , 1h ) , 6.96 ( t , j = 7.2 hz , 1h ) , 5.41 ( s , 1h ) , 3.913.86 ( m , 1h ) , 3.032.98 ( m , 1h ) , 2.922.88 ( m , 1h ) , 2.812.76 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.3 , 165.0 , 149.3 , 149.1 , 143.9 , 140.6 , 136.3 , 133.9 , 131.8 , 128.6 , 126.9 , 125.9 , 123.4 , 122.9 , 121.1 , 118.4 , 118.2 , 111.5 , 110.8 , 60.1 , 41.0 , 23.7 ( note : two of either carbons 1 , 2 , or 3 are absent ) ; mp > 250 c . hms ( apci ) calcd for c26h22n4o5s 503.1384 ; found 503.1381 [ m + h ] . compound 93 was prepared via procedure i from 4-formyl - n - methylbenzenesulfonamide ( 0.20 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield an orange - yellow solid ( 0.11 g , 21% ) . h nmr ( 600 mhz , dmso - d6 ) 10.84 ( s , 1h ) , 8.80 ( s , 1h ) , 8.50 ( d , j = 4.8 hz , 1h ) , 8.028.00 ( m , 2h ) , 7.71 ( d , j = 8.4 hz , 2h ) , 7.48 ( d , j = 7.8 hz , 2h ) , 7.40 ( d , j = 4.8 hz , 1h ) , 7.347.29 ( m , 3h ) , 7.097.05 ( m , 2h ) , 6.94 ( t , j = 7.8 hz , 1h ) , 3.843.79 ( m , 1h ) , 3.012.95 ( m , 1h ) , 2.892.85 ( m , 1h ) , 2.702.65 ( m , 1h ) , 2.39 ( d , j = 4.8 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 169.7 , 149.9 , 149.6 , 149.5 , 146.1 , 138.0 , 136.4 , 136.3 , 135.9 , 128.5 , 128.1 , 127.0 , 126.5 , 125.6 , 123.4 , 122.7 , 122.5 , 121.0 , 118.5 , 118.3 , 118.1 , 111.5 , 111.1 , 60.3 , 41.1 , 28.7 , 23.6 ; mp > 220 c . hms ( apci ) calcd for c27h24n4o5s 517.1540 ; found 517.1545 [ m + h ] . compound 94 was prepared via procedure i from 4-(trifluoromethyl)benzaldehyde ( 0.17 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a yellow solid ( 0.24 g , 49% ) . h nmr ( 600 mhz , dmso - d6 ) 10.94 ( s , 1h ) , 8.83 ( d , j = 1.2 hz , 1h ) , 8.70 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 8.20 ( br s , 1h ) , 8.04 ( d , j = 8.4 hz , 1h ) , 7.66 ( d , j = 7.8 hz , 2h ) , 7.547.48 ( m , 3h ) , 7.34 ( d , j = 8.4 hz , 1h ) , 7.24 ( d , j = 7.8 hz , 1h ) , 7.13 ( s , 1h ) , 7.05 ( t , j = 7.8 hz , 1h ) , 6.91 ( t , j = 7.2 hz , 1h ) , 5.46 ( s , 1h ) , 3.883.83 ( m , 1h ) , 3.022.92 ( m , 2h ) , 2.782.73 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.2 , 165.3 , 151.8 , 149.0 , 141.9 , 136.6 , 136.3 , 134.2 , 128.9 , 128.2 , 126.9 , 125.5 , 125.4 , 123.5 , 122.9 , 121.2 , 121.1 , 118.2 , 118.0 , 111.5 , 110.7 , 60.3 , 41.2 , 23.7 ( note : either carbon 1 or 2 is absent ) ; mp 235240 c . hms ( apci ) calcd for c27h20f3n3o3 492.1535 ; found 492.1532 [ m + h ] . compound 95 was prepared via procedure i from 35 ( 0.15 g , 0.83 mmol ) , tryptamine ( 0.13 g , 0.83 mmol ) , and methyl acetopyruvate ( 0.12 g , 0.83 mmol ) to yield a brown solid ( 0.10 g , 27% ) . h nmr ( 400 mhz , dmso - d6 ) 10.82 ( s , 1h ) , 10.49 ( s , 1h ) , 7.68 ( dd , j = 8.0 hz , j = 2.4 hz , 1h ) , 7.347.30 ( m , 2h ) , 7.10 ( s , 1h ) , 7.05 ( t , j = 6.8 hz , 1h ) , 6.92 ( t , j = 6.8 hz , 1h ) , 6.84 ( s , 1h ) , 6.64 ( d , j = 8.0 hz , 1h ) , 5.12 ( s , 1h ) , 3.86 ( s , 3h ) , 3.833.76 ( m , 1h ) , 2.982.83 ( m , 2h ) , 2.752.68 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.7 , 168.8 , 165.0 , 159.8 , 154.4 , 154.1 , 136.0 , 130.3 , 126.9 , 122.8 , 121.0 , 119.6 , 118.3 , 118.2 , 118.1 , 117.0 , 112.8 , 111.4 , 110.7 , 59.6 , 52.4 , 40.9 , 29.8 , 23.5 ; mp 188190 c . hms ( apci ) calcd for c24h22n2o6 435.1551 ; found 435.1549 [ m + h ] . compound 96 was prepared via procedure i from 33 ( 0.1 g , 0.52 mmol ) , tryptamine ( 0.083 g , 0.52 mmol ) , and methyl acetopyruvate ( 0.074 g , 0.52 mmol ) to yield a cream - colored solid ( 0.17 g , 74% ) . h nmr ( 600 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.55 ( d , j = 8.0 hz , 1h ) , 7.347.31 ( m , 2h ) , 7.11 ( s , 1h ) , 7.06 ( t , j = 6.8 hz , 1h ) , 6.946.91 ( m , 2h ) , 6.70 ( d , j = 8.0 hz , 1h ) , 5.14 ( s , 1h ) , 3.833.76 ( m , 7h ) , 2.992.84 ( m , 2h ) , 2.752.69 ( m , 1h ) , 2.28 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 165.9 , 165.0 , 158.1 , 136.2 , 130.9 , 128.1 , 126.9 , 125.5 , 125.0 , 122.9 , 121.0 , 119.6 , 118.6 , 118.3 , 118.1 , 111.5 , 110.8 , 60.0 , 55.9 , 51.9 , 40.9 , 40.0 , 23.6 ( note : carbons 3 and 4 are absent ) ; mp 130135 c . hms ( apci ) calcd for c25h24n2o6 449.1707 ; found 449.1709 [ m + h ] . compound 97 was prepared via procedure i from 40 ( 0.10 g , 0.56 mmol ) , tryptamine ( 0.090 g , 0.56 mmol ) , and methyl acetopyruvate ( 0.081 g , 0.56 mmol ) to yield a pale - orange solid ( 0.13 g , 53% ) . h nmr ( 400 mhz , cdcl3 ) 8.14 ( s , 1h ) , 7.83 ( d , j = 8.4 hz , 1h ) , 7.407.36 ( m , 2h ) , 7.23 ( t , j = 7.6 hz , 1h ) , 7.11 ( t , j = 7.6 hz , 1h ) , 7.00 ( s , 1h ) , 6.83 ( d , j = 7.6 hz , 1h ) , 6.74 ( s , 1h ) , 4.76 ( s , 1h ) , 4.074.02 ( m , 1h ) , 3.90 ( s , 3h ) , 3.112.93 ( m , 3h ) , 2.51 ( s , 3h ) , 1.98 ( s , 3h ) . c nmr ( 150 mhz , cdcl3 ) 194.6 , 167.6 , 164.6 , 159.8 , 141.4 , 139.0 , 136.5 , 131.5 , 131.3 , 130.5 , 127.2 , 125.2 , 122.6 , 122.3 , 119.8 , 119.5 , 118.7 , 112.4 , 111.6 , 61.4 , 52.2 , 41.3 , 28.2 , 24.4 , 21.9 ; mp 4043 c . hms ( apci ) calcd for c25h24n2o5 433.1745 ; found 433.1745 [ m + h ] . compound 98 was prepared via procedure i from 39 ( 0.09 g , 0.45 mmol ) , tryptamine ( 0.073 g , 0.45 mmol ) , and methyl acetopyruvate ( 0.065 g , 0.45 mmol ) to yield a pale - orange , amorphous solid ( 0.14 g , 68% ) . h nmr ( 400 mhz , dmso - d6 ) 10.85 ( s , 1h ) , 7.71 ( d , j = 8.0 hz , 1h ) , 7.407.23 ( m , 4h ) , 7.147.03 ( m , 2h ) , 6.93 ( t , j = 7.6 hz , 1h ) , 5.13 ( s , 1h ) , 3.833.78 ( m , 4h ) , 2.982.82 ( m , 2h ) , 2.752.68 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 190.8 , 165.2 , 142.8 , 136.2 , 131.8 , 131.2 , 130.5 , 129.4 , 128.0 , 126.8 , 126.0 , 122.9 , 121.0 , 118.3 , 118.0 , 111.4 , 110.7 , 59.1 , 52.5 , 48.6 , 40.8 , 23.6 ( note : carbons 1 and 2 are absent ) . hms ( apci ) calcd for 453.1225 ; found 453.1219 [ m + h ] . compound 99 was prepared via procedure i from 38 ( 0.08 g , 0.44 mmol ) , tryptamine ( 0.070 g , 0.44 mmol ) , and methyl acetopyruvate ( 0.063 g , 0.44 mmol ) to yield a pale - orange solid ( 0.096 g , 50% ) . h nmr ( 400 mhz , cdcl3 ) 8.42 ( s , 1h ) , 7.81 ( t , j = 7.6 hz , 1h ) , 7.407.27 ( m , 2h ) , 7.20 ( t , j = 7.2 hz , 1h ) , 7.147.06 ( m , 1h ) , 6.95 ( d , j = 1.2 hz , 1h ) , 6.78 ( dd , j = 1.2 hz , j = 7.6 hz , 1h ) , 6.70 ( dd , j = 1.2 hz , j = 10.8 hz , 1h ) , 4.80 ( s , 1h ) , 4.094.03 ( m , 1h ) , 3.92 ( s , 3h ) , 3.102.96 ( m , 3h ) , 2.19 ( s , 3h ) . c nmr ( 100 mhz , cdcl3 ) 198.1 , 193.6 , 165.5 , 162.0 ( d , j = 260.4 hz ) , 142.8 ( d , j = 7.4 hz ) , 136.5 , 132.8 , 127.0 , 123.5 , 123.4 ( d , j = 26.0 hz ) , 122.5 , 122.3 , 122.1 , 120.1 , 119.7 , 118.7 , 118.5 , 111.9 , 111.7 , 61.2 , 52.6 , 41.6 , 29.2 , 24.4 ; mp 4045 c . hms ( apci ) calcd for c24h21fn2o5 437.1512 ; found 437.1512 [ m + h ] . compound 100 was prepared via procedure i from 34 ( 0.1 g , 0.56 mmol ) , tryptamine ( 0.089 g , 0.52 mmol ) , and methyl acetopyruvate ( 0.080 g , 0.56 mmol ) to yield an off - white solid ( 0.020 g , 8% ) . h nmr ( 400 mhz , dmso - d6 ) 10.68 ( s , 1h ) , 10.07 ( br s , 1h ) , 7.47 ( s , 1h ) , 7.357.29 ( m , 3h ) , 7.057.02 ( m , 3h ) , 6.91 ( t , j = 10.8 hz , 1h ) , 5.58 ( s , 1h ) , 3.83 ( s , 3h ) , 3.803.74 ( m , 1h ) , 3.022.88 ( m , 2h ) , 2.762.68 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 196.6 , 190.2 , 163.6 , 151.5 , 136.4 , 136.2 , 127.0 , 126.9 , 123.5 , 123.0 , 122.5 , 121.0 , 118.32 , 118.25 , 118.0 , 111.4 , 111.2 , 110.4 , 94.5 , 52.7 , 52.2 , 44.8 , 29.3 , 26.7 ; mp 194197 c . hms ( apci ) calcd for c24h22n2o6 435.1551 ; found 435.1552 [ m + h ] . compound 101 was prepared via procedure i from 41 ( 0.20 g , 1.0 mmol ) , tryptamine ( 0.17 g , 1.0 mmol ) , and methyl acetopyruvate ( 0.15 g , 1.0 mmol ) to yield an off - white solid ( 0.16 g , 36% ) . h nmr ( 600 mhz , dmso - d6 , 56 c ) 10.68 ( s , 1h ) , 7.53 ( s , 1h ) , 7.48 ( dd , j = 1.6 hz , j = 8.0 hz , 1h ) , 7.327.28 ( m , 2h ) , 7.067.02 ( m , 3h ) , 6.92 ( td , j = 7.2 hz , j = 0.8 hz , 1h ) , 5.59 ( s , 1h ) , 3.86 ( s , 6h ) , 3.813.72 ( m , 1h ) , 2.972.85 ( m , 2h ) , 2.842.69 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.5 , 165.9 , 165.2 , 157.9 , 154.8 , 136.2 , 130.6 , 126.9 , 126.6 , 122.7 , 121.9 , 121.0 , 118.3 , 117.8 , 111.7 , 111.5 , 110.7 , 56.0 , 52.3 , 41.0 , 40.1 , 29.7 , 23.4 ( note : carbon 3 and either carbon 1 or 2 are absent ) ; mp 103107 c . hms ( apci ) calcd for c25h24n2o6 449.1707 ; found 449.1704 [ m + h ] . compound 102 was prepared via procedure i from 36 ( 0.10 g , 0.56 mmol ) , tryptamine ( 0.090 g , 0.56 mmol ) , and methyl acetopyruvate ( 0.081 g , 0.56 mmol ) to yield an orange solid ( 0.12 g , 50% ) . h nmr ( 600 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.75 ( s , 1h ) , 7.66 ( d , j = 8.4 hz , 1h ) , 7.31 ( d , j = 8.4 hz , 1h ) , 7.22 ( d , j = 8.4 hz , 1h ) , 7.09 ( d , j = 1.8 hz , 1h ) , 7.04 ( t , j = 7.2 hz , 1h ) , 6.90 ( t , j = 7.8 hz , 1h ) , 6.84 ( d , j = 8.4 hz , 1h ) , 5.27 ( s , 1h ) , 3.81 ( s , 3h ) , 3.75 ( dt , j = 8.4 hz , j = 13.8 hz , 1h ) , 2.942.89 ( m , 1h ) , 2.762.69 ( m , 2h ) , 2.31 ( s , 3h ) , 2.25 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 166.0 , 165.5 , 140.6 , 138.2 , 136.3 , 131.0 , 128.8 , 127.0 , 126.8 , 125.4 , 122.9 , 121.1 , 118.3 , 117.7 , 111.5 , 110.7 , 55.6 , 41.5 , 40.1 , 23.6 , 18.5 , 14.1 ( note : carbons 3 and 4 , and either carbons 1 or 2 are absent ) ; mp 6070 c . hms ( apci ) calcd for c25h24n2o5 433.1763 ; found 433.1764 [ m + h ] . compound 103 was prepared via procedure i from 32 ( 0.10 g , 0.50 mmol ) , tryptamine ( 0.081 g , 0.50 mmol ) , and methyl acetopyruvate ( 0.073 g , 0.50 mmol ) to yield a pale - yellow solid ( 0.080 g , 35% ) . h nmr ( 400 mhz , dmso - d6 ) 12.50 ( br s , 1h ) , 10.81 ( s , 1h ) , 7.95 ( d , j = 1.6 hz , 1h ) , 7.76 ( dd , j = 1.2 hz , j = 8.0 hz , 1h ) , 7.29 ( d , j = 8.4 hz , 2h ) , 7.097.01 ( m , 3h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.68 ( s , 1h ) , 3.85 ( s , 3h ) , 3.803.73 ( m , 1h ) , 2.972.84 ( m , 2h ) , 2.772.72 ( m , 1h ) , 2.28 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 192.5 , 170.4 , 165.5 , 164.8 , 139.8 , 136.2 , 134.7 , 130.8 , 129.8 , 128.2 , 127.8 , 126.9 , 122.8 , 121.0 , 118.3 , 117.7 , 111.5 , 110.4 , 59.8 , 55.6 , 52.6 , 41.5 , 23.5 ( note : carbon 3 is absent ) ; mp 5560 c . hms ( apci ) calcd for c24h21cln2o5 453.1225 ; found 453.1222 [ m + h ] . compound 104 was prepared via procedure i from 37 ( 0.12 g , 0.67 mmol ) , tryptamine ( 0.11 g , 0.67 mmol ) , and methyl acetopyruvate ( 0.097 g , 0.67 mmol ) to yield an orange , amorphous solid ( 0.033 g , 11% ) . h nmr ( 400 mhz , cdcl3 ) 8.58 ( s , 1h ) , 7.65 ( d , j = 8.8 hz , 2h ) , 7.42 ( d , j = 7.6 hz , 1h ) , 7.317.27 ( m , 2h ) , 7.11 ( t , j = 7.2 hz , 1h ) , 7.20 ( t , j = 7.6 hz , 1h ) , 6.93 ( s , 1h ) , 5.52 ( s , 1h ) , 4.023.97 ( m , 1h ) , 3.88 ( s , 3h ) , 3.022.87 ( m , 3h ) , 2.35 ( s , 3h ) . c nmr ( 100 mhz , cdcl3 ) 192.9 , 191.4 , 171.1 , 167.1 ( d , j = 186.7 hz ) , 162.7 , 136.4 , 132.6 , 130.9 , 127.4 , 125.4 , 122.3 , 121.9 , 119.2 , 118.7 , 116.9 ( d , j = 23.8 ) , 114.0 , 112.5 , 111.3 , 102.3 , 52.4 , 45.9 , 41.3 , 28.4 , 24.1 . hms ( apci ) calcd for c24h21fn2o5 437.1507 ; found 437.1509 [ m + h ] . compound 105 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(1-methyl-1h - indol-3-yl)ethanamine ( 0.17 g , 1.0 mmol ) to yield cream - colored solid ( 0.21 g , 43% ) . h nmr ( 600 mhz , dmso - d6 ) 8.81 ( d , j = 1.8 hz , 1h ) , 8.70 ( dd , j = 1.8 hz , j = 4.8 , 1h ) , 8.01 ( dt , j = 1.8 hz , 8.4 hz , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.507.46 ( m , 3h ) , 7.36 ( d , j = 9.0 hz , 1h ) , 7.32 ( d , j = 8.4 hz , 1h ) , 7.147.10 ( m , 2h ) , 6.96 ( t , j = 7.8 hz , 1h ) , 5.50 ( s , 1h ) , 3.853.80 ( m , 4h ) , 3.70 ( s , 3h ) , 3.002.92 ( m , 2h ) , 2.762.72 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.2 , 165.9 , 165.0 , 153.9 , 152.2 , 149.1 , 142.0 , 136.6 , 136.3 , 133.9 , 129.5 , 129.4 , 128.4 , 127.3 , 127.2 , 123.5 , 121.2 , 118.4 , 118.3 , 110.1 , 109.7 , 60.4 , 52.2 , 41.3 , 32.2 , 23.5 ( note : either carbon 1 or 2 is absent ) ; mp 215218 c . hms ( apci ) calcd for c29h25n3o5 496.1867 ; found 496.1872 [ m + h ] . compound 106 was prepared via procedure i from methyl 4-formylbenzoate ( 0.094 g , 0.57 mmol ) , 2-(2-methyl-1h - indol-3-yl)ethanamine ( 0.10 g , 0.57 mmol ) , and methyl acetopyruvate ( 0.083 g , 0.57 mmol ) to yield a cream - colored solid ( 0.18 g , 73% ) . h nmr ( 600 mhz , dmso - d6 ) 10.73 ( s , 1h ) , 7.85 ( d , j = 9.0 hz , 2h ) , 7.21 ( d , j = 7.8 hz , 1h ) , 7.187.15 ( m , 3h ) , 6.97 ( t , j = 7.8 hz , 1h ) , 6.86 ( t , j = 7.8 hz , 1h ) , 5.03 ( s , 1h ) , 3.83 ( s , 3h ) , 3.643.59 ( m , 1h ) , 2.922.87 ( m , 1h ) , 2.772.72 ( m , 1h ) , 2.602.56 ( m , 1h ) , 2.26 ( s , 3h ) , 2.17 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.1 , 165.9 , 165.0 , 142.4 , 135.1 , 132.2 , 129.8 , 129.7 , 129.3 , 128.1 , 127.9 , 125.6 , 120.1 , 118.2 , 117.0 , 110.5 , 106.5 , 60.1 , 52.1 , 40.9 , 39.9 , 24.5 , 10.9 ; mp 182187 c . hms ( apci ) calcd for c25h24n2o5 433.1758 ; found 433.1759 [ m + h ] . compound 107 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(4-methyl-1h - indol-3-yl)ethanamine ( 0.17 g , 1.0 mmol ) to yield a pale - yellow solid ( 0.05 g , 11% ) . h nmr ( 600 mhz , dmso - d6 ) 10.84 ( d , j = 1.8 hz , 1h ) , 8.82 ( d , j = 1.8 hz , 1h ) , 8.70 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 8.01 ( dt , j = 1.8 hz , j = 8.4 hz , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.497.44 ( m , 3h ) , 7.15 ( d , j = 8.4 hz , 1h ) , 7.04 ( d , j = 2.4 hz , 1h ) , 6.92 ( t , j = 6.6 hz , 1h ) , 6.67 ( d , j = 7.2 hz , 1h ) , 5.48 ( s , 1h ) , 3.893.81 ( m , 4h ) , 3.143.09 ( m , 1h ) , 2.982.87 ( m , 2h ) , 2.44 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 186.9 , 165.9 , 165.1 , 152.3 , 149.3 , 142.2 , 136.7 , 136.2 , 133.9 , 129.5 , 129.4 , 128.3 , 125.4 , 123.4 , 123.1 , 122.9 , 121.1 , 120.1 , 119.9 , 118.2 , 111.5 , 109.6 , 66.4 , 60.4 , 52.2 , 25.5 , 19.7 ; mp 170175 c . hms ( apci ) calcd for c29h25n3o5 496.1845 ; found 496.1850 [ m + h ] . compound 108 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(5-methoxy-1h - indol-3-yl)ethanamine ( 0.19 g , 1.0 mmol ) to yield a yellow solid ( 0.35 g , 68% ) . h nmr ( 600 mhz , dmso - d6 ) 10.72 ( s , 1h ) , 8.79 ( d , j = 1.8 hz , 1h ) , 8.68 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 7.99 ( dt , j = 1.8 hz , j = 7.8 hz , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.487.46 ( m , 1h ) , 7.44 ( d , j = 7.8 hz , 2h ) , 7.227.21 ( m , 2h ) , 7.09 ( d , j = 2.4 hz , 1h ) , 6.75 ( d , j = 2.4 hz , 1h ) , 6.70 ( dd , j = 2.4 hz , j = 9.0 hz , 1h ) , 5.44 ( s , h ) , 3.853.80 ( m , 4h ) , 2.68 ( s , 3h ) , 2.982.89 ( m , 2h ) , 2.732.70 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.7 , 181.1 , 165.9 , 165.2 , 153.0 , 152.0 , 149.1 , 142.4 , 136.3 , 134.1 , 131.4 , 129.5 , 129.4 , 128.3 , 127.2 , 123.6 , 123.5 , 117.9 , 112.2 , 111.3 , 110.5 , 99.7 , 60.4 , 55.2 , 52.2 , 41.1 , 23.8 ; mp 222225 c . hms ( apci ) calcd for c29h25n3o6 512.1816 ; found 512.1822 [ m + h ] . compound 109 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 3-(6-fluoro-1h - indol-3-yl)ethanamine ( 0.18 g , 1.0 mmol ) to yield a pale - orange solid ( 0.44 g , 87% ) . h nmr ( 600 mhz , dmso - d6 ) 10.94 ( s , 1h ) , 8.82 ( d , j = 0.6 hz , 1h ) , 8.69 ( d , j = 4.8 hz , 1h ) , 8.01 ( d , j = 7.8 hz , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.80 ( br s , 1h ) , 7.497.47 ( m , 1h ) , 7.43 ( d , j = 7.8 hz , 2h ) , 7.337.30 ( m , 1h ) , 7.317.10 ( m , 2h ) , 6.79 ( td , j = 9.6 hz , j = 1.8 hz , 1h ) , 5.44 ( s , 1h ) , 3.893.82 ( m , 4h ) , 2.982.91 ( m , 2h ) , 2.802.76 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.9 , 181.1 , 165.9 , 165.1 , 159.7 , 158.1 , 152.3 , 142.2 , 136.3 , 136.1 , 133.9 , 129.5 , 129.3 , 128.3 , 125.5 , 123.8 , 123.4 , 119.1 , 118.1 , 111.1 , 106.7 , 106.6 , 60.4 ( d , j = 14.4 hz ) , 52.1 , 41.1 , 23.1 ; mp 162167 c . hms ( apci ) calcd for c28h22fn3o5 500.1595 ; found 500.1600 [ m + h ] . compound 110 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(6-chloro-1h - indol-3-yl)ethanamine ( 0.20 g , 1.0 mmol ) to yield a yellow solid ( 0.44 g , 85% ) . h nmr ( 600 mhz , dmso - d6 ) 11.00 ( s , 1h ) , 8.80 ( s , 1h ) , 8.68 ( d , j = 3.6 hz , 1h ) , 8.00 ( d , j = 8.4 hz , 1h ) , 7.87 ( d , j = 7.8 hz , 2h ) , 7.77 ( br s , 1h ) , 7.487.41 ( m , 3h ) , 7.37 ( d , j = 1.2 hz , 1h ) , 7.33 ( d , j = 8.4 hz , 1h ) , 7.17 ( s , 1h ) , 6.94 ( dd , j = 1.2 hz , j = 8.4 hz , 1h ) , 3.873.82 ( m , 4h ) , 2.972.89 ( m , 2h ) , 2.792.76 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.2 , 165.9 , 165.3 , 149.2 , 136.6 , 136.2 , 129.44 , 129.36 , 128.3 , 128.1 , 125.8 , 125.7 , 125.5 , 124.7 , 124.1 , 123.3 , 119.5 , 118.8 , 118.6 , 111.2 , 111.1 , 109.8 , 60.3 , 52.1 , 41.0 , 23.4 ; mp 184189 c . hms ( apci ) calcd for c28h22cln3o5 516.1321 ; found 516.1324 [ m + h ] . compound 111 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(6-methyl-1h - indol-3-yl)ethanamine ( 0.17 g , 1.0 mmol ) to yield a cream - colored solid ( 0.10 g , 20% ) . h nmr ( 600 mhz , dmso - d6 ) 10.71 ( s , 1h ) , 8.79 ( s , 1h ) , 8.68 ( d , j = 3.6 hz , 1h ) , 7.99 ( d , j = 6.6 hz , 1h ) , 7.87 ( d , j = 7.8 hz , 2h ) , 7.47 ( t , j = 6.0 hz , 1h ) , 7.42 ( d , j = 7.8 hz , 2h ) , 7.17 ( d , j = 7.8 hz , 1h ) , 7.11 ( s , 1h ) , 7.02 ( s , 1h ) , 6.75 ( d , j = 7.8 hz , 1h ) , 5.40 ( s , 1h ) , 3.903.82 ( m , 4h ) , 2.992.89 ( m , 2h ) , 2.742.71 ( m , 1h ) , 2.37 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 186.7 , 165.9 , 165.1 , 152.1 , 149.1 , 142.3 , 136.7 , 136.2 , 134.0 , 130.0 , 129.5 , 129.4 , 128.4 , 128.1 , 125.5 , 124.9 , 123.4 , 122.2 , 120.0 , 117.8 , 111.3 , 110.6 , 60.4 , 52.2 , 41.1 , 23.8 , 21.4 ; mp 202207 c . hms ( apci ) calcd for c29h25n3o5 496.1867 ; found 496.1868 [ m + h ] . compound 112 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(6-methoxy-1h - indol-3-yl)ethanamine ( 0.19 g , 1.0 mmol ) to yield a pale - orange solid ( 0.39 g , 76% ) . h nmr ( 600 mhz , dmso - d6 ) 10.64 ( s , 1h ) , 8.78 ( s , 1h ) , 8.67 ( s , 1h ) , 8.06 ( d , j = 7.8 hz , 1h ) , 7.87 ( d , j = 7.8 hz , 2h ) , 7.55 ( d , j = 7.2 hz , 1h ) , 7.41 ( d , j = 7.8 hz , 2h ) , 7.11 ( d , j = 7.8 hz , 1h ) , 6.96 ( s , 1h ) , 6.83 ( s , 1h ) , 6.58 ( d , j = 7.8 hz , 1h ) , 5.39 ( s , 1h ) , 3.82 ( s , 3h ) , 3.753.70 ( m , 4h ) , 2.942.90 ( m , 2h ) , 2.712.69 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 165.8 , 155.6 , 145.7 , 137.6 , 137.4 , 137.0 , 130.8 , 130.4 , 129.5 , 129.4 , 128.3 , 128.11 , 128.07 , 125.5 , 121.3 , 118.7 , 110.8 , 108.5 , 107.5 , 94.5 , 60.4 , 55.2 , 40.9 , 23.8 , 20.8 ( note : two of either carbon 1 , 2 , or 3 are absent ) ; mp 195200 c . hms ( apci ) calcd for c29h25n3o6 512.1816 ; found 512.1821 [ m + h ] . to a slurry of 2-(7-fluoro-1h - indol-3-yl)ethanamine hydrochloride ( 0.05 g , 0.23 mmol ) in meoh ( 0.026 ml ) was added triethylamine ( 0.039 ml , 0.28 mmol ) . ether ( 1.3 ml ) was added , and the mixture was stirred at 10 c for 1 h. the resulting triethylamine hydrochloride salt was filtered off , and the filtrate was concentrated in vacuo to afford a white solid ( 0.040 g , > 99% ) which was carried on immediately . compound 113 was prepared via procedure i from methyl 4-formylbenzoate ( 0.039 g , 0.24 mmol ) , 19 ( 0.052 g , 0.24 mmol ) , and 2-(7-fluoro-1h - indol-3-yl)ethanamine hydrochloride ( 0.040 g , 0.24 mmol ) to yield a pale - yellow solid ( 0.11 g , 97% ) . h nmr ( 600 mhz , dmso - d6 ) 11.30 ( s , 1h ) , 10.11 ( s , 1h ) , 8.74 ( m , 1h ) , 8.46 ( m , 1h ) , 7.987.97 ( m , 1h ) , 7.877.86 ( m , 1h ) , 7.377.33 ( m , 2h ) , 7.28 ( m , 1h ) , 7.167.14 ( m , 2h ) , 6.896.87 ( m , 2h ) , 5.23 ( s , 1h ) , 3.843.76 ( m , 4h ) , 2.92 ( m , 1h ) , 2.79 ( m , 1h ) , 2.732.68 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 193.0 ( d , j = 13.4 hz ) , 169.4 , 166.2 , 165.5 , 150.0 , 149.5 , 148.4 , 147.7 , 139.1 , 136.6 , 134.3 , 131.1 , 129.7 , 129.0 , 128.7 , 128.3 , 127.7 , 124.0 , 118.6 , 114.7 , 112.4 , 105.8 , 60.0 ( d , j = 45.5 hz ) , 52.0 ( d , j = 41.2 hz ) , 40.1 ( d , j = 21.8 hz ) , 23.3 ; mp 6569 c . hms ( apci ) calcd for c28h22fn3o5 500.1616 ; found 500.1616 [ m + h ] . to a slurry of 2-(7-chloro-1h - indol-3-yl)ethanamine hydrochloride ( 0.15 g , 0.65 mmol ) in meoh ( 0.072 ml ) ether ( 3.62 ml ) was added , and the mixture was stirred at 10 c for 1 h. the resulting triethylamine hydrochloride salt was filtered off , and the filtrate was concentrated in vacuo to afford a white solid ( 0.074 g , 58% ) which was carried on immediately . compound 114 was prepared via procedure i from methyl 4-formylbenzoate ( 0.064 g , 0.39 mmol ) , 19 ( 0.086 g , 0.39 mmol ) , and 2-(7-chloro-1h - indol-3-yl)ethanamine hydrochloride ( 0.074 g , 0.39 mmol ) to yield a yellow solid ( 0.009 g , 5% ) . h nmr ( 600 mhz , dmso - d6 ) 11.22 ( s , 1h ) , 8.80 ( s , 1h ) , 8.69 ( d , j = 4.2 hz , 1h ) , 8.00 ( d , j = 7.8 hz , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.497.44 ( m , 3h ) , 7.31 ( d , j = 7.8 hz , 1h ) , 7.22 ( d , j = 1.8 hz , 1h ) , 7.14 ( d , j = 7.2 hz , 1h ) , 6.94 ( t , j = 7.2 hz , 1h ) , 5.49 ( s , 1h ) , 3.893.82 ( m , 4h ) , 3.002.91 ( m , 2h ) , 2.832.78 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.3 , 165.9 , 165.0 , 152.4 , 149.3 , 142.0 , 136.2 , 133.9 , 133.0 , 129.5 , 129.4 , 129.0 , 128.3 , 124.4 , 123.5 , 120.6 , 119.4 , 118.2 , 117.3 , 115.9 , 112.3 , 60.2 , 52.2 , 41.0 , 23.6 ( note : one of either carbon 1 , 2 , or 3 are absent ) ; mp 246249 c . hms ( apci ) calcd for c28h22cln3o5 516.1321 ; found 516.1325 [ m + h ] . compound 115 was prepared via procedure i from methyl 4-formylbenzoate ( 0.094 g , 0.57 mmol ) , 2-(7-methyl-1h - indol-3-yl ) ethanamine ( 0.10 g , 0.57 mmol ) , and methyl acetopyruvate ( 0.083 g , 0.57 mmol ) to yield a white solid ( 0.16 g , 66% ) . h nmr ( 400 mhz , dmso - d6 ) 12.50 ( br s , 1h ) , 10.78 ( s , 1h ) , 7.88 ( d , j = 8.0 hz , 2h ) , 7.26 ( d , j = 8.4 hz , 2h ) , 7.127.07 ( m , 2h ) , 6.836.82 ( m , 2h ) , 5.20 ( s , 1h ) , 3.833.76 ( m , 4h ) , 2.982.80 ( m , 2h ) , 2.802.66 ( m , 1h ) , 2.41 ( s , 3h ) , 2.26 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 165.9 , 165.0 , 142.4 , 135.7 , 129.3 , 128.1 , 126.5 , 125.5 , 122.5 , 121.5 , 120.5 , 118.5 , 115.7 , 111.1 , 109.7 , 59.7 , 52.1 , 40.8 , 40.0 , 23.7 , 16.7 ( note : carbons 3 and 4 are absent ) ; mp 220227 c . hms ( apci ) calcd from c25h24n2o5 433.1758 ; found 433.1758 [ m + h ] . compound 116 was prepared via procedure i from 19 ( 0.15 g , 0.68 mmol ) , tryptamine ( 0.11 g , 0.68 mmol ) , and 35 ( 0.12 g , 0.68 mmol ) to yield a yellow solid ( 0.027 g , 8% ) . h nmr ( 400 mhz , dmso - d6 ) 10.84 ( s , 1h ) , 8.75 ( s , 1h ) , 8.48 ( d , j = 3.2 hz , 1h ) , 7.94 ( d , j = 7.2 hz , 1h ) , 7.83 ( d , j = 8.0 hz , 2h ) , 7.347.27 ( m , 5h ) , 7.087.04 ( m , 2h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.33 ( s , 1h ) , 4.28 ( q , j = 7.6 hz , 2h ) , 3.843.77 ( m , 1h ) , 3.002.93 ( m , 1h ) , 2.872.80 ( m , 1h ) , 2.732.66 ( m , 1h ) , 1.28 ( t , j = 6.8 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 186.8 , 182.1 , 162.9 , 155.0 , 148.3 , 148.1 , 136.4 , 136.3 , 127.0 , 123.8 , 123.4 , 123.2 , 123.1 , 121.5 , 121.3 , 120.8 , 118.5 , 118.2 , 117.8 , 111.8 , 111.2 , 109.5 , 60.6 , 45.3 , 23.6 , 23.3 , 14.0 ; mp > 250 c . hms ( apci ) calcd for c29h25n3o5 496.1867 ; found 496.1872 [ m + h ] . compound 117 was prepared via procedure i from 45 ( 0.40 g , 2.3 mmol ) , tryptamine ( 0.36 g , 2.3 mmol ) , and 20 ( 0.50 g , 2.3 mmol ) to yield a yellow solid ( 0.019 g , 2% ) . h nmr ( 600 mhz , dmso - d6 ) 10.84 ( s , 1h ) , 8.68 ( d , j = 5.4 hz , 2h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.51 ( d , j = 5.4 hz , 2h ) , 7.40 ( d , j = 8.4 hz , 2h ) , 7.34 ( d , j = 8.4 hz , 1h ) , 7.30 ( d , j = 8.4 hz , 1h ) , 7.12 ( d , j = 1.8 hz , 1h ) , 7.06 ( t , j = 7.8 hz , 1h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.40 ( s , 1h ) , 4.29 ( q , j = 7.2 hz , 2h ) , 3.883.82 ( m , 1h ) , 3.002.90 ( m , 2h ) , 2.782.73 ( m , 1h ) , 1.29 ( 7.2 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 189.0 , 165.4 , 165.0 , 149.6 , 145.8 , 142.2 , 136.2 , 129.8 , 129.7 , 129.3 , 128.3 , 126.9 , 122.9 , 121.8 , 121.1 , 118.3 , 118.1 , 117.35 , 111.5 , 110.7 , 60.7 , 60.3 , 41.1 , 23.6 , 14.2 ; mp 169172 c . hms ( apci ) calcd for c29h25n3o5 496.1880 ; found 496.1877 [ m + h ] . compound 118 was prepared via procedure i from 19 ( 0.15 g , 0.68 mmol ) , 2-(2-methyl-1h - indol-3-yl)ethanamine ( 0.12 g , 0.68 mmol ) , and methyl 4-formylbenzoate ( 0.11 g , 0.68 mmol ) to yield an orange solid ( 0.046 g , 14% ) . h nmr ( 400 mhz , dmso - d6 ) 10.75 ( s , 1h ) , 8.73 ( s , 1h ) , 8.48 ( d , j = 4.4 hz , 1h ) , 7.93 ( s , 1h ) , 7.82 ( d , j = 8.4 hz , 2h ) , 7.307.17 ( m , 5h ) , 6.97 ( t , j = 6.4 hz , 1h ) , 6.86 ( t , j = 7.2 hz , 1h ) , 5.23 ( s , 1h ) , 3.81 ( s , 3h ) , 3.633.56 ( m , 1h ) , 2.962.88 ( m , 1h ) , 2.762.69 ( m , 1h ) , 2.572.50 ( m , 1h ) , 2.18 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 182.6 , 166.0 , 150.4 , 150.1 , 149.2 , 136.8 , 136.1 , 135.5 , 135.2 , 132.2 , 129.0 , 128.6 , 128.0 , 123.6 , 122.6 , 120.1 , 118.2 , 117.0 , 110.6 , 106.7 , 61.2 , 52.0 , 41.3 , 22.6 , 11.0 ( note : two of carbons 1 , 2 , 3 , or 4 are absent ) ; mp > 250 c . hms ( apci ) calcd for c29h25n3o5 496.1867 ; found 496.1872 [ m + h ] . compound 119 was prepared via procedure i from 45 ( 0.15 g , 0.84 mmol ) , 2-(2-methyl-1h - indol-3-yl)ethanamine ( 0.15 g , 0.84 mmol ) , and methyl acetopyruvate ( 0.12 g , 0.84 mmol ) to yield a cream - colored solid ( 0.078 g , 21% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.5 ( br s , 1h ) , 7.83 ( d , j = 7.2 hz , 2h ) , 7.237.18 ( m , 4h ) , 6.95 ( t , j = 7.2 hz , 1h ) , 6.86 ( t , j = 7.2 hz , 1h ) , 5.09 ( s , 1h ) , 4.30 ( q , j = 7.2 hz , 2h ) , 3.613.56 ( m , 1h ) , 2.922.87 ( m , 1h ) , 2.802.75 ( m , 1h ) , 2.572.53 ( m , 1h ) , 2.19 ( s , 3h ) , 2.05 ( s , 3h ) , 1.30 ( t , j = 7.2 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.3 , 189.3 , 165.5 , 135.1 , 132.1 , 129.1 , 127.9 , 120.1 , 118.1 , 117.0 , 112.1 , 110.5 , 108.9 , 106.6 , 98.5 , 90.2 , 54.9 , 48.7 , 48.6 , 40.0 , 29.0 , 14.2 , 11.0 ( note : one of either carbon 1 , 2 , or 4 is absent ) ; mp 190195 c . hms ( apci ) calcd for c26h26n2o5 447.1928 ; found 447.30 [ m + h ] . compound 120 was prepared via procedure i from 189 ( 0.15 g , 0.77 mmol ) , tryptamine ( 0.12 g , 0.77 mmol ) , and methyl acetopyruvate ( 0.11 g , 0.77 mmol ) to yield a cream - colored solid ( 0.20 g , 57% ) . h nmr ( 400 mhz , dmso - d6 ) 10.81 ( s , 1h ) , 10.42 ( s , 1h ) , 7.597.46 ( m , 1h ) , 7.347.23 ( m , 3h ) , 7.127.02 ( m , 2h ) , 6.976.89 ( m , 2h ) , 5.76 ( s , 1h ) , 4.28 ( q , j = 7.2 hz , 2h ) , 3.783.74 ( m , 1h ) , 2.982.85 ( m , 2h ) , 2.732.68 ( m , 1h ) , 2.28 ( s , 3h ) , 1.29 ( t , j = 7.2 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.7 , 165.5 , 165.1 , 156.2 , 154.8 , 136.2 , 130.5 , 128.1 , 127.0 , 126.7 , 125.5 , 122.7 , 121.0 , 120.2 , 118.3 , 118.0 , 116.1 , 111.4 , 110.8 , 60.7 , 41.0 , 40.0 , 29.7 , 23.4 , 14.2 ; mp 200205 c . hms ( apci ) calcd for c25h24n2o6 449.1721 ; found 449.1723 [ m + h ] . compound 121 was prepared via procedure i from methyl 4-formylbenzoate ( 0.28 g , 1.7 mmol ) , ( 1h - indol-3-yl)methanamine ( 0.25 g , 1.7 mmol ) , and 20 ( 0.38 g , 1.7 mmol ) to yield an orange solid ( 0.78 g , 98% ) . h nmr ( 400 mhz , dmso - d6 ) 11.08 ( s , 1h ) , 8.66 ( d , j = 5.6 hz , 2h ) , 7.92 ( d , j = 8.0 hz , 2h ) , 7.517.37 ( m , 6h ) , 7.137.08 ( m , 2h ) , 6.97 ( t , j = 7.2 hz , 1h ) , 5.115.07 ( m , 2h ) , 3.84 ( s , 3h ) , 3.80 ( d , j = 14.8 hz , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 166.0 , 165.1 , 149.2 , 129.45 , 129.36 , 128.2 , 128.1 , 126.2 , 125.5 , 125.1 , 122.0 , 121.7 , 121.5 , 119.0 , 118.9 , 118.6 , 118.2 , 111.7 , 109.3 , 59.2 , 52.2 , 35.5 ( note : carbon 4 is absent ) ; mp 240243 c . hms ( apci ) calcd for c27h21n3o5 468.1567 ; found 468.1566 [ m + h ] . compound 122 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 3-(1h - indol-3-yl)propan-1-amine ( 0.17 g , 1.0 mmol ) to yield a yellow solid ( 0.35 g , 71% ) . h nmr ( 600 mhz , dmso - d6 ) 10.75 ( s , 1h ) , 8.82 ( s , 1h ) , 8.69 ( d , j = 4.8 hz , 1h ) , 8.02 ( d , j = 7.8 hz , 1h ) , 7.87 ( d , j = 8.4 hz , 2h ) , 7.497.47 ( m , 3h ) , 7.37 ( d , j = 7.8 hz , 1h ) , 7.31 ( d , j = 8.4 hz , 1h ) , 7.067.03 ( m , 2h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.54 ( s , 1h ) , 3.623.55 ( m , 4h ) , 2.832.79 ( m , 1h ) , 2.622.55 ( m , 2h ) , 1.841.80 ( m , 1h ) , 1.731.69 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.9 , 165.9 , 165.2 , 154.4 , 152.1 , 149.2 , 142.4 , 136.3 , 134.0 , 129.5 , 128.3 , 127.0 , 123.5 , 122.4 , 122.3 , 120.8 , 118.3 , 118.0 , 113.4 , 111.4 , 60.4 , 52.3 , 40.7 , 28.0 , 22.1 ( note : either carbon 1 or 2 and carbon 3 are absent ) ; mp 221226 c . hms ( apci ) calcd for c29h25n3o5 496.1845 ; found 496.1852 [ m + h ] . to a solution of 1 ( 0.50 g , 1.2 mmol ) in dcm : meoh ( 1:1 , 0.13 m ) was added ( diazomethyl)trimethylsilane ( 0.72 ml , 1.4 mmol ) . the reaction mixture continued to stir at rt for 5 h before being concentrated in vacuo . the crude residue was then purified using flash column chromatography on sio2 ( 3% meoh / dcm ) to yield a pale - yellow solid ( 0.24 g , 46% ) . h nmr ( 400 mhz , dmso - d6 ) 10.82 ( s , 1h ) , 7.88 ( dd , j = 1.6 hz , j = 8.0 hz , 2h ) , 7.337.24 ( m , 4h ) , 7.097.03 ( m , 2h ) , 6.92 ( t , j = 7.6 hz , 1h ) , 5.20 ( s , 1h ) , 4.36 ( s , 3h ) , 3.84 ( s , 3h ) , 3.803.71 ( m , 1h ) , 2.962.89 ( m , 1h ) , 2.842.77 ( m , 1h ) , 2.722.63 ( m , 1h ) , 2.25 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.9 , 165.9 , 164.2 , 154.0 , 141.7 , 136.2 , 129.5 , 129.3 , 128.2 , 126.8 , 126.2 , 122.9 , 121.0 , 118.3 , 118.0 , 111.5 , 110.7 , 59.5 , 59.1 , 52.2 , 40.9 , 30.3 , 23.6 ; mp 4045 c . hms ( apci ) calcd for c25h24n2o5 433.1763 ; found 433.1761 [ m + h ] . to a solution of 1 ( 0.50 g , 1.2 mmol ) in 2-methoxyethanol ( 8.36 ml , 0.14 m ) was added ammonium formate ( 0.11 ml , 2.2 mmol , 1.8 equiv ) . the reaction mixture was refluxed for 3 h before being concentrated in vacuo , ground with a mortar and pestle , and triturated with et2o . further purification was achieved via flash column chromatography on sio2 ( 10% meoh / dcm ) to yield a pale - yellow solid ( 0.070 g , 14% ) . h nmr ( 400 mhz , cdcl3 , 56 c ) 10.02 ( br s , 1h ) , 8.36 ( br s , 1h ) , 7.92 ( d , j = 8.0 hz , 2h ) , 7.397.34 ( m , 2h ) , 7.17 ( t , j = 7.6 hz , 1h ) , 7.087.02 ( m , 3h ) , 6.97 ( s , 1h ) , 6.44 ( br s , 1h ) , 4.77 ( s , 1h ) , 4.043.97 ( m , 1h ) , 3.91 ( s , 3h ) , 3.092.99 ( m , 2h ) , 2.922.85 ( m , 1h ) , 1.56 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 177.8 , 165.9 , 164.4 , 163.2 , 144.7 , 136.2 , 129.7 , 129.5 , 128.3 , 126.9 , 122.7 , 121.0 , 118.2 , 118.0 , 111.4 , 110.8 , 105.6 , 58.0 , 52.1 , 48.6 , 41.0 , 23.2 ; mp 5054 c . hms ( apci ) calcd for c24h23n3o4 418.1766 ; found 418.1766 [ m + h ] . to a solution of 1 ( 0.50 g , 1.2 mmol ) in dcm ( 11 ml , 0.11 m ) was added acetic anhydride ( 0.14 ml , 1.4 mmol , 1.2 equiv ) and pyridine ( 0.14 ml , 1.8 mmol , 1.5 equiv ) . the reaction mixture was stirred at rt for 6/2 h before being concentrated in vacuo . the crude material was then purified by flash column chromatography on sio2 ( 3% meoh / dcm ) . additional purification was achieved using hplc ( 75% acn with 0.1% formic acid ) to give a yellow oil ( 0.038 g , 7% ) . h nmr ( 400 mhz , cdcl3 ) 8.06 ( s , 1h ) , 7.947.92 ( m , 2h ) , 7.38 ( d , j = 8.4 hz , 2h ) , 7.21 ( t , j = 8.0 hz , 1h ) , 7.107.05 ( m , 3h ) , 6.98 ( d , j = 2.0 hz , 1h ) , 4.93 ( s , 1h ) , 4.074.00 ( m , 1h ) , 3.91 ( s , 3h ) , 3.082.89 ( m , 3h ) , 2.47 ( s , 3h ) , 2.26 ( s , 3h ) ; c nmr ( 150 mhz , cdcl3 ) 191.5 , 167.0 , 166.6 , 163.8 , 147.7 , 139.2 , 137.0 , 136.6 , 131.0 , 130.4 , 128.1 , 127.4 , 122.6 , 122.2 , 119.9 , 118.7 , 112.6 , 111.5 , 62.3 , 62.4 , 41.5 , 30.1 , 24.4 , 20.8 . hms ( apci ) calcd for c26h24n2o6 461.1721 ; found 461.1717 [ m + h ] . to a solution of 106 ( 0.30 g , 0.69 mmol ) and triethylamine ( 0.19 ml , 1.4 mmol , 2.0 equiv ) in thf ( 0.69 ml , 1.0 m ) at 30 c was added butyryl chloride ( 0.072 ml , 0.69 mmol , 1.0 equiv ) dropwise over 20 min . the mixture was allowed to stir at 30 c for 2 h before being concentrated in vacuo . the crude material was dissolved in etoac , washed with water and brine , dried over mgso4 , filtered , and concentrated in vacuo . purification was achieved via flash column chromatography on sio2 ( 10% etoac : dcm ) to afford a yellow , amorphous solid ( 0.12 g , 35% ) . h nmr ( 600 mhz , cdcl3 ) 7.96 ( s , 1h ) , 7.88 ( d , j = 7.8 hz , 2h ) , 7.25 ( d , j = 8.4 hz , 1h ) , 7.20 ( d , j = 7.2 hz , 1h ) , 7.11 ( t , j = 7.2 hz , 1h ) , 7.01 ( t , j = 7.2 hz , 1h ) , 6.94 ( d , j = 7.8 hz , 2h ) , 4.78 ( s , 1h ) , 3.89 ( s , 3h ) , 3.873.82 ( m , 1h ) , 3.02 ( dt , j = 13.8 hz , j = 8.4 hz , 1h ) , 2.91 ( dt , j = 13.8 hz , j = 7.8 hz , 1h ) , 2.822.78 ( m , 1h ) , 2.70 ( t , j = 7.8 hz , 2h ) , 2.24 ( s , 3h ) , 2.23 ( s , 3h ) , 1.85 ( sextet , 7.8 hz , 2h ) , 1.09 ( t , j = 7.2 hz , 3h ) . c nmr ( 150 mhz , cdcl3 ) 191.6 , 170.0 , 166.6 , 163.7 , 147.9 , 139.1 , 136.9 , 135.4 , 132.1 , 130.8 , 130.2 , 128.3 , 128.0 , 121.5 , 119.7 , 117.8 , 110.6 , 108.0 , 62.5 , 52.4 , 41.4 , 35.9 , 30.2 , 23.3 , 18.4 , 13.7 , 11.5 . hms ( apci ) calcd for c29h30n2o6 503.2168 ; found 503.2172 [ m + h ] . to a solution of 106 ( 3.0 g , 6.9 mmol ) and triethylamine ( 1.9 ml , 14 mmol , 2.0 equiv ) in thf ( 6.9 ml , 1.0 m ) at 30 c was added acryloyl chloride ( 0.72 ml , 6.9 mmol , 1.0 equiv ) dropwise over 20 min . the mixture was allowed to stir at 30 c for 2 h before being concentrated in vacuo . the crude material was dissolved in etoac , washed with water and brine , dried over mgso4 , filtered , and concentrated in vacuo . purification was achieved via flash column chromatography on sio2 ( 10% etoac : dcm ) to afford a yellow , amorphous solid ( 0.68 g , 20% ) . h nmr ( 300 mhz , cdcl3 ) 8.00 ( s , 1h ) , 7.89 ( d , j = 8.7 hz , 2h ) , 7.277.20 ( m , 2h ) , 7.11 ( t , j = 7.2 hz , 1h ) , 7.036.94 ( m , 3h ) , 6.71 ( d , j = 0.9 hz , 1h ) , 6.43 ( d , j = 10.2 hz , 1h ) , 6.20 ( d , j = 0.6 hz , 1h ) , 4.81 ( s , 1h ) , 3.893.81 ( m , 4h ) , 3.082.76 ( m , 3h ) , 2.24 ( s , 6h ) . c nmr ( 150 mhz , cdcl3 ) 196.1 , 191.6 , 186.7 , 166.6 , 163.6 , 162.2 , 147.6 , 139.0 , 137.3 , 135.7 , 135.4 , 132.1 , 130.8 , 130.2 , 128.3 , 128.0 , 126.0 , 121.5 , 119.6 , 117.7 , 110.7 , 107.9 , 62.6 , 52.4 , 41.5 , 30.2 , 23.3 , 11.5 . hms ( apci ) calcd for c28h26n2o6 487.1837 ; found 487.1860 [ m + h ] . compound 161 was prepared via procedure i from methyl 4-formylbenzoate ( 0.34 g , 2.1 mmol ) , ethyl acetopyruvate ( 0.33 g , 2.1 mmol ) , and 2-phenylethanamine ( 0.25 g , 2.1 mmol ) to yield a white solid ( 0.73 g , 93% ) . h nmr ( 400 mhz , dmso - d6 ) 7.92 ( d , j = 8.4 hz , 2h ) , 7.317.24 ( m , 4h ) , 7.19 ( d , j = 7.2 hz , 1h ) , 7.10 ( d , j = 6.8 hz , 2h ) , 5.15 ( s , 1h ) , 3.833.76 ( m , 4h ) , 2.822.60 ( m , 3h ) , 2.26 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 190.9 , 165.9 , 165.0 , 142.4 , 138.5 , 129.4 , 129.4 , 128.6 , 128.5 , 128.1 , 126.4 , 125.6 , 119.7 , 66.4 , 59.7 , 52.2 , 41.5 , 33.5 ; mp 123128 c . hms ( apci ) calcd for c22h21no5 380.1493 ; found 380.1494 [ m + h ] . compound 162 was prepared via procedure i from methyl 4-formylbenzoate ( 0.40 g , 2.4 mmol ) , 188 ( 0.41 g , 2.4 mmol ) , and 20 ( 0.53 g , 2.4 mmol ) to yield a yellow solid ( 0.67 g , 56% ) . h nmr ( 600 mhz , dmso - d6 ) 8.70 ( d , j = 3.6 hz , 2h ) , 7.937.84 ( m , 4h ) , 7.81 ( d , j = 7.8 hz , 1h ) , 7.577.40 ( m , 7h ) , 7.30 ( d , j = 6.6 hz , 1h ) , 5.40 ( s , 1h ) , 3.843.80 ( m , 4h ) , 3.373.34 ( m , 1h ) , 3.133.08 ( m , 1h ) , 3.033.00 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 196.1 , 165.9 , 162.1 , 160.1 , 136.4 , 136.3 , 130.7 , 129.5 , 128.2 , 128.0 , 125.5 , 123.4 , 122.8 , 121.2 , 120.8 , 118.48 , 118.45 , 118.2 , 118.1 , 115.2 , 111.6 , 111.3 , 61.5 , 52.2 , 48.6 , 26.2 ; mp 221224 c . hms ( apci ) calcd for c30h24n2o5 493.1758 ; found 493.1756 [ m + h ] . compound 163 was prepared via procedure i from methyl 4-formylbenzoate ( 0.20 g , 1.2 mmol ) , 19 ( 0.27 g , 1.2 mmol ) , and 2-(benzofuran-3-yl)ethanamine ( 0.20 g , 1.2 mmol ) to yield a pale - yellow solid ( 0.028 g , 4.7% ) . h nmr ( 600 mhz , dmso - d6 ) 8.78 ( s , 1h ) , 8.57 ( s , 1h ) , 7.99 ( d , j = 7.2 hz , 1h ) , 7.86 ( d , j = 7.8 hz , 2h ) , 7.77 ( s , 1h ) , 7.52 ( d , j = 8.4 hz , 1h ) , 7.477.42 ( m , 3h ) , 7.37 ( t , j = 5.4 hz , 1h ) , 7.29 ( t , j = 7.2 hz , 1h ) , 7.20 ( t , j = 7.2 hz , 1h ) , 5.44 ( s , 1h ) , 3.873.82 ( m , 4h ) , 2.972.92 ( m , 2h ) , 2.762.75 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 189.3 , 181.3 , 166.0 , 154.6 , 150.6 , 149.5 , 142.4 , 135.9 , 129.1 , 128.8 , 128.1 , 127.5 , 124.4 , 122.7 , 122.4 , 119.6 , 117.0 , 115.6 , 111.3 , 60.2 , 52.1 , 40.0 , 21.7 ( note : carbons 1 , 2 , and 3 are absent ) ; mp 225230 c . hms ( apci ) calcd for c28h22n2o6 481.1397 ; found 481.1396 [ m h ] . compound 164 was prepared via procedure i from methyl 4-formylbenzoate ( 0.19 g , 1.1 mmol ) , 2-(1h - benzo[d]imidazol-1-yl)ethanamine ( 0.18 g , 1.1 mmol ) , and 20 ( 0.25 g , 1.1 mmol ) to yield a yellow solid ( 0.40 g , 73% ) . h nmr ( 400 mhz , dmso - d6 ) 8.66 ( d , j = 1.3 hz , 2h ) , 8.59 ( s , 1h ) , 7.80 ( d , j = 8.4 hz , 2h ) , 7.67 ( t , j = 5.2 hz , 1h ) , 7.61 ( t , j = 5.2 hz , 1h ) , 7.52 ( d , j = 5.6 hz , 2h ) , 7.337.29 ( m , 4h ) , 5.37 ( s , 1h ) , 4.614.54 ( m , 1h ) , 4.484.44 ( m , 1h ) , 4.033.98 ( m , 1h ) , 3.82 ( s , 3h ) , 3.083.04 ( m , 1h ) . c nmr ( 100 mhz , dmso - d6 ) 186.2 , 166.4 , 165.9 , 149.2 , 146.4 , 143.4 , 142.6 , 139.6 , 132.9 , 129.4 , 128.4 , 128.14 , 128.06 , 125.5 , 123.5 , 123.1 , 122.1 , 118.2 , 111.0 , 60.08 , 52.2 , 43.1 ( note : one sp carbon is under the dmso peak ) ; mp 135140 c . hms ( apci ) calcd for c27h22n4o5 483.1676 ; found 483.1674 [ m + h ] . compound 165 was prepared via procedure i from methyl 4-formylbenzoate ( 0.37 g , 2.3 mmol ) , 2-(1h - imidazol-4-yl)ethanamine ( 0.25 g , 2.3 mmol ) , and 20 ( 0.50 g , 2.3 mmol ) to yield an orange solid ( 0.031 g , 3% ) . h nmr ( 400 mhz , dmso - d6 ) 8.61 ( s , 1h ) , 8.50 ( d , j = 5.2 hz , 2h ) , 7.88 ( d , j = 8.0 hz , 2h ) , 7.51 ( d , j = 5.2 hz , 2h ) , 7.40 ( d , j = 8.0 hz , 2h ) , 7.26 ( s , 1h ) , 7.11 ( s , 1h ) , 5.27 ( s , 1h ) , 3.903.82 ( m , 4h ) , 2.832.76 ( m , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 182.5 , 169.1 , 166.1 , 148.8 , 148.0 , 134.0 , 131.2 , 129.0 , 128.5 , 128.1 , 127.8 , 127.6 , 122.4 , 116.4 , 111.6 , 66.3 , 52.0 , 40.0 , 22.3 ; mp 6470 c . hms ( apci ) calcd for c23h20n4o5 433.1512 ; found 433.1513 [ m + h ] . compound 166 was prepared via procedure i from methyl 4-formylbenzoate ( 0.30 g , 1.8 mmol ) , ethyl acetopyruvate ( 0.29 g , 1.8 mmol ) , and 2-(m - tolyl)ethanamine ( 0.25 g , 1.8 mmol ) to yield a white solid ( 0.56 g , 76% ) . h nmr ( 400 mhz , dmso - d6 ) 7.90 ( d , j = 7.6 hz , 2h ) , 7.28 ( d , j = 7.6 hz , 2h ) , 7.12 ( t , j = 8.0 hz , 1h ) , 6.99 ( d , j = 7.6 hz , 1h ) , 6.886.86 ( m , 2h ) , 5.13 ( s , 1h ) , 3.83 ( s , 3h ) , 3.793.73 ( m , 1h ) , 2.772.70 ( m , 2h ) , 2.612.57 ( m , 1h ) , 2.26 ( s , 3h ) , 2.22 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 191.5 , 166.0 , 165.1 , 142.4 , 138.4 , 137.5 , 129.4 , 129.2 , 128.4 , 128.1 , 127.1 , 126.9 , 125.62 , 125.56 , 119.7 , 66.4 , 59.7 , 52.2 , 41.6 , 33.4 , 21.0 ; mp 118123 c . hms ( apci ) calcd for c23h23no5 394.1649 ; found 394.1651 [ m + h ] . compound 167 was prepared via procedure i from methyl 4-formylbenzoate ( 0.26 g , 1.6 mmol ) , ethyl acetopyruvate ( 0.25 g , 1.6 mmol ) , and 2-(3-chlorophenyl)ethanamine ( 0.25 g , 1.6 mmol ) to yield a pale - yellow solid ( 0.50 g , 76% ) . h nmr ( 400 mhz , dmso - d6 ) 7.90 ( d , j = 8.4 hz , 2h ) , 7.327.20 ( m , 5h ) , 7.08 ( d , j = 7.2 hz , 1h ) , 5.22 ( s , 1h ) , 3.833.79 ( m , 4h ) , 2.792.69 ( m , 3h ) , 2.26 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 165.9 , 165.1 , 142.3 , 141.2 , 133.0 , 130.5 , 130.2 , 129.4 , 128.5 , 128.1 , 127.6 , 127.4 , 126.4 , 125.5 , 59.5 , 52.2 , 41.1 , 32.9 , 29.7 ( note : carbon 4 is absent ) ; mp 118122 c . hms ( apci ) calcd for c22h20clno5 414.1108 ; found 414.1109 [ m + h ] . compound 168 was prepared via procedure i from methyl 4-formylbenzoate ( 0.30 g , 1.8 mmol ) , ethyl acetopyruvate ( 0.28 g , 1.8 mmol ) , and 2-(3-fluorophenyl)ethanamine ( 0.25 g , 1.8 mmol ) to yield an off - white solid ( 0.57 g , 79% ) . h nmr ( 400 mhz , dmso - d6 ) 7.90 ( d , j = 8.4 hz , 2h ) , 7.31 ( d , j = 8.0 hz , 2h ) , 7.297.25 ( m , 1h ) , 7.006.94 ( m , 3h ) , 5.22 ( s , 1h ) , 3.833.79 ( m , 4h ) , 2.812.69 ( m , 3h ) , 2.26 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 165.9 , 165.1 , 162.2 ( d , j = 241.8 hz ) , 142.3 , 141.6 , 141.5 , 130.3 ( d , j = 8.1 hz ) , 129.44 , 129.40 , 128.1 , 125.6 , 124.8 , 115.3 ( d , j = 20.9 hz ) , 113.2 ( d , j = 20.9 hz ) , 59.5 , 52.2 , 41.1 , 33.0 , 15.2 ( note : carbon 4 is absent ) ; mp 114119 c . hms ( apci ) calcd for c22h20fno5 398.1403 ; found 398.1404 [ m + h ] . compound 169 was prepared via procedure i from methyl 4-formylbenzoate ( 0.27 g , 1.7 mmol ) , ethyl acetopyruvate ( 0.26 g , 1.7 mmol ) , and 2-(3-methoxyphenyl)ethanamine ( 0.25 g , 1.7 mmol ) to yield an off - white solid ( 0.52 g , 76% ) . h nmr ( 400 mhz , dmso - d6 ) 7.90 ( d , j = 8.4 hz , 2h ) , 7.30 ( d , j = 8.0 hz , 2h ) , 7.16 ( t , j = 8.0 hz , 1h ) , 6.75 ( d , j = 7.6 hz , 1h ) , 6.686.66 ( m , 2h ) , 5.15 ( s , 1h ) , 3.833.76 ( m , 4h ) , 3.69 ( s , 3h ) , 2.772.70 ( m , 2h ) , 2.652.60 ( m , 1h ) , 2.26 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 166.0 , 165.0 , 159.3 , 145.8 , 142.4 , 140.1 , 129.5 , 129.42 , 129.38 , 128.1 , 125.5 , 120.8 , 114.1 , 111.9 , 59.6 , 54.9 , 52.2 , 41.4 , 33.4 , 29.7 ( note : carbon 4 is absent ) ; mp 150153 c . hms ( apci ) calcd for c23h23no6 410.1603 ; found 410.1604 [ m + h ] . compound 170 was prepared via procedure i from methyl 4-formylbenzoate ( 0.55 g , 3.4 mmol ) , ethyl acetopyruvate ( 0.53 g , 3.4 mmol ) , and 190 ( 0.46 g , 3.4 mmol ) to yield a cream - colored solid ( 1.0 g , 78% ) . h nmr ( 400 mhz , dmso - d6 ) 9.34 ( br s , 1h ) , 7.93 ( d , j = 8.8 hz , 2h ) , 7.33 ( d , j = 8.8 hz , 2h ) , 7.08 ( t , j = 7.6 hz , 1h ) , 6.61 ( dt , j = 1.6 hz , j = 6.8 hz , 1h ) , 6.546.52 ( m , 2h ) , 5.16 ( s , 1h ) , 3.873.83 ( m , 4h ) , 2.742.69 ( m , 2h ) , 2.562.52 ( m , 1h ) , 2.30 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 193.0 , 166.0 , 165.0 , 157.5 , 142.4 , 139.9 , 129.9 , 129.7 , 129.5 , 129.2 , 128.1 , 127.0 , 119.2 , 115.4 , 113.5 , 59.7 , 52.2 , 48.7 , 41.6 , 33.6 ; mp 98104 c . hms ( apci ) calcd for c22h21no6 396.1447 ; found 396.1446 [ m + h ] . compound 171 was prepared via procedure i from methyl 4-formylbenzoate ( 0.19 g , 1.1 mmol ) , 2-(pyridin-4-yl)ethanamine ( 0.14 g , 1.1 mmol ) , and 20 ( 0.25 g , 1.1 mmol ) to yield a yellow solid ( 0.47 g , 95% ) . h nmr ( 400 mhz , dmso - d6 ) 8.65 ( d , j = 6.0 hz , 2h ) , 8.498.48 ( m , 2h ) , 7.92 ( d , j = 8.0 hz , 2h ) , 7.567.53 ( m , 2h ) , 7.50 ( d , j = 8.0 hz , 2h ) , 7.297.26 ( m , 2h ) , 5.47 ( s , 1h ) , 3.913.83 ( m , 4h ) , 2.882.78 ( m , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 190.1 , 185.8 , 182.0 , 166.3 , 166.0 , 149.5 , 149.2 , 148.3 , 146.6 , 143.4 , 129.4 , 128.2 , 124.6 , 122.2 , 115.6 , 59.9 , 52.2 , 40.6 , 32.7 ; mp 126129 c . hms ( apci ) calcd for c25h21n3o5 444.1567 ; found 444.1566 [ m + h ] . compound 172 was prepared via procedure i from methyl 4-formylbenzoate ( 0.19 g , 1.1 mmol ) , 2-(pyridin-3-yl)ethanamine ( 0.14 g , 1.1 mmol ) , and 20 ( 0.25 g , 1.1 mmol ) to yield a yellow solid ( 0.47 g , 93% ) . h nmr ( 400 mhz , dmso - d6 ) 8.67 ( d , j = 6.0 hz , 2h ) , 8.44 ( dd , j = 1.2 hz , j = 4.8 hz , 1h ) , 8.41 ( d , j = 1.6 hz , 1h ) , 7.92 ( d , j = 8.4 hz , 2h ) , 7.66 ( d , j = 7.6 hz , 1h ) , 7.55 ( d , j = 6.0 hz , 2h ) , 7.50 ( d , j = 8.4 hz , 2h ) , 7.35 ( dd , j = 4.8 hz , j = 7.6 hz , 1h ) , 5.51 ( s , 1h ) , 3.913.83 ( m , 4h ) , 2.912.77 ( m , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 206.6 , 186.6 , 165.9 , 165.6 , 149.3 , 148.9 , 146.9 , 146.1 , 142.7 , 137.3 , 134.7 , 129.5 , 128.2 , 128.1 , 123.8 , 122.0 , 116.6 , 59.9 , 52.2 , 41.3 , 30.5 ; mp 160163 c . hms ( apci ) calcd for c25h21n3o5 444.1567 ; found 444.1565 [ m + h ] . compound 173 was prepared via procedure i from methyl 4-formylbenzoate ( 0.19 g , 1.1 mmol ) , 2-(pyridin-2-yl)ethanamine ( 0.14 g , 1.1 mmol ) , and 20 ( 0.25 g , 1.1 mmol ) to yield a yellow solid ( 0.50 g , > 99% ) . h nmr ( 400 mhz , dmso - d6 ) 8.67 ( d , j = 6.0 hz , 2h ) , 8.48 ( dd , j = 1.6 hz , j = 5.2 hz , 1h ) , 7.91 ( d , j = 8.4 hz , 2h ) , 7.73 ( td , j = 2.0 hz , j = 7.6 hz , 1h ) , 7.53 ( dd , j = 1.2 hz , j = 4.4 hz , 2h ) , 7.46 ( d , j = 8.0 hz , 2h ) , 7.27 ( s , 1h ) , 7.25 ( t , j = 3.6 hz , 1h ) , 5.44 ( s , 1h ) , 4.003.93 ( m , 1h ) , 3.82 ( s , 3h ) , 3.072.97 ( m , 2h ) , 2.922.84 ( m , 1h ) . c nmr ( 100 mhz , dmso - d6 ) 206.6 , 186.7 , 165.9 , 165.5 , 158.1 , 156.6 , 149.4 , 148.7 , 146.1 , 142.6 , 137.3 , 129.5 , 128.2 , 125.6 , 123.6 , 122.0 , 116.9 , 60.1 , 52.2 , 40.3 , 35.4 ; mp 187190 c . hms ( apci ) calcd for c25h21n3o5 444.1567 ; found 444.1564 [ m + h ] . compound 174 was prepared via procedure i from isonicotinaldehyde ( 0.11 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a mustard - colored solid ( 0.32 g , 76% ) . h nmr ( 600 mhz , dmso - d6 ) 10.93 ( s , 1h ) , 8.84 ( d , j = 1.8 hz , 1h ) , 8.67 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 8.53 ( d , j = 5.4 hz , 2h ) , 8.05 ( dt , j = 2.4 hz , j = 8.4 hz , 1h ) , 7.497.47 ( m , 2h ) , 7.427.34 ( m , 3h ) , 7.30 ( br s , 1h ) , 7.13 ( d , j = 1.8 hz , 1h ) , 7.06 ( t , j = 7.8 hz , 1h ) , 6.94 ( t , j = 8.4 hz , 1h ) , 5.34 ( s , 1h ) , 3.923.87 ( m , 1h ) , 3.022.91 ( m , 2h ) , 2.822.77 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 185.5 , 166.1 , 151.3 , 148.9 , 148.4 , 136.7 , 136.3 , 134.5 , 126.9 , 125.5 , 123.6 , 123.4 , 123.0 , 121.1 , 118.3 , 118.1 , 116.1 , 111.6 , 110.8 , 59.7 , 41.2 , 23.7 ( note : either carbon 1 or 2 is absent ) ; mp 225230 c . hms ( apci ) calcd for c25h20n4o3 425.1608 ; found 425.1610 [ m + h ] . compound 175 was prepared via procedure i from nicotinaldehyde ( 0.11 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield an orange solid ( 0.29 g , 67% ) . h nmr ( 600 mhz , dmso - d6 ) 10.90 ( s , 1h ) , 8.83 ( d , j = 2.4 hz , 1h ) , 8.68 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 8.57 ( d , j = 1.8 hz , 1h ) , 8.49 ( dd , j = 2.4 hz , j = 4.8 hz , 1h ) , 8.04 ( dt , j = 1.8 hz , j = 7.8 hz , 1h ) , 7.74 ( d , j = 8.4 hz , 1h ) , 7.497.47 ( m , 1h ) , 7.367.32 ( m , 3h ) , 7.24 ( s , 1h ) , 7.13 ( d , j = 1.8 hz , 1h ) , 7.06 ( t , j = 7.8 hz , 1h ) , 6.94 ( t , j = 8.4 hz , 1h ) , 5.39 ( s , 1h ) , 3.893.85 ( m , 1h ) , 3.022.93 ( m , 2h ) , 2.792.75 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 165.3 , 151.9 , 149.3 , 149.1 , 148.9 , 136.4 , 136.3 , 135.7 , 134.1 , 128.1 , 126.9 , 125.5 , 124.0 , 123.4 , 122.9 , 121.1 , 118.3 , 118.1 , 111.5 , 110.7 , 58.4 , 41.0 , 23.7 ( note : carbons 1 and 2 are absent ) ; mp 225227 c . hms ( apci ) calcd for c25h20n4o3 425.1608 ; found 425.1610 [ m + h ] . compound 176 was prepared via procedure i from picolinaldehyde ( 0.11 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a yellow solid ( 0.30 g , 71% ) . h nmr ( 600 mhz , dmso - d6 ) 10.91 ( s , 1h ) , 8.80 ( d , j = 1.2 hz , 1h ) , 8.69 ( dd , j = 1.2 hz , j = 4.8 hz , 8.55 ( d , j = 4.2 hz , 1h ) , 8.00 ( d , j = 7.2 hz , 1h ) , 7.77 ( td , j = 1.2 hz , j = 7.2 hz , 1h ) , 7.507.46 ( m , 2h ) , 7.387.30 ( m , 4h ) , 7.12 ( d , j = 1.8 hz , 1h ) , 7.05 ( t , j = 7.8 hz , 1h ) , 6.95 ( t , j = 7.8 hz , 1h ) , 5.54 ( s , 1h ) , 3.873.82 ( m , 1h ) , 3.012.91 ( m , 2h ) , 2.722.67 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 189.2 , 165.4 , 156.1 , 151.9 , 149.4 , 149.0 , 137.2 , 136.3 , 134.2 , 128.2 , 126.9 , 125.5 , 123.8 , 123.4 , 122.8 , 121.0 , 118.3 , 118.1 , 111.5 , 110.8 , 62.1 , 41.4 , 23.6 ( note : either carbon 1 or 2 and carbon 3 are absent ) ; mp 218223 c . hms ( apci ) calcd for c25h20n4o3 425.1613 ; found 425.1613 [ m + h ] . compound 177 was prepared via procedure i from furan-3-carbaldehyde ( 0.10 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield an orange solid ( 0.12 g , 28% ) . h nmr ( 600 mhz , dmso - d6 ) 10.86 ( s , 1h ) , 8.85 ( d , j = 1.8 hz , 1h ) , 8.71 ( dd , j = 1.2 hz , j = 4.8 hz , 1h ) , 8.05 ( dt , j = 1.8 hz , j = 7.8 hz , 1h ) , 7.74 ( s , 1h ) , 7.507.48 ( m , 1h ) , 7.45 ( d , j = 7.8 hz , 1h ) , 7.34 ( d , j = 7.8 hz , 1h ) , 7.18 ( s , 1h ) , 7.15 ( d , j = 1.8 hz , 1h ) , 7.10 ( s , 1h ) , 7.07 ( t , j = 7.2 hz , 1h ) , 6.98 ( t , j = 7.8 hz , 1h ) , 6.48 ( d , j = 1.2 hz , 1h ) , 5.40 ( s , 1h ) , 3.893.84 ( m , 1h ) , 3.123.00 ( m , 2h ) , 2.842.80 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 164.4 , 152.4 , 149.5 , 144.1 , 142.7 , 136.3 , 133.8 , 127.0 , 125.5 , 123.4 , 122.9 , 121.1 , 120.8 , 118.3 , 118.2 , 117.5 , 111.5 , 110.9 , 108.6 , 52.4 , 40.7 , 23.7 ( note : carbon 1 and 2 are absent ) ; mp 211217 c . hms ( apci ) calcd for c24h19n3o4 414.1448 ; found 414.1449 [ m + h ] . compound 178 was prepared via procedure i from furfural ( 0.10 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a mustard - colored solid ( 0.06 g , 14% ) . h nmr ( 600 mhz , dmso - d6 ) 10.87 ( s , 1h ) , 8.82 ( d , j = 1.2 hz , 1h ) , 8.72 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 8.03 ( dt , j = 1.8 hz , j = 5.4 hz , 1h ) , 7.62 ( t , j = 0.6 hz , 1h ) , 7.537.52 ( m , 1h ) , 7.48 ( d , j = 7.8 hz , 1h ) , 7.34 ( d , j = 7.8 hz , 1h ) , 7.18 ( s , 1h ) , 7.15 ( d , j = 2.4 hz , 1h ) , 7.107.06 ( m , 2h ) , 6.99 ( t , j = 6.6 hz , 1h ) , 6.52 ( d , j = 3.0 hz , 1h ) , 6.4336.425 ( m , 1h ) , 3.823.77 ( m , 1h ) , 3.193.14 ( m , 1h ) , 3.002.95 ( m , 1h ) , 2.662.61 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.9 , 164.5 , 152.3 , 149.1 , 148.9 , 143.4 , 143.2 , 136.3 , 134.0 , 127.0 , 123.5 , 122.9 , 122.8 , 121.0 , 118.4 , 118.3 , 118.1 , 115.0 , 111.5 , 110.8 , 110.2 , 54.5 , 41.4 , 23.7 ; mp 211216 c . hms ( apci ) calcd for c24h19n3o4 414.1448 ; found 414.1452 [ m + h ] . compound 179 was prepared via procedure i from thiophene-2-carbaldehyde ( 0.11 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield an orange solid ( 0.07 g , 16% ) . h nmr ( 600 mhz , dmso - d6 ) 10.87 ( s , 1h ) , 8.81 ( s , 1h ) , 8.72 ( d , j = 4.8 hz , 1h ) , 8.02 ( dd , j = 1.8 hz , j = 6.0 hz , 1h ) , 7.53 - 7.51 ( m , 1h ) , 7.487.44 ( m , 2h ) , 7.34 ( d , j = 7.8 , 1h ) , 7.20 ( d , j = 3.0 hz , 1h ) , 7.15 ( d , j = 1.8 hz , 1h ) , 7.07 ( t , j = 7.8 hz , 2h ) , 7.006.96 ( m , 2h ) , 5.76 ( s , 1h ) , 3.873.83 ( m , 1h ) , 3.143.09 ( m , 1h ) , 3.053.00 ( m , 1h ) , 2.772.72 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 164.2 , 152.4 , 149.2 , 140.2 , 136.3 , 133.8 , 130.3 , 128.7 , 127.02 , 126.96 , 126.5 , 123.6 , 122.9 , 121.1 , 118.3 , 118.2 , 111.5 , 110.8 , 56.1 , 40.9 , 23.6 ( note : carbons 1 , 2 , and 3 are absent ) ; mp 150155 c . hms ( apci ) calcd for c24h19n3o3s 430.1226 ; found 430.1223 [ m + h ] . compound 180 was prepared via procedure i from thiophene-3-carbaldehyde ( 0.11 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a yellow solid ( 0.11 g , 25% ) . h nmr ( 600 mhz , dmso - d6 ) 10.87 ( s , 1h ) , 8.86 ( s , 1h ) , 8.71 ( d , j = 4.8 hz , 1h ) , 8.06 ( d , j = 7.8 hz , 1h ) , 7.70 ( d , j = 1.8 hz , 1h ) , 7.507.47 ( m , 2h ) , 7.40 ( d , j = 7.8 hz , 1h ) , 7.34 ( d , j = 7.8 hz , 1h ) , 7.25 ( s , 1h ) , 7.14 ( s , 1h ) , 7.087.06 ( m , 2h ) , 6.96 ( t , j = 7.8 hz , 1h ) , 5.55 ( s , 1h ) , 3.863.80 ( m , 1h ) , 3.062.98 ( m , 2h ) , 2.762.70 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 187.4 , 181.2 , 164.5 , 152.5 , 137.2 , 136.3 , 133.8 , 127.05 , 126.98 , 126.2 , 126.0 , 125.4 , 123.5 , 122.9 , 122.8 , 121.1 , 118.4 , 118.2 , 118.0 , 111.5 , 110.9 , 55.0 , 41.2 , 23.9 ; mp 238242 c . hms ( apci ) calcd for c24h19n3o3s 430.1198 ; found 430.1201 [ m + h ] .

nmda receptors are tetrameric complexes composed of glun1 and glun2a d subunits that mediate a slow ca2 + -permeable component of excitatory synaptic transmission . nmda receptors have been implicated in a wide range of neurological diseases and thus represent an important therapeutic target . we herein describe a novel series of pyrrolidinones that selectively potentiate only nmda receptors that contain the glun2c subunit . the most active analogues tested were over 100-fold selective for recombinant glun2c - containing receptors over glun2a / b / d - containing nmda receptors as well as ampa and kainate receptors . this series represents the first class of allosteric potentiators that are selective for diheteromeric glun2c - containing nmda receptors .

<s>[INST]n - methyl - d - aspartate ( nmda ) receptors are members of the family of ionotropic glutamate receptors that mediate excitatory neurotransmission . nmda receptors are tetrameric assemblies of two glun1 subunits , which bind the coagonist glycine , and two glun2 subunits , which bind glutamate . both glun1 and glun2 subunits share a similar architecture , comprised of an extracellular amino - terminal domain ( atd ) , an extracellular ligand - binding domain ( lbd ) , a transmembrane domain ( tmd ) , and an intracellular carboxyl - terminal domain ( ctd ) . the glun2 subunit is encoded by four distinct gene products ( glun2a - d ) , which have temporally and spatially distinct expression patterns in the brain . the glun2 subunit controls pharmacological characteristics such as agonist sensitivity , deactivation time course , mean open time , and open probability . the distinct anatomical locations of the glun2 subunits could allow subunit - selective modulators ( either potentiators or inhibitors ) to target specific brain regions for therapeutic gain . nmda receptors are thought to play a role in neuronal development , learning , and memory formation , as well as being implicated in ischemia , dementia , schizophrenia , treatment resistant depression , and parkinson s disease . recently discovered modulators have demonstrated selectivity for glun2a , 3-chloro-4-fluoro - n-[4-[[2-(phenylcarbonyl)hydrazino]carbonyl]benzyl]benzenesulfonamide ( tcn201 ) ; glun2a / glun2b , 9-cyclopropylphenanthrene-3-carboxylic acid ( ubp710 ) ; and glun2c / glun2d , ( 3-chlorophenyl ) [ 3,4-dihydro-6,7-dimethoxy-1-[(4-methoxyphenoxy)methyl]-2(1h)-isoquinolinyl]methanone ( ciq ) , 4-[6-methoxy-2-[(1e)-2-(3-nitrophen yl)ethenyl]-4-oxo-3(4h)quinazolinyl]benzoic acid ( qnz46 ) , 5-(4-bromophenyl)-3-(1,2-dihydro-6- methyl-2-oxo-4-phenyl-3-quinolinyl)-4,5-dihydro - g - oxo-1h - pyrazole-1-butanoic acid ( dqp1105 ) , and ( 2r,3s)-1-(phenanthrenyl-3-carbonyl)piperazine-2,3-dicarboxylic acid ( ubp141 ) . here , we describe the development of the first class of positive allosteric modulators that are selective for glun2c - containing nmda receptors over glun2a- , glun2b- , and glun2d - containing receptors . to identify this class of ligands , a glun1/glun2c cell line and multiwell fluorescence - based assay were developed to enable screening of compound libraries for nmda receptor modulators . we screened two commercial diversity libraries to identify several compounds that modulate glun2c - containing nmda receptors . one of these screening hits established a novel class of subunit - selective potentiators for recombinant glun1/glun2c nmda receptors , exemplified by compound 1 ( figure 1 ) . optimization of the initial lead pyrrolidinone scaffold involved the development of a structure activity relationship , which led to the identification of a novel series of compounds with potency in the low micromolar range and high selectivity for recombinant glun2c - containing receptors over glun2a / b / d - containing nmda receptors . in addition , no detectable potentiation was observed at recombinant ampa , kainate , gaba , glycine , serotonin , nicotinic , or purinergic receptors ( data not shown ) . these analogues represent a novel class of nmda receptor modulators that are highly selective for diheteromeric glun1/glun2c receptor subtypes and provide a useful tool with which to evaluate the physiological role of glun2c in normal and neuropathological conditions . chemical structure of methyl 4-(1-(2-(1h - indol-3-yl)ethyl)-3-acetyl-4-hydroxy-5-oxo-2,5-dihydro-1h - pyrrol-2-yl)benzoate ( compound 1 ) that was identified as a positive modulator using a fluorescence - based screen of compound libraries in a cell line expressing diheteromeric glun1/glun2c nmda receptors . we used bioinformatic searches and medicinal chemistry to obtain analogues for our initial screening hit , compound 1 ( see below ) . both commercially available analogues and compounds synthesized via a mi - component biginelli - like reaction ( scheme 1 ) were assessed at 30 m . we determined the ec50 and maximal potentiation from concentration effect curves for compounds that showed potentiation of more than 120% of control at 30 m . no compounds in this class potentiated glun2a- , glun2b- , or glun2d - containing receptors , suggesting remarkable selectivity for this class ( see below ) . modifications were made at either r , the a - ring , or the b - ring using alternative methodologies to access the appropriate precursor . reaction conditions : ppts , rt , 124 h , 2% to > 99% ( procedure i ) . final compounds 161180 , in which either the a or b ring is replaced , were also prepared using these conditions . addition of diethyl oxalate and sodium ethoxide to a methyl ketone generated a series of pyruvate analogues ( 320 ) containing modifications at r ( scheme 2 ) . only when r was a phenol was it necessary to first protect the hydroxyl group with triisopropyl chloride ( tipscl ) before the addition of diethyl oxalate . reaction conditions : ( a ) diethyl oxalate , naoet , etoh , 0 c to rt , 4 h , 15% to > 99% ( procedure ii ) ; ( b ) tipscl , imidazole , rt , 6 h , > 99% ; ( c ) diethyl oxalate , naoet , etoh , 0 c to rt , 4 h , 28% ( procedure ii ) ; ( d ) tbaf , 0 c to rt , 1 h , 43% . analogues containing disubstituted a - rings were synthesized using several procedures based on the commercially available precursors ( scheme 3 ) . suzuki coupling between dibutyl vinylboronate and the appropriately substituted methyl 4-iodobenzoate , followed by ozonolysis , gave phenols 34 and 35 . alternatively , addition of a grignard reagent and n , n - dimethylformamide ( dmf ) led to isolation of benzaldehyde 36 . finally , anisole 41 was prepared via a dialkylation of both the hydroxyl and carboxylic acid functional groups . reaction conditions : ( a ) 2.0 equiv nbs , ( phcoo)2 , reflux , 4 h , then agno3 , rt , 3 h , 3863% ; ( b ) dibutyl vinylboronate , 5 mol % ( pph3)2pdcl2 , naco3 , reflux , 2 h , 6880% ; ( c ) o3 ; then ( ch3)2s , 78 c to rt , 12 h , 6087% ; ( d ) i - prmgcl , dmf , 15 c to rt , 3 h , 70% ; ( e ) co(g ) , ( pph3)2pdcl2 , naco3 , 110 c , 824% ( procedure iv ) ; ( f ) ch3i , k2co3 , rt , 3 h , 58% . benzaldehydes containing a para - amide ( 4244 ) or para - ester ( 4547 ) substituent were synthesized as illustrated in scheme 4 . primary amide 42 was synthesized from carboxylic acid 155 by generating the acid chloride in situ . standard amide coupling conditions were employed for the preparation of amides 43 and 44 . alkylation of carboxylic acid 155 with the appropriate alkyl iodide afforded esters 45 and 46 , while t - butyl ester 47 was prepared using a method previously described . reaction conditions : ( a ) vilsmeier reagent , aq nh3 , 0 c , 16 h , 30% ; ( b ) rrn where r = h and r = me or where r = r = me , dmap , edci , 0 c to rt , 24 h , 1451% ; ( c ) ri where r = et or r = i - pr , k2co3 , rt , 4 h , 2487% ; ( d ) ( ch3)2nch(ot - bu)2 , reflux , 1/2 h , 81% . an alternative strategy was used to synthesize analogues containing a modification at r starting from pyrrolidinones 1 and 106 ( scheme 5 ) . alternatively , esters 159 and 160 were synthesized from enol 106 using the appropriate acyl chloride and triethylamine . reaction conditions : ( a ) tmsch2n2 , rt , 5 h , 46% ; ( b ) nh4hco2 , reflux , 3 h , 14% ; ( c ) ac2o , pyridine , rt , 6/2 h , 7% ; ( d ) rc(o)cl where r = ch2ch2ch3 or r = ch = ch2 , tea , 30 c , 2 h , 2035% . a fluorescence - based screen of 57504 compounds obtained from asinex and chemdiv libraries was performed in bhk cells with inducible expression of glun1/glun2c receptors . hits were defined as compounds that produced changes that were 2.5 standard deviations away from the average response to maximally effective agonist ( i.e. , glutamate and glycine ) application . in this primary screen , 1% of the compounds met these criteria . compounds that showed potentiation were further evaluated for their ability to produce responses in cells with no nmda receptor expression ( in uninduced cells ) in order to identify false positive hits . false positive results can occur when the compounds directly release ca from intracellular stores , enhance ca channel function , possess fluorescent properties in the excitation / emission range of fluo-4 , or otherwise produce an increase in intracellular ca signal independent of nmda receptor activation . compounds that showed potentiation of glutamate responses in induced cells and did not produce responses in uninduced cells were subsequently studied by two - electrode voltage - clamp recording of nmda receptor responses . a single compound was found to selectively potentiate the glun1/glun2c receptors and did not show any activity at glun2a / b / d - containing nmda receptors expressed in xenopus laevis oocytes ( figure 2a ) . compound 1 , which contains a pyrrolidinone core motif , potentiated glun1/glun2c responses to 238 8.2% of control at 100 m with an ec50 of 24 2.4 m ( n = 12 ) ( figure 2b ) . compound 1 had no agonist activity on its own in that it did not induce current responses in oocytes expressing glun1/glun2c in the absence of glutamate and glycine ( n = 4 ) . in addition , 30 m of compound 1 did not potentiate homomeric recombinant glua1 ampa receptor responses ( 97 1.1% control , n = 16 ) . in addition , 120 m of compound 1 did not potentiate homomeric gluk2 recombinant kainate receptors ( 95 2.3% of control , n = 5 ) . ( a ) current traces for 1 at the glun1/glun2a , glun1/glun2b , glun1/glun2c , and the glun1/glun2d receptors . ( b ) compound 1 selectively potentiates the glun1/glun2c receptor to a fitted maximum of 275 10% with an ec50 of 24 2.4 , n = 12 . ( c ) the ec50 for glycine in the absence and presence of 1 is 0.20 0.01 m ( n = 6 ) and 0.16 0.02 m ( n = 4 ) , respectively . the ec50 for glutamate in the absence and presence of 1 is 0.8 0.07 m ( n = 8) and 1.2 0.04 m ( n = 6 ) , respectively . the presence of 1 did not shift the glycine or glutamate ec50 values significantly . ( d ) the reversal potential is 5.1 0.8 mv when activated by coagonists ( 100 m glutamate and 30 m glycine ) and is 5.0 1.2 mv ( n = 6 ) when the glun1/glun2c receptor is potentiated by 1 . the reversal potential was not significantly shifted in the presence of 1 , suggesting that potentiation is independent of membrane potential . compound 1 ( 68 m ) did not detectably alter the ec50 of glycine or glutamate ( n = 46 ; figure 2c ) . additionally , the reversal potential of glutamate and glycine induced current responses was unchanged in the presence ( 5.0 + 1.2 mv , n = 6 ) or absence ( 5.1 + 0.8 mv , n = 6 ) of compound 1 . potentiation was not significantly different at 40 mv ( 202 11% ) compared to + 30 mv ( 180 12% ; p = 0.2679 ; paired t test ) , indicating that potentiation of glun2c - containing receptors by compound 1 at 20 m was voltage - independent ( n = 6 ; figure 2d ) . we subsequently evaluated the response to 30 m of all pyrrolidinone analogues at glun1/glun2a , glun1/glun2b , glun1/glun2c , and glun1/glun2d and proceeded to determine the concentration exploration of the effects of keto - linked r ( scheme 1 ; see chemistry section ) substitutions on potentiation of glun2c - containing receptors in oocytes revealed that additional steric bulk was tolerated , with only minimal improvements in potency ( table 1 , 6265 ) . for example , replacement of r with a phenyl group , as in 65 , produced a small increase in potency ( ec50 = 17 2.3 ) accompanied by a modest decrease in maximal potentiation compared to compound 1 ( table 1 ) . analogues containing m - substituted phenyl rings ( 6670 ) offered variable potentiation , while analogues with o- and p - substituted phenyl rings were inactive ( data not shown ) . notably , 66 , with a meta - hydroxyl group , displayed a considerably higher potency at glun2c - containing receptors ( 7.0 0.9 m ) but caused significant inhibition of glun2a- , glun2b- , and glun2d - containing receptors at 100 m ( responses were 76 2.0% , 42 1.6% , and 48 2.4% of control , respectively , normalized to agonist activated current ) . such mixed - action modulators that potentiate one subunit while inhibiting another are intriguing but of little utility as pharmacological probes . two compounds containing a pyridine ring at r potentiated responses up to 200% with ec50 values of 12 1.9 m ( 72 ) and 8.9 1.3 m ( 73 ) . interestingly , 71 , which contains a 2-substituted pyridine ring , was inactive at all receptor subunits . these initial experiments confirmed the ability of derivatives within this class to selectively potentiate glun2c - containing receptors compared to other nmda receptor subtypes . fitted ec50 values are shown for glun1/glun2c to two significant figures when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 6 and 12 oocytes from 23 frogs for each compound . when no effect was found ( n = 315 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 3 oocytes all compounds ) . for all tables , glun2 subunits were coexpressed with glun1 in xenopus oocytes and evaluated using two - electrode voltage - clamp recordings . the response to 100 m of test compound was greater than 140% of control . next , we evaluated the effects of various a - ring substituents ( table 2 ) utilizing r substitutions shown to offer the desired activity . one compound , 84 , which contains an ethyl ester at ring position r , displayed comparable potency compared to screening hit 1 . analogues containing bulkier ester substituents ( e.g. , 85 with an iso - propyl ester and 86 with a tert - butyl ester ) led to inactivity . a series of compounds containing ester isosteres including a nitrile ( 87 ) , nitro ( 88 ) , amide ( 8991 ) , and sulfonamide ( 92 and 93 ) were also evaluated for their ability to potentiate glun2c - containing nmda receptors . fitted ec50 values are shown for glun1/glun2c to two significant figures when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 8 and 12 oocytes from 23 frogs for each compound . when no effect was found ( n = 311 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 3 oocytes all compounds ) . a variety of substituents at a - ring positions r and r were systematically tested while holding the para - methyl ester constant at r ( table 3 ) . substitution at the meta position ( r ) revealed either a reduction in potency ( 95 ) or complete inactivity ( 9699 ) . evaluation of a series of ortho ( r ) ring substituents demonstrated a preference for electron donating groups . for example , analogues containing an ortho - hydroxyl ( 100 ) exhibited potentiation with a modest increase in potency , whereas ortho - chloro ( 103 ) or -fluoro ( 104 ) substituents were slightly less active . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response ; hill slopes ranged between 1.3 and 1.8 . data for active compounds at glun1/glun2c are from between 3 and 12 oocytes from 23 frogs for each compound . when no effect was found ( n = 315 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 5 oocytes for all compounds ) . replacement of the b - ring with an assortment of acyclic , cyclic , and heterocyclic systems generated a series of compounds that were evaluated for potency and subunit selectivity while retaining optimal r and a - ring substitutions ( table 4 ) . interestingly , substitution with a napthyl derivative , as in 162 , led to strong inhibition at all four subunits . replacement of the indole nh with an oxygen atom led only to weak activity ( 163 ) , suggesting the presence of a hydrogen bond in the binding pocket . in all other instances , removal of the indole led to complete inactivity ( i.e. , 164 and 165 ) . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . when no effect was found , the lack of effect was confirmed by testing at 100 m ( data not shown , n 3 oocytes for all compounds ) . inhibited at glun1/glun2a with an ic50 of 18 m , at glun1/glun2b with an ic50 of 7.2 m , at glun1/glun2c with an ic50 of 11 m , and glun1/glun2d with an ic50 of 5.7 m . this led us to examine b - ring substituents as an alternative strategy to access increased potency . methylation of the indole nitrogen led to inactivity ( 105 ) , further suggesting the importance of a hydrogen atom at this position in the binding pocket . the best potency was obtained for analogues with substitutions at b - ring position r. compound 111 demonstrated an ability to selectively potentiate glun2c - containing nmda receptors up to 218% with an ec50 value of 4.3 0.3 m . it is unclear whether the increase in potency observed for 111 can be ascribed to a steric effect or , alternatively , to a mildly electropositive effect . consistent with a steric effect , analogues which contain larger r substituents such as r = ome ( 112 ) revealed a loss of potency compared to 111 . analogues containing strongly electron withdrawing r substituents such as r = f ( 109 ) also decreased the observed activity . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 6 and 27 oocytes from 23 frogs for each compound . when no effect was found ( n = 411 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 4 oocytes for all compounds ) . we subsequently evaluated the effect of combining modifications at r , the a - ring and the b - ring that had previously demonstrated an improvement in potency ( table 6 ) . substitution with either a meta- or para - substituted pyridine ring at r and a para - ethyl ester at r revealed potentiation of glun1/glun2c responses with ec50 values of 8.2 0.9 m ( 116 ) and 9.7 0.6 m ( 117 ) , respectively . modification of the b - ring and either r ( r = m - pyridine ) or r ( r = p - co2et ) exhibited a similar increase in on - target potency . for example , substitution with a methyl group at r and a para - ethyl ester at r , as in analogue 119 , resulted in a 2-fold potency enhancement . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 8 and 14 oocytes from 2 frogs for each compound ; the hill slope varied between 1.2 and 1.5 . when no effect was found at 30 m ( n = 36 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 7 oocytes for all compounds ) . the original screening hit , 1 , contains a two carbon region linking the b - ring with the core pyrrolidinone . the linker modifications explored are illustrated in table 7 . both shortening ( 121 ) and extending ( 122 ) the linker eliminated all activity , suggesting that the potency of pyrrolidinone analogues is highly dependent on the length of the carbon linkage . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 7 and 8 oocytes from 2 frogs for each compound tested ; the hill slope varied between 1.3 and 1.4 . when no effect was found at 30 m ( n = 311 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 4 oocytes for all compounds ) . several modifications were made at r to determine the significance of the enol in controlling potency and selectivity ( table 8) . replacement with an amine , as in 157 , led to a complete loss of potentiation at concentrations up to 100 m . in most instances , compounds containing in contrast , propyl ester 159 maintained activity comparable to lead analogue 1 , with an ec50 of 17 1.8 m . these data suggest that enhancements in potency can not be gained though modifications of the enol . fitted ec50 values are shown for glun1/glun2c to two significant digits when potentiation at 30 m of the test compound exceeded 120% of control ; values in parentheses are the fitted maximum response as a percentage of the initial glutamate ( 100 m ) and glycine ( 30 m ) response . data for active compounds at glun1/glun2c are from between 5 and 9 oocytes from 23 frogs for each compound . the hill slope varied between 1.2 and 1.8 and was fixed to be 1.5 for less potent analogues ( 157 , 159 ) . when no effect was found ( n = 39 oocytes ) , the lack of effect was confirmed by testing at 100 m ( data not shown , n 4 oocytes for all compounds ) . to enable evaluation of potential stereoselectivity for pyrrolidinone analogues at glun1/glun2c , we separated the enantiomers of 106 using a semipreparatory od - rh chiral hplc column ( see chemistry experimentals ) . each enantiomer was subjected to two - electrode voltage clamp analysis in xenopus laevis oocytes . the results , illustrated in figure 3 , indicate that only one enantiomer ( 106a ) is active and may account for the activity of 106 . compound 106a potentiated glun2c response by 259 7.8% with an estimated ec50 value of 18 0.6 m ( n = 6 ) . in contrast , no activity was observed for the other enantiomer ( 106b ) ( n = 6 ) . the active analogue demonstrated weak inhibition at glun2d - containing receptors and had no effect at glun2a- or glun2b - containing receptors . these data suggest that the activity of pyrrolidinone analogues may rely on a single enantiomer and that the binding pocket can distinguish between the enantiomers . effect curves for the enantiomers of 106 demonstrate that only one enantiomer , 106a , is active , potentiating the glun1/glun2c receptor to a fitted maximum of 259 8% of control with an ec50 of 18 0.6 m ( n = 6 ) . the incorporation of a methyl group at the c-7 position of the indole of initial screening hit 1 afforded 111 , which selectively potentiates glun2c - containing nmda receptors with a potency of 4.3 0.3 m . in addition , the activity of this series appears to originate from one enantiomer . these compounds represent the first class of allosteric potentiators selective for diheteromeric glun1/glun2c receptors over receptors containing glun2a- , glun2b- , and glun2d subunits . future studies will address the activity of this series of modulators on triheteromeric glun2c - containing nmda receptors containing two different glun2 subunits ( e.g. , glun1/glun2a this series of molecules may serve as a pharmacological tool to evaluate the role of the glun2c subunit in normal and neuropathological function . all protocols involving xenopus laevis were approved by the emory university institutional animal care and use committee . two - electrode voltage - clamp recordings were made from xenopus laevis oocytes expressing recombinant glun1/glun2a , glun1/glun2b , glun1/glun2c , glun1/glun2d , glua1 , or gluk2 receptors following injection of crna . cdnas for rat glun11a ( genbank accession numbers u11418 and u08261 ; hereafter glun1 ) , glun2a ( d13211 ) , glun2b ( u11419 ) , glun2c ( m91563 ) , glun2d ( l31611 ) , glua1 ( x17184 ) , and gluk2 ( z11548 ) were provided by drs . s. heinemann ( salk institute ) , s. nakanishi ( kyoto university ) , and p. seeburg ( university of heidelberg ) . oocyte isolation , crna synthesis , and crna injection have been previously described ; some experiments were performed with oocytes obtained from ecocyte ( austin , tx ) . voltage - clamp recordings from oocytes were made during perfusion with recording solution containing 90 mm nacl , 1.0 mm kcl , 0.5 mm bacl2 , 0.005 mm edta , and 10 mm hepes at ph 7.4 ( 23 c ) . glass microelectrodes had resistances of 0.31.0 m and were filled with 0.33.0 m kcl ; the membrane potential was held at 40 mv for all recordings . compounds were made as 20 mm stock solutions in dmso and diluted to the final concentration in recording solution ; final dmso content was 0.050.5% ( v / v ) . oocytes expressing gluk2 receptors were pretreated with 10 m concanavalin a for 10 min . nmda receptors were activated by 100 m glutamate plus 30 m glycine ; glua1 and gluk2 receptors were activated by 100 m glutamate . to prevent a gradual increase in current response over the course of the experiment of glun1/glun2a receptor responses in oocytes , some oocytes expressing glun1/glun2a were injected with 2050 nl of 2 mm k - bapta ( potassium 1,2-bis(o - aminophenoxy)ethane - n , n , n,n-tetraacetic acid ) . when the response to agonist in the presence of 30 m of a test compound exceeded 120% of control , the response to glutamate and glycine in the absence and presence of 57 concentrations of active analogues were recorded in multiple oocytes obtained from two or more different frogs for all experiments . the ec50 ( half - maximally effective concentration of potentiator ) was determined by fitting the equation1to the concentration response data normalized to the current in the absence of potentiator ( 100% ) for each oocyte , and the mean ( sem ) presented . n is the hill slope , which ranged between 1 and 2 and is not reported ; maximum is the fitted maximal response expressed as a percent of control to a saturating concentration of potentiator . when responses were inhibited by test compound at 30 m to less than 60% of control , the ic50 value was determined by fitting the equation2to the concentration for some compounds , visual detection of precipitation led to inclusion of 110 mm 2-hydroxypropyl--cyclodextrin in the recording solution to enhance solubility and enable generation of the full concentration response data . to generate a cell line with inducible nmda receptor expression , we used a previously described tet - on ( tetracycline - inducible promoter ; clontech , mountain view , ca ) baby hamster kidney ( bhk-21 , atcc ccl-10 ) cell line . the bhk-21 tet - on cell line was maintained at 37 c , 5% co2 , and 95% relative humidity in culture medium composed of dulbecco s modified eagle medium ( dmem ) containing glutamax - i , 4500 mg / l glucose , and 110 mg / l sodium pyruvate ( invitrogen , carlsbad , ca ) supplemented with penicillin ( 100 units / ml ) , streptomycin ( 100 g / ml ) , ( invitrogen , carlsbad , ca ) , 10% dialyzed fetal bovine serum ( invitrogen , carlsbad , ca ) , and 1 mg / ml g418 ( invitrogen , carlsbad , ca ) . the selection marker g418 was always included to provide continuous selection of tet - on - compatible bhk-21 cells . u11418 ) in the inducible ptre2 vector and rat glun2c ( genbank accession no . d13212 ) in the pci - ires - bla vector ( see ref ( 16 ) for details on this vector ) using fugene 6 transfection reagent ( promega , madison , wi ) . the nmda receptor antagonists dl-2-amino-5-phosphonopentanoate ( ap5 ) ( 200 m ; abcam , cambridge , ma ) and 7-chloro - kynurenate ( 7-cka ) ( 200 m ; abcam , cambridge , ma ) were added to the culture medium to prevent nmda receptor - mediated cell death . the following day , the cells were diluted 1:1000 and 1:10,000 and seeded in 144 mm dishes . the next day ( e.g. , two days after transfection ) , 10 g / ml blasticidin s ( invivogen , san diego , ca ) was added to the culture medium to select for transfected cells . unless otherwise stated , the culture medium for the cell lines always contained 1 mg / ml g418 and 10 g / ml blasticidin s for selection as well as 200 m ap5 and 200 m dcka to prevent nmda receptor - mediated cell death . the media was changed every 23 days , and blasticidin s - resistant clones were isolated 1020 days after transfection and evaluated for their response properties . fluorescence - based assays were conducted as previously described , and test compounds were screened at 10 m . purity of purchased compounds was greater than 90% , as determined by the suppliers , via hplc or nmr . precoated glass plates ( silica gel 60 f254 , 0.25 mm ) were used to monitor the progress of reactions by thin layer chromatography ( tlc ) . purification by flash column chromatography was performed on a teledyne isco combiflash companion using prepackaged teledyne redisep disposable normal phase silica columns . h and c nmr experiments were each carried out on an inova-400 ( 400 mhz ) , vnmr 400 ( 400 mhz ) , inova-600 ( 600 mhz ) , unity-600 ( 600 mhz ) , or mercury 300 vx ( 300 mhz ) . all chemical shifts are reported in parts per million and referenced to the residual solvent peak . mass spectra were performed by the emory university mass spectrometry center on a vg 70-s nier johnson or jeol instrument . purity of all final compounds was found to be 95% by lc / ms analysis unless otherwise noted . the separation of the enantiomers of 106 was obtained using a chiralpak od - rh 30 mm 250 mm , 5 m column with the following conditions : flow rate 10 ml / min , injection volume 12 ml ( 5 mg / ml ) , 44% acn/66% water with 0.1% formic acid ; 106atr = 121.3 min ; 106btr = 129.3 min . enantiomeric excess ( ee ) of both enantiomers 106a and 106b was determined using a chiralpak od - rh 4.6 mm 150 mm , 5 m column with the following conditions : flow rate 0.5 ml / min , injection volume 10 l , 44% acn/66% water with 0.1% formic acid ; 106a [ ]d20 18 ( c = 0.10 , methanol ) , tr = 26.1 min , 98% ee ; 106b [ ]d20 + 9 ( c = 0.10 , methanol ) , tr = 29.1 min , 96% ee . a perkin - elmer 314 instrument was used to obtain optical rotation data . to a stirred solution of aldehyde ( 1.0 mmol ) in dioxane ( 1.0 m ) was added tryptamine ( 1.0 equiv ) and 10 mol % pyridinium 4-methylbenzenesulfonate . upon the formation of a slurry , methyl acetopyruvate ( 1.0 equiv ) was added . the resulting mixture was allowed to stir at rt for up to 12 h. in most instances , a precipitate was visible , which was collected via filtration and washed with et2o . the solid was dissolved in an appropriate solvent and washed with saturated ammonium chloride and brine before being dried over mgso4 , filtered , and concentrated in vacuo . if a precipitate did not form , the mixture was concentrated in vacuo before being subjected to the workup as described above . purification was achieved via flash column chromatography on sio2 ( meoh / dcm ) to afford the desired pyrrolidinone . additional purification was obtained by hplc ( 85% acn/15% water with 0.1% formic acid ) as needed . to a solution of sodium ethanolate ( 1.0 equiv ) in etoh ( 0.72 m ) at 0 c was added a mixture of diethyl oxalate ( 1.0 equiv ) and ethanone ( 1.0 mmol ) over 20 min . the mixture was allowed to stir at rt for 4 h. in most instances , a precipitate had formed which was collected via filtration and washed with absolute etoh . if no precipitate was evident , a minimal amount of water was added and the mixture was concentrated in vacuo . the residue was dissolved in water , neutralized with acetic acid , and extracted with et2o ( 3 ) . the combined organic layers were dried over mgso4 , filtered , and concentrated in vacuo . purification was achieved as needed via flash column chromatography on sio2 ( hexanes / etoac : 4/1 ) to obtain the product . to a solution of 4-bromobenzoic acid ( 1.0 mmol ) in thf : meoh ( 4:1 , 0.3 m ) at 0 c was added ( diazomethyl)trimethylsilane ( 2.4 equiv ) . the reaction was allowed to warm to rt over the period of 1 h. at this time , the mixture was concentrated in vacuo and 1.0 m hcl was added . the mixture was extracted with etoac ( 2 ) , dried over mgso4 , filtered , and concentrated in vacuo to afford the product . to a solution of methyl 4-bromobenzoate ( 1.0 mmol ) in dmf ( 0.6 m ) was added 17 mol % bis(triphenylphosphine)palladium(ii ) dichloride and sodium formate ( 1.5 equiv ) . the reaction mixture was stirred at 110 c under a steady stream of co(g ) for 2 h. at this time , the mixture was cooled to rt , diluted with saturated sodium carbonate , and extracted with etoac ( 2 ) . the combined organic layers were washed with brine , dried over mgso4 , filtered , and concentrated in vacuo . purification was achieved via flash column chromatography on sio2 ( hexanes / etoac : 3/1 ) to yield the desired product , which was taken on without further purification . compound 1 was prepared via procedure i from methyl 4-formylbenzoate ( 3.0 g , 18 mmol ) , tryptamine ( 2.9 g , 18 mmol ) , and methyl acetopyruvate ( 2.6 g , 18 mmol ) to yield a cream - colored solid ( 5.5 g , 72% ) . h nmr ( 400 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.88 ( d , j = 8.0 hz , 2h ) , 7.337.24 ( m , 4h ) , 7.127.03 ( m , 2h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.17 ( s , 1h ) , 3.83 ( s , 3h ) , 3.833.77 ( m , 1h ) , 3.002.90 ( m , 1h ) , 2.872.80 ( m , 1h ) , 2.742.67 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 165.6 , 165.1 , 142.5 , 136.3 , 129.3 , 128.1 , 126.9 , 125.5 , 122.9 , 121.2 , 121.1 , 118.4 , 118.3 , 118.1 , 111.6 , 111.5 , 110.8 , 66.4 , 59.8 , 52.2 , 40.8 , 23.6 ; mp 99105 c . hms ( apci ) calcd for c24h22n2o5 419.1607 ; found 419.1606 [ m + h ] . compound 62 was prepared via procedure i from methyl 4-formylbenzoate ( 0.095 g , 0.58 mmol ) , tryptamine ( 0.93 g , 0.58 mmol ) , and 3 ( 0.10 g , 0.58 mmol ) to yield a cream - colored solid ( 0.16 g , 64% ) . h nmr ( 400 mhz , dmso - d6 ) 10.84 ( s , 1h ) , 7.87 ( d , j = 8.4 hz , 2h ) , 7.337.23 ( m , 4h ) , 7.09 ( d , j = 2.4 hz , 1h ) , 7.05 ( t , j = 8.0 hz , 1h ) , 6.91 ( t , j = 6.8 hz , 1h ) , 5.17 ( s , 1h ) , 3.833.76 ( m , 4h ) , 2.962.89 ( m , 1h ) , 2.862.79 ( m , 1h ) , 2.752.57 ( m , 3h ) , 0.85 ( t , j = 7.6 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 165.9 , 165.1 , 142.5 , 136.2 , 129.7 , 129.3 , 128.1 , 126.9 , 125.5 , 122.9 , 121.0 , 118.2 , 118.1 , 111.5 , 110.7 , 59.8 , 54.9 , 52.2 , 40.8 , 40.0 , 23.6 ( note : carbons 1 and 2 are absent ) ; mp 175180 c . hms ( apci ) calcd c25h24n2o5 433.1758 ; found 433.1756 [ m + h ] . compound 63 was prepared via procedure i from methyl 4-formylbenzoate ( 0.088 g , 0.54 mmol ) , tryptamine ( 0.086 g , 0.54 mmol ) , and 4 ( 0.10 g , 0.54 mmol ) to yield a light - brown , amorphous solid ( 0.067 g , 28% ) . h nmr ( 600 mhz , dmso - d6 , 70 c ) 10.65 ( s , 1h ) , 7.84 ( d , j = 7.8 hz , 2h ) , 7.32 ( d , j = 7.8 hz , 2h ) , 7.28 ( d , j = 7.8 hz , 2h ) , 7.067.03 ( m , 2h ) , 6.92 ( t , j = 8.4 hz , 1h ) , 5.18 ( s , 1h ) , 3.83 ( s , 3h ) , 3.793.75 ( m , 1h ) , 3.403.20 ( m , 2h ) , 2.982.93 ( m , 1h ) , 2.912.86 ( m , 1h ) , 2.722.67 ( m , 1h ) , 0.86 ( d , j = 4.8 hz , 6h ) . c nmr ( 150 mhz , dmso - d6 ) 182.1 , 166.0 , 136.2 , 129.2 , 128.1 , 128.0 , 126.9 , 125.5 , 123.4 , 122.8 , 121.1 , 121.0 , 118.5 , 118.2 , 118.1 , 111.6 , 111.5 , 110.9 , 109.5 , 60.0 , 52.1 , 40.9 , 23.7 , 23.2 , 18.5 , 17.7 . hms ( apci ) calcd for c26h26n2o5 447.1915 ; found 447.1916 [ m + h ] . compound 64 was prepared via procedure i from methyl 4-formylbenzoate ( 0.082 g , 0.50 mmol ) , tryptamine ( 0.080 g , 0.50 mmol ) , and 5 ( 0.10 g , 0.50 mmol ) to yield an orange oil ( 0.092 g , 40% ) . h nmr ( 600 mhz , cdcl3 ) 8.17 ( br s , 1h ) , 7.93 ( d , j = 7.8 hz , 2h ) , 7.407.35 ( m , 2h ) , 7.20 ( t , j = 7.2 hz , 1h ) , 7.09 ( t , j = 7.2 hz , 1h ) , 7.04 ( dd , j = 1.2 hz , j = 7.8 hz , 2h ) , 6.96 ( s , 1h ) , 5.04 ( s , 1h ) , 4.023.99 ( m , 1h ) , 3.91 ( s , 3h ) , 3.093.00 ( m , 2h ) , 2.952.91 ( m , 1h ) , 1.06 ( s , 9h ) . c nmr ( 150 mhz , cdcl3 ) 202.2 , 181.2 , 166.7 , 141.2 , 136.5 , 130.6 , 130.2 , 128.0 , 127.2 , 122.5 , 122.2 , 119.8 , 118.8 , 118.7 , 111.6 , 111.4 , 63.0 , 52.4 , 41.7 , 27.7 , 25.3 , 24.5 ( note : either carbon 1 or 2 is absent ) . hms ( apci ) calcd for c27h28n2o5 461.2071 ; found 461.2077 [ m + h ] . compound 65 was prepared via procedure i from 6 ( 0.15 g , 0.68 mmol ) , tryptamine ( 0.11 g , 0.68 mmol ) , and methyl 4-formylbenzoate ( 0.11 g , 0.68 mmol ) to yield a cream - colored solid ( 0.031 g , 9% ) . h nmr ( 400 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.79 ( d , j = 7.2 hz , 2h ) , 7.597.48 ( m , 2h ) , 7.407.28 ( m , 3h ) , 7.247.21 ( m , 3h ) , 7.117.04 ( m , 2h ) , 6.92 ( t , j = 7.6 hz , 1h ) , 6.74 ( s , 1h ) , 5.25 ( s , 1h ) , 3.803.74 ( m , 4h ) , 3.002.90 ( m , 1h ) , 2.822.67 ( m , 2h ) . c nmr ( 150 mhz , dmso - d6 ) 190.1 , 188.9 , 165.9 , 165.4 , 142.1 , 138.2 , 136.4 , 132.4 , 129.6 , 129.5 , 128.7 , 128.3 , 128.1 , 127.0 , 123.0 , 121.1 , 118.9 , 118.4 , 118.2 , 111.6 , 110.9 , 60.8 , 52.1 , 41.2 , 23.8 ; mp 200205 c . hms ( apci ) calcd for c29h24n2o5 481.1771 ; found 481.1765 [ m + h ] . compound 66 was prepared via procedure i from methyl 4-formylbenzoate ( 0.35 g , 2.1 mmol ) , tryptamine ( 0.34 g , 2.1 mmol ) , and 21 ( 0.50 g , 2.1 mmol ) to yield a cream - colored solid ( 1.0 g , 96% ) . h nmr ( 600 mhz , dmso - d6 ) 10.77 ( s , 1h ) , 7.83 ( d , j = 7.8 hz , 2h ) , 7.377.29 ( m , 6h ) , 7.137.12 ( m , 1h ) , 7.077.03 ( m , 3h ) , 6.91 ( t , j = 7.8 hz , 1h ) , 5.36 ( s , 1h ) , 3.873.81 ( m , 4h ) , 3.002.93 ( m , 2h ) , 2.782.73 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 198.0 , 166.0 , 157.1 , 136.40 , 136.3 , 129.4 , 128.4 , 128.2 , 125.6 , 123.4 , 122.9 , 121.2 , 121.1 , 119.5 , 118.6 , 118.4 , 118.25 , 118.19 , 115.2 , 111.7 , 111.6 , 110.9 , 109.7 , 66.5 , 52.2 , 41.2 , 23.8 ; mp 7880 c . hms ( apci ) calcd for c29h24n2o6 497.1707 ; found 497.1707 [ m + h ] . compound 67 was prepared via procedure i from methyl 4-formylbenzoate ( 0.066 g , 0.40 mmol ) , tryptamine ( 0.064 g , 0.40 mmol ) , and 7 ( 0.10 g , 0.40 mmol ) to yield a pale - yellow , amorphous solid ( 0.046 g , 23% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.64 ( s , 1h ) , 7.897.82 ( m , 3h ) , 7.357.22 ( m , 6h ) , 7.077.05 ( m , 2h ) , 6.986.91 ( m , 2h ) , 5.34 ( s , 1h ) , 4.26 ( m , 1h ) , 3.82 ( s , 3h ) , 3.74 ( s , 3h ) , 3.012.90 ( m , 2h ) , 2.782.75 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 188.6 , 165.9 , 165.1 , 158.9 , 141.9 , 139.3 , 136.3 , 129.6 , 129.4 , 129.3 , 128.3 , 128.1 , 126.9 , 125.5 , 122.9 , 121.2 , 121.1 , 119.0 , 118.3 , 118.1 , 113.5 , 111.5 , 110.8 , 60.7 , 55.3 , 52.2 , 41.1 , 23.8 . hms ( apci ) calcd for c30h26n2o6 511.1877 ; found 511.1871 [ m + h ] . compound 68 was prepared via procedure i from methyl 4-formylbenzoate ( 0.17 g , 1.0 mmol ) , tryptamine ( 0.17 g , 1.0 mmol ) , and 8 ( 0.24 g , 1.0 mmol ) to yield a pale - yellow , amorphous solid ( 0.029 g , 6% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.67 ( s , 1h ) , 7.72 ( m , 2h ) , 7.367.33 ( m , 2h ) , 7.287.21 ( m , 2h ) , 7.117.04 ( m , 6h ) , 6.93 ( t , j = 7.2 hz , 1h ) , 5.29 ( s , 1h ) , 3.863.78 ( m , 4h ) , 3.012.96 ( m , 1h ) , 2.912.86 ( m , 1h ) , 2.762.72 ( m , 1h ) , 2.23 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 190.2 , 190.0 , 182.1 , 182.0 , 166.0 , 145.4 , 144.7 , 136.2 , 128.8 , 127.9 , 126.9 , 122.9 , 122.8 , 121.0 , 118.3 , 118.1 , 111.5 , 111.1 , 109.2 , 52.0 , 48.6 , 41.1 , 23.6 , 20.9 ( note : carbons 1 , 2 , 3 , and 4 are absent ) . hms ( apci ) calcd for c30h26n2o5 493.1769 ; found 493.1768 [ m h ] . compound 69 was prepared via procedure i from methyl 4-formylbenzoate ( 0.064 g , 0.39 mmol ) , tryptamine ( 0.063 g , 0.39 mmol ) , and 9 ( 0.10 g , 0.39 mmol ) to yield a pale - yellow , amorphous solid ( 0.045 g , 22% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.69 ( s , 1h ) , 7.82 ( d , j = 8.4 hz , 2h ) , 7.69 ( s , 1h ) , 7.58 ( d , j = 6.0 hz , 1h ) , 7.357.32 ( m , 3h ) , 7.297.26 ( m , 3h ) , 7.077.05 ( m , 2h ) , 6.93 ( t , j = 7.2 hz , 1h ) , 5.28 ( s , 1h ) , 3.823.79 ( m , 4h ) , 2.982.94 ( m , 1h ) , 2.882.84 ( m , 1h ) , 2.742.68 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 182.1 , 166.1 , 145.4 , 137.9 , 136.4 , 136.3 , 129.2 , 128.2 , 127.0 , 126.8 , 125.5 , 123.44 , 123.43 , 122.8 , 121.2 , 121.0 , 118.5 , 118.3 , 118.1 , 111.6 , 111.5 , 111.0 , 109.5 , 60.5 , 52.1 , 23.2 , 20.8 . hms ( apci ) calcd for c29h23cln2o5 513.1223 ; found 513.1219 [ m h ] . compound 70 was prepared via procedure i from methyl 4-formylbenzoate ( 0.069 g , 0.42 mmol ) , tryptamine ( 0.067 g , 0.42 mmol ) , and 10 ( 0.10 g , 0.42 mmol ) to yield a yellow , amorphous solid ( 0.028 g , 14% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.66 ( s , 1h ) , 7.79 ( d , j = 8.4 hz , 2h ) , 7.537.45 ( m , 2h ) , 7.34 ( dd , j = 3.0 hz , j = 8.4 hz , 2h ) , 7.297.26 ( m , 1h ) , 7.22 ( d , j = 7.8 hz , 2h ) , 7.137.10 ( m , 1h ) , 7.077.04 ( m , 2h ) , 6.93 ( t , j = 7.8 hz , 1h ) , 5.32 ( s , 1h ) , 3.843.79 ( m , 4h ) , 3.012.96 ( m , 1h ) , 2.922.88 ( m , 1h ) , 2.762.71 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 191.7 , 167.0 , 161.5 ( d , j = 241.7 hz ) , 143.0 , 137.6 , 136.2 , 129.3 , 128.9 , 128.6 , 128.1 , 127.9 , 126.9 , 125.5 , 124.1 , 122.8 , 121.0 , 118.3 , 118.1 , 116.6 , 116.5 , 111.5 , 110.9 , 61.0 , 52.0 , 41.2 , 23.5 ( note : carbon 3 is absent ) . hms ( apci ) calcd for c29h23fn2o5 497.1510 ; found 497.1513 [ m h ] . compound 71 was prepared via procedure i from methyl 4-formylbenzoate ( 0.074 g , 0.45 mmol ) , tryptamine ( 0.072 g , 0.45 mmol ) , and 18 ( 0.10 g , 0.45 mmol ) to yield a yellow , amorphous solid ( 0.037 g , 17% ) . h nmr ( 600 mhz , cdcl3 ) 8.66 ( d , j = 4.2 hz , 1h ) , 8.21 ( s , 1h ) , 8.14 ( d , j = 7.8 hz , 1h ) , 8.07 ( dt , j = 1.2 hz , j = 7.8 hz , 1h ) , 7.94 ( d , j = 8.4 hz , 2h ) , 7.71 ( dt , j = 0.6 hz , j = 6.0 hz , 1h ) , 7.39 ( d , j = 7.2 hz , 1h ) , 7.36 ( d , j = 7.8 hz , 1h ) , 7.217.17 ( m , 3h ) , 7.07 ( t , j = 8.4 hz , 1h ) , 7.01 ( d , j = 1.8 hz , 1h ) , 5.14 ( s , 1h ) , 4.154.10 ( m , 1h ) , 3.89 ( s , 3h ) , 3.112.95 ( m , 3h ) . c nmr ( 150 mhz , cdcl3 ) 181.8 , 173.2 , 166.8 , 165.7 , 151.7 , 145.3 , 142.5 , 140.6 , 136.5 , 130.3 , 130.0 , 128.3 , 128.1 , 127.3 , 125.2 , 122.3 , 119.6 , 118.7 , 112.5 , 111.5 , 109.6 , 61.6 , 41.4 , 29.9 , 24.3 ( note : carbon 3 is absent ) . hms ( apci ) calcd for c28h23n3o5 482.1710 ; found 482.1708 [ m + h ] . compound 72 was prepared via procedure i from methyl 4-formylbenzoate ( 0.079 g , 0.48 mmol ) , tryptamine ( 0.077 g , 0.45 mmol ) , and 19 ( 0.10 g , 0.48 mmol ) to yield a yellow solid ( 0.11 g , 49% ) . h nmr ( 400 mhz , dmso - d6 ) 10.89 ( s , 1h ) , 8.80 ( s , 1h ) , 8.69 ( d , j = 4.4 hz , 1h ) , 8.00 ( d , j = 7.6 hz , 1h ) , 7.88 ( d , j = 7.2 hz , 2h ) , 7.437.42 ( m , 2h ) , 7.347.29 ( m , 2h ) , 7.14 ( d , j = 8.0 hz , 2h ) , 7.06 ( t , j = 6.8 hz , 1h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.42 ( s , 1h ) , 3.873.82 ( m , 4h ) , 3.022.89 ( m , 2h ) , 2.792.74 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.8 , 165.9 , 165.0 , 152.1 , 149.1 , 142.1 , 136.3 , 133.9 , 129.5 , 129.4 , 128.3 , 128.1 , 126.9 , 125.5 , 123.5 , 122.9 , 121.0 , 118.3 , 118.1 , 111.5 , 110.7 , 109.5 , 60.4 , 52.2 , 41.1 , 23.7 ; mp 199205 c . hms ( apci ) calcd for c28h23n3o5 482.1711 ; found 482.1707 [ m + h ] . compound 73 was prepared via procedure i from methyl 4-formylbenzoate ( 0.15 g , 0.9 mmol ) , tryptamine ( 0.15 g , 0.9 mmol ) , and 20 ( 0.20 g , 0.9 mmol ) to yield a yellow solid ( 0.13 g , 30% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.63 ( s , 1h ) , 8.47 ( d , j = 2.8 hz , 1h ) , 7.766.92 ( m , 12h ) , 5.27 ( s , 1h ) , 3.823.78 ( m , 4h ) , 3.002.95 ( m , 1h ) , 2.912.86 ( m , 1h ) , 2.742.72 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 191.3 , 166.0 , 149.5 , 149.0 , 146.6 , 136.3 , 128.9 , 128.5 , 128.0 , 127.0 , 122.8 , 122.3 , 121.1 , 120.7 , 118.3 , 118.1 , 111.5 , 111.0 , 52.0 , 48.6 , 41.1 , 23.5 ( note : carbons 1 and 2 are absent ) ; mp > 250 c . hms ( apci ) calcd for c28h23n3o5 480.1570 ; found 480.1568 [ m h ] . compound 74 was prepared via procedure i from methyl 4-formylbenzoate ( 0.13 g , 0.80 mmol ) , tryptamine ( 0.13 g , 0.80 mmol ) , and 11 ( 0.20 g , 0.80 mmol ) to yield a pink , amorphous solid ( 0.028 g , 7% ) . h nmr ( 600 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.89 ( s , 1h ) , 7.50 ( d , j = 6.0 hz , 1h ) , 7.347.18 ( m , 5h ) , 7.097.04 ( m , 3h ) , 6.966.88 ( m , 3h ) , 5.27 ( s , 1h ) , 3.833.74 ( m , 6h ) , 2.992.87 ( m , 2h ) , 2.732.65 ( m , 2h ) . c nmr ( 150 mhz , dmso - d6 ) 190.1 , 182.1 , 166.2 , 156.0 , 146.1 , 137.3 , 132.7 , 129.1 , 128.8 , 128.4 , 128.1 , 128.0 , 127.7 , 127.0 , 125.6 , 122.8 , 121.0 , 119.7 , 118.2 , 118.1 , 111.5 , 111.1 , 111.0 , 60.3 , 56.1 , 55.2 , 52.1 , 40.9 , 23.6 , 18.6 . hms ( apci ) calcd for c30h26n2o6 509.1710 ; found 509.1711 [ m h ] . compound 75 was prepared via procedure i from methyl 4-formylbenzoate ( 0.14 g , 0.85 mmol ) , tryptamine ( 0.14 g , 0.85 mmol ) , and 12 ( 0.20 g , 0.85 mmol ) to yield a pale - yellow , amorphous solid ( 0.040 g , 9% ) . h nmr ( 600 mhz , dmso - d6 , 70 c ) 10.71 ( br s , 1h ) , 7.67 ( d , j = 7.2 hz , 2h ) , 7.37 ( d , j = 9.0 hz , 1h ) , 7.30 ( d , j = 7.8 hz , 1h ) , 7.136.99 ( m , 4h ) , 6.946.91 ( m , 2h ) , 6.846.74 ( m , 3h ) , 4.96 ( s , 1h ) , 3.823.76 ( m , 4h ) , 2.972.92 ( m , 1h ) , 2.822.71 ( m , 2h ) , 1.78 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 190.1 , 182.1 , 182.03 , 182.01 , 165.9 , 144.4 , 139.4 , 136.3 , 134.2 , 129.3 , 128.8 , 128.3 , 127.9 , 127.0 , 124.7 , 123.0 , 122.7 , 121.1 , 118.3 , 118.1 , 111.6 , 111.2 , 108.9 , 60.3 , 52.0 , 48.6 , 41.1 , 23.6 . hms ( apci ) calcd for c30h26n2o5 493.1761 ; found 493.1763 [ m h ] . compound 76 was prepared via procedure i from methyl 4-formylbenzoate ( 0.13 g , 0.79 mmol ) , tryptamine ( 0.13 g , 0.79 mmol ) , and 13 ( 0.20 g , 0.79 mmol ) to yield a cream - colored solid ( 0.27 g , 66% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.64 ( s,1h ) , 7.67 ( m , 2h ) , 7.35 ( d , j = 8.4 hz , 1h ) , 7.30 ( d , j = 7.8 hz , 1h ) , 7.247.18 ( m , 2h ) , 7.107.03 ( m , 4h ) , 6.92 ( t , j = 7.2 hz , 2h ) , 6.78 ( m , 1h ) , 5.04 ( s , 1h ) , 3.863.75 ( m , 4h ) , 2.972.92 ( m , 1h ) , 2.852.83 ( m , 1h ) , 2.732.68 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 185.2 , 165.9 , 144.1 , 136.3 , 130.0 , 129.5 , 129.1 , 128.8 , 128.7 , 128.6 , 128.1 , 128.0 , 126.9 , 126.5 , 123.0 , 121.0 , 118.3 , 118.1 , 111.5 , 111.0 , 67.1 , 52.1 , 40.0 , 25.2 ( note : carbons 1 , 2 , and 3 are absent ) ; mp 248253 c . hms ( apci ) calcd for c29h23cln2o5 513.1214 ; found 513.1215 [ m h ] . compound 77 was prepared via procedure i from methyl 4-formylbenzoate ( 0.19 g , 0.84 mmol ) , tryptamine ( 0.14 g , 0.84 mmol ) , and 14 ( 0.20 g , 0.84 mmol ) to yield a brown , amorphous solid ( 0.070 g , 17% ) . h nmr ( 600 mhz , dmso - d6 , 70 c ) 10.68 ( s , 1h ) , 7.807.54 ( m , 2h ) , 7.357.30 ( m , 4h ) , 7.116.78 ( m , 7h ) , 5.07 ( s , 1h ) , 3.813.74 ( m , 4h ) , 2.972.92 ( m , 1h ) , 2.872.82 ( m , 1h ) , 2.722.67 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 172.6 , 165.9 , 161.2 , 156.0 , 155.1 , 139.5 , 136.3 , 135.0 , 130.0 , 129.6 , 128.6 , 126.8 , 126.7 , 126.3 , 125.3 , 124.8 , 123.1 , 121.1 , 119.3 , 118.3 , 118.0 , 111.5 , 110.6 , 59.1 , 52.3 , 41.2 , 23.8 . hms ( apci ) calcd for c29h23fn2o5 497.1510 ; found 497.1513 [ m h ] . compound 78 was prepared via procedure i from methyl 4-formylbenzoate ( 0.42 g , 2.6 mmol ) , tryptamine ( 0.41 g , 2.6 mmol ) , and 15 ( 0.50 g , 2.6 mmol ) to yield an orange solid ( 0.079 g , 7% ) . h nmr ( 600 mhz , cdcl3 ) 8.32 ( s , 1h ) , 8.05 ( s , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.437.41 ( m , 2h ) , 7.32 ( d , j = 8.4 hz , 1h ) , 7.25 ( d , j = 8.4 hz , 2h ) , 7.16 ( t , j = 7.2 hz , 1h ) , 7.06 ( t , j = 7.2 hz , 1h ) , 6.94 ( s , 1h ) , 6.39 ( dd , j = 1.8 hz , j = 3.6 hz , 1h ) , 5.39 ( s , 1h ) , 4.043.99 ( m , 1h ) , 3.88 ( s , 3h ) , 3.072.96 ( m , 2h ) , 2.932.89 ( m , 1h ) . c nmr ( 150 mhz , cdcl3 ) 173.9 , 167.1 , 153.1 , 145.1 , 136.5 , 129.8 , 129.7 , 129.2 , 128.4 , 128.2 , 127.4 , 122.3 , 122.2 , 119.5 , 118.9 , 117.1 , 114.2 , 112.7 , 111.7 , 111.4 , 111.3 , 61.3 , 52.2 , 41.3 , 24.3 ; mp 6065 c . hms ( apci ) calcd for c27h22n2o6 471.1551 ; found 471.1547 [ m + h ] . compound 79 was prepared via procedure i from methyl 4-formylbenzoate ( 0.073 g , 0.44 mmol ) , tryptamine ( 0.071 g , 0.44 mmol ) , and 16 ( 0.10 g , 0.44 mmol ) to yield a yellow , amorphous solid ( 0.043 g , 20% ) . h nmr ( 400 mhz , dmso - d6 ) 10.80 ( s , 1h ) , 7.83 ( d , j = 8.4 hz , 2h ) , 7.55 ( d , j = 4.0 hz , 1h ) , 7.347.29 ( m , 4h ) , 7.067.02 ( m , 3h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.805.70 ( m , 1h ) , 5.28 ( s , 1h ) , 3.863.74 ( m , 4h ) , 3.002.89 ( m , 1h ) , 2.852.78 ( m , 1h ) , 2.732.67 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 165.8 , 144.7 , 136.2 , 129.0 , 128.2 , 126.9 , 126.8 , 123.4 , 122.9 , 121.2 , 121.0 , 118.5 , 118.3 , 118.1 , 111.6 , 111.5 , 111.1 , 109.5 , 52.0 , 48.6 , 40.0 , 23.5 ( note : carbons 1 , 2 , and 4 are absent ) ; mp 190195 c . hms ( apci ) calcd for c27h22n2o5s 485.1177 ; found 485.1173 [ m h ] . compound 80 was prepared via procedure i from methyl 4-formylbenzoate ( 0.36 g , 2.2 mmol ) , tryptamine ( 0.35 g , 2.2 mmol ) , and 17 ( 0.50 g , 2.2 mmol ) to yield a cream - colored solid ( 0.70 g , 65% ) . h nmr ( 400 mhz , dmso - d6 ) 10.86 ( s , 1h ) , 8.38 ( d , j = 2.8 hz , 1h ) , 7.85 ( d , j = 7.6 hz , 2h ) , 7.49 ( t , j = 4.0 hz , 1h ) , 7.377.31 ( m , 4h ) , 7.13 ( s , 1h ) , 7.07 ( t , j = 7.6 hz , 1h ) , 6.93 ( t , j = 6.8 hz , 1h ) , 5.76 ( d , j = 1.2 hz , 1h ) , 5.44 ( s , 1h ) , 3.893.81 ( m , 4h ) , 3.022.90 ( m , 2h ) , 2.802.74 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.8 , 165.9 , 142.1 , 141.6 , 136.3 , 134.2 , 129.5 , 129.4 , 128.3 , 128.1 , 127.3 , 126.9 , 126.3 , 125.5 , 122.9 , 121.1 , 118.3 , 118.1 , 111.5 , 110.8 , 60.7 , 52.1 , 41.1 , 23.8 ; mp 189192 c . hms ( apci ) calcd for c27h22n2o5s 487.1336 ; found 487.1335 [ m + h ] . compound 81 was prepared via procedure i from methyl 3-formylbenzoate ( 0.50 g , 3.1 mmol ) , tryptamine ( 0.49 g , 3.1 mmol ) , and methyl acetopyruvate ( 0.44 g , 3.1 mmol ) to yield a pale - pink solid ( 0.77 g , 60% ) . h nmr ( 400 mhz , dmso - d6 ) 10.82 ( s , 1h ) , 7.87 ( d , j = 7.6 hz , 1h ) , 7.73 ( s , 1h ) , 7.45 ( t , j = 7.2 hz , 1h ) , 7.397.26 ( m , 3h ) , 7.10 ( d , j = 2.0 hz , 1h ) , 7.05 ( t , j = 7.2 hz , 1h ) , 6.89 ( t , j = 8.0 hz , 1h ) , 5.24 ( s , 1h ) , 3.853.76 ( m , 4h ) , 2.982.91 ( m , 1h ) , 2.872.80 ( m , 1h ) , 2.722.65 ( m , 1h ) , 2.72 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 191.5 , 166.0 , 165.1 , 154.8 , 137.8 , 136.3 , 132.5 , 129.9 , 129.1 , 129.0 , 128.4 , 126.9 , 122.9 , 121.1 , 119.8 , 118.3 , 118.1 , 111.5 , 110.8 , 59.8 , 52.3 , 40.8 , 29.8 , 23.7 ; mp 218220 c . hms ( apci ) calcd for c24h22n2o5 419.1593 ; found 419.1596 [ m + h ] . compound 82 was prepared via procedure i from methyl 2-formylbenzoate ( 0.10 g , 0.61 mmol ) , tryptamine ( 0.098 g , 0.61 mmol ) , and methyl acetopyruvate ( 0.088 g , 0.61 mmol ) to yield a white solid ( 0.18 g , 72% ) . h nmr ( 400 mhz , dmso - d6 ) 10.82 ( s , 1h ) , 7.87 ( d , j = 7.6 hz , 1h ) , 7.72 ( s , 1h ) , 7.46 ( t , j = 7.6 hz , 1h ) , 7.38 ( d , j = 7.6 hz , 1h ) , 7.327.25 ( m , 2h ) , 7.10 ( d , j = 1.6 hz , 1h ) , 7.02 ( t , j = 7.6 hz , 1h ) , 6.89 ( t , j = 7.6 hz , 1h ) , 5.24 ( s , 1h ) , 3.86 ( s , 3h ) , 3.823.75 ( m , 1h ) , 2.972.90 ( m , 1h ) , 2.862.79 ( m , 1h ) , 2.712.66 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.6 , 166.0 , 165.0 , 154.5 , 137.8 , 136.2 , 132.5 , 129.8 , 129.0 , 128.9 , 128.3 , 126.8 , 122.9 , 121.0 , 119.9 , 118.2 , 118.0 , 111.4 , 110.7 , 59.7 , 52.2 , 40.8 , 29.8 , 23.6 ; mp 210218 c . hms ( apci ) calcd for c24h22n2o5 419.1602 ; found 419.1599 [ m + h ] . to a suspension of 1 ( 0.10 g , 0.24 mmol ) in etoh ( 3.5 ml ) was added a 2n aq sodium hydroxide solution ( 0.8 ml ) . the reaction was heated at reflux for 2 h. the solution was then cooled to 0 c , and concentrated hcl was added carefully . the precipitate was filtered off , rinsed with cold water , and dried under vacuum for 12 h to afford a white powder ( 0.090 g , 93% ) . h nmr ( 400 mhz , dmso - d6 ) 10.89 ( br s , 1h ) , 10.79 ( br s , 1h ) , 8.09 ( d , j = 8.0 hz , 2h ) , 7.307.28 ( m , 2h ) , 7.23 ( d , j = 8.0 hz , 2h ) , 7.037.01 ( m , 2h ) , 6.90 ( app t , j = 8.0 hz , 1h ) , 5.56 ( s , 1h ) , 3.773.74 ( m , 1h ) , 2.892.71 ( m , 1h ) , 2.712.61 ( m , 2h ) , 2.10 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 196.5 , 179.9 , 169.3 , 164.3 , 146.9 , 136.5 , 130.1 ( 2 ) , 128.5 , 127.8 ( 2 ) , 127.4 , 123.0 , 119.1 , 121.7 , 119.8 , 118.8 , 113.0 , 111.1 , 54.7 , 49.1 , 26.6 , 24.3 ; mp > 250 c . hms ( esi ) calcd for c23h20n2nao5 427.1270 ; found 427.1263 [ m + na ] . compound 84 was prepared via procedure i from 45 ( 0.20 g , 1.1 mmol ) , tryptamine ( 0.18 g , 1.1 mmol ) , and methyl acetopyruvate ( 0.16 g , 1.1 mmol ) to yield a pale - pink solid ( 0.20 g , 42% ) . h nmr ( 400 mhz , dmso - d6 ) 12.48 ( br s , 1h ) , 10.82 ( s , 1h ) , 7.87 ( d , j = 8.4 hz , 2h ) , 7.337.24 ( m , 4h ) , 7.09 ( d , j = 2.4 hz , 1h ) , 7.05 ( t , j = 7.2 hz , 1h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.18 ( s , 1h ) , 4.30 ( q , j = 7.2 hz , 2h ) , 3.833.76 ( m , 1h ) , 2.972.89 ( m , 1h ) , 2.872.80 ( m , 1h ) , 2.742.67 ( m , 1h ) , 2.26 ( s , 3h ) , 1.30 ( t , j = 7.2 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.6 , 165.4 , 165.1 , 142.4 , 136.2 , 129.6 , 129.3 , 128.1 , 126.9 , 122.9 , 121.0 , 118.3 , 118.1 , 111.5 , 110.7 , 60.7 , 59.8 , 40.8 , 39.9 , 23.6 , 14.2 ( note : carbon 3 and either carbon 1 or 2 are absent ) ; mp 180183 c . hms ( apci ) calcd for c25h24n2o5 433.1771 ; found 433.1765 [ m + h ] . compound 85 was prepared via procedure i from 46 ( 0.20 g , 1.0 mmol ) , tryptamine ( 0.17 g , 1.0 mmol ) , and methyl acetopyruvate ( 0.15 g , 1.0 mmol ) to yield an orange , amorphous solid ( 0.028 g , 6% ) . h nmr ( 400 mhz , dmso - d6 ) 10.70 ( s , 1h ) , 7.86 ( d , j = 8.4 hz , 2h ) , 7.337.23 ( m , 3h ) , 7.117.00 ( m , 3h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.165.11 ( m , 2h ) , 3.823.77 ( m , 1h ) , 3.022.85 ( m , 2h ) , 2.762.71 ( m , 1h ) , 2.26 ( s , 3h ) , 1.32 ( s , 3h ) , 1.31 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 190.0 , 164.9 , 136.2 , 129.2 , 128.1 , 126.8 , 125.5 , 123.5 , 122.8 , 121.2 , 121.0 , 118.5 , 118.3 , 118.1 , 111.5 , 110.8 , 68.1 , 59.8 , 40.9 , 39.9 , 23.6 , 21.6 ( note : carbons 1 and 2 are absent ) . hms ( apci ) calcd for c26h26n2o5 447.1928 ; found 447.1922 [ m + h ] . compound 86 was prepared via procedure i from 47 ( 0.50 g , 2.4 mmol ) , tryptamine ( 0.39 g , 2.4 mmol ) , and methyl acetopyruvate ( 0.35 g , 2.4 mmol ) to yield a pale - yellow solid ( 0.92 g , 83% ) . h nmr ( 400 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.81 ( d , j = 8.4 hz , 2h ) , 7.337.22 ( m , 4h ) , 7.10 ( d , j = 2.0 hz , 1h ) , 7.05 ( t , j = 7.2 hz , 1h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.17 ( s , 1h ) , 3.833.76 ( m , 1h ) , 2.962.89 ( m , 1h ) , 2.862.81 ( m , 1h ) , 2.792.67 ( m , 1h ) , 2.26 ( s , 3h ) , 1.53 ( s , 9h ) . c nmr ( 150 mhz , dmso - d6 ) 191.5 , 165.1 , 164.6 , 154.4 , 142.0 , 131.1 , 129.1 , 127.9 , 126.9 , 126.2 , 122.8 , 121.0 , 119.8 , 118.2 , 118.1 , 111.4 , 110.7 , 80.7 , 59.8 , 40.8 , 29.7 , 27.8 , 23.6 ; mp 145150 c . hms ( apci ) calcd for c27h28n2o5 461.2063 ; found 461.2065 [ m + h ] . compound 87 was prepared via procedure i from 4-formylbenzonitrile ( 0.15 g , 1.1 mmol ) , tryptamine ( 0.18 g , 1.1 mmol ) , and 19 ( 0.25 g , 1.1 mmol ) to yield a yellow solid ( 0.084 g , 17% ) . h nmr ( 600 mhz , dmso - d6 ) 10.84 ( s , 1h ) , 8.81 ( s , 1h ) , 8.69 ( d , j = 3.6 hz , 1h ) , 8.01 ( d , j = 7.8 hz , 1h ) , 7.75 ( d , j = 7.8 hz , 2h ) , 7.507.47 ( m , 3h ) , 7.33 ( d , j = 8.4 hz , 1h ) , 7.31 ( d , j = 7.8 hz , 1h ) , 7.13 ( s , 1h ) , 7.07 ( t , j = 7.8 hz , 1h ) , 6.94 ( t , j = 7.2 hz , 1h ) , 5.44 ( s , 1h ) , 3.883.83 ( m , 1h ) , 3.012.90 ( m , 2h ) , 2.792.75 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 189.3 , 165.1 , 152.1 , 150.2 , 149.2 , 142.5 , 136.3 , 133.9 , 132.4 , 129.0 , 126.9 , 123.9 , 123.4 , 122.9 , 121.1 , 118.6 , 118.3 , 118.1 , 117.7 , 111.5 , 111.0 , 110.7 , 60.3 , 41.2 , 23.7 ; mp > 250 c . hms ( apci ) calcd for c27h20n4o3 449.1608 ; found 449.1607 [ m + h ] . compound 88 was prepared via procedure i from 4-nitrobenzaldehyde ( 0.50 g , 3.3 mmol ) , tryptamine ( 0.53 g , 3.3 mmol ) , and methyl acetopyruvate ( 0.48 g , 3.3 mmol ) to yield a pale - yellow solid ( 1.0 g , 75% ) . h nmr ( 400 mhz , dmso - d6 ) 12.62 ( br s , 1h ) , 10.82 ( s , 1h ) , 8.10 ( d , j = 8.8 hz , 2h ) , 7.37 ( d , j = 8.8 hz , 2h ) , 7.31 ( d , j = 8.4 hz , 2h ) , 7.09 ( d , j = 1.6 hz , 1h ) , 7.04 ( t , j = 8.0 hz , 1h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.26 ( s , 1h ) , 3.853.78 ( m , 1h ) , 2.972.84 ( m , 2h ) , 2.802.77 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.6 , 165.2 , 154.7 , 147.1 , 144.9 , 136.2 , 129.0 , 126.8 , 123.5 , 122.9 , 121.0 , 118.2 , 118.0 , 111.4 , 110.7 , 59.4 , 41.0 , 29.8 , 23.5 ( note : carbon 3 is absent ) ; mp 142150 c . hms ( apci ) calcd for c22h19n3o5 406.1398 ; found 406.1395 [ m + h ] . compound 89 was prepared via procedure i from 42 ( 0.29 g , 2.0 mmol ) , tryptamine ( 0.32 g , 2.0 mmol ) , and 19 ( 0.44 g , 2.0 mmol ) to yield a yellow solid ( 0.70 g , 76% ) . h nmr ( 600 mhz , dmso - d6 ) 10.65 ( s , 1h ) , 8.81 ( s , 1h ) , 8.66 ( s , 1h ) , 7.99 ( d , j = 7.8 hz , 1h ) , 7.81 ( d , j = 8.4 hz , 2h ) , 7.457.32 ( m , 6h ) , 7.127.06 ( m , 3h ) , 6.95 ( t , j = 7.2 hz , 1h ) , 5.39 ( s , 1h ) , 3.913.86 ( m , 1h ) , 3.042.98 ( m , 2h ) , 2.832.79 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.1 , 175.4 , 167.3 , 165.0 , 148.7 , 139.8 , 136.1 , 135.7 , 135.3 , 134.0 , 133.9 , 127.4 , 127.2 , 126.7 , 122.8 , 122.7 , 122.4 , 120.6 , 117.7 , 111.1 , 110.7 , 108.5 , 60.2 , 39.9 , 13.7 ; mp 175180 c . hms ( apci ) calcd for c27h22n4o4 467.17138 ; found 467.17160 [ m + h ] . compound 90 was prepared via procedure i from 43 ( 0.15 g , 0.93 mmol ) , tryptamine ( 0.15 g , 0.93 mmol ) , and 19 ( 0.21 g , 0.93 mmol ) to yield a yellow solid ( 0.33 g , 73% ) . h nmr ( 600 mhz , dmso - d6 ) 10.72 ( s , 1h ) , 8.79 ( s , 1h ) , 8.67 ( d , j = 4.8 hz , 1h ) , 8.24 ( d , j = 3.6 hz , 1h ) , 7.99 ( d , j = 7.8 hz , 1h ) , 7.75 ( d , j = 7.8 hz , 2h ) , 7.45 ( t , j = 5.4 hz , 1h ) , 7.397.34 ( m , 4h ) , 7.117.05 ( m , 2h ) , 6.94 ( t , j = 7.2 hz , 1h ) , 5.38 ( s , 1h ) , 3.883.84 ( m , 1h ) , 3.113.09 ( m , 1h ) , 3.022.94 ( m , 2h ) , 2.76 ( d , j = 4.8 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 166.3 , 165.0 , 152.3 , 149.3 , 136.3 , 136.1 , 134.5 , 128.1 , 127.9 , 127.3 , 125.5 , 123.4 , 122.4 , 122.9 , 121.0 , 118.5 , 118.3 , 118.14 , 118.1 , 111.6 , 110.8 , 60.4 , 41.0 , 26.2 , 23.7 ( note : carbon 4 is absent ) ; mp 240245 c . hms ( apci ) calcd for c28h24n4o4 481.1876 ; found 481.1879 [ m + h ] . compound 91 was prepared via procedure i from 19 ( 0.38 g , 1.7 mmol ) , tryptamine ( 0.27 g , 1.7 mmol ) , and 44 ( 0.30 g , 1.7 mmol ) to yield a yellow solid ( 0.33 g , 39% ) . h nmr ( 600 mhz , dmso - d6 ) 10.85 ( s , 1h ) , 8.81 ( s , 1h ) , 8.69 ( d , j = 4.8 hz , 1h ) , 8.01 ( d , j = 7.8 hz , 1h ) , 7.497.47 ( m , 2h ) , 7.367.29 ( m , 4h ) , 7.147.10 ( m , 2h ) , 7.06 ( t , j = 7.8 hz , 1h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.42 ( s , 1h ) , 3.883.82 ( m , 1h ) , 3.022.95 ( m , 5h ) , 2.84 ( s , 3h ) , 2.772.71 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 169.71 , 164.9 , 152.3 , 149.3 , 136.4 , 136.3 , 136.2 , 128.1 , 127.8 , 127.2 , 125.5 , 123.4 , 122.9 , 121.2 , 121.0 , 118.5 , 118.3 , 118.1 , 111.6 , 111.5 , 110.8 , 60.5 , 41.0 , 40.0 , 23.8 , 23.2 ( note : carbon 4 is absent ) ; mp 210212 c . hms ( apci ) calcd for c29h26n4o4 495.2040 ; found 495.2036 [ m + h ] . compound 92 was prepared via procedure i from 4-formylbenzenesulfonamide ( 0.19 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a pale - orange solid ( 0.024 g , 5% ) . h nmr ( 600 mhz , dmso - d6 ) 10.86 ( s , 1h ) , 8.81 ( s , 1h ) , 8.69 ( d , j = 4.2 hz , 1h ) , 8.01 ( d , j = 7.8 hz , 1h ) , 7.76 ( d , j = 9.0 hz , 2h ) , 7.507.47 ( m , 3h ) , 7.34 ( d , j = 7.8 hz , 2h ) , 7.32 ( s , 2h ) , 7.14 ( d , j = 1.8 hz , 1h ) , 7.07 ( t , j = 8.4 hz , 1h ) , 6.96 ( t , j = 7.2 hz , 1h ) , 5.41 ( s , 1h ) , 3.913.86 ( m , 1h ) , 3.032.98 ( m , 1h ) , 2.922.88 ( m , 1h ) , 2.812.76 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.3 , 165.0 , 149.3 , 149.1 , 143.9 , 140.6 , 136.3 , 133.9 , 131.8 , 128.6 , 126.9 , 125.9 , 123.4 , 122.9 , 121.1 , 118.4 , 118.2 , 111.5 , 110.8 , 60.1 , 41.0 , 23.7 ( note : two of either carbons 1 , 2 , or 3 are absent ) ; mp > 250 c . hms ( apci ) calcd for c26h22n4o5s 503.1384 ; found 503.1381 [ m + h ] . compound 93 was prepared via procedure i from 4-formyl - n - methylbenzenesulfonamide ( 0.20 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield an orange - yellow solid ( 0.11 g , 21% ) . h nmr ( 600 mhz , dmso - d6 ) 10.84 ( s , 1h ) , 8.80 ( s , 1h ) , 8.50 ( d , j = 4.8 hz , 1h ) , 8.028.00 ( m , 2h ) , 7.71 ( d , j = 8.4 hz , 2h ) , 7.48 ( d , j = 7.8 hz , 2h ) , 7.40 ( d , j = 4.8 hz , 1h ) , 7.347.29 ( m , 3h ) , 7.097.05 ( m , 2h ) , 6.94 ( t , j = 7.8 hz , 1h ) , 3.843.79 ( m , 1h ) , 3.012.95 ( m , 1h ) , 2.892.85 ( m , 1h ) , 2.702.65 ( m , 1h ) , 2.39 ( d , j = 4.8 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 169.7 , 149.9 , 149.6 , 149.5 , 146.1 , 138.0 , 136.4 , 136.3 , 135.9 , 128.5 , 128.1 , 127.0 , 126.5 , 125.6 , 123.4 , 122.7 , 122.5 , 121.0 , 118.5 , 118.3 , 118.1 , 111.5 , 111.1 , 60.3 , 41.1 , 28.7 , 23.6 ; mp > 220 c . hms ( apci ) calcd for c27h24n4o5s 517.1540 ; found 517.1545 [ m + h ] . compound 94 was prepared via procedure i from 4-(trifluoromethyl)benzaldehyde ( 0.17 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a yellow solid ( 0.24 g , 49% ) . h nmr ( 600 mhz , dmso - d6 ) 10.94 ( s , 1h ) , 8.83 ( d , j = 1.2 hz , 1h ) , 8.70 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 8.20 ( br s , 1h ) , 8.04 ( d , j = 8.4 hz , 1h ) , 7.66 ( d , j = 7.8 hz , 2h ) , 7.547.48 ( m , 3h ) , 7.34 ( d , j = 8.4 hz , 1h ) , 7.24 ( d , j = 7.8 hz , 1h ) , 7.13 ( s , 1h ) , 7.05 ( t , j = 7.8 hz , 1h ) , 6.91 ( t , j = 7.2 hz , 1h ) , 5.46 ( s , 1h ) , 3.883.83 ( m , 1h ) , 3.022.92 ( m , 2h ) , 2.782.73 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.2 , 165.3 , 151.8 , 149.0 , 141.9 , 136.6 , 136.3 , 134.2 , 128.9 , 128.2 , 126.9 , 125.5 , 125.4 , 123.5 , 122.9 , 121.2 , 121.1 , 118.2 , 118.0 , 111.5 , 110.7 , 60.3 , 41.2 , 23.7 ( note : either carbon 1 or 2 is absent ) ; mp 235240 c . hms ( apci ) calcd for c27h20f3n3o3 492.1535 ; found 492.1532 [ m + h ] . compound 95 was prepared via procedure i from 35 ( 0.15 g , 0.83 mmol ) , tryptamine ( 0.13 g , 0.83 mmol ) , and methyl acetopyruvate ( 0.12 g , 0.83 mmol ) to yield a brown solid ( 0.10 g , 27% ) . h nmr ( 400 mhz , dmso - d6 ) 10.82 ( s , 1h ) , 10.49 ( s , 1h ) , 7.68 ( dd , j = 8.0 hz , j = 2.4 hz , 1h ) , 7.347.30 ( m , 2h ) , 7.10 ( s , 1h ) , 7.05 ( t , j = 6.8 hz , 1h ) , 6.92 ( t , j = 6.8 hz , 1h ) , 6.84 ( s , 1h ) , 6.64 ( d , j = 8.0 hz , 1h ) , 5.12 ( s , 1h ) , 3.86 ( s , 3h ) , 3.833.76 ( m , 1h ) , 2.982.83 ( m , 2h ) , 2.752.68 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.7 , 168.8 , 165.0 , 159.8 , 154.4 , 154.1 , 136.0 , 130.3 , 126.9 , 122.8 , 121.0 , 119.6 , 118.3 , 118.2 , 118.1 , 117.0 , 112.8 , 111.4 , 110.7 , 59.6 , 52.4 , 40.9 , 29.8 , 23.5 ; mp 188190 c . hms ( apci ) calcd for c24h22n2o6 435.1551 ; found 435.1549 [ m + h ] . compound 96 was prepared via procedure i from 33 ( 0.1 g , 0.52 mmol ) , tryptamine ( 0.083 g , 0.52 mmol ) , and methyl acetopyruvate ( 0.074 g , 0.52 mmol ) to yield a cream - colored solid ( 0.17 g , 74% ) . h nmr ( 600 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.55 ( d , j = 8.0 hz , 1h ) , 7.347.31 ( m , 2h ) , 7.11 ( s , 1h ) , 7.06 ( t , j = 6.8 hz , 1h ) , 6.946.91 ( m , 2h ) , 6.70 ( d , j = 8.0 hz , 1h ) , 5.14 ( s , 1h ) , 3.833.76 ( m , 7h ) , 2.992.84 ( m , 2h ) , 2.752.69 ( m , 1h ) , 2.28 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 165.9 , 165.0 , 158.1 , 136.2 , 130.9 , 128.1 , 126.9 , 125.5 , 125.0 , 122.9 , 121.0 , 119.6 , 118.6 , 118.3 , 118.1 , 111.5 , 110.8 , 60.0 , 55.9 , 51.9 , 40.9 , 40.0 , 23.6 ( note : carbons 3 and 4 are absent ) ; mp 130135 c . hms ( apci ) calcd for c25h24n2o6 449.1707 ; found 449.1709 [ m + h ] . compound 97 was prepared via procedure i from 40 ( 0.10 g , 0.56 mmol ) , tryptamine ( 0.090 g , 0.56 mmol ) , and methyl acetopyruvate ( 0.081 g , 0.56 mmol ) to yield a pale - orange solid ( 0.13 g , 53% ) . h nmr ( 400 mhz , cdcl3 ) 8.14 ( s , 1h ) , 7.83 ( d , j = 8.4 hz , 1h ) , 7.407.36 ( m , 2h ) , 7.23 ( t , j = 7.6 hz , 1h ) , 7.11 ( t , j = 7.6 hz , 1h ) , 7.00 ( s , 1h ) , 6.83 ( d , j = 7.6 hz , 1h ) , 6.74 ( s , 1h ) , 4.76 ( s , 1h ) , 4.074.02 ( m , 1h ) , 3.90 ( s , 3h ) , 3.112.93 ( m , 3h ) , 2.51 ( s , 3h ) , 1.98 ( s , 3h ) . c nmr ( 150 mhz , cdcl3 ) 194.6 , 167.6 , 164.6 , 159.8 , 141.4 , 139.0 , 136.5 , 131.5 , 131.3 , 130.5 , 127.2 , 125.2 , 122.6 , 122.3 , 119.8 , 119.5 , 118.7 , 112.4 , 111.6 , 61.4 , 52.2 , 41.3 , 28.2 , 24.4 , 21.9 ; mp 4043 c . hms ( apci ) calcd for c25h24n2o5 433.1745 ; found 433.1745 [ m + h ] . compound 98 was prepared via procedure i from 39 ( 0.09 g , 0.45 mmol ) , tryptamine ( 0.073 g , 0.45 mmol ) , and methyl acetopyruvate ( 0.065 g , 0.45 mmol ) to yield a pale - orange , amorphous solid ( 0.14 g , 68% ) . h nmr ( 400 mhz , dmso - d6 ) 10.85 ( s , 1h ) , 7.71 ( d , j = 8.0 hz , 1h ) , 7.407.23 ( m , 4h ) , 7.147.03 ( m , 2h ) , 6.93 ( t , j = 7.6 hz , 1h ) , 5.13 ( s , 1h ) , 3.833.78 ( m , 4h ) , 2.982.82 ( m , 2h ) , 2.752.68 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 190.8 , 165.2 , 142.8 , 136.2 , 131.8 , 131.2 , 130.5 , 129.4 , 128.0 , 126.8 , 126.0 , 122.9 , 121.0 , 118.3 , 118.0 , 111.4 , 110.7 , 59.1 , 52.5 , 48.6 , 40.8 , 23.6 ( note : carbons 1 and 2 are absent ) . hms ( apci ) calcd for 453.1225 ; found 453.1219 [ m + h ] . compound 99 was prepared via procedure i from 38 ( 0.08 g , 0.44 mmol ) , tryptamine ( 0.070 g , 0.44 mmol ) , and methyl acetopyruvate ( 0.063 g , 0.44 mmol ) to yield a pale - orange solid ( 0.096 g , 50% ) . h nmr ( 400 mhz , cdcl3 ) 8.42 ( s , 1h ) , 7.81 ( t , j = 7.6 hz , 1h ) , 7.407.27 ( m , 2h ) , 7.20 ( t , j = 7.2 hz , 1h ) , 7.147.06 ( m , 1h ) , 6.95 ( d , j = 1.2 hz , 1h ) , 6.78 ( dd , j = 1.2 hz , j = 7.6 hz , 1h ) , 6.70 ( dd , j = 1.2 hz , j = 10.8 hz , 1h ) , 4.80 ( s , 1h ) , 4.094.03 ( m , 1h ) , 3.92 ( s , 3h ) , 3.102.96 ( m , 3h ) , 2.19 ( s , 3h ) . c nmr ( 100 mhz , cdcl3 ) 198.1 , 193.6 , 165.5 , 162.0 ( d , j = 260.4 hz ) , 142.8 ( d , j = 7.4 hz ) , 136.5 , 132.8 , 127.0 , 123.5 , 123.4 ( d , j = 26.0 hz ) , 122.5 , 122.3 , 122.1 , 120.1 , 119.7 , 118.7 , 118.5 , 111.9 , 111.7 , 61.2 , 52.6 , 41.6 , 29.2 , 24.4 ; mp 4045 c . hms ( apci ) calcd for c24h21fn2o5 437.1512 ; found 437.1512 [ m + h ] . compound 100 was prepared via procedure i from 34 ( 0.1 g , 0.56 mmol ) , tryptamine ( 0.089 g , 0.52 mmol ) , and methyl acetopyruvate ( 0.080 g , 0.56 mmol ) to yield an off - white solid ( 0.020 g , 8% ) . h nmr ( 400 mhz , dmso - d6 ) 10.68 ( s , 1h ) , 10.07 ( br s , 1h ) , 7.47 ( s , 1h ) , 7.357.29 ( m , 3h ) , 7.057.02 ( m , 3h ) , 6.91 ( t , j = 10.8 hz , 1h ) , 5.58 ( s , 1h ) , 3.83 ( s , 3h ) , 3.803.74 ( m , 1h ) , 3.022.88 ( m , 2h ) , 2.762.68 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 196.6 , 190.2 , 163.6 , 151.5 , 136.4 , 136.2 , 127.0 , 126.9 , 123.5 , 123.0 , 122.5 , 121.0 , 118.32 , 118.25 , 118.0 , 111.4 , 111.2 , 110.4 , 94.5 , 52.7 , 52.2 , 44.8 , 29.3 , 26.7 ; mp 194197 c . hms ( apci ) calcd for c24h22n2o6 435.1551 ; found 435.1552 [ m + h ] . compound 101 was prepared via procedure i from 41 ( 0.20 g , 1.0 mmol ) , tryptamine ( 0.17 g , 1.0 mmol ) , and methyl acetopyruvate ( 0.15 g , 1.0 mmol ) to yield an off - white solid ( 0.16 g , 36% ) . h nmr ( 600 mhz , dmso - d6 , 56 c ) 10.68 ( s , 1h ) , 7.53 ( s , 1h ) , 7.48 ( dd , j = 1.6 hz , j = 8.0 hz , 1h ) , 7.327.28 ( m , 2h ) , 7.067.02 ( m , 3h ) , 6.92 ( td , j = 7.2 hz , j = 0.8 hz , 1h ) , 5.59 ( s , 1h ) , 3.86 ( s , 6h ) , 3.813.72 ( m , 1h ) , 2.972.85 ( m , 2h ) , 2.842.69 ( m , 1h ) , 2.27 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.5 , 165.9 , 165.2 , 157.9 , 154.8 , 136.2 , 130.6 , 126.9 , 126.6 , 122.7 , 121.9 , 121.0 , 118.3 , 117.8 , 111.7 , 111.5 , 110.7 , 56.0 , 52.3 , 41.0 , 40.1 , 29.7 , 23.4 ( note : carbon 3 and either carbon 1 or 2 are absent ) ; mp 103107 c . hms ( apci ) calcd for c25h24n2o6 449.1707 ; found 449.1704 [ m + h ] . compound 102 was prepared via procedure i from 36 ( 0.10 g , 0.56 mmol ) , tryptamine ( 0.090 g , 0.56 mmol ) , and methyl acetopyruvate ( 0.081 g , 0.56 mmol ) to yield an orange solid ( 0.12 g , 50% ) . h nmr ( 600 mhz , dmso - d6 ) 10.83 ( s , 1h ) , 7.75 ( s , 1h ) , 7.66 ( d , j = 8.4 hz , 1h ) , 7.31 ( d , j = 8.4 hz , 1h ) , 7.22 ( d , j = 8.4 hz , 1h ) , 7.09 ( d , j = 1.8 hz , 1h ) , 7.04 ( t , j = 7.2 hz , 1h ) , 6.90 ( t , j = 7.8 hz , 1h ) , 6.84 ( d , j = 8.4 hz , 1h ) , 5.27 ( s , 1h ) , 3.81 ( s , 3h ) , 3.75 ( dt , j = 8.4 hz , j = 13.8 hz , 1h ) , 2.942.89 ( m , 1h ) , 2.762.69 ( m , 2h ) , 2.31 ( s , 3h ) , 2.25 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 166.0 , 165.5 , 140.6 , 138.2 , 136.3 , 131.0 , 128.8 , 127.0 , 126.8 , 125.4 , 122.9 , 121.1 , 118.3 , 117.7 , 111.5 , 110.7 , 55.6 , 41.5 , 40.1 , 23.6 , 18.5 , 14.1 ( note : carbons 3 and 4 , and either carbons 1 or 2 are absent ) ; mp 6070 c . hms ( apci ) calcd for c25h24n2o5 433.1763 ; found 433.1764 [ m + h ] . compound 103 was prepared via procedure i from 32 ( 0.10 g , 0.50 mmol ) , tryptamine ( 0.081 g , 0.50 mmol ) , and methyl acetopyruvate ( 0.073 g , 0.50 mmol ) to yield a pale - yellow solid ( 0.080 g , 35% ) . h nmr ( 400 mhz , dmso - d6 ) 12.50 ( br s , 1h ) , 10.81 ( s , 1h ) , 7.95 ( d , j = 1.6 hz , 1h ) , 7.76 ( dd , j = 1.2 hz , j = 8.0 hz , 1h ) , 7.29 ( d , j = 8.4 hz , 2h ) , 7.097.01 ( m , 3h ) , 6.91 ( t , j = 7.6 hz , 1h ) , 5.68 ( s , 1h ) , 3.85 ( s , 3h ) , 3.803.73 ( m , 1h ) , 2.972.84 ( m , 2h ) , 2.772.72 ( m , 1h ) , 2.28 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 192.5 , 170.4 , 165.5 , 164.8 , 139.8 , 136.2 , 134.7 , 130.8 , 129.8 , 128.2 , 127.8 , 126.9 , 122.8 , 121.0 , 118.3 , 117.7 , 111.5 , 110.4 , 59.8 , 55.6 , 52.6 , 41.5 , 23.5 ( note : carbon 3 is absent ) ; mp 5560 c . hms ( apci ) calcd for c24h21cln2o5 453.1225 ; found 453.1222 [ m + h ] . compound 104 was prepared via procedure i from 37 ( 0.12 g , 0.67 mmol ) , tryptamine ( 0.11 g , 0.67 mmol ) , and methyl acetopyruvate ( 0.097 g , 0.67 mmol ) to yield an orange , amorphous solid ( 0.033 g , 11% ) . h nmr ( 400 mhz , cdcl3 ) 8.58 ( s , 1h ) , 7.65 ( d , j = 8.8 hz , 2h ) , 7.42 ( d , j = 7.6 hz , 1h ) , 7.317.27 ( m , 2h ) , 7.11 ( t , j = 7.2 hz , 1h ) , 7.20 ( t , j = 7.6 hz , 1h ) , 6.93 ( s , 1h ) , 5.52 ( s , 1h ) , 4.023.97 ( m , 1h ) , 3.88 ( s , 3h ) , 3.022.87 ( m , 3h ) , 2.35 ( s , 3h ) . c nmr ( 100 mhz , cdcl3 ) 192.9 , 191.4 , 171.1 , 167.1 ( d , j = 186.7 hz ) , 162.7 , 136.4 , 132.6 , 130.9 , 127.4 , 125.4 , 122.3 , 121.9 , 119.2 , 118.7 , 116.9 ( d , j = 23.8 ) , 114.0 , 112.5 , 111.3 , 102.3 , 52.4 , 45.9 , 41.3 , 28.4 , 24.1 . hms ( apci ) calcd for c24h21fn2o5 437.1507 ; found 437.1509 [ m + h ] . compound 105 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(1-methyl-1h - indol-3-yl)ethanamine ( 0.17 g , 1.0 mmol ) to yield cream - colored solid ( 0.21 g , 43% ) . h nmr ( 600 mhz , dmso - d6 ) 8.81 ( d , j = 1.8 hz , 1h ) , 8.70 ( dd , j = 1.8 hz , j = 4.8 , 1h ) , 8.01 ( dt , j = 1.8 hz , 8.4 hz , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.507.46 ( m , 3h ) , 7.36 ( d , j = 9.0 hz , 1h ) , 7.32 ( d , j = 8.4 hz , 1h ) , 7.147.10 ( m , 2h ) , 6.96 ( t , j = 7.8 hz , 1h ) , 5.50 ( s , 1h ) , 3.853.80 ( m , 4h ) , 3.70 ( s , 3h ) , 3.002.92 ( m , 2h ) , 2.762.72 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.2 , 165.9 , 165.0 , 153.9 , 152.2 , 149.1 , 142.0 , 136.6 , 136.3 , 133.9 , 129.5 , 129.4 , 128.4 , 127.3 , 127.2 , 123.5 , 121.2 , 118.4 , 118.3 , 110.1 , 109.7 , 60.4 , 52.2 , 41.3 , 32.2 , 23.5 ( note : either carbon 1 or 2 is absent ) ; mp 215218 c . hms ( apci ) calcd for c29h25n3o5 496.1867 ; found 496.1872 [ m + h ] . compound 106 was prepared via procedure i from methyl 4-formylbenzoate ( 0.094 g , 0.57 mmol ) , 2-(2-methyl-1h - indol-3-yl)ethanamine ( 0.10 g , 0.57 mmol ) , and methyl acetopyruvate ( 0.083 g , 0.57 mmol ) to yield a cream - colored solid ( 0.18 g , 73% ) . h nmr ( 600 mhz , dmso - d6 ) 10.73 ( s , 1h ) , 7.85 ( d , j = 9.0 hz , 2h ) , 7.21 ( d , j = 7.8 hz , 1h ) , 7.187.15 ( m , 3h ) , 6.97 ( t , j = 7.8 hz , 1h ) , 6.86 ( t , j = 7.8 hz , 1h ) , 5.03 ( s , 1h ) , 3.83 ( s , 3h ) , 3.643.59 ( m , 1h ) , 2.922.87 ( m , 1h ) , 2.772.72 ( m , 1h ) , 2.602.56 ( m , 1h ) , 2.26 ( s , 3h ) , 2.17 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.1 , 165.9 , 165.0 , 142.4 , 135.1 , 132.2 , 129.8 , 129.7 , 129.3 , 128.1 , 127.9 , 125.6 , 120.1 , 118.2 , 117.0 , 110.5 , 106.5 , 60.1 , 52.1 , 40.9 , 39.9 , 24.5 , 10.9 ; mp 182187 c . hms ( apci ) calcd for c25h24n2o5 433.1758 ; found 433.1759 [ m + h ] . compound 107 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(4-methyl-1h - indol-3-yl)ethanamine ( 0.17 g , 1.0 mmol ) to yield a pale - yellow solid ( 0.05 g , 11% ) . h nmr ( 600 mhz , dmso - d6 ) 10.84 ( d , j = 1.8 hz , 1h ) , 8.82 ( d , j = 1.8 hz , 1h ) , 8.70 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 8.01 ( dt , j = 1.8 hz , j = 8.4 hz , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.497.44 ( m , 3h ) , 7.15 ( d , j = 8.4 hz , 1h ) , 7.04 ( d , j = 2.4 hz , 1h ) , 6.92 ( t , j = 6.6 hz , 1h ) , 6.67 ( d , j = 7.2 hz , 1h ) , 5.48 ( s , 1h ) , 3.893.81 ( m , 4h ) , 3.143.09 ( m , 1h ) , 2.982.87 ( m , 2h ) , 2.44 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 186.9 , 165.9 , 165.1 , 152.3 , 149.3 , 142.2 , 136.7 , 136.2 , 133.9 , 129.5 , 129.4 , 128.3 , 125.4 , 123.4 , 123.1 , 122.9 , 121.1 , 120.1 , 119.9 , 118.2 , 111.5 , 109.6 , 66.4 , 60.4 , 52.2 , 25.5 , 19.7 ; mp 170175 c . hms ( apci ) calcd for c29h25n3o5 496.1845 ; found 496.1850 [ m + h ] . compound 108 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(5-methoxy-1h - indol-3-yl)ethanamine ( 0.19 g , 1.0 mmol ) to yield a yellow solid ( 0.35 g , 68% ) . h nmr ( 600 mhz , dmso - d6 ) 10.72 ( s , 1h ) , 8.79 ( d , j = 1.8 hz , 1h ) , 8.68 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 7.99 ( dt , j = 1.8 hz , j = 7.8 hz , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.487.46 ( m , 1h ) , 7.44 ( d , j = 7.8 hz , 2h ) , 7.227.21 ( m , 2h ) , 7.09 ( d , j = 2.4 hz , 1h ) , 6.75 ( d , j = 2.4 hz , 1h ) , 6.70 ( dd , j = 2.4 hz , j = 9.0 hz , 1h ) , 5.44 ( s , h ) , 3.853.80 ( m , 4h ) , 2.68 ( s , 3h ) , 2.982.89 ( m , 2h ) , 2.732.70 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.7 , 181.1 , 165.9 , 165.2 , 153.0 , 152.0 , 149.1 , 142.4 , 136.3 , 134.1 , 131.4 , 129.5 , 129.4 , 128.3 , 127.2 , 123.6 , 123.5 , 117.9 , 112.2 , 111.3 , 110.5 , 99.7 , 60.4 , 55.2 , 52.2 , 41.1 , 23.8 ; mp 222225 c . hms ( apci ) calcd for c29h25n3o6 512.1816 ; found 512.1822 [ m + h ] . compound 109 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 3-(6-fluoro-1h - indol-3-yl)ethanamine ( 0.18 g , 1.0 mmol ) to yield a pale - orange solid ( 0.44 g , 87% ) . h nmr ( 600 mhz , dmso - d6 ) 10.94 ( s , 1h ) , 8.82 ( d , j = 0.6 hz , 1h ) , 8.69 ( d , j = 4.8 hz , 1h ) , 8.01 ( d , j = 7.8 hz , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.80 ( br s , 1h ) , 7.497.47 ( m , 1h ) , 7.43 ( d , j = 7.8 hz , 2h ) , 7.337.30 ( m , 1h ) , 7.317.10 ( m , 2h ) , 6.79 ( td , j = 9.6 hz , j = 1.8 hz , 1h ) , 5.44 ( s , 1h ) , 3.893.82 ( m , 4h ) , 2.982.91 ( m , 2h ) , 2.802.76 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.9 , 181.1 , 165.9 , 165.1 , 159.7 , 158.1 , 152.3 , 142.2 , 136.3 , 136.1 , 133.9 , 129.5 , 129.3 , 128.3 , 125.5 , 123.8 , 123.4 , 119.1 , 118.1 , 111.1 , 106.7 , 106.6 , 60.4 ( d , j = 14.4 hz ) , 52.1 , 41.1 , 23.1 ; mp 162167 c . hms ( apci ) calcd for c28h22fn3o5 500.1595 ; found 500.1600 [ m + h ] . compound 110 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(6-chloro-1h - indol-3-yl)ethanamine ( 0.20 g , 1.0 mmol ) to yield a yellow solid ( 0.44 g , 85% ) . h nmr ( 600 mhz , dmso - d6 ) 11.00 ( s , 1h ) , 8.80 ( s , 1h ) , 8.68 ( d , j = 3.6 hz , 1h ) , 8.00 ( d , j = 8.4 hz , 1h ) , 7.87 ( d , j = 7.8 hz , 2h ) , 7.77 ( br s , 1h ) , 7.487.41 ( m , 3h ) , 7.37 ( d , j = 1.2 hz , 1h ) , 7.33 ( d , j = 8.4 hz , 1h ) , 7.17 ( s , 1h ) , 6.94 ( dd , j = 1.2 hz , j = 8.4 hz , 1h ) , 3.873.82 ( m , 4h ) , 2.972.89 ( m , 2h ) , 2.792.76 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.2 , 165.9 , 165.3 , 149.2 , 136.6 , 136.2 , 129.44 , 129.36 , 128.3 , 128.1 , 125.8 , 125.7 , 125.5 , 124.7 , 124.1 , 123.3 , 119.5 , 118.8 , 118.6 , 111.2 , 111.1 , 109.8 , 60.3 , 52.1 , 41.0 , 23.4 ; mp 184189 c . hms ( apci ) calcd for c28h22cln3o5 516.1321 ; found 516.1324 [ m + h ] . compound 111 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(6-methyl-1h - indol-3-yl)ethanamine ( 0.17 g , 1.0 mmol ) to yield a cream - colored solid ( 0.10 g , 20% ) . h nmr ( 600 mhz , dmso - d6 ) 10.71 ( s , 1h ) , 8.79 ( s , 1h ) , 8.68 ( d , j = 3.6 hz , 1h ) , 7.99 ( d , j = 6.6 hz , 1h ) , 7.87 ( d , j = 7.8 hz , 2h ) , 7.47 ( t , j = 6.0 hz , 1h ) , 7.42 ( d , j = 7.8 hz , 2h ) , 7.17 ( d , j = 7.8 hz , 1h ) , 7.11 ( s , 1h ) , 7.02 ( s , 1h ) , 6.75 ( d , j = 7.8 hz , 1h ) , 5.40 ( s , 1h ) , 3.903.82 ( m , 4h ) , 2.992.89 ( m , 2h ) , 2.742.71 ( m , 1h ) , 2.37 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 186.7 , 165.9 , 165.1 , 152.1 , 149.1 , 142.3 , 136.7 , 136.2 , 134.0 , 130.0 , 129.5 , 129.4 , 128.4 , 128.1 , 125.5 , 124.9 , 123.4 , 122.2 , 120.0 , 117.8 , 111.3 , 110.6 , 60.4 , 52.2 , 41.1 , 23.8 , 21.4 ; mp 202207 c . hms ( apci ) calcd for c29h25n3o5 496.1867 ; found 496.1868 [ m + h ] . compound 112 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 2-(6-methoxy-1h - indol-3-yl)ethanamine ( 0.19 g , 1.0 mmol ) to yield a pale - orange solid ( 0.39 g , 76% ) . h nmr ( 600 mhz , dmso - d6 ) 10.64 ( s , 1h ) , 8.78 ( s , 1h ) , 8.67 ( s , 1h ) , 8.06 ( d , j = 7.8 hz , 1h ) , 7.87 ( d , j = 7.8 hz , 2h ) , 7.55 ( d , j = 7.2 hz , 1h ) , 7.41 ( d , j = 7.8 hz , 2h ) , 7.11 ( d , j = 7.8 hz , 1h ) , 6.96 ( s , 1h ) , 6.83 ( s , 1h ) , 6.58 ( d , j = 7.8 hz , 1h ) , 5.39 ( s , 1h ) , 3.82 ( s , 3h ) , 3.753.70 ( m , 4h ) , 2.942.90 ( m , 2h ) , 2.712.69 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 165.8 , 155.6 , 145.7 , 137.6 , 137.4 , 137.0 , 130.8 , 130.4 , 129.5 , 129.4 , 128.3 , 128.11 , 128.07 , 125.5 , 121.3 , 118.7 , 110.8 , 108.5 , 107.5 , 94.5 , 60.4 , 55.2 , 40.9 , 23.8 , 20.8 ( note : two of either carbon 1 , 2 , or 3 are absent ) ; mp 195200 c . hms ( apci ) calcd for c29h25n3o6 512.1816 ; found 512.1821 [ m + h ] . to a slurry of 2-(7-fluoro-1h - indol-3-yl)ethanamine hydrochloride ( 0.05 g , 0.23 mmol ) in meoh ( 0.026 ml ) was added triethylamine ( 0.039 ml , 0.28 mmol ) . ether ( 1.3 ml ) was added , and the mixture was stirred at 10 c for 1 h. the resulting triethylamine hydrochloride salt was filtered off , and the filtrate was concentrated in vacuo to afford a white solid ( 0.040 g , > 99% ) which was carried on immediately . compound 113 was prepared via procedure i from methyl 4-formylbenzoate ( 0.039 g , 0.24 mmol ) , 19 ( 0.052 g , 0.24 mmol ) , and 2-(7-fluoro-1h - indol-3-yl)ethanamine hydrochloride ( 0.040 g , 0.24 mmol ) to yield a pale - yellow solid ( 0.11 g , 97% ) . h nmr ( 600 mhz , dmso - d6 ) 11.30 ( s , 1h ) , 10.11 ( s , 1h ) , 8.74 ( m , 1h ) , 8.46 ( m , 1h ) , 7.987.97 ( m , 1h ) , 7.877.86 ( m , 1h ) , 7.377.33 ( m , 2h ) , 7.28 ( m , 1h ) , 7.167.14 ( m , 2h ) , 6.896.87 ( m , 2h ) , 5.23 ( s , 1h ) , 3.843.76 ( m , 4h ) , 2.92 ( m , 1h ) , 2.79 ( m , 1h ) , 2.732.68 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 193.0 ( d , j = 13.4 hz ) , 169.4 , 166.2 , 165.5 , 150.0 , 149.5 , 148.4 , 147.7 , 139.1 , 136.6 , 134.3 , 131.1 , 129.7 , 129.0 , 128.7 , 128.3 , 127.7 , 124.0 , 118.6 , 114.7 , 112.4 , 105.8 , 60.0 ( d , j = 45.5 hz ) , 52.0 ( d , j = 41.2 hz ) , 40.1 ( d , j = 21.8 hz ) , 23.3 ; mp 6569 c . hms ( apci ) calcd for c28h22fn3o5 500.1616 ; found 500.1616 [ m + h ] . to a slurry of 2-(7-chloro-1h - indol-3-yl)ethanamine hydrochloride ( 0.15 g , 0.65 mmol ) in meoh ( 0.072 ml ) ether ( 3.62 ml ) was added , and the mixture was stirred at 10 c for 1 h. the resulting triethylamine hydrochloride salt was filtered off , and the filtrate was concentrated in vacuo to afford a white solid ( 0.074 g , 58% ) which was carried on immediately . compound 114 was prepared via procedure i from methyl 4-formylbenzoate ( 0.064 g , 0.39 mmol ) , 19 ( 0.086 g , 0.39 mmol ) , and 2-(7-chloro-1h - indol-3-yl)ethanamine hydrochloride ( 0.074 g , 0.39 mmol ) to yield a yellow solid ( 0.009 g , 5% ) . h nmr ( 600 mhz , dmso - d6 ) 11.22 ( s , 1h ) , 8.80 ( s , 1h ) , 8.69 ( d , j = 4.2 hz , 1h ) , 8.00 ( d , j = 7.8 hz , 1h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.497.44 ( m , 3h ) , 7.31 ( d , j = 7.8 hz , 1h ) , 7.22 ( d , j = 1.8 hz , 1h ) , 7.14 ( d , j = 7.2 hz , 1h ) , 6.94 ( t , j = 7.2 hz , 1h ) , 5.49 ( s , 1h ) , 3.893.82 ( m , 4h ) , 3.002.91 ( m , 2h ) , 2.832.78 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 181.3 , 165.9 , 165.0 , 152.4 , 149.3 , 142.0 , 136.2 , 133.9 , 133.0 , 129.5 , 129.4 , 129.0 , 128.3 , 124.4 , 123.5 , 120.6 , 119.4 , 118.2 , 117.3 , 115.9 , 112.3 , 60.2 , 52.2 , 41.0 , 23.6 ( note : one of either carbon 1 , 2 , or 3 are absent ) ; mp 246249 c . hms ( apci ) calcd for c28h22cln3o5 516.1321 ; found 516.1325 [ m + h ] . compound 115 was prepared via procedure i from methyl 4-formylbenzoate ( 0.094 g , 0.57 mmol ) , 2-(7-methyl-1h - indol-3-yl ) ethanamine ( 0.10 g , 0.57 mmol ) , and methyl acetopyruvate ( 0.083 g , 0.57 mmol ) to yield a white solid ( 0.16 g , 66% ) . h nmr ( 400 mhz , dmso - d6 ) 12.50 ( br s , 1h ) , 10.78 ( s , 1h ) , 7.88 ( d , j = 8.0 hz , 2h ) , 7.26 ( d , j = 8.4 hz , 2h ) , 7.127.07 ( m , 2h ) , 6.836.82 ( m , 2h ) , 5.20 ( s , 1h ) , 3.833.76 ( m , 4h ) , 2.982.80 ( m , 2h ) , 2.802.66 ( m , 1h ) , 2.41 ( s , 3h ) , 2.26 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 165.9 , 165.0 , 142.4 , 135.7 , 129.3 , 128.1 , 126.5 , 125.5 , 122.5 , 121.5 , 120.5 , 118.5 , 115.7 , 111.1 , 109.7 , 59.7 , 52.1 , 40.8 , 40.0 , 23.7 , 16.7 ( note : carbons 3 and 4 are absent ) ; mp 220227 c . hms ( apci ) calcd from c25h24n2o5 433.1758 ; found 433.1758 [ m + h ] . compound 116 was prepared via procedure i from 19 ( 0.15 g , 0.68 mmol ) , tryptamine ( 0.11 g , 0.68 mmol ) , and 35 ( 0.12 g , 0.68 mmol ) to yield a yellow solid ( 0.027 g , 8% ) . h nmr ( 400 mhz , dmso - d6 ) 10.84 ( s , 1h ) , 8.75 ( s , 1h ) , 8.48 ( d , j = 3.2 hz , 1h ) , 7.94 ( d , j = 7.2 hz , 1h ) , 7.83 ( d , j = 8.0 hz , 2h ) , 7.347.27 ( m , 5h ) , 7.087.04 ( m , 2h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.33 ( s , 1h ) , 4.28 ( q , j = 7.6 hz , 2h ) , 3.843.77 ( m , 1h ) , 3.002.93 ( m , 1h ) , 2.872.80 ( m , 1h ) , 2.732.66 ( m , 1h ) , 1.28 ( t , j = 6.8 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 186.8 , 182.1 , 162.9 , 155.0 , 148.3 , 148.1 , 136.4 , 136.3 , 127.0 , 123.8 , 123.4 , 123.2 , 123.1 , 121.5 , 121.3 , 120.8 , 118.5 , 118.2 , 117.8 , 111.8 , 111.2 , 109.5 , 60.6 , 45.3 , 23.6 , 23.3 , 14.0 ; mp > 250 c . hms ( apci ) calcd for c29h25n3o5 496.1867 ; found 496.1872 [ m + h ] . compound 117 was prepared via procedure i from 45 ( 0.40 g , 2.3 mmol ) , tryptamine ( 0.36 g , 2.3 mmol ) , and 20 ( 0.50 g , 2.3 mmol ) to yield a yellow solid ( 0.019 g , 2% ) . h nmr ( 600 mhz , dmso - d6 ) 10.84 ( s , 1h ) , 8.68 ( d , j = 5.4 hz , 2h ) , 7.88 ( d , j = 8.4 hz , 2h ) , 7.51 ( d , j = 5.4 hz , 2h ) , 7.40 ( d , j = 8.4 hz , 2h ) , 7.34 ( d , j = 8.4 hz , 1h ) , 7.30 ( d , j = 8.4 hz , 1h ) , 7.12 ( d , j = 1.8 hz , 1h ) , 7.06 ( t , j = 7.8 hz , 1h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.40 ( s , 1h ) , 4.29 ( q , j = 7.2 hz , 2h ) , 3.883.82 ( m , 1h ) , 3.002.90 ( m , 2h ) , 2.782.73 ( m , 1h ) , 1.29 ( 7.2 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 189.0 , 165.4 , 165.0 , 149.6 , 145.8 , 142.2 , 136.2 , 129.8 , 129.7 , 129.3 , 128.3 , 126.9 , 122.9 , 121.8 , 121.1 , 118.3 , 118.1 , 117.35 , 111.5 , 110.7 , 60.7 , 60.3 , 41.1 , 23.6 , 14.2 ; mp 169172 c . hms ( apci ) calcd for c29h25n3o5 496.1880 ; found 496.1877 [ m + h ] . compound 118 was prepared via procedure i from 19 ( 0.15 g , 0.68 mmol ) , 2-(2-methyl-1h - indol-3-yl)ethanamine ( 0.12 g , 0.68 mmol ) , and methyl 4-formylbenzoate ( 0.11 g , 0.68 mmol ) to yield an orange solid ( 0.046 g , 14% ) . h nmr ( 400 mhz , dmso - d6 ) 10.75 ( s , 1h ) , 8.73 ( s , 1h ) , 8.48 ( d , j = 4.4 hz , 1h ) , 7.93 ( s , 1h ) , 7.82 ( d , j = 8.4 hz , 2h ) , 7.307.17 ( m , 5h ) , 6.97 ( t , j = 6.4 hz , 1h ) , 6.86 ( t , j = 7.2 hz , 1h ) , 5.23 ( s , 1h ) , 3.81 ( s , 3h ) , 3.633.56 ( m , 1h ) , 2.962.88 ( m , 1h ) , 2.762.69 ( m , 1h ) , 2.572.50 ( m , 1h ) , 2.18 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 182.6 , 166.0 , 150.4 , 150.1 , 149.2 , 136.8 , 136.1 , 135.5 , 135.2 , 132.2 , 129.0 , 128.6 , 128.0 , 123.6 , 122.6 , 120.1 , 118.2 , 117.0 , 110.6 , 106.7 , 61.2 , 52.0 , 41.3 , 22.6 , 11.0 ( note : two of carbons 1 , 2 , 3 , or 4 are absent ) ; mp > 250 c . hms ( apci ) calcd for c29h25n3o5 496.1867 ; found 496.1872 [ m + h ] . compound 119 was prepared via procedure i from 45 ( 0.15 g , 0.84 mmol ) , 2-(2-methyl-1h - indol-3-yl)ethanamine ( 0.15 g , 0.84 mmol ) , and methyl acetopyruvate ( 0.12 g , 0.84 mmol ) to yield a cream - colored solid ( 0.078 g , 21% ) . h nmr ( 600 mhz , dmso - d6 , 80 c ) 10.5 ( br s , 1h ) , 7.83 ( d , j = 7.2 hz , 2h ) , 7.237.18 ( m , 4h ) , 6.95 ( t , j = 7.2 hz , 1h ) , 6.86 ( t , j = 7.2 hz , 1h ) , 5.09 ( s , 1h ) , 4.30 ( q , j = 7.2 hz , 2h ) , 3.613.56 ( m , 1h ) , 2.922.87 ( m , 1h ) , 2.802.75 ( m , 1h ) , 2.572.53 ( m , 1h ) , 2.19 ( s , 3h ) , 2.05 ( s , 3h ) , 1.30 ( t , j = 7.2 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.3 , 189.3 , 165.5 , 135.1 , 132.1 , 129.1 , 127.9 , 120.1 , 118.1 , 117.0 , 112.1 , 110.5 , 108.9 , 106.6 , 98.5 , 90.2 , 54.9 , 48.7 , 48.6 , 40.0 , 29.0 , 14.2 , 11.0 ( note : one of either carbon 1 , 2 , or 4 is absent ) ; mp 190195 c . hms ( apci ) calcd for c26h26n2o5 447.1928 ; found 447.30 [ m + h ] . compound 120 was prepared via procedure i from 189 ( 0.15 g , 0.77 mmol ) , tryptamine ( 0.12 g , 0.77 mmol ) , and methyl acetopyruvate ( 0.11 g , 0.77 mmol ) to yield a cream - colored solid ( 0.20 g , 57% ) . h nmr ( 400 mhz , dmso - d6 ) 10.81 ( s , 1h ) , 10.42 ( s , 1h ) , 7.597.46 ( m , 1h ) , 7.347.23 ( m , 3h ) , 7.127.02 ( m , 2h ) , 6.976.89 ( m , 2h ) , 5.76 ( s , 1h ) , 4.28 ( q , j = 7.2 hz , 2h ) , 3.783.74 ( m , 1h ) , 2.982.85 ( m , 2h ) , 2.732.68 ( m , 1h ) , 2.28 ( s , 3h ) , 1.29 ( t , j = 7.2 hz , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.7 , 165.5 , 165.1 , 156.2 , 154.8 , 136.2 , 130.5 , 128.1 , 127.0 , 126.7 , 125.5 , 122.7 , 121.0 , 120.2 , 118.3 , 118.0 , 116.1 , 111.4 , 110.8 , 60.7 , 41.0 , 40.0 , 29.7 , 23.4 , 14.2 ; mp 200205 c . hms ( apci ) calcd for c25h24n2o6 449.1721 ; found 449.1723 [ m + h ] . compound 121 was prepared via procedure i from methyl 4-formylbenzoate ( 0.28 g , 1.7 mmol ) , ( 1h - indol-3-yl)methanamine ( 0.25 g , 1.7 mmol ) , and 20 ( 0.38 g , 1.7 mmol ) to yield an orange solid ( 0.78 g , 98% ) . h nmr ( 400 mhz , dmso - d6 ) 11.08 ( s , 1h ) , 8.66 ( d , j = 5.6 hz , 2h ) , 7.92 ( d , j = 8.0 hz , 2h ) , 7.517.37 ( m , 6h ) , 7.137.08 ( m , 2h ) , 6.97 ( t , j = 7.2 hz , 1h ) , 5.115.07 ( m , 2h ) , 3.84 ( s , 3h ) , 3.80 ( d , j = 14.8 hz , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 166.0 , 165.1 , 149.2 , 129.45 , 129.36 , 128.2 , 128.1 , 126.2 , 125.5 , 125.1 , 122.0 , 121.7 , 121.5 , 119.0 , 118.9 , 118.6 , 118.2 , 111.7 , 109.3 , 59.2 , 52.2 , 35.5 ( note : carbon 4 is absent ) ; mp 240243 c . hms ( apci ) calcd for c27h21n3o5 468.1567 ; found 468.1566 [ m + h ] . compound 122 was prepared via procedure i from methyl 4-formylbenzoate ( 0.16 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and 3-(1h - indol-3-yl)propan-1-amine ( 0.17 g , 1.0 mmol ) to yield a yellow solid ( 0.35 g , 71% ) . h nmr ( 600 mhz , dmso - d6 ) 10.75 ( s , 1h ) , 8.82 ( s , 1h ) , 8.69 ( d , j = 4.8 hz , 1h ) , 8.02 ( d , j = 7.8 hz , 1h ) , 7.87 ( d , j = 8.4 hz , 2h ) , 7.497.47 ( m , 3h ) , 7.37 ( d , j = 7.8 hz , 1h ) , 7.31 ( d , j = 8.4 hz , 1h ) , 7.067.03 ( m , 2h ) , 6.92 ( t , j = 7.2 hz , 1h ) , 5.54 ( s , 1h ) , 3.623.55 ( m , 4h ) , 2.832.79 ( m , 1h ) , 2.622.55 ( m , 2h ) , 1.841.80 ( m , 1h ) , 1.731.69 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.9 , 165.9 , 165.2 , 154.4 , 152.1 , 149.2 , 142.4 , 136.3 , 134.0 , 129.5 , 128.3 , 127.0 , 123.5 , 122.4 , 122.3 , 120.8 , 118.3 , 118.0 , 113.4 , 111.4 , 60.4 , 52.3 , 40.7 , 28.0 , 22.1 ( note : either carbon 1 or 2 and carbon 3 are absent ) ; mp 221226 c . hms ( apci ) calcd for c29h25n3o5 496.1845 ; found 496.1852 [ m + h ] . to a solution of 1 ( 0.50 g , 1.2 mmol ) in dcm : meoh ( 1:1 , 0.13 m ) was added ( diazomethyl)trimethylsilane ( 0.72 ml , 1.4 mmol ) . the reaction mixture continued to stir at rt for 5 h before being concentrated in vacuo . the crude residue was then purified using flash column chromatography on sio2 ( 3% meoh / dcm ) to yield a pale - yellow solid ( 0.24 g , 46% ) . h nmr ( 400 mhz , dmso - d6 ) 10.82 ( s , 1h ) , 7.88 ( dd , j = 1.6 hz , j = 8.0 hz , 2h ) , 7.337.24 ( m , 4h ) , 7.097.03 ( m , 2h ) , 6.92 ( t , j = 7.6 hz , 1h ) , 5.20 ( s , 1h ) , 4.36 ( s , 3h ) , 3.84 ( s , 3h ) , 3.803.71 ( m , 1h ) , 2.962.89 ( m , 1h ) , 2.842.77 ( m , 1h ) , 2.722.63 ( m , 1h ) , 2.25 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 191.9 , 165.9 , 164.2 , 154.0 , 141.7 , 136.2 , 129.5 , 129.3 , 128.2 , 126.8 , 126.2 , 122.9 , 121.0 , 118.3 , 118.0 , 111.5 , 110.7 , 59.5 , 59.1 , 52.2 , 40.9 , 30.3 , 23.6 ; mp 4045 c . hms ( apci ) calcd for c25h24n2o5 433.1763 ; found 433.1761 [ m + h ] . to a solution of 1 ( 0.50 g , 1.2 mmol ) in 2-methoxyethanol ( 8.36 ml , 0.14 m ) was added ammonium formate ( 0.11 ml , 2.2 mmol , 1.8 equiv ) . the reaction mixture was refluxed for 3 h before being concentrated in vacuo , ground with a mortar and pestle , and triturated with et2o . further purification was achieved via flash column chromatography on sio2 ( 10% meoh / dcm ) to yield a pale - yellow solid ( 0.070 g , 14% ) . h nmr ( 400 mhz , cdcl3 , 56 c ) 10.02 ( br s , 1h ) , 8.36 ( br s , 1h ) , 7.92 ( d , j = 8.0 hz , 2h ) , 7.397.34 ( m , 2h ) , 7.17 ( t , j = 7.6 hz , 1h ) , 7.087.02 ( m , 3h ) , 6.97 ( s , 1h ) , 6.44 ( br s , 1h ) , 4.77 ( s , 1h ) , 4.043.97 ( m , 1h ) , 3.91 ( s , 3h ) , 3.092.99 ( m , 2h ) , 2.922.85 ( m , 1h ) , 1.56 ( s , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 177.8 , 165.9 , 164.4 , 163.2 , 144.7 , 136.2 , 129.7 , 129.5 , 128.3 , 126.9 , 122.7 , 121.0 , 118.2 , 118.0 , 111.4 , 110.8 , 105.6 , 58.0 , 52.1 , 48.6 , 41.0 , 23.2 ; mp 5054 c . hms ( apci ) calcd for c24h23n3o4 418.1766 ; found 418.1766 [ m + h ] . to a solution of 1 ( 0.50 g , 1.2 mmol ) in dcm ( 11 ml , 0.11 m ) was added acetic anhydride ( 0.14 ml , 1.4 mmol , 1.2 equiv ) and pyridine ( 0.14 ml , 1.8 mmol , 1.5 equiv ) . the reaction mixture was stirred at rt for 6/2 h before being concentrated in vacuo . the crude material was then purified by flash column chromatography on sio2 ( 3% meoh / dcm ) . additional purification was achieved using hplc ( 75% acn with 0.1% formic acid ) to give a yellow oil ( 0.038 g , 7% ) . h nmr ( 400 mhz , cdcl3 ) 8.06 ( s , 1h ) , 7.947.92 ( m , 2h ) , 7.38 ( d , j = 8.4 hz , 2h ) , 7.21 ( t , j = 8.0 hz , 1h ) , 7.107.05 ( m , 3h ) , 6.98 ( d , j = 2.0 hz , 1h ) , 4.93 ( s , 1h ) , 4.074.00 ( m , 1h ) , 3.91 ( s , 3h ) , 3.082.89 ( m , 3h ) , 2.47 ( s , 3h ) , 2.26 ( s , 3h ) ; c nmr ( 150 mhz , cdcl3 ) 191.5 , 167.0 , 166.6 , 163.8 , 147.7 , 139.2 , 137.0 , 136.6 , 131.0 , 130.4 , 128.1 , 127.4 , 122.6 , 122.2 , 119.9 , 118.7 , 112.6 , 111.5 , 62.3 , 62.4 , 41.5 , 30.1 , 24.4 , 20.8 . hms ( apci ) calcd for c26h24n2o6 461.1721 ; found 461.1717 [ m + h ] . to a solution of 106 ( 0.30 g , 0.69 mmol ) and triethylamine ( 0.19 ml , 1.4 mmol , 2.0 equiv ) in thf ( 0.69 ml , 1.0 m ) at 30 c was added butyryl chloride ( 0.072 ml , 0.69 mmol , 1.0 equiv ) dropwise over 20 min . the mixture was allowed to stir at 30 c for 2 h before being concentrated in vacuo . the crude material was dissolved in etoac , washed with water and brine , dried over mgso4 , filtered , and concentrated in vacuo . purification was achieved via flash column chromatography on sio2 ( 10% etoac : dcm ) to afford a yellow , amorphous solid ( 0.12 g , 35% ) . h nmr ( 600 mhz , cdcl3 ) 7.96 ( s , 1h ) , 7.88 ( d , j = 7.8 hz , 2h ) , 7.25 ( d , j = 8.4 hz , 1h ) , 7.20 ( d , j = 7.2 hz , 1h ) , 7.11 ( t , j = 7.2 hz , 1h ) , 7.01 ( t , j = 7.2 hz , 1h ) , 6.94 ( d , j = 7.8 hz , 2h ) , 4.78 ( s , 1h ) , 3.89 ( s , 3h ) , 3.873.82 ( m , 1h ) , 3.02 ( dt , j = 13.8 hz , j = 8.4 hz , 1h ) , 2.91 ( dt , j = 13.8 hz , j = 7.8 hz , 1h ) , 2.822.78 ( m , 1h ) , 2.70 ( t , j = 7.8 hz , 2h ) , 2.24 ( s , 3h ) , 2.23 ( s , 3h ) , 1.85 ( sextet , 7.8 hz , 2h ) , 1.09 ( t , j = 7.2 hz , 3h ) . c nmr ( 150 mhz , cdcl3 ) 191.6 , 170.0 , 166.6 , 163.7 , 147.9 , 139.1 , 136.9 , 135.4 , 132.1 , 130.8 , 130.2 , 128.3 , 128.0 , 121.5 , 119.7 , 117.8 , 110.6 , 108.0 , 62.5 , 52.4 , 41.4 , 35.9 , 30.2 , 23.3 , 18.4 , 13.7 , 11.5 . hms ( apci ) calcd for c29h30n2o6 503.2168 ; found 503.2172 [ m + h ] . to a solution of 106 ( 3.0 g , 6.9 mmol ) and triethylamine ( 1.9 ml , 14 mmol , 2.0 equiv ) in thf ( 6.9 ml , 1.0 m ) at 30 c was added acryloyl chloride ( 0.72 ml , 6.9 mmol , 1.0 equiv ) dropwise over 20 min . the mixture was allowed to stir at 30 c for 2 h before being concentrated in vacuo . the crude material was dissolved in etoac , washed with water and brine , dried over mgso4 , filtered , and concentrated in vacuo . purification was achieved via flash column chromatography on sio2 ( 10% etoac : dcm ) to afford a yellow , amorphous solid ( 0.68 g , 20% ) . h nmr ( 300 mhz , cdcl3 ) 8.00 ( s , 1h ) , 7.89 ( d , j = 8.7 hz , 2h ) , 7.277.20 ( m , 2h ) , 7.11 ( t , j = 7.2 hz , 1h ) , 7.036.94 ( m , 3h ) , 6.71 ( d , j = 0.9 hz , 1h ) , 6.43 ( d , j = 10.2 hz , 1h ) , 6.20 ( d , j = 0.6 hz , 1h ) , 4.81 ( s , 1h ) , 3.893.81 ( m , 4h ) , 3.082.76 ( m , 3h ) , 2.24 ( s , 6h ) . c nmr ( 150 mhz , cdcl3 ) 196.1 , 191.6 , 186.7 , 166.6 , 163.6 , 162.2 , 147.6 , 139.0 , 137.3 , 135.7 , 135.4 , 132.1 , 130.8 , 130.2 , 128.3 , 128.0 , 126.0 , 121.5 , 119.6 , 117.7 , 110.7 , 107.9 , 62.6 , 52.4 , 41.5 , 30.2 , 23.3 , 11.5 . hms ( apci ) calcd for c28h26n2o6 487.1837 ; found 487.1860 [ m + h ] . compound 161 was prepared via procedure i from methyl 4-formylbenzoate ( 0.34 g , 2.1 mmol ) , ethyl acetopyruvate ( 0.33 g , 2.1 mmol ) , and 2-phenylethanamine ( 0.25 g , 2.1 mmol ) to yield a white solid ( 0.73 g , 93% ) . h nmr ( 400 mhz , dmso - d6 ) 7.92 ( d , j = 8.4 hz , 2h ) , 7.317.24 ( m , 4h ) , 7.19 ( d , j = 7.2 hz , 1h ) , 7.10 ( d , j = 6.8 hz , 2h ) , 5.15 ( s , 1h ) , 3.833.76 ( m , 4h ) , 2.822.60 ( m , 3h ) , 2.26 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 190.9 , 165.9 , 165.0 , 142.4 , 138.5 , 129.4 , 129.4 , 128.6 , 128.5 , 128.1 , 126.4 , 125.6 , 119.7 , 66.4 , 59.7 , 52.2 , 41.5 , 33.5 ; mp 123128 c . hms ( apci ) calcd for c22h21no5 380.1493 ; found 380.1494 [ m + h ] . compound 162 was prepared via procedure i from methyl 4-formylbenzoate ( 0.40 g , 2.4 mmol ) , 188 ( 0.41 g , 2.4 mmol ) , and 20 ( 0.53 g , 2.4 mmol ) to yield a yellow solid ( 0.67 g , 56% ) . h nmr ( 600 mhz , dmso - d6 ) 8.70 ( d , j = 3.6 hz , 2h ) , 7.937.84 ( m , 4h ) , 7.81 ( d , j = 7.8 hz , 1h ) , 7.577.40 ( m , 7h ) , 7.30 ( d , j = 6.6 hz , 1h ) , 5.40 ( s , 1h ) , 3.843.80 ( m , 4h ) , 3.373.34 ( m , 1h ) , 3.133.08 ( m , 1h ) , 3.033.00 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 196.1 , 165.9 , 162.1 , 160.1 , 136.4 , 136.3 , 130.7 , 129.5 , 128.2 , 128.0 , 125.5 , 123.4 , 122.8 , 121.2 , 120.8 , 118.48 , 118.45 , 118.2 , 118.1 , 115.2 , 111.6 , 111.3 , 61.5 , 52.2 , 48.6 , 26.2 ; mp 221224 c . hms ( apci ) calcd for c30h24n2o5 493.1758 ; found 493.1756 [ m + h ] . compound 163 was prepared via procedure i from methyl 4-formylbenzoate ( 0.20 g , 1.2 mmol ) , 19 ( 0.27 g , 1.2 mmol ) , and 2-(benzofuran-3-yl)ethanamine ( 0.20 g , 1.2 mmol ) to yield a pale - yellow solid ( 0.028 g , 4.7% ) . h nmr ( 600 mhz , dmso - d6 ) 8.78 ( s , 1h ) , 8.57 ( s , 1h ) , 7.99 ( d , j = 7.2 hz , 1h ) , 7.86 ( d , j = 7.8 hz , 2h ) , 7.77 ( s , 1h ) , 7.52 ( d , j = 8.4 hz , 1h ) , 7.477.42 ( m , 3h ) , 7.37 ( t , j = 5.4 hz , 1h ) , 7.29 ( t , j = 7.2 hz , 1h ) , 7.20 ( t , j = 7.2 hz , 1h ) , 5.44 ( s , 1h ) , 3.873.82 ( m , 4h ) , 2.972.92 ( m , 2h ) , 2.762.75 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 189.3 , 181.3 , 166.0 , 154.6 , 150.6 , 149.5 , 142.4 , 135.9 , 129.1 , 128.8 , 128.1 , 127.5 , 124.4 , 122.7 , 122.4 , 119.6 , 117.0 , 115.6 , 111.3 , 60.2 , 52.1 , 40.0 , 21.7 ( note : carbons 1 , 2 , and 3 are absent ) ; mp 225230 c . hms ( apci ) calcd for c28h22n2o6 481.1397 ; found 481.1396 [ m h ] . compound 164 was prepared via procedure i from methyl 4-formylbenzoate ( 0.19 g , 1.1 mmol ) , 2-(1h - benzo[d]imidazol-1-yl)ethanamine ( 0.18 g , 1.1 mmol ) , and 20 ( 0.25 g , 1.1 mmol ) to yield a yellow solid ( 0.40 g , 73% ) . h nmr ( 400 mhz , dmso - d6 ) 8.66 ( d , j = 1.3 hz , 2h ) , 8.59 ( s , 1h ) , 7.80 ( d , j = 8.4 hz , 2h ) , 7.67 ( t , j = 5.2 hz , 1h ) , 7.61 ( t , j = 5.2 hz , 1h ) , 7.52 ( d , j = 5.6 hz , 2h ) , 7.337.29 ( m , 4h ) , 5.37 ( s , 1h ) , 4.614.54 ( m , 1h ) , 4.484.44 ( m , 1h ) , 4.033.98 ( m , 1h ) , 3.82 ( s , 3h ) , 3.083.04 ( m , 1h ) . c nmr ( 100 mhz , dmso - d6 ) 186.2 , 166.4 , 165.9 , 149.2 , 146.4 , 143.4 , 142.6 , 139.6 , 132.9 , 129.4 , 128.4 , 128.14 , 128.06 , 125.5 , 123.5 , 123.1 , 122.1 , 118.2 , 111.0 , 60.08 , 52.2 , 43.1 ( note : one sp carbon is under the dmso peak ) ; mp 135140 c . hms ( apci ) calcd for c27h22n4o5 483.1676 ; found 483.1674 [ m + h ] . compound 165 was prepared via procedure i from methyl 4-formylbenzoate ( 0.37 g , 2.3 mmol ) , 2-(1h - imidazol-4-yl)ethanamine ( 0.25 g , 2.3 mmol ) , and 20 ( 0.50 g , 2.3 mmol ) to yield an orange solid ( 0.031 g , 3% ) . h nmr ( 400 mhz , dmso - d6 ) 8.61 ( s , 1h ) , 8.50 ( d , j = 5.2 hz , 2h ) , 7.88 ( d , j = 8.0 hz , 2h ) , 7.51 ( d , j = 5.2 hz , 2h ) , 7.40 ( d , j = 8.0 hz , 2h ) , 7.26 ( s , 1h ) , 7.11 ( s , 1h ) , 5.27 ( s , 1h ) , 3.903.82 ( m , 4h ) , 2.832.76 ( m , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 182.5 , 169.1 , 166.1 , 148.8 , 148.0 , 134.0 , 131.2 , 129.0 , 128.5 , 128.1 , 127.8 , 127.6 , 122.4 , 116.4 , 111.6 , 66.3 , 52.0 , 40.0 , 22.3 ; mp 6470 c . hms ( apci ) calcd for c23h20n4o5 433.1512 ; found 433.1513 [ m + h ] . compound 166 was prepared via procedure i from methyl 4-formylbenzoate ( 0.30 g , 1.8 mmol ) , ethyl acetopyruvate ( 0.29 g , 1.8 mmol ) , and 2-(m - tolyl)ethanamine ( 0.25 g , 1.8 mmol ) to yield a white solid ( 0.56 g , 76% ) . h nmr ( 400 mhz , dmso - d6 ) 7.90 ( d , j = 7.6 hz , 2h ) , 7.28 ( d , j = 7.6 hz , 2h ) , 7.12 ( t , j = 8.0 hz , 1h ) , 6.99 ( d , j = 7.6 hz , 1h ) , 6.886.86 ( m , 2h ) , 5.13 ( s , 1h ) , 3.83 ( s , 3h ) , 3.793.73 ( m , 1h ) , 2.772.70 ( m , 2h ) , 2.612.57 ( m , 1h ) , 2.26 ( s , 3h ) , 2.22 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 191.5 , 166.0 , 165.1 , 142.4 , 138.4 , 137.5 , 129.4 , 129.2 , 128.4 , 128.1 , 127.1 , 126.9 , 125.62 , 125.56 , 119.7 , 66.4 , 59.7 , 52.2 , 41.6 , 33.4 , 21.0 ; mp 118123 c . hms ( apci ) calcd for c23h23no5 394.1649 ; found 394.1651 [ m + h ] . compound 167 was prepared via procedure i from methyl 4-formylbenzoate ( 0.26 g , 1.6 mmol ) , ethyl acetopyruvate ( 0.25 g , 1.6 mmol ) , and 2-(3-chlorophenyl)ethanamine ( 0.25 g , 1.6 mmol ) to yield a pale - yellow solid ( 0.50 g , 76% ) . h nmr ( 400 mhz , dmso - d6 ) 7.90 ( d , j = 8.4 hz , 2h ) , 7.327.20 ( m , 5h ) , 7.08 ( d , j = 7.2 hz , 1h ) , 5.22 ( s , 1h ) , 3.833.79 ( m , 4h ) , 2.792.69 ( m , 3h ) , 2.26 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 165.9 , 165.1 , 142.3 , 141.2 , 133.0 , 130.5 , 130.2 , 129.4 , 128.5 , 128.1 , 127.6 , 127.4 , 126.4 , 125.5 , 59.5 , 52.2 , 41.1 , 32.9 , 29.7 ( note : carbon 4 is absent ) ; mp 118122 c . hms ( apci ) calcd for c22h20clno5 414.1108 ; found 414.1109 [ m + h ] . compound 168 was prepared via procedure i from methyl 4-formylbenzoate ( 0.30 g , 1.8 mmol ) , ethyl acetopyruvate ( 0.28 g , 1.8 mmol ) , and 2-(3-fluorophenyl)ethanamine ( 0.25 g , 1.8 mmol ) to yield an off - white solid ( 0.57 g , 79% ) . h nmr ( 400 mhz , dmso - d6 ) 7.90 ( d , j = 8.4 hz , 2h ) , 7.31 ( d , j = 8.0 hz , 2h ) , 7.297.25 ( m , 1h ) , 7.006.94 ( m , 3h ) , 5.22 ( s , 1h ) , 3.833.79 ( m , 4h ) , 2.812.69 ( m , 3h ) , 2.26 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 165.9 , 165.1 , 162.2 ( d , j = 241.8 hz ) , 142.3 , 141.6 , 141.5 , 130.3 ( d , j = 8.1 hz ) , 129.44 , 129.40 , 128.1 , 125.6 , 124.8 , 115.3 ( d , j = 20.9 hz ) , 113.2 ( d , j = 20.9 hz ) , 59.5 , 52.2 , 41.1 , 33.0 , 15.2 ( note : carbon 4 is absent ) ; mp 114119 c . hms ( apci ) calcd for c22h20fno5 398.1403 ; found 398.1404 [ m + h ] . compound 169 was prepared via procedure i from methyl 4-formylbenzoate ( 0.27 g , 1.7 mmol ) , ethyl acetopyruvate ( 0.26 g , 1.7 mmol ) , and 2-(3-methoxyphenyl)ethanamine ( 0.25 g , 1.7 mmol ) to yield an off - white solid ( 0.52 g , 76% ) . h nmr ( 400 mhz , dmso - d6 ) 7.90 ( d , j = 8.4 hz , 2h ) , 7.30 ( d , j = 8.0 hz , 2h ) , 7.16 ( t , j = 8.0 hz , 1h ) , 6.75 ( d , j = 7.6 hz , 1h ) , 6.686.66 ( m , 2h ) , 5.15 ( s , 1h ) , 3.833.76 ( m , 4h ) , 3.69 ( s , 3h ) , 2.772.70 ( m , 2h ) , 2.652.60 ( m , 1h ) , 2.26 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 166.0 , 165.0 , 159.3 , 145.8 , 142.4 , 140.1 , 129.5 , 129.42 , 129.38 , 128.1 , 125.5 , 120.8 , 114.1 , 111.9 , 59.6 , 54.9 , 52.2 , 41.4 , 33.4 , 29.7 ( note : carbon 4 is absent ) ; mp 150153 c . hms ( apci ) calcd for c23h23no6 410.1603 ; found 410.1604 [ m + h ] . compound 170 was prepared via procedure i from methyl 4-formylbenzoate ( 0.55 g , 3.4 mmol ) , ethyl acetopyruvate ( 0.53 g , 3.4 mmol ) , and 190 ( 0.46 g , 3.4 mmol ) to yield a cream - colored solid ( 1.0 g , 78% ) . h nmr ( 400 mhz , dmso - d6 ) 9.34 ( br s , 1h ) , 7.93 ( d , j = 8.8 hz , 2h ) , 7.33 ( d , j = 8.8 hz , 2h ) , 7.08 ( t , j = 7.6 hz , 1h ) , 6.61 ( dt , j = 1.6 hz , j = 6.8 hz , 1h ) , 6.546.52 ( m , 2h ) , 5.16 ( s , 1h ) , 3.873.83 ( m , 4h ) , 2.742.69 ( m , 2h ) , 2.562.52 ( m , 1h ) , 2.30 ( s , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 193.0 , 166.0 , 165.0 , 157.5 , 142.4 , 139.9 , 129.9 , 129.7 , 129.5 , 129.2 , 128.1 , 127.0 , 119.2 , 115.4 , 113.5 , 59.7 , 52.2 , 48.7 , 41.6 , 33.6 ; mp 98104 c . hms ( apci ) calcd for c22h21no6 396.1447 ; found 396.1446 [ m + h ] . compound 171 was prepared via procedure i from methyl 4-formylbenzoate ( 0.19 g , 1.1 mmol ) , 2-(pyridin-4-yl)ethanamine ( 0.14 g , 1.1 mmol ) , and 20 ( 0.25 g , 1.1 mmol ) to yield a yellow solid ( 0.47 g , 95% ) . h nmr ( 400 mhz , dmso - d6 ) 8.65 ( d , j = 6.0 hz , 2h ) , 8.498.48 ( m , 2h ) , 7.92 ( d , j = 8.0 hz , 2h ) , 7.567.53 ( m , 2h ) , 7.50 ( d , j = 8.0 hz , 2h ) , 7.297.26 ( m , 2h ) , 5.47 ( s , 1h ) , 3.913.83 ( m , 4h ) , 2.882.78 ( m , 3h ) . c nmr ( 150 mhz , dmso - d6 ) 190.1 , 185.8 , 182.0 , 166.3 , 166.0 , 149.5 , 149.2 , 148.3 , 146.6 , 143.4 , 129.4 , 128.2 , 124.6 , 122.2 , 115.6 , 59.9 , 52.2 , 40.6 , 32.7 ; mp 126129 c . hms ( apci ) calcd for c25h21n3o5 444.1567 ; found 444.1566 [ m + h ] . compound 172 was prepared via procedure i from methyl 4-formylbenzoate ( 0.19 g , 1.1 mmol ) , 2-(pyridin-3-yl)ethanamine ( 0.14 g , 1.1 mmol ) , and 20 ( 0.25 g , 1.1 mmol ) to yield a yellow solid ( 0.47 g , 93% ) . h nmr ( 400 mhz , dmso - d6 ) 8.67 ( d , j = 6.0 hz , 2h ) , 8.44 ( dd , j = 1.2 hz , j = 4.8 hz , 1h ) , 8.41 ( d , j = 1.6 hz , 1h ) , 7.92 ( d , j = 8.4 hz , 2h ) , 7.66 ( d , j = 7.6 hz , 1h ) , 7.55 ( d , j = 6.0 hz , 2h ) , 7.50 ( d , j = 8.4 hz , 2h ) , 7.35 ( dd , j = 4.8 hz , j = 7.6 hz , 1h ) , 5.51 ( s , 1h ) , 3.913.83 ( m , 4h ) , 2.912.77 ( m , 3h ) . c nmr ( 100 mhz , dmso - d6 ) 206.6 , 186.6 , 165.9 , 165.6 , 149.3 , 148.9 , 146.9 , 146.1 , 142.7 , 137.3 , 134.7 , 129.5 , 128.2 , 128.1 , 123.8 , 122.0 , 116.6 , 59.9 , 52.2 , 41.3 , 30.5 ; mp 160163 c . hms ( apci ) calcd for c25h21n3o5 444.1567 ; found 444.1565 [ m + h ] . compound 173 was prepared via procedure i from methyl 4-formylbenzoate ( 0.19 g , 1.1 mmol ) , 2-(pyridin-2-yl)ethanamine ( 0.14 g , 1.1 mmol ) , and 20 ( 0.25 g , 1.1 mmol ) to yield a yellow solid ( 0.50 g , > 99% ) . h nmr ( 400 mhz , dmso - d6 ) 8.67 ( d , j = 6.0 hz , 2h ) , 8.48 ( dd , j = 1.6 hz , j = 5.2 hz , 1h ) , 7.91 ( d , j = 8.4 hz , 2h ) , 7.73 ( td , j = 2.0 hz , j = 7.6 hz , 1h ) , 7.53 ( dd , j = 1.2 hz , j = 4.4 hz , 2h ) , 7.46 ( d , j = 8.0 hz , 2h ) , 7.27 ( s , 1h ) , 7.25 ( t , j = 3.6 hz , 1h ) , 5.44 ( s , 1h ) , 4.003.93 ( m , 1h ) , 3.82 ( s , 3h ) , 3.072.97 ( m , 2h ) , 2.922.84 ( m , 1h ) . c nmr ( 100 mhz , dmso - d6 ) 206.6 , 186.7 , 165.9 , 165.5 , 158.1 , 156.6 , 149.4 , 148.7 , 146.1 , 142.6 , 137.3 , 129.5 , 128.2 , 125.6 , 123.6 , 122.0 , 116.9 , 60.1 , 52.2 , 40.3 , 35.4 ; mp 187190 c . hms ( apci ) calcd for c25h21n3o5 444.1567 ; found 444.1564 [ m + h ] . compound 174 was prepared via procedure i from isonicotinaldehyde ( 0.11 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a mustard - colored solid ( 0.32 g , 76% ) . h nmr ( 600 mhz , dmso - d6 ) 10.93 ( s , 1h ) , 8.84 ( d , j = 1.8 hz , 1h ) , 8.67 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 8.53 ( d , j = 5.4 hz , 2h ) , 8.05 ( dt , j = 2.4 hz , j = 8.4 hz , 1h ) , 7.497.47 ( m , 2h ) , 7.427.34 ( m , 3h ) , 7.30 ( br s , 1h ) , 7.13 ( d , j = 1.8 hz , 1h ) , 7.06 ( t , j = 7.8 hz , 1h ) , 6.94 ( t , j = 8.4 hz , 1h ) , 5.34 ( s , 1h ) , 3.923.87 ( m , 1h ) , 3.022.91 ( m , 2h ) , 2.822.77 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 185.5 , 166.1 , 151.3 , 148.9 , 148.4 , 136.7 , 136.3 , 134.5 , 126.9 , 125.5 , 123.6 , 123.4 , 123.0 , 121.1 , 118.3 , 118.1 , 116.1 , 111.6 , 110.8 , 59.7 , 41.2 , 23.7 ( note : either carbon 1 or 2 is absent ) ; mp 225230 c . hms ( apci ) calcd for c25h20n4o3 425.1608 ; found 425.1610 [ m + h ] . compound 175 was prepared via procedure i from nicotinaldehyde ( 0.11 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield an orange solid ( 0.29 g , 67% ) . h nmr ( 600 mhz , dmso - d6 ) 10.90 ( s , 1h ) , 8.83 ( d , j = 2.4 hz , 1h ) , 8.68 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 8.57 ( d , j = 1.8 hz , 1h ) , 8.49 ( dd , j = 2.4 hz , j = 4.8 hz , 1h ) , 8.04 ( dt , j = 1.8 hz , j = 7.8 hz , 1h ) , 7.74 ( d , j = 8.4 hz , 1h ) , 7.497.47 ( m , 1h ) , 7.367.32 ( m , 3h ) , 7.24 ( s , 1h ) , 7.13 ( d , j = 1.8 hz , 1h ) , 7.06 ( t , j = 7.8 hz , 1h ) , 6.94 ( t , j = 8.4 hz , 1h ) , 5.39 ( s , 1h ) , 3.893.85 ( m , 1h ) , 3.022.93 ( m , 2h ) , 2.792.75 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 165.3 , 151.9 , 149.3 , 149.1 , 148.9 , 136.4 , 136.3 , 135.7 , 134.1 , 128.1 , 126.9 , 125.5 , 124.0 , 123.4 , 122.9 , 121.1 , 118.3 , 118.1 , 111.5 , 110.7 , 58.4 , 41.0 , 23.7 ( note : carbons 1 and 2 are absent ) ; mp 225227 c . hms ( apci ) calcd for c25h20n4o3 425.1608 ; found 425.1610 [ m + h ] . compound 176 was prepared via procedure i from picolinaldehyde ( 0.11 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a yellow solid ( 0.30 g , 71% ) . h nmr ( 600 mhz , dmso - d6 ) 10.91 ( s , 1h ) , 8.80 ( d , j = 1.2 hz , 1h ) , 8.69 ( dd , j = 1.2 hz , j = 4.8 hz , 8.55 ( d , j = 4.2 hz , 1h ) , 8.00 ( d , j = 7.2 hz , 1h ) , 7.77 ( td , j = 1.2 hz , j = 7.2 hz , 1h ) , 7.507.46 ( m , 2h ) , 7.387.30 ( m , 4h ) , 7.12 ( d , j = 1.8 hz , 1h ) , 7.05 ( t , j = 7.8 hz , 1h ) , 6.95 ( t , j = 7.8 hz , 1h ) , 5.54 ( s , 1h ) , 3.873.82 ( m , 1h ) , 3.012.91 ( m , 2h ) , 2.722.67 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 189.2 , 165.4 , 156.1 , 151.9 , 149.4 , 149.0 , 137.2 , 136.3 , 134.2 , 128.2 , 126.9 , 125.5 , 123.8 , 123.4 , 122.8 , 121.0 , 118.3 , 118.1 , 111.5 , 110.8 , 62.1 , 41.4 , 23.6 ( note : either carbon 1 or 2 and carbon 3 are absent ) ; mp 218223 c . hms ( apci ) calcd for c25h20n4o3 425.1613 ; found 425.1613 [ m + h ] . compound 177 was prepared via procedure i from furan-3-carbaldehyde ( 0.10 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield an orange solid ( 0.12 g , 28% ) . h nmr ( 600 mhz , dmso - d6 ) 10.86 ( s , 1h ) , 8.85 ( d , j = 1.8 hz , 1h ) , 8.71 ( dd , j = 1.2 hz , j = 4.8 hz , 1h ) , 8.05 ( dt , j = 1.8 hz , j = 7.8 hz , 1h ) , 7.74 ( s , 1h ) , 7.507.48 ( m , 1h ) , 7.45 ( d , j = 7.8 hz , 1h ) , 7.34 ( d , j = 7.8 hz , 1h ) , 7.18 ( s , 1h ) , 7.15 ( d , j = 1.8 hz , 1h ) , 7.10 ( s , 1h ) , 7.07 ( t , j = 7.2 hz , 1h ) , 6.98 ( t , j = 7.8 hz , 1h ) , 6.48 ( d , j = 1.2 hz , 1h ) , 5.40 ( s , 1h ) , 3.893.84 ( m , 1h ) , 3.123.00 ( m , 2h ) , 2.842.80 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 164.4 , 152.4 , 149.5 , 144.1 , 142.7 , 136.3 , 133.8 , 127.0 , 125.5 , 123.4 , 122.9 , 121.1 , 120.8 , 118.3 , 118.2 , 117.5 , 111.5 , 110.9 , 108.6 , 52.4 , 40.7 , 23.7 ( note : carbon 1 and 2 are absent ) ; mp 211217 c . hms ( apci ) calcd for c24h19n3o4 414.1448 ; found 414.1449 [ m + h ] . compound 178 was prepared via procedure i from furfural ( 0.10 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a mustard - colored solid ( 0.06 g , 14% ) . h nmr ( 600 mhz , dmso - d6 ) 10.87 ( s , 1h ) , 8.82 ( d , j = 1.2 hz , 1h ) , 8.72 ( dd , j = 1.8 hz , j = 4.8 hz , 1h ) , 8.03 ( dt , j = 1.8 hz , j = 5.4 hz , 1h ) , 7.62 ( t , j = 0.6 hz , 1h ) , 7.537.52 ( m , 1h ) , 7.48 ( d , j = 7.8 hz , 1h ) , 7.34 ( d , j = 7.8 hz , 1h ) , 7.18 ( s , 1h ) , 7.15 ( d , j = 2.4 hz , 1h ) , 7.107.06 ( m , 2h ) , 6.99 ( t , j = 6.6 hz , 1h ) , 6.52 ( d , j = 3.0 hz , 1h ) , 6.4336.425 ( m , 1h ) , 3.823.77 ( m , 1h ) , 3.193.14 ( m , 1h ) , 3.002.95 ( m , 1h ) , 2.662.61 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 186.9 , 164.5 , 152.3 , 149.1 , 148.9 , 143.4 , 143.2 , 136.3 , 134.0 , 127.0 , 123.5 , 122.9 , 122.8 , 121.0 , 118.4 , 118.3 , 118.1 , 115.0 , 111.5 , 110.8 , 110.2 , 54.5 , 41.4 , 23.7 ; mp 211216 c . hms ( apci ) calcd for c24h19n3o4 414.1448 ; found 414.1452 [ m + h ] . compound 179 was prepared via procedure i from thiophene-2-carbaldehyde ( 0.11 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield an orange solid ( 0.07 g , 16% ) . h nmr ( 600 mhz , dmso - d6 ) 10.87 ( s , 1h ) , 8.81 ( s , 1h ) , 8.72 ( d , j = 4.8 hz , 1h ) , 8.02 ( dd , j = 1.8 hz , j = 6.0 hz , 1h ) , 7.53 - 7.51 ( m , 1h ) , 7.487.44 ( m , 2h ) , 7.34 ( d , j = 7.8 , 1h ) , 7.20 ( d , j = 3.0 hz , 1h ) , 7.15 ( d , j = 1.8 hz , 1h ) , 7.07 ( t , j = 7.8 hz , 2h ) , 7.006.96 ( m , 2h ) , 5.76 ( s , 1h ) , 3.873.83 ( m , 1h ) , 3.143.09 ( m , 1h ) , 3.053.00 ( m , 1h ) , 2.772.72 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 164.2 , 152.4 , 149.2 , 140.2 , 136.3 , 133.8 , 130.3 , 128.7 , 127.02 , 126.96 , 126.5 , 123.6 , 122.9 , 121.1 , 118.3 , 118.2 , 111.5 , 110.8 , 56.1 , 40.9 , 23.6 ( note : carbons 1 , 2 , and 3 are absent ) ; mp 150155 c . hms ( apci ) calcd for c24h19n3o3s 430.1226 ; found 430.1223 [ m + h ] . compound 180 was prepared via procedure i from thiophene-3-carbaldehyde ( 0.11 g , 1.0 mmol ) , 19 ( 0.22 g , 1.0 mmol ) , and tryptamine ( 0.16 g , 1.0 mmol ) to yield a yellow solid ( 0.11 g , 25% ) . h nmr ( 600 mhz , dmso - d6 ) 10.87 ( s , 1h ) , 8.86 ( s , 1h ) , 8.71 ( d , j = 4.8 hz , 1h ) , 8.06 ( d , j = 7.8 hz , 1h ) , 7.70 ( d , j = 1.8 hz , 1h ) , 7.507.47 ( m , 2h ) , 7.40 ( d , j = 7.8 hz , 1h ) , 7.34 ( d , j = 7.8 hz , 1h ) , 7.25 ( s , 1h ) , 7.14 ( s , 1h ) , 7.087.06 ( m , 2h ) , 6.96 ( t , j = 7.8 hz , 1h ) , 5.55 ( s , 1h ) , 3.863.80 ( m , 1h ) , 3.062.98 ( m , 2h ) , 2.762.70 ( m , 1h ) . c nmr ( 150 mhz , dmso - d6 ) 187.4 , 181.2 , 164.5 , 152.5 , 137.2 , 136.3 , 133.8 , 127.05 , 126.98 , 126.2 , 126.0 , 125.4 , 123.5 , 122.9 , 122.8 , 121.1 , 118.4 , 118.2 , 118.0 , 111.5 , 110.9 , 55.0 , 41.2 , 23.9 ; mp 238242 c . hms ( apci ) calcd for c24h19n3o3s 430.1198 ; found 430.1201 [ m + h ] .[/INST]nmda receptors are tetrameric complexes composed of glun1 and glun2a d subunits that mediate a slow ca2 + -permeable component of excitatory synaptic transmission . nmda receptors have been implicated in a wide range of neurological diseases and thus represent an important therapeutic target . we herein describe a novel series of pyrrolidinones that selectively potentiate only nmda receptors that contain the glun2c subunit . the most active analogues tested were over 100-fold selective for recombinant glun2c - containing receptors over glun2a / b / d - containing nmda receptors as well as ampa and kainate receptors . this series represents the first class of allosteric potentiators that are selective for diheteromeric glun2c - containing nmda receptors .</s>

small leucine - rich proteoglycans ( slrps ) are biologically active components of the extracellular matrix ( ecm ) and are structurally characterized by a central protein core made up of leucine - rich repeats ( lrrs ) flanked by cysteine - clusters and substituted with covalently linked glycosaminoglycan ( gag ) side chains ( huxley - jones et al . , these proteoglycans are secreted into the pericellular space and abound in the majority of tissues . they are divided into five distinct classes , based on n - terminal cys - rich clusters of the protein core and ear repeats ( c - terminal repeats specific to slrps ) ( mcewan et al . 2006 ) , chromosomal organization and homologies at the protein and genomic levels ( table 1 ; ( schaefer and iozzo 2008 ) . the gag chains of slrps are sulphated , linear disaccharide repeating units made from acetylated amino sugar moieties and uronic acid , forming negatively charged chondroitin sulphate ( cs ) or dermatan sulphate ( ds ) chains . they are covalently linked to the respective protein core via serine residues ( gandhi and mancera 2008 ; iozzo 1998 ) . by contrast , the keratan sulphate ( ks ) gags are composed of repeating disaccharide units containing galactose ( -4n - acetyl - glucosamine-1,3-galactose-1 ) . decorin , biglycan ( cs / ds class i proteoglycans ) and lumican ( ks class ii proteoglycan ) are the best characterized members of the slrp family . table 1classification of slrpsclass iclass iiclass iiiclass ivclass vbiglycanfibromodulinepiphycanchondroadherinpodocandecorinlumicanopticinnyctalopinpodocan like protein-1asporinprelposteoglycantsukushiecm2keratocanecmxosteoadherinbased on several parameters including conservation and homology at the protein and genomic level , the presence of characteristic n - terminal cys - rich clusters with defined spacing , and chromosomal organization ( schaefer and iozzo 2008 ) classification of slrps based on several parameters including conservation and homology at the protein and genomic level , the presence of characteristic n - terminal cys - rich clusters with defined spacing , and chromosomal organization ( schaefer and iozzo 2008 ) slrps consist of two different structural components , namely a conserved protein core involved in protein / protein interactions ( hocking et al . 1998 ; iozzo 1997 ; kresse et al . along with their pericellular localization , this allows slrps to interact with different molecules and cell - surface receptors , thereby modulating a wide range of cell - matrix interactions ( brandan et al . 2008 ; iozzo 1998 ; perrimon and bernfield 2001 ; roughley 2006 ; schaefer and iozzo 2008 ) . these functions were mostly elucidated by the characterization of specific slrp - deficient mice ( ameye et al . 1999 ; xu et al . 1998 ; young et al . 2002 ) and are briefly summarized in table 2 . slrps were long known to be able to bind to various types of collagens thereby regulating the kinetics , assembly , and special organization of fibrils in skin , tendons , and cornea ( iozzo 1999 ; kalamajski and oldberg 2009 ; kresse et al . 2006 ; schonherr et al . 1995b ; svensson et al . 1995 ; wiberg et al . 2002 ; zhang et al . protein core fragments serve as biological markers for various degenerative cartilage disorders ( melrose et al . table 2characteristics of slrp - deficient micegene disruptedphenotypereferencebiglycanreduced bone mass with decreased production of bone marrow stromal cells and larger irregular collagen fibrils indicating an osteoporosis - like phenotype ; spontaneous aortic dissection and rupture(chen et al . fragility phenotype with loosely packed collagen networks resembling ehlers - danlos syndrome ; intestinal tumor formation(bi et al . 1998)fibromodulinabnormal collagen fibrillogenesis in tendons(svensson et al . 1999)biglycan and decorinsevere osteopenia and increased skin fragility(young et al . 2002)biglycan and fibromodulinseverely altered collagen fibril assembly with ectopic ossification of tendons and premature arthritis(ameye et al . 2002 ) characteristics of slrp - deficient mice however , the biological functions of slrps extend far beyond their interactions with collagens . slrps interact with various cytokines , including transforming growth factor beta ( tgf- ) , bone morphogenic protein ( bmp-4 ) , wnt - i - induced secreted protein - i ( wisp-1 ) , von willebrand factor ( vwf ) , platelet - derived growth factor ( pdgf ) and tumor necrosis factor - alpha ( tnf ) ( bi et al . 2007 ; chen et al . 2009 ; kolb et al . 2001 ; kresse and schonherr 2001 ; nili et al . 2003 ; tufvesson and westergren - thorsson 2002 ) , leading to modulation of their diverse biological functions . pharmacologic manipulations of these interactions could potentially be exploited for the treatment of proliferative , inflammatory , and fibrotic disorders ( goldoni and iozzo 2008 ; schaefer and iozzo 2008 ; schaefer et al . 2002 ; schaefer et al . 2004 ) . as extracellular compounds slrps engage various signaling receptors , including toll - like receptors ( tlrs ) ( schaefer et al . 2005 ) , insulin - like growth factor receptor ( igf - ir ) ( schaefer et al . 2007 ) , epidermal growth factor receptor ( egf - r ) ( iozzo et al . 1999 ) , low - density lipoprotein receptor - related protein ( lrp-1 ) ( brandan et al . 2006 ) , integrin 21 ( fiedler et al . 2008 ; guidetti et al . 2002 ) , and c - met ( goldoni et al . 2009 ) , thereby acting as direct triggers of signal transduction . these interactions result in modulation of cellular growth , proliferation , differentiation , survival , adhesion and migration under developmental , physiological and pathological conditions ( brandan et al . for further details regarding the interaction of slrps with cell membrane receptors we refer to more extensive reviews ( brandan et al . 2008 ; goldoni and iozzo 2008 ; schaefer and iozzo 2008 ; schaefer and schaefer 2009 ) . thus , slrps aptly fit the definition of matricellular proteins due to their : ( i ) extracellular location , ( ii ) modulatory effects on synthesis , assembly and degradation of fibrils without being part of the fibrillar structure itself , and ( iii ) direct ( receptor - mediated ) and indirect ( via interaction with cytokines , growth factors and other ecm components ) regulation of cell - matrix crosstalk , influencing a host of biological processes ( e. g. inflammation , fibrosis , tumorigenesis , angiogenesis , coagulation and wound healing ) . in the present review , we focus primarily on the matricellular functions of decorin , biglycan ( class i proteoglycans ) , and lumican ( class ii proteoglycan ) , which are briefly summarized in table 3 . table 3matricellular functions modulated by the slrps decorin , biglycan and lumicanbiological function modulatedmechanism mediated / involved in modulationreceptor - binding associated with signal transductionegf - r(d1 ) , igf - ir(d ) , lrp-1(d ) , c - met(d ) , tlr2(b ) , tlr4(b ) and cd14(l)modulation of cytokine bio - activitybmp-4(b ) , pdgf(d , b ) , tgf-(d , b ) , tnf(d , b ) , vwf(d ) and wisp-1(d , b)fibrillogenesis , fibrillar organization and degradationbind collagens(d , b , l ) and elastic fibril components(d , b ) regulating fibrillar kinetics(d ) , assembly(d , l ) and degradation(d , l ) , thereby modulating the structure , stability and integrity of the ecm.adhesion and migrationby binding to adhesion(d ) and anti - adhesion molecules(d ) and also by signaling via igf - ir(d ) , integrin 21(d , l ) , rhoa(d , b ) , rac1(d , b ) , syk(d ) and erk1/2(l ) , inhibits or enhances adhesion and migration in a cell type specific manner.cellular proliferationby binding and modulating receptor mediate signaling ( egfr , erbb4 and vegf - r2)(d ) ; by modulating : ( i ) growth factor bioactivity ( tgf-(d ) and pdgf - bb(b ) ) ; ( ii ) cell cycle ( influencing expression of p21(d , l ) , p27(d , b ) , cdk2(b ) and cyclin d1(l ) ) and ( iii ) the myostatin pathway , regulate cellular growth in a cell and stage - specific manner(d).cellular survivalregulate cellular survival by modulating igf - ir signaling(d ) , egfr(d ) , caspase-3 activity(d , b ) and fas / fasl - mediated apoptotic pathway(l).inflammation and innate immunityacts as pamp(b ) or presents pamps(l ) to the receptor thereby triggering or enhancing the inflammatory response . also sustains inflammation by regulating chemokine gradient(d , b , l ) and complement activity(d , b).fibrosispotent antifibrotic agent(d ) , influencing fibrogenesis in different organs by a number of distinct mechanisms : ( i ) inhibition of tgf- , ( ii ) regulation of ecm synthesis and turnover and by ( iii ) regulating cell death , adhesion and migration.the slrp modulating the respective matricellular function is indicated as subscript and abbreviated as follows : d , decorin ; b , biglycan ; l , lumican matricellular functions modulated by the slrps decorin , biglycan and lumican the slrp modulating the respective matricellular function is indicated as subscript and abbreviated as follows : d , decorin ; b , biglycan ; l , lumican by their ability to bind to different types of collagens and elastic fibril components , slrps impact on extracellular matrix organization , modulating the structural and functional environment of cells . the interaction of slrps with collagens has been shown to enhance fibril stability ( keene et al . 2000 ; neame et al . 2000 ) and to protect fibrils from proteolytic cleavage by various collagenases ( geng et al . the role of decorin in regulating collagen fibrillogenesis was elucidated by studies using knockout mice , which exhibit loosely packed collagen fiber networks with increased fibril diameter , leading to a skin fragility phenotype ( danielson et al . the functional importance of decorin in regulating collagen fibrillogenesis was further emphasized by the altered mechanical function of lung tissue in decorin - deficient mice ( fust et al . 2005 ) . decorin is involved in lateral growth of collagen fibrils and regulates fibril diameter in vitro ( danielson et al . it binds to collagen type i , ii , iii , iv , vi , and xiv ( bidanset et al . 1992 ; ehnis et al . 1997 ; reed and iozzo 2002 ) and has been localized to the d and e bands of tendon collagen in the gap zone ( pringle and dodd 1990 ; weber et al . decorin is also involved in lateral fusion of collagen i fibrils by binding to the c - terminus via lrr4 - 6 of the protein core through protein / protein interactions , which involves more than one binding domain ( keene et al . 2000 ; kresse et al . . the gag chain of decorin binds tenascin - x and mediates its interaction with collagen fibrils , thereby contributing to extracellular matrix integrity ( elefteriou et al . 2001 ) . furthermore , the gag chains are involved in the maintenance of interfibrillar spacing , which also effects fibril diameter ( iozzo 1999 ; raspanti et al . biglycan - deficient mice do not suffer from increased skin fragility , but exhibit larger and irregular fibrils leading to thin dermis and reduced bone mass ( corsi et al . biglycan binds to collagen type i , ii , and iii but unlike decorin its interaction with collagen does not appear to influence fibril diameter or fibrillar kinetics . however , due to its trivalency biglycan could have a special organizing function on assembly of the extracellular matrix ( douglas et al . this notion is supported by the binding of biglycan to the n - terminal ends of the collagen vi tetramers . this leads to supramolecular organization of collagen into hexagonal networks , with biglycan being localized at the intra - network junctions of the collagen vi filaments ( wiberg et al . intact biglycan with gag chains is required for complex formation and interaction with the tgf--inducible gene - h3 ( beta ig - h3 ) and collagen vi ( reinboth et al . the influence of biglycan on collagen fibrillogenesis is further demonstrated by the presence of high amounts of biglycan in keloids ( hunzelmann et al . 1996 ) and by its localization in the decidualized regions of the endometrium , regulating fibril thickness in the murine decidua ( san martin and zorn 2003 ) . decorin and biglycan also regulate collagen fibril assembly coordinately in the cornea ( zhang et al . there is some evidence that both slrps may also be involved in elastic fiber biology . decorin forms complexes with fibrillin-1 , tropoelastin ( the soluble precursor of mature elastin ) and microfibril - associated glycoprotein 1 ( mapg-1 ) ( kielty et al . 1996 ; trask et al . 2000 ) . therefore , both proteoglycans were classified as microfibril- and elastic fiber - associated molecules ( kielty et al . biglycan regulates elastogenesis as shown by the ability of its gag chains to inhibit elastin synthesis and assembly in the vessel wall ( hwang et al . recent studies have established a molecular link between decorin and the igf - ir signaling pathway and the synthesis of fibrillin-1 in renal fibroblasts . translational regulation of fibrillin-1 involves the igf - ir and the phosphoinositide 3-kinase ( pi3k)/akt pathway , with mammalian target of rapamycin ( mtor ) and p70 s6 kinase as downstream targets ( fig . 1 ) ( schaefer et al . this intriguing finding indicates that the ecm component decorin is capable of directly regulating the synthesis of another matrix constituent ( fibrillin-1 ) . this together with the ability of decorin to regulate the activity of mmps ( schonherr et al . 2001 ) , underlines the complexity of ecm synthesis and turnover under physiological and pathological conditions . 1cell type - specific functions mediated by decorin via modulation of igf - ir signaling . decorin binds and induces phosphorylation of the insulin - like growth factor - i ( igf - i ) receptor , causing downstream activation of phosphoinositide-3 kinase ( pi3k ) and the akt / protein kinase b ( akt / pkb ) pathway . in endothelial and renal tubular epithelial cells this signaling cascade leads to an inhibition of apoptosis , whereas in renal fibroblasts signaling through mammalian target of rapamycin ( mtor ) and p70s6 kinase ( p70s6k ) leads to increased translation and synthesis of fibrillin-1 . these pathways demonstrate the intricate regulatory mechanisms whereby decorin modulates igf - ir signaling in a cell type - specific manner , thereby giving rise to different biological outcomes cell type - specific functions mediated by decorin via modulation of igf - ir signaling . decorin binds and induces phosphorylation of the insulin - like growth factor - i ( igf - i ) receptor , causing downstream activation of phosphoinositide-3 kinase ( pi3k ) and the akt / protein kinase b ( akt / pkb ) pathway . in endothelial and renal tubular epithelial cells this signaling cascade leads to an inhibition of apoptosis , whereas in renal fibroblasts signaling through mammalian target of rapamycin ( mtor ) and p70s6 kinase ( p70s6k ) leads to increased translation and synthesis of fibrillin-1 . these pathways demonstrate the intricate regulatory mechanisms whereby decorin modulates igf - ir signaling in a cell type - specific manner , thereby giving rise to different biological outcomes lumican - deficient mice suffer from increased skin fragility and corneal opacities due to abnormal fibril assembly and altered interfibrillar spacing , indicating a role in lateral fusion of collagen fibrils ( chakravarti et al . 1998 ) . besides maintaining normal fibril architecture of the cornea by regulating fibril assembly in the posterior stroma , lumican provides an optimal ks content required for corneal transparency ( chakravarti et al . lumican regulates the assembly of fibrils at an early stage of collagen fibrillogenesis ( ezura et al . recently , the binding site of the lumican protein core to collagen type i via asp-213 of lrr7 has been reported ( kalamajski and oldberg , 2009 ) . fibromodulin , another class ii keratan sulphate slrp binds to collagen and also regulates fibrillogenesis . its deficiency leads to an abnormal tendon phenotype with impaired collagen fibrils ( svensson et al . 1999 ; viola et al . 2007 ) . during tendon development , fibromodulin is involved in collagen fibrillogenesis , regulating fibril assembly and maturation ( ezura et al . the interaction of fibromodulin with collagen requires more than one binding domain , similar to class i slrps . one of these domains appears to be the c - terminal end of the molecule containing the disulfide loop ( font et al . 1998 ) , and the binding to collagen i involves lrr5 - 7 of the protein core ( kalamajski and oldberg 2009 ) . the multitude of matricellular functions performed by slrps is further evidenced by their ability to regulate cellular proliferation . decorin has long been known to regulate cellular growth , as ectopic overexpression of decorin retarded cell growth ( yamaguchi and ruoslahti 1988 ) . diverse mechanisms of growth regulation by decorin have been revealed over the years and these were attributed to its ability to , ( i ) engage receptors modulating signaling pathways , ( ii ) act as a growth factor , and ( iii ) influence regulation at certain cell cycle checkpoints . decorin inhibits cellular proliferation in a tgf--dependent manner in chinese hamster ovary ( cho ) cells ( yamaguchi et al . 1990 ) , arterial smooth muscle cells ( fischer et al . 2001 ) , human hepatic stellate cells ( shi et al . 2006 ) , and fibroblasts ( zhang et al . however , the majority of data concerning decorin - mediated regulation of proliferation was generated in carcinoma cell lines . in tumor cells , decorin binds egfr and erbb4 , leading to activation of the mitogen - activated protein kinase ( mapk ) pathway , ca influx , induction of the cyclin - dependent kinase ( cdk ) inhibitor p21 with subsequent downregulation of the receptor ( csordas et al . thus , these extensive studies provide a molecular explanation for the antiproliferative and antioncogenic effects of decorin ( reed et al . moreover , there is a direct link between decorin deficiency and spontaneous tumor formation ( bi et al . 2008 ) . for further details more extensive reviews are suggested ( goldoni and iozzo 2008 ; nikitovic et al . recently , decorin has been shown to inhibit proliferation of trophoblasts through the egfr and vascular endothelial growth factor receptor-2 ( vegf - r2 ) signaling pathways ( iacob et al . 2008 ) , indicating that these mechanisms are not restricted to regulation of carcinoma cell proliferation . interestingly , by binding myostatin and modulating its down - stream signals , decorin can rescue the inhibitory effects of myostatin on myoblast proliferation , thereby acting indirectly as a promoter of cell proliferation ( brandan et al . 2006 ) . the role of biglycan in regulating cellular proliferation was addressed only by a limited number of studies . antiproliferative effects of biglycan were observed in mesangial cells of the kidney , where it inhibited pdgf - bb - induced proliferation ( schaefer et al . 2003 ) and in bone marrow stromal cells , where wisp-1 blocked the antiproliferative effects of biglycan ( inkson et al . in pancreatic cancer cells , biglycan induced g1 arrest , thereby inhibiting tumor cell proliferation . this effect was associated with upregulation of the cdk inhibitor p27 and downregulation of cyclin a and proliferating cell nuclear antigen , along with decreased activation of ras and erk ( weber et al . however , in vascular smooth muscle cells biglycan has been shown to favor proliferation in a cdk2- and p27-dependent manner ( shimizu - hirota et al . moreover , the proliferative phase of osteoblast development was associated with increased expression of biglycan , indirectly indicating that biglycan might promote proliferation ( waddington et al . it is tempting to speculate that similar to decorin , biglycan might regulate proliferation in a cell type - specific manner , either directly via a specific receptor or by contributing to the crosstalk between signaling pathways , or by an indirect mechanism . to interpret these data in more detail , studies on biglycan - mediated signaling are warranted . up to now , the toll - like receptors-2 and -4 have been identified as signaling receptors for biglycan ( schaefer et al . 2005 ) , whereas unlike decorin it was found not to signal through the egfr ( moscatello et al . similar to decorin , lumican also acts as a negative regulator of cellular proliferation , by upregulating the expression of the cdk inhibitor p21 ( li et al . lumican inhibits proliferation of mouse embryonic fibroblasts by upregulating p21 in a p53-dependent mechanism with decreased cyclin a , d1 and e ( vij et al . 2004 ) . lack of lumican has been shown to promote proliferation of stromal keratinocytes and embryonic fibroblasts ( vij et al . its inhibitory effects on growth are extended to tumor cells , with some of these cells secreting lumican in an autocrine manner ( sifaki et al . lumican regulates vertical growth and inhibits anchorage - independent proliferation and cyclin d1 expression in melanoma cells ( brezillon et al . further details concerning the role of lumican in controlling tumor growth are included in recent reviews ( goldoni and iozzo 2008 ; naito 2005 ; nikitovic et al . 2002 ) , endothelial cells , and bone marrow stromal cells ( bi et al . 2005 ) . in tubular epithelial and endothelial cells , the anti - apoptotic effects of decorin are mediated by binding to the igf - ir and signaling via the pi3k / akt pathway , which also plays a role in fibrosis ( details are described in the section fibrosis below ) and angiogenesis ( fig . 1 ) ( schaefer et al . it appears that signaling through the canonical igf pathway may represent a common mechanism by which decorin protects non - carcinoma cells from programmed cell death . conversely , in carcinoma cells decorin has been shown to enhance apoptosis via the egfr and enhanced caspase-3 activity , indicating an additional mechanism , which might explain the anti - oncogenic effects of decorin ( seidler et al . 2003 ) . the role of biglycan and lumican in the regulation of cell survival has not been studied in detail . biglycan has been shown to protect mesangial cells from apoptosis by decreasing caspase-3 activity ( schaefer et al . by contrast , lumican mediates fas - fasl - induced apoptosis by inducing fas ( cd95 ) in mouse embryonic fibroblasts ( vij et al . the ability of lumican to induce apoptosis has also been reported in tumor cells and could be used to control tumor progression ( vuillermoz et al . decorin , biglycan , asporin , and fibromodulin bind the profibrotic cytokine tgf- ( hildebrand et al . 1994 ; nakajima et al . 2007 ) . however , since tgf- interacts with conserved leucine - rich repeat structures ( schonherr et al . 1998 ) , it is likely that other slrps are also able to form complexes with this cytokine . a lot of attention has been focused on the interaction of decorin with tgf- , as it had been demonstrated unequivocally that decorin treatment exerts beneficial effects in fibrotic disorders involving tgf- overproduction in the kidney and other organs ( border et al . 1992 ; kolb et al . 2001 ) . besides inhibition of tgf--mediated fibrosis , the binding of decorin to tgf- has significant biological implications in regulating a number of cellular processes , e. g. ( i ) modulation of cell proliferation ( li et al . 2008 ; yamaguchi et al . 1990 ) , ( ii ) inhibition of repressive effects of tgf- on macrophages leading to their activation ( comalada et al . 2003 ) , and ( iii ) suppression of tgf--dependent apoptosis in bone marrow stromal cells ( bi et al . 2005 ) . several mechanisms for the decorin - mediated inactivation of tgf- have been postulated , e. g. ( i ) interaction with tgf- signaling , either directly or indirectly by regulating modulators of the tgf- pathway ( e. g. fibrillin-1 , myostatin ) ( abdel - wahab et al . ; yamaguchi et al . 1990 ; zhu et al . 2007 ) , ( ii ) formation of decorin / tgf- complexes , which are either eliminated from the tissue ( via the circulation or by urinary excretion ) or in the presence of collagen i are sequestered in the ecm ( schaefer et al . conversely , the interaction of decorin with tgf- could also enhance the bioactivity of tgf- , as seen in the process of bone formation during remodeling ( takeuchi et al . the mechanism of interaction of decorin with tgf- has been described at length in earlier reviews ( iozzo , 1998 ; kresse and schonherr 2001 ) . besides its interaction with the igf - ir , decorin can also bind igf - i but with a 1000-fold lower affinity than the classical igf - i - binding proteins , indicating that decorin is more likely to compete with igf - i for binding to the igf - ir , rather than with the binding proteins which have kd values in the range of 10 m. this suggests that only in situations where decorin is expressed abundantly relevant competition with the classical binding proteins might occur ( schonherr et al . decorin binds pdgf , inhibiting downstream phosphorylation of the pdgfr and signaling in aortic smooth muscle cells . these effects could be exploited therapeutically to prevent intimal hyperplasia ( nili et al . 2003 ) . through its gag chains , decorin interacts with the von willebrand factor and is involved in the modulation of ecm organization ( guidetti et al . decorin and biglycan also bind and immobilize the proinflammatory cytokine tnf ( tufvesson and westergren - thorsson 2002 ) . both slrps interact with wisp - i , regulating its function in fibroblasts and osteogenic cells ( desnoyers et al . biglycan also modulates the activity of bmp-4 on osteoblast differentiation ( chen et al . 2004 ) . furthermore , biglycan and fibromodulin were found to modulate bone morphogenic protein signaling , affecting differentiation of tendon stem progenitor cells , thereby influencing tendon formation ( bi et al . the slrps have been shown to regulate embryonic development by modulating the activity of various growth factors . biglycan forms complexes with bmp-4 enhancing its binding to chordin , which leads to its inactivation by the chordin - tsg ( twisted gastrulation ) complex ( moreno et al . tsukushi , another member of the slrp family , acts as a modulator of cellular functions by regulating bmp-4 , fibroblast growth factor ( fgf ) and xenopus nodal - related protein-2 ( xnr2 ) signaling ( kuriyama et al . the binding and regulation of asporin to growth factors and its modulatory effects have been considered in a recent review ( ikegawa 2008 ) . by their ability to interact with different growth factors , the slrps exhibit regulatory effects on various cellular processes , including development . there is growing evidence for a significant role of slrps as direct and indirect endogenous modulators of inflammation and innate immunity ( al haj zen et al . 2006 ; schaefer et al . biglycan , besides being sequestered in the ecm , can also exist as a soluble molecule , e.g. when it is released from the ecm by proteolytic digestion of injured tissues or secreted by activated macrophages ( for schematic drawing please see schaefer and schaefer 2009 ) . similar to pathogen - associated molecular patterns ( pamps ) , soluble biglycan acts as an endogenous ligand of tlr4 and tlr2 in macrophages . these interactions lead to activation and downstream signaling , via p38 , p42/44 , and nfb in a myd88-dependent manner and subsequent synthesis and secretion of pro - inflammatory cytokines ( schaefer et al . both the protein core and the gag chains of biglycan are required for activation of these pathways . generation of tnf and mip2 enhances recruitment of macrophages and neutrophils , which in turn secrete additional biglycan , thereby creating a positive feedback loop that stimulates autocrine and paracrine inflammatory responses . the clinical significance of this has been shown by a survival benefit of biglycan - null mice in tlr4- ( gram - negative ) or tlr2-dependent ( gram - positive ) sepsis . improved survival in this model was associated with lower plasma levels of tnf and reduced infiltration of mononuclear cells into the lung , a major target organ of sepsis in mice ( schaefer et al . 2005 ) . in a model of non - infectious inflammatory renal injury , overexpression of biglycan in the kidney was associated with increased numbers of infiltrating mononuclear cells ( babelova et al . what is more , soluble biglycan activates the nlrp3/asc inflammasome by inducing caspase-1 and releasing mature il-1 without further need for additional costimulatory factors . in terms of receptors involved , biglycan interacts with tlr2/4 and purinergic p2x4/p2x7 receptors , thereby inducing receptor cooperativity ( babelova et al . in addition , formation of reactive oxygen species ( ros ) appears also to be involved in biglycan - mediated activation of the inflammasome ( babelova et al . 2009 ) . under pathological conditions , in a model of inflammatory renal injury ( unilateral ureteral obstruction ) and in lps - induced sepsis , biglycan deficiency was associated with lower levels of active caspase-1 and mature il-1 in kidneys , lungs and in the circulation ( babelova et al . it is tempting to speculate that biglycan upon its release from the ecm acts as an autonomous trigger of the inflammatory response reaction . on the other hand , in pathogen - driven inflammation biglycan might potentiate pamp - triggered inflammation by engaging a second tlr that is not involved in pathogen - sensing . this is evident in the ability of lumican core protein to bind and present lipopolysaccharide to cd14 , thereby activating the tlr4 pathway ( wu et al . in addition , slrps enhance the activation of the immune system by their ability to modulate the activity of tgf- , a potent immunosuppressive cytokine ( wojtowicz - praga 2003 ) . similar to biglycan , decorin is also capable of modulating inflammation by various mechanisms , especially by its effects on macrophages . furthermore , it inhibits macrophage proliferation and apoptosis and enhances the synthesis of proinflammatory cytokines and inducible nitric oxide synthase ( inos ) ( comalada et al . 2003 ) . the anti - proliferative and anti - apoptotic effects of decorin on macrophages are mediated by inducing the inhibitors of the cdks p27(kip1 ) and p21(waf1 ) , which are important for cell cycle regulation . what is more , decorin also inhibits the effects of the macrophage colony stimulating factor ( xaus et al . the slrps are also involved in the recruitment of immune cells to the site of injury , either directly by acting as ligands to cell surface receptors or indirectly by different mechanisms . decorin stimulates the production of mcp-1 , a mononuclear cell - recruiting chemokine , thereby sustaining the inflammatory state ( koninger et al . 2005 ) , acts as a ligand for selectin l / cd44 and is directly involved in the recruitment of cd16(- ) natural killer cells ( kitaya and yasuo 2009 ) . lumican , by binding and signaling via fasl , enhances the synthesis and secretion of proinflammatory cytokines and the recruitment of macrophages and neutrophils ( funderburgh et al . the core protein of lumican binds the cxc - chemokine kc ( cxcl1 ) , establishing a chemokine gradient that regulates neutrophil infiltration ( carlson et al . 2007 ) . furthermore , decorin , biglycan , fibromodulin , osteoadherin and chondroadherin bind c1q , resulting in the case of fibromodulin , osteoadherin , and chondroadherin in activation of the classical complement pathway , and leading to an enhanced inflammatory response ( sjoberg et al . thus , slrps by : ( i ) acting as pamp analogues , ( ii ) aiding the presentation of pamps to the receptor complex , or ( iii ) interacting with various cytokines , chemokines and complement factors , modulate inflammation and innate immunity by a host of mechanisms , both in non - infectious and in pathogen - mediated inflammatory conditions . taking into account all matricellular functions of slrps mentioned above , including the regulation of cell behavior , the synthesis and degradation of the ecm , the activity of profibrotic factors , and the recruitment of infiltrating cells , slrps are undoubtedly important players in fibrogenesis . while fibrosis occurs in diverse organs , its pathological hallmarks are quite comparable , irrespective of the tissue affected . these include : ( i ) enhanced and aberrant activation of profibrotic growth factors ( e. g. tgf- ) ; ( ii ) accumulation of activated ( myo)fibroblasts ; ( iii ) altered composition and increased deposition of ecm ; and ( iv ) persistent inflammation , which perpetuates fibrotic transformation ( hewitson 2009 ) . among various slrps , a lot of attention has been focused on the antifibrotic effects of decorin as a neutralizing factor of tgf- ( border et al . it was shown that treatment with decorin considerably attenuated fibrogenesis , regardless of tissue and mode of decorin administration ( al haj zen et al . ; fukui et al . 2001 ; grisanti et al . 2005 ; huijun et al . 2005 ; isaka et al . ( 1992 ) confirmed the antifibrotic effects of decorin in a host of organs , such as the kidney ( schaefer et al . 2007 ) , lung ( kolb et al . 2001 ) , heart ( weis et al . 2005 ) , skeletal muscle ( brandan et al . 2008 ) , liver ( shi et al . 2006 ) , blood vessels ( al haj zen et al . 2006 ) , skin ( krishna et al . 2006 ) , and conjunctiva ( grisanti et al . 2005 ) . furthermore there is now good evidence that decorin involves multiple signaling pathways by its interactions with the igf - ir , egfr , lrp-1 and c - met ( goldoni et al . thus , it appears that it is not the direct physical interaction of decorin with tgf- ( hildebrand et al . 1998 ) but rather its interference with the tgf- signaling cascade ( described in the section interactions with cytokines and growth factors , above ) that plays a key role in the neutralization of this cytokine . furthermore , the binding of decorin to tgf- and collagen i has been shown to be important for sequestration of the cytokine in the ecm ( markmann et al . interestingly , even by triggering the same pathway decorin may give rise to distinct biological outcomes ( fig . 1 ) , depending on the cell type and biological context . in this light , previous observations regarding the consequences of decorin / tgf- interactions , implicating inactivation ( border et al . 1992 ) , activation ( takeuchi et al . 1994 ) or lack of effects on tgf- activity ( hausser et al . the antifibrotic effects of decorin are not only limited to its interaction with tgf- but involve other mechanisms as well ( schaefer et al . decorin deficiency ( danielson et al . 1997 ) aggravated renal fibrosis significantly in unilateral ureteral obstruction or diabetic nephropathy due to enhanced apoptosis of tubular epithelial cells ( schaefer et al . 2002 ) . acceleration of apoptosis was independent of tgf- and was based on direct interaction of decorin with the igf - ir in tubular epithelial cells , followed by phosphorylation of the receptor and activation of akt / pkb ( fig . 1 ) ( merline et al . 2009 ; schaefer et al . 2002 ; schaefer et al . 2007 ; schonherr et al . 2005 ) . furthermore : ( i ) collagen i deposition was diminished in fibrotic decorin - null kidneys even though synthesis was enhanced , suggesting that decorin may protect collagen fibrils from proteolytic digestion ( geng et al . 2006 ; schaefer et al . 2002 ) ; ( ii ) tgf- activity was enhanced , underlining the importance of decorin in tgf- inactivation ; and ( iii ) proinflammatory biglycan was upregulated , resulting in enhanced infiltration of mononuclear cells . in the heart , the absence of decorin resulted in abnormal scar formation after myocardial infarction ( weis et al . the ability of decorin to regulate adhesion and migration in a cell - dependent manner further underlines its complex role in fibrogenesis . in fibroblasts deficient in decorin , increased cell spreading was reported ( gu and wada 1996 ) , while exogenous addition of decorin inhibited fibroblast adhesion to a variety of substrates , indicating the anti - adhesive effects of decorin ( gu and wada 1996 ; winnemoller et al . conversely , by binding and signaling via the igf - ir and integrin 21 , decorin promotes endothelial cell adhesion and migration on collagen type i ( fiedler et al . 2008 ) . in fibroblasts , the core protein of decorin induced increased synthesis and activation of rhoa and rac1 and has been shown to remodel lung fibroblasts enhancing their migration by inducing morphological and cytoskeletal changes ( tufvesson and westergren - thorsson 2003 ) . thus , decorin appears to be a potent antifibrotic molecule , influencing fibrogenesis in different organs by a number of distinct mechanisms , i.e. by inhibition of tgf- , regulation of ecm synthesis and turnover , modulation of cell death , and adhesion and migration ) . no beneficial effects were seen in pulmonary fibrosis when biglycan instead of decorin was adenovirally induced ( kolb et al . this is conceivable , taking into account that the proinflammatory effects of biglycan are mediated via tlr2/4 ( described in the section inflammation and innate immunity ) . recently , biglycan has been shown to be protective in cardiac fibrosis following myocardial infarction , based on its ability to regulate collagen formation ( westermann et al . it is tempting to speculate that slrps may have different functions resulting in different biological outcomes , depending on whether these molecules are soluble and can engage cell surface receptors or are incorporated in the ecm and are therefore unable to act as receptor ligands . taking into account the many modulatory functions exhibited by slrps at the molecular and cellular levels , i.e. controlling morphogenesis , cellular growth , apoptosis and inflammation among other functions , makes the study of slrps as matricellular proteins aptly worthwhile . future research should aim at translating our rapidly expanding knowledge of these matricellular proteins into the clinical setting by identifying promising drug targets and defining new therapeutic strategies to treat inflammatory , fibrotic , and malignant disorders .

the small leucine - rich proteoglycans ( slrps ) are biologically active components of the extracellular matrix ( ecm ) , consisting of a protein core with leucine rich - repeat ( lrr ) motifs covalently linked to glycosaminoglycan ( gag ) side chains . the diversity in composition resulting from the various combinations of protein cores substituted with one or more gag chains along with their pericellular localization enables slrps to interact with a host of different cell surface receptors , cytokines , growth factors , and other ecm components , leading to modulation of cellular functions . slrps are capable of binding to : ( i ) different types of collagens , thereby regulating fibril assembly , organization , and degradation ; ( ii ) toll - like receptors ( tlrs ) , complement c1q , and tumor necrosis factor - alpha ( tnf ) , regulating innate immunity and inflammation ; ( iii ) epidermal growth factor receptor ( egf - r ) , insulin - like growth factor receptor ( igf - ir ) , and c - met , influencing cellular proliferation , survival , adhesion , migration , tumor growth and metastasis as well as synthesis of other ecm components ; ( iv ) low - density lipoprotein receptor - related protein ( lrp-1 ) and tgf- , modulating cytokine activity and fibrogenesis ; and ( v ) growth factors such as bone morphogenic protein ( bmp-4 ) and wnt - i - induced secreted protein-1 ( wisp-1 ) , controlling cell proliferation and differentiation . thus , the ability of slrps , as ecm components , to directly or indirectly regulate cell - matrix crosstalk , resulting in the modulation of various biological processes , aptly qualifies these compounds as matricellular proteins .

<s>[INST]small leucine - rich proteoglycans ( slrps ) are biologically active components of the extracellular matrix ( ecm ) and are structurally characterized by a central protein core made up of leucine - rich repeats ( lrrs ) flanked by cysteine - clusters and substituted with covalently linked glycosaminoglycan ( gag ) side chains ( huxley - jones et al . , these proteoglycans are secreted into the pericellular space and abound in the majority of tissues . they are divided into five distinct classes , based on n - terminal cys - rich clusters of the protein core and ear repeats ( c - terminal repeats specific to slrps ) ( mcewan et al . 2006 ) , chromosomal organization and homologies at the protein and genomic levels ( table 1 ; ( schaefer and iozzo 2008 ) . the gag chains of slrps are sulphated , linear disaccharide repeating units made from acetylated amino sugar moieties and uronic acid , forming negatively charged chondroitin sulphate ( cs ) or dermatan sulphate ( ds ) chains . they are covalently linked to the respective protein core via serine residues ( gandhi and mancera 2008 ; iozzo 1998 ) . by contrast , the keratan sulphate ( ks ) gags are composed of repeating disaccharide units containing galactose ( -4n - acetyl - glucosamine-1,3-galactose-1 ) . decorin , biglycan ( cs / ds class i proteoglycans ) and lumican ( ks class ii proteoglycan ) are the best characterized members of the slrp family . table 1classification of slrpsclass iclass iiclass iiiclass ivclass vbiglycanfibromodulinepiphycanchondroadherinpodocandecorinlumicanopticinnyctalopinpodocan like protein-1asporinprelposteoglycantsukushiecm2keratocanecmxosteoadherinbased on several parameters including conservation and homology at the protein and genomic level , the presence of characteristic n - terminal cys - rich clusters with defined spacing , and chromosomal organization ( schaefer and iozzo 2008 ) classification of slrps based on several parameters including conservation and homology at the protein and genomic level , the presence of characteristic n - terminal cys - rich clusters with defined spacing , and chromosomal organization ( schaefer and iozzo 2008 ) slrps consist of two different structural components , namely a conserved protein core involved in protein / protein interactions ( hocking et al . 1998 ; iozzo 1997 ; kresse et al . along with their pericellular localization , this allows slrps to interact with different molecules and cell - surface receptors , thereby modulating a wide range of cell - matrix interactions ( brandan et al . 2008 ; iozzo 1998 ; perrimon and bernfield 2001 ; roughley 2006 ; schaefer and iozzo 2008 ) . these functions were mostly elucidated by the characterization of specific slrp - deficient mice ( ameye et al . 1999 ; xu et al . 1998 ; young et al . 2002 ) and are briefly summarized in table 2 . slrps were long known to be able to bind to various types of collagens thereby regulating the kinetics , assembly , and special organization of fibrils in skin , tendons , and cornea ( iozzo 1999 ; kalamajski and oldberg 2009 ; kresse et al . 2006 ; schonherr et al . 1995b ; svensson et al . 1995 ; wiberg et al . 2002 ; zhang et al . protein core fragments serve as biological markers for various degenerative cartilage disorders ( melrose et al . table 2characteristics of slrp - deficient micegene disruptedphenotypereferencebiglycanreduced bone mass with decreased production of bone marrow stromal cells and larger irregular collagen fibrils indicating an osteoporosis - like phenotype ; spontaneous aortic dissection and rupture(chen et al . fragility phenotype with loosely packed collagen networks resembling ehlers - danlos syndrome ; intestinal tumor formation(bi et al . 1998)fibromodulinabnormal collagen fibrillogenesis in tendons(svensson et al . 1999)biglycan and decorinsevere osteopenia and increased skin fragility(young et al . 2002)biglycan and fibromodulinseverely altered collagen fibril assembly with ectopic ossification of tendons and premature arthritis(ameye et al . 2002 ) characteristics of slrp - deficient mice however , the biological functions of slrps extend far beyond their interactions with collagens . slrps interact with various cytokines , including transforming growth factor beta ( tgf- ) , bone morphogenic protein ( bmp-4 ) , wnt - i - induced secreted protein - i ( wisp-1 ) , von willebrand factor ( vwf ) , platelet - derived growth factor ( pdgf ) and tumor necrosis factor - alpha ( tnf ) ( bi et al . 2007 ; chen et al . 2009 ; kolb et al . 2001 ; kresse and schonherr 2001 ; nili et al . 2003 ; tufvesson and westergren - thorsson 2002 ) , leading to modulation of their diverse biological functions . pharmacologic manipulations of these interactions could potentially be exploited for the treatment of proliferative , inflammatory , and fibrotic disorders ( goldoni and iozzo 2008 ; schaefer and iozzo 2008 ; schaefer et al . 2002 ; schaefer et al . 2004 ) . as extracellular compounds slrps engage various signaling receptors , including toll - like receptors ( tlrs ) ( schaefer et al . 2005 ) , insulin - like growth factor receptor ( igf - ir ) ( schaefer et al . 2007 ) , epidermal growth factor receptor ( egf - r ) ( iozzo et al . 1999 ) , low - density lipoprotein receptor - related protein ( lrp-1 ) ( brandan et al . 2006 ) , integrin 21 ( fiedler et al . 2008 ; guidetti et al . 2002 ) , and c - met ( goldoni et al . 2009 ) , thereby acting as direct triggers of signal transduction . these interactions result in modulation of cellular growth , proliferation , differentiation , survival , adhesion and migration under developmental , physiological and pathological conditions ( brandan et al . for further details regarding the interaction of slrps with cell membrane receptors we refer to more extensive reviews ( brandan et al . 2008 ; goldoni and iozzo 2008 ; schaefer and iozzo 2008 ; schaefer and schaefer 2009 ) . thus , slrps aptly fit the definition of matricellular proteins due to their : ( i ) extracellular location , ( ii ) modulatory effects on synthesis , assembly and degradation of fibrils without being part of the fibrillar structure itself , and ( iii ) direct ( receptor - mediated ) and indirect ( via interaction with cytokines , growth factors and other ecm components ) regulation of cell - matrix crosstalk , influencing a host of biological processes ( e. g. inflammation , fibrosis , tumorigenesis , angiogenesis , coagulation and wound healing ) . in the present review , we focus primarily on the matricellular functions of decorin , biglycan ( class i proteoglycans ) , and lumican ( class ii proteoglycan ) , which are briefly summarized in table 3 . table 3matricellular functions modulated by the slrps decorin , biglycan and lumicanbiological function modulatedmechanism mediated / involved in modulationreceptor - binding associated with signal transductionegf - r(d1 ) , igf - ir(d ) , lrp-1(d ) , c - met(d ) , tlr2(b ) , tlr4(b ) and cd14(l)modulation of cytokine bio - activitybmp-4(b ) , pdgf(d , b ) , tgf-(d , b ) , tnf(d , b ) , vwf(d ) and wisp-1(d , b)fibrillogenesis , fibrillar organization and degradationbind collagens(d , b , l ) and elastic fibril components(d , b ) regulating fibrillar kinetics(d ) , assembly(d , l ) and degradation(d , l ) , thereby modulating the structure , stability and integrity of the ecm.adhesion and migrationby binding to adhesion(d ) and anti - adhesion molecules(d ) and also by signaling via igf - ir(d ) , integrin 21(d , l ) , rhoa(d , b ) , rac1(d , b ) , syk(d ) and erk1/2(l ) , inhibits or enhances adhesion and migration in a cell type specific manner.cellular proliferationby binding and modulating receptor mediate signaling ( egfr , erbb4 and vegf - r2)(d ) ; by modulating : ( i ) growth factor bioactivity ( tgf-(d ) and pdgf - bb(b ) ) ; ( ii ) cell cycle ( influencing expression of p21(d , l ) , p27(d , b ) , cdk2(b ) and cyclin d1(l ) ) and ( iii ) the myostatin pathway , regulate cellular growth in a cell and stage - specific manner(d).cellular survivalregulate cellular survival by modulating igf - ir signaling(d ) , egfr(d ) , caspase-3 activity(d , b ) and fas / fasl - mediated apoptotic pathway(l).inflammation and innate immunityacts as pamp(b ) or presents pamps(l ) to the receptor thereby triggering or enhancing the inflammatory response . also sustains inflammation by regulating chemokine gradient(d , b , l ) and complement activity(d , b).fibrosispotent antifibrotic agent(d ) , influencing fibrogenesis in different organs by a number of distinct mechanisms : ( i ) inhibition of tgf- , ( ii ) regulation of ecm synthesis and turnover and by ( iii ) regulating cell death , adhesion and migration.the slrp modulating the respective matricellular function is indicated as subscript and abbreviated as follows : d , decorin ; b , biglycan ; l , lumican matricellular functions modulated by the slrps decorin , biglycan and lumican the slrp modulating the respective matricellular function is indicated as subscript and abbreviated as follows : d , decorin ; b , biglycan ; l , lumican by their ability to bind to different types of collagens and elastic fibril components , slrps impact on extracellular matrix organization , modulating the structural and functional environment of cells . the interaction of slrps with collagens has been shown to enhance fibril stability ( keene et al . 2000 ; neame et al . 2000 ) and to protect fibrils from proteolytic cleavage by various collagenases ( geng et al . the role of decorin in regulating collagen fibrillogenesis was elucidated by studies using knockout mice , which exhibit loosely packed collagen fiber networks with increased fibril diameter , leading to a skin fragility phenotype ( danielson et al . the functional importance of decorin in regulating collagen fibrillogenesis was further emphasized by the altered mechanical function of lung tissue in decorin - deficient mice ( fust et al . 2005 ) . decorin is involved in lateral growth of collagen fibrils and regulates fibril diameter in vitro ( danielson et al . it binds to collagen type i , ii , iii , iv , vi , and xiv ( bidanset et al . 1992 ; ehnis et al . 1997 ; reed and iozzo 2002 ) and has been localized to the d and e bands of tendon collagen in the gap zone ( pringle and dodd 1990 ; weber et al . decorin is also involved in lateral fusion of collagen i fibrils by binding to the c - terminus via lrr4 - 6 of the protein core through protein / protein interactions , which involves more than one binding domain ( keene et al . 2000 ; kresse et al . . the gag chain of decorin binds tenascin - x and mediates its interaction with collagen fibrils , thereby contributing to extracellular matrix integrity ( elefteriou et al . 2001 ) . furthermore , the gag chains are involved in the maintenance of interfibrillar spacing , which also effects fibril diameter ( iozzo 1999 ; raspanti et al . biglycan - deficient mice do not suffer from increased skin fragility , but exhibit larger and irregular fibrils leading to thin dermis and reduced bone mass ( corsi et al . biglycan binds to collagen type i , ii , and iii but unlike decorin its interaction with collagen does not appear to influence fibril diameter or fibrillar kinetics . however , due to its trivalency biglycan could have a special organizing function on assembly of the extracellular matrix ( douglas et al . this notion is supported by the binding of biglycan to the n - terminal ends of the collagen vi tetramers . this leads to supramolecular organization of collagen into hexagonal networks , with biglycan being localized at the intra - network junctions of the collagen vi filaments ( wiberg et al . intact biglycan with gag chains is required for complex formation and interaction with the tgf--inducible gene - h3 ( beta ig - h3 ) and collagen vi ( reinboth et al . the influence of biglycan on collagen fibrillogenesis is further demonstrated by the presence of high amounts of biglycan in keloids ( hunzelmann et al . 1996 ) and by its localization in the decidualized regions of the endometrium , regulating fibril thickness in the murine decidua ( san martin and zorn 2003 ) . decorin and biglycan also regulate collagen fibril assembly coordinately in the cornea ( zhang et al . there is some evidence that both slrps may also be involved in elastic fiber biology . decorin forms complexes with fibrillin-1 , tropoelastin ( the soluble precursor of mature elastin ) and microfibril - associated glycoprotein 1 ( mapg-1 ) ( kielty et al . 1996 ; trask et al . 2000 ) . therefore , both proteoglycans were classified as microfibril- and elastic fiber - associated molecules ( kielty et al . biglycan regulates elastogenesis as shown by the ability of its gag chains to inhibit elastin synthesis and assembly in the vessel wall ( hwang et al . recent studies have established a molecular link between decorin and the igf - ir signaling pathway and the synthesis of fibrillin-1 in renal fibroblasts . translational regulation of fibrillin-1 involves the igf - ir and the phosphoinositide 3-kinase ( pi3k)/akt pathway , with mammalian target of rapamycin ( mtor ) and p70 s6 kinase as downstream targets ( fig . 1 ) ( schaefer et al . this intriguing finding indicates that the ecm component decorin is capable of directly regulating the synthesis of another matrix constituent ( fibrillin-1 ) . this together with the ability of decorin to regulate the activity of mmps ( schonherr et al . 2001 ) , underlines the complexity of ecm synthesis and turnover under physiological and pathological conditions . 1cell type - specific functions mediated by decorin via modulation of igf - ir signaling . decorin binds and induces phosphorylation of the insulin - like growth factor - i ( igf - i ) receptor , causing downstream activation of phosphoinositide-3 kinase ( pi3k ) and the akt / protein kinase b ( akt / pkb ) pathway . in endothelial and renal tubular epithelial cells this signaling cascade leads to an inhibition of apoptosis , whereas in renal fibroblasts signaling through mammalian target of rapamycin ( mtor ) and p70s6 kinase ( p70s6k ) leads to increased translation and synthesis of fibrillin-1 . these pathways demonstrate the intricate regulatory mechanisms whereby decorin modulates igf - ir signaling in a cell type - specific manner , thereby giving rise to different biological outcomes cell type - specific functions mediated by decorin via modulation of igf - ir signaling . decorin binds and induces phosphorylation of the insulin - like growth factor - i ( igf - i ) receptor , causing downstream activation of phosphoinositide-3 kinase ( pi3k ) and the akt / protein kinase b ( akt / pkb ) pathway . in endothelial and renal tubular epithelial cells this signaling cascade leads to an inhibition of apoptosis , whereas in renal fibroblasts signaling through mammalian target of rapamycin ( mtor ) and p70s6 kinase ( p70s6k ) leads to increased translation and synthesis of fibrillin-1 . these pathways demonstrate the intricate regulatory mechanisms whereby decorin modulates igf - ir signaling in a cell type - specific manner , thereby giving rise to different biological outcomes lumican - deficient mice suffer from increased skin fragility and corneal opacities due to abnormal fibril assembly and altered interfibrillar spacing , indicating a role in lateral fusion of collagen fibrils ( chakravarti et al . 1998 ) . besides maintaining normal fibril architecture of the cornea by regulating fibril assembly in the posterior stroma , lumican provides an optimal ks content required for corneal transparency ( chakravarti et al . lumican regulates the assembly of fibrils at an early stage of collagen fibrillogenesis ( ezura et al . recently , the binding site of the lumican protein core to collagen type i via asp-213 of lrr7 has been reported ( kalamajski and oldberg , 2009 ) . fibromodulin , another class ii keratan sulphate slrp binds to collagen and also regulates fibrillogenesis . its deficiency leads to an abnormal tendon phenotype with impaired collagen fibrils ( svensson et al . 1999 ; viola et al . 2007 ) . during tendon development , fibromodulin is involved in collagen fibrillogenesis , regulating fibril assembly and maturation ( ezura et al . the interaction of fibromodulin with collagen requires more than one binding domain , similar to class i slrps . one of these domains appears to be the c - terminal end of the molecule containing the disulfide loop ( font et al . 1998 ) , and the binding to collagen i involves lrr5 - 7 of the protein core ( kalamajski and oldberg 2009 ) . the multitude of matricellular functions performed by slrps is further evidenced by their ability to regulate cellular proliferation . decorin has long been known to regulate cellular growth , as ectopic overexpression of decorin retarded cell growth ( yamaguchi and ruoslahti 1988 ) . diverse mechanisms of growth regulation by decorin have been revealed over the years and these were attributed to its ability to , ( i ) engage receptors modulating signaling pathways , ( ii ) act as a growth factor , and ( iii ) influence regulation at certain cell cycle checkpoints . decorin inhibits cellular proliferation in a tgf--dependent manner in chinese hamster ovary ( cho ) cells ( yamaguchi et al . 1990 ) , arterial smooth muscle cells ( fischer et al . 2001 ) , human hepatic stellate cells ( shi et al . 2006 ) , and fibroblasts ( zhang et al . however , the majority of data concerning decorin - mediated regulation of proliferation was generated in carcinoma cell lines . in tumor cells , decorin binds egfr and erbb4 , leading to activation of the mitogen - activated protein kinase ( mapk ) pathway , ca influx , induction of the cyclin - dependent kinase ( cdk ) inhibitor p21 with subsequent downregulation of the receptor ( csordas et al . thus , these extensive studies provide a molecular explanation for the antiproliferative and antioncogenic effects of decorin ( reed et al . moreover , there is a direct link between decorin deficiency and spontaneous tumor formation ( bi et al . 2008 ) . for further details more extensive reviews are suggested ( goldoni and iozzo 2008 ; nikitovic et al . recently , decorin has been shown to inhibit proliferation of trophoblasts through the egfr and vascular endothelial growth factor receptor-2 ( vegf - r2 ) signaling pathways ( iacob et al . 2008 ) , indicating that these mechanisms are not restricted to regulation of carcinoma cell proliferation . interestingly , by binding myostatin and modulating its down - stream signals , decorin can rescue the inhibitory effects of myostatin on myoblast proliferation , thereby acting indirectly as a promoter of cell proliferation ( brandan et al . 2006 ) . the role of biglycan in regulating cellular proliferation was addressed only by a limited number of studies . antiproliferative effects of biglycan were observed in mesangial cells of the kidney , where it inhibited pdgf - bb - induced proliferation ( schaefer et al . 2003 ) and in bone marrow stromal cells , where wisp-1 blocked the antiproliferative effects of biglycan ( inkson et al . in pancreatic cancer cells , biglycan induced g1 arrest , thereby inhibiting tumor cell proliferation . this effect was associated with upregulation of the cdk inhibitor p27 and downregulation of cyclin a and proliferating cell nuclear antigen , along with decreased activation of ras and erk ( weber et al . however , in vascular smooth muscle cells biglycan has been shown to favor proliferation in a cdk2- and p27-dependent manner ( shimizu - hirota et al . moreover , the proliferative phase of osteoblast development was associated with increased expression of biglycan , indirectly indicating that biglycan might promote proliferation ( waddington et al . it is tempting to speculate that similar to decorin , biglycan might regulate proliferation in a cell type - specific manner , either directly via a specific receptor or by contributing to the crosstalk between signaling pathways , or by an indirect mechanism . to interpret these data in more detail , studies on biglycan - mediated signaling are warranted . up to now , the toll - like receptors-2 and -4 have been identified as signaling receptors for biglycan ( schaefer et al . 2005 ) , whereas unlike decorin it was found not to signal through the egfr ( moscatello et al . similar to decorin , lumican also acts as a negative regulator of cellular proliferation , by upregulating the expression of the cdk inhibitor p21 ( li et al . lumican inhibits proliferation of mouse embryonic fibroblasts by upregulating p21 in a p53-dependent mechanism with decreased cyclin a , d1 and e ( vij et al . 2004 ) . lack of lumican has been shown to promote proliferation of stromal keratinocytes and embryonic fibroblasts ( vij et al . its inhibitory effects on growth are extended to tumor cells , with some of these cells secreting lumican in an autocrine manner ( sifaki et al . lumican regulates vertical growth and inhibits anchorage - independent proliferation and cyclin d1 expression in melanoma cells ( brezillon et al . further details concerning the role of lumican in controlling tumor growth are included in recent reviews ( goldoni and iozzo 2008 ; naito 2005 ; nikitovic et al . 2002 ) , endothelial cells , and bone marrow stromal cells ( bi et al . 2005 ) . in tubular epithelial and endothelial cells , the anti - apoptotic effects of decorin are mediated by binding to the igf - ir and signaling via the pi3k / akt pathway , which also plays a role in fibrosis ( details are described in the section fibrosis below ) and angiogenesis ( fig . 1 ) ( schaefer et al . it appears that signaling through the canonical igf pathway may represent a common mechanism by which decorin protects non - carcinoma cells from programmed cell death . conversely , in carcinoma cells decorin has been shown to enhance apoptosis via the egfr and enhanced caspase-3 activity , indicating an additional mechanism , which might explain the anti - oncogenic effects of decorin ( seidler et al . 2003 ) . the role of biglycan and lumican in the regulation of cell survival has not been studied in detail . biglycan has been shown to protect mesangial cells from apoptosis by decreasing caspase-3 activity ( schaefer et al . by contrast , lumican mediates fas - fasl - induced apoptosis by inducing fas ( cd95 ) in mouse embryonic fibroblasts ( vij et al . the ability of lumican to induce apoptosis has also been reported in tumor cells and could be used to control tumor progression ( vuillermoz et al . decorin , biglycan , asporin , and fibromodulin bind the profibrotic cytokine tgf- ( hildebrand et al . 1994 ; nakajima et al . 2007 ) . however , since tgf- interacts with conserved leucine - rich repeat structures ( schonherr et al . 1998 ) , it is likely that other slrps are also able to form complexes with this cytokine . a lot of attention has been focused on the interaction of decorin with tgf- , as it had been demonstrated unequivocally that decorin treatment exerts beneficial effects in fibrotic disorders involving tgf- overproduction in the kidney and other organs ( border et al . 1992 ; kolb et al . 2001 ) . besides inhibition of tgf--mediated fibrosis , the binding of decorin to tgf- has significant biological implications in regulating a number of cellular processes , e. g. ( i ) modulation of cell proliferation ( li et al . 2008 ; yamaguchi et al . 1990 ) , ( ii ) inhibition of repressive effects of tgf- on macrophages leading to their activation ( comalada et al . 2003 ) , and ( iii ) suppression of tgf--dependent apoptosis in bone marrow stromal cells ( bi et al . 2005 ) . several mechanisms for the decorin - mediated inactivation of tgf- have been postulated , e. g. ( i ) interaction with tgf- signaling , either directly or indirectly by regulating modulators of the tgf- pathway ( e. g. fibrillin-1 , myostatin ) ( abdel - wahab et al . ; yamaguchi et al . 1990 ; zhu et al . 2007 ) , ( ii ) formation of decorin / tgf- complexes , which are either eliminated from the tissue ( via the circulation or by urinary excretion ) or in the presence of collagen i are sequestered in the ecm ( schaefer et al . conversely , the interaction of decorin with tgf- could also enhance the bioactivity of tgf- , as seen in the process of bone formation during remodeling ( takeuchi et al . the mechanism of interaction of decorin with tgf- has been described at length in earlier reviews ( iozzo , 1998 ; kresse and schonherr 2001 ) . besides its interaction with the igf - ir , decorin can also bind igf - i but with a 1000-fold lower affinity than the classical igf - i - binding proteins , indicating that decorin is more likely to compete with igf - i for binding to the igf - ir , rather than with the binding proteins which have kd values in the range of 10 m. this suggests that only in situations where decorin is expressed abundantly relevant competition with the classical binding proteins might occur ( schonherr et al . decorin binds pdgf , inhibiting downstream phosphorylation of the pdgfr and signaling in aortic smooth muscle cells . these effects could be exploited therapeutically to prevent intimal hyperplasia ( nili et al . 2003 ) . through its gag chains , decorin interacts with the von willebrand factor and is involved in the modulation of ecm organization ( guidetti et al . decorin and biglycan also bind and immobilize the proinflammatory cytokine tnf ( tufvesson and westergren - thorsson 2002 ) . both slrps interact with wisp - i , regulating its function in fibroblasts and osteogenic cells ( desnoyers et al . biglycan also modulates the activity of bmp-4 on osteoblast differentiation ( chen et al . 2004 ) . furthermore , biglycan and fibromodulin were found to modulate bone morphogenic protein signaling , affecting differentiation of tendon stem progenitor cells , thereby influencing tendon formation ( bi et al . the slrps have been shown to regulate embryonic development by modulating the activity of various growth factors . biglycan forms complexes with bmp-4 enhancing its binding to chordin , which leads to its inactivation by the chordin - tsg ( twisted gastrulation ) complex ( moreno et al . tsukushi , another member of the slrp family , acts as a modulator of cellular functions by regulating bmp-4 , fibroblast growth factor ( fgf ) and xenopus nodal - related protein-2 ( xnr2 ) signaling ( kuriyama et al . the binding and regulation of asporin to growth factors and its modulatory effects have been considered in a recent review ( ikegawa 2008 ) . by their ability to interact with different growth factors , the slrps exhibit regulatory effects on various cellular processes , including development . there is growing evidence for a significant role of slrps as direct and indirect endogenous modulators of inflammation and innate immunity ( al haj zen et al . 2006 ; schaefer et al . biglycan , besides being sequestered in the ecm , can also exist as a soluble molecule , e.g. when it is released from the ecm by proteolytic digestion of injured tissues or secreted by activated macrophages ( for schematic drawing please see schaefer and schaefer 2009 ) . similar to pathogen - associated molecular patterns ( pamps ) , soluble biglycan acts as an endogenous ligand of tlr4 and tlr2 in macrophages . these interactions lead to activation and downstream signaling , via p38 , p42/44 , and nfb in a myd88-dependent manner and subsequent synthesis and secretion of pro - inflammatory cytokines ( schaefer et al . both the protein core and the gag chains of biglycan are required for activation of these pathways . generation of tnf and mip2 enhances recruitment of macrophages and neutrophils , which in turn secrete additional biglycan , thereby creating a positive feedback loop that stimulates autocrine and paracrine inflammatory responses . the clinical significance of this has been shown by a survival benefit of biglycan - null mice in tlr4- ( gram - negative ) or tlr2-dependent ( gram - positive ) sepsis . improved survival in this model was associated with lower plasma levels of tnf and reduced infiltration of mononuclear cells into the lung , a major target organ of sepsis in mice ( schaefer et al . 2005 ) . in a model of non - infectious inflammatory renal injury , overexpression of biglycan in the kidney was associated with increased numbers of infiltrating mononuclear cells ( babelova et al . what is more , soluble biglycan activates the nlrp3/asc inflammasome by inducing caspase-1 and releasing mature il-1 without further need for additional costimulatory factors . in terms of receptors involved , biglycan interacts with tlr2/4 and purinergic p2x4/p2x7 receptors , thereby inducing receptor cooperativity ( babelova et al . in addition , formation of reactive oxygen species ( ros ) appears also to be involved in biglycan - mediated activation of the inflammasome ( babelova et al . 2009 ) . under pathological conditions , in a model of inflammatory renal injury ( unilateral ureteral obstruction ) and in lps - induced sepsis , biglycan deficiency was associated with lower levels of active caspase-1 and mature il-1 in kidneys , lungs and in the circulation ( babelova et al . it is tempting to speculate that biglycan upon its release from the ecm acts as an autonomous trigger of the inflammatory response reaction . on the other hand , in pathogen - driven inflammation biglycan might potentiate pamp - triggered inflammation by engaging a second tlr that is not involved in pathogen - sensing . this is evident in the ability of lumican core protein to bind and present lipopolysaccharide to cd14 , thereby activating the tlr4 pathway ( wu et al . in addition , slrps enhance the activation of the immune system by their ability to modulate the activity of tgf- , a potent immunosuppressive cytokine ( wojtowicz - praga 2003 ) . similar to biglycan , decorin is also capable of modulating inflammation by various mechanisms , especially by its effects on macrophages . furthermore , it inhibits macrophage proliferation and apoptosis and enhances the synthesis of proinflammatory cytokines and inducible nitric oxide synthase ( inos ) ( comalada et al . 2003 ) . the anti - proliferative and anti - apoptotic effects of decorin on macrophages are mediated by inducing the inhibitors of the cdks p27(kip1 ) and p21(waf1 ) , which are important for cell cycle regulation . what is more , decorin also inhibits the effects of the macrophage colony stimulating factor ( xaus et al . the slrps are also involved in the recruitment of immune cells to the site of injury , either directly by acting as ligands to cell surface receptors or indirectly by different mechanisms . decorin stimulates the production of mcp-1 , a mononuclear cell - recruiting chemokine , thereby sustaining the inflammatory state ( koninger et al . 2005 ) , acts as a ligand for selectin l / cd44 and is directly involved in the recruitment of cd16(- ) natural killer cells ( kitaya and yasuo 2009 ) . lumican , by binding and signaling via fasl , enhances the synthesis and secretion of proinflammatory cytokines and the recruitment of macrophages and neutrophils ( funderburgh et al . the core protein of lumican binds the cxc - chemokine kc ( cxcl1 ) , establishing a chemokine gradient that regulates neutrophil infiltration ( carlson et al . 2007 ) . furthermore , decorin , biglycan , fibromodulin , osteoadherin and chondroadherin bind c1q , resulting in the case of fibromodulin , osteoadherin , and chondroadherin in activation of the classical complement pathway , and leading to an enhanced inflammatory response ( sjoberg et al . thus , slrps by : ( i ) acting as pamp analogues , ( ii ) aiding the presentation of pamps to the receptor complex , or ( iii ) interacting with various cytokines , chemokines and complement factors , modulate inflammation and innate immunity by a host of mechanisms , both in non - infectious and in pathogen - mediated inflammatory conditions . taking into account all matricellular functions of slrps mentioned above , including the regulation of cell behavior , the synthesis and degradation of the ecm , the activity of profibrotic factors , and the recruitment of infiltrating cells , slrps are undoubtedly important players in fibrogenesis . while fibrosis occurs in diverse organs , its pathological hallmarks are quite comparable , irrespective of the tissue affected . these include : ( i ) enhanced and aberrant activation of profibrotic growth factors ( e. g. tgf- ) ; ( ii ) accumulation of activated ( myo)fibroblasts ; ( iii ) altered composition and increased deposition of ecm ; and ( iv ) persistent inflammation , which perpetuates fibrotic transformation ( hewitson 2009 ) . among various slrps , a lot of attention has been focused on the antifibrotic effects of decorin as a neutralizing factor of tgf- ( border et al . it was shown that treatment with decorin considerably attenuated fibrogenesis , regardless of tissue and mode of decorin administration ( al haj zen et al . ; fukui et al . 2001 ; grisanti et al . 2005 ; huijun et al . 2005 ; isaka et al . ( 1992 ) confirmed the antifibrotic effects of decorin in a host of organs , such as the kidney ( schaefer et al . 2007 ) , lung ( kolb et al . 2001 ) , heart ( weis et al . 2005 ) , skeletal muscle ( brandan et al . 2008 ) , liver ( shi et al . 2006 ) , blood vessels ( al haj zen et al . 2006 ) , skin ( krishna et al . 2006 ) , and conjunctiva ( grisanti et al . 2005 ) . furthermore there is now good evidence that decorin involves multiple signaling pathways by its interactions with the igf - ir , egfr , lrp-1 and c - met ( goldoni et al . thus , it appears that it is not the direct physical interaction of decorin with tgf- ( hildebrand et al . 1998 ) but rather its interference with the tgf- signaling cascade ( described in the section interactions with cytokines and growth factors , above ) that plays a key role in the neutralization of this cytokine . furthermore , the binding of decorin to tgf- and collagen i has been shown to be important for sequestration of the cytokine in the ecm ( markmann et al . interestingly , even by triggering the same pathway decorin may give rise to distinct biological outcomes ( fig . 1 ) , depending on the cell type and biological context . in this light , previous observations regarding the consequences of decorin / tgf- interactions , implicating inactivation ( border et al . 1992 ) , activation ( takeuchi et al . 1994 ) or lack of effects on tgf- activity ( hausser et al . the antifibrotic effects of decorin are not only limited to its interaction with tgf- but involve other mechanisms as well ( schaefer et al . decorin deficiency ( danielson et al . 1997 ) aggravated renal fibrosis significantly in unilateral ureteral obstruction or diabetic nephropathy due to enhanced apoptosis of tubular epithelial cells ( schaefer et al . 2002 ) . acceleration of apoptosis was independent of tgf- and was based on direct interaction of decorin with the igf - ir in tubular epithelial cells , followed by phosphorylation of the receptor and activation of akt / pkb ( fig . 1 ) ( merline et al . 2009 ; schaefer et al . 2002 ; schaefer et al . 2007 ; schonherr et al . 2005 ) . furthermore : ( i ) collagen i deposition was diminished in fibrotic decorin - null kidneys even though synthesis was enhanced , suggesting that decorin may protect collagen fibrils from proteolytic digestion ( geng et al . 2006 ; schaefer et al . 2002 ) ; ( ii ) tgf- activity was enhanced , underlining the importance of decorin in tgf- inactivation ; and ( iii ) proinflammatory biglycan was upregulated , resulting in enhanced infiltration of mononuclear cells . in the heart , the absence of decorin resulted in abnormal scar formation after myocardial infarction ( weis et al . the ability of decorin to regulate adhesion and migration in a cell - dependent manner further underlines its complex role in fibrogenesis . in fibroblasts deficient in decorin , increased cell spreading was reported ( gu and wada 1996 ) , while exogenous addition of decorin inhibited fibroblast adhesion to a variety of substrates , indicating the anti - adhesive effects of decorin ( gu and wada 1996 ; winnemoller et al . conversely , by binding and signaling via the igf - ir and integrin 21 , decorin promotes endothelial cell adhesion and migration on collagen type i ( fiedler et al . 2008 ) . in fibroblasts , the core protein of decorin induced increased synthesis and activation of rhoa and rac1 and has been shown to remodel lung fibroblasts enhancing their migration by inducing morphological and cytoskeletal changes ( tufvesson and westergren - thorsson 2003 ) . thus , decorin appears to be a potent antifibrotic molecule , influencing fibrogenesis in different organs by a number of distinct mechanisms , i.e. by inhibition of tgf- , regulation of ecm synthesis and turnover , modulation of cell death , and adhesion and migration ) . no beneficial effects were seen in pulmonary fibrosis when biglycan instead of decorin was adenovirally induced ( kolb et al . this is conceivable , taking into account that the proinflammatory effects of biglycan are mediated via tlr2/4 ( described in the section inflammation and innate immunity ) . recently , biglycan has been shown to be protective in cardiac fibrosis following myocardial infarction , based on its ability to regulate collagen formation ( westermann et al . it is tempting to speculate that slrps may have different functions resulting in different biological outcomes , depending on whether these molecules are soluble and can engage cell surface receptors or are incorporated in the ecm and are therefore unable to act as receptor ligands . taking into account the many modulatory functions exhibited by slrps at the molecular and cellular levels , i.e. controlling morphogenesis , cellular growth , apoptosis and inflammation among other functions , makes the study of slrps as matricellular proteins aptly worthwhile . future research should aim at translating our rapidly expanding knowledge of these matricellular proteins into the clinical setting by identifying promising drug targets and defining new therapeutic strategies to treat inflammatory , fibrotic , and malignant disorders .[/INST]the small leucine - rich proteoglycans ( slrps ) are biologically active components of the extracellular matrix ( ecm ) , consisting of a protein core with leucine rich - repeat ( lrr ) motifs covalently linked to glycosaminoglycan ( gag ) side chains . the diversity in composition resulting from the various combinations of protein cores substituted with one or more gag chains along with their pericellular localization enables slrps to interact with a host of different cell surface receptors , cytokines , growth factors , and other ecm components , leading to modulation of cellular functions . slrps are capable of binding to : ( i ) different types of collagens , thereby regulating fibril assembly , organization , and degradation ; ( ii ) toll - like receptors ( tlrs ) , complement c1q , and tumor necrosis factor - alpha ( tnf ) , regulating innate immunity and inflammation ; ( iii ) epidermal growth factor receptor ( egf - r ) , insulin - like growth factor receptor ( igf - ir ) , and c - met , influencing cellular proliferation , survival , adhesion , migration , tumor growth and metastasis as well as synthesis of other ecm components ; ( iv ) low - density lipoprotein receptor - related protein ( lrp-1 ) and tgf- , modulating cytokine activity and fibrogenesis ; and ( v ) growth factors such as bone morphogenic protein ( bmp-4 ) and wnt - i - induced secreted protein-1 ( wisp-1 ) , controlling cell proliferation and differentiation . thus , the ability of slrps , as ecm components , to directly or indirectly regulate cell - matrix crosstalk , resulting in the modulation of various biological processes , aptly qualifies these compounds as matricellular proteins .</s>

iran , which is located in southwest asia , located in an epidemiologic transition and faces the double burden of diseases . breast cancer is the most common cancer in iranian women ; meanwhile the iranian patients are relatively young . given that iran has a female population of about 38 million , this corresponds to a total number of 8500 new cases of breast cancer annually . breast cancer has more frequently occurred in wealthy countries due to a higher prevalence of bc risk factors , such as aged population , older age at first pregnancy , nulliparity , inappropriate breastfeeding , high - calorie intake , sedentary occupation and steroid hormonal consumption . on the other hand , bc survival would be lower in less affluent countries , and in women with low income , or educational level . based on the report from the ministry of health and medical education ( mohme ) ; cancer is the third cause of death in iran after cardiovascular heart disease , then the injuries [ 3 , 4 ] . experimental data has strongly suggested that estrogens have a role in the development and growth of breast cancer . tumor formation may also result from excessive hormonal stimulation of an organ in which normal growth and function would be under endocrine control . the response of an organ to the proliferative effects of a hormone might be a progression from normal growth , to hyperplasia , then to neoplasia . indirect evidence of this sequence has included the increased risk of breast cancer associated with early menarche , late first full - term pregnancy , and late menopause as well as the reduced risk associated with early menopause . immune surveillance has described the process whereby precancerous and malignant cells have recognized by the immune system as damaged , and then would be consequently targeted for elimination . natural killer ( nk ) cells and cytotoxic t lymphocytes ( ctls ) both have played important roles in the innate and adaptive immunity against intracellular pathogens and tumor cells . granule exocytosis is the main pathway for immune elimination of virus - infected cells and tumor cells by ctls and nk cells . after target - cell recognition , release of the cytotoxic granule contents in to the immunological synapse , have formed between the killer cell and its target induces apoptosis . the perforin / granzyme ( gzm ) pathway is a major mechanism for these cytotoxic lymphocytes to kill their targets . granzyme h ( gzm h ) has regarded as an orphan granzyme with unknown biologic functions in immune defense cells . gzm h , which expands the cell death - inducing repertoire of innate immune system , was a functional cytotoxic serine protease of nk cell granule . several studies have recently shown gzmh to be constitutively and highly expressed in human nk cells and to possess chymotrypsin - like ( chymase ) enzymatic activity . human gzmh triggers rapid cell death of target tumor cells that is characteristic of dna fragmentation and mitochondrial damage and generation of reactive oxygen species [ 8 , 12 ] . the steroid hormones , estradiol , plays an important role in the progression of breast cancer , and a majority of the human breast cancers start out as estrogen dependent and express the estrogen receptor ( er ) . the biological effects of estrogen have mediated by its binding to one of the structurally and functionally distinct ers ( er and er ) . the action of progesterone has mediated through its intracellular cognate receptor , the progesterone receptor ( pr ) , which functions as a transcription factor that regulates gene expression . mutation or aberrant expression of the coregulators might thus affect the normal function of the pr , and hence disrupt the normal development of the mammary gland , which might lead to breast cancer . 30 breast cancer patients who were under study at cancer research center , shahid beheshti university of medical sciences ( crc , sbums ) , and 30 control women in premenopausal status , have participated in this study . a total four ml blood has drawn from patients and control women with a 21-gauge needle by syringe . radioimmunoassay ( ria ) has applied for measurement of serum estrogen ( bio source , kip0629 ) . a sandwich enzyme - linked immunosorbent assay ( elisa ) has applied for measurement of granzyme h in serum ( cusabio , gzmh - e17366h ) . immunohistochemistry ( ihc ) for assaying estrogen and progesterone receptors ( novocastra , product code : rtu - cb11 , rtu - pcr-312 ) result have expressed as meansd of experiments . student 's t - test has used for comparison the means between two groups , logistic regression for bc risk . to assess correlation between granzymeh and estrogen , correlation bivariate test mean of serum levels of granzyme h patients was 71.612.2 and 96.1613.4 in control group ( p<0.0001 ) . mean of serum estrogen in patients group was 107.523.8 and in control group was 90.514.8 ( p<0.003 ) ( table1 ) . there was a weak inverse correlation between gzmh and estrogen levels in patient group ( r=-0.3 p<0.02 ) . spearman correlation analysis between estrogen , er , and pr has indicated a weak positive non - significant correlation in patient group . they are secreted towards a neoplastic target cell subsequent to perforin - dependent delivery to target cell cytosol where they have caused apoptosis in target cell ( tumor ) . according to our finding , experimental data have strongly suggested that estrogens play a great role in development and growth of breast cancer . mean levels of serum estrogen in patients group were statistically higher than controls group ( p<0.003 ) . there was a weak correlation between gzmh and estrogen levels in patient group ( r=-0.3 ) . according to study of jiang x et al . , estrogen has induced increasing levels of granzyme b inhibitor , and caused blocking cell death induced by natural killer cells . so our study has implicated existence of suppressor or problem for producing of gzmh in patients group , but it has seemed to be , that contrary to granzyme b. according to our finding levels of estrogen could nt affect on making positive er , pr . some factors like hormone consumption could increase the risk of bc . logistic regression analysis between hormone consumption with breast cancer , have indicated significant statistically relationship ( p<0.01 , or=32.6 , ci : 1.8 - 57.3 ) ( table 2 ) . epidemiologic data have provided strong evidence for an association between plasma estrogens and breast cancer risk . the 1996 , large meta - analysis of the relationship between oral contraceptive use and breast cancer risk , have shown that a history of recent oral contraceptive use , rather than duration of use , was a better predictor of breast cancer risk . these data have based primarily on older high - dose and moderate - dose oral contraceptive pills and not the recently introduced low - dose pills . it is , therefore , likely that the small increase in breast cancer risk associated with the early formulations of oral contraceptives would diminish with the new low - dose pills . human gzmh triggers rapid cell death of target tumor cells that is characteristic of dna fragmentation and mitochondrial damage and generation of reactive oxygen species .we have observed that decreasing level of granzyme h has increased the risk of breast cancer ( p<0.009,or=0.8,ci:0.8 - 0.9 ) ( table 2 ) . but our study has shown that bmi , number of delivery or breastfeeding , and age at monarch could nt affect on risk of bc . early age at menarche has been found to be one of the important determinants in etiology of breast cancer . many epidemiologic studies have suggested that as younger a woman s age at monarch , would be the higher her risk of breast cancer . since monarch at a young age has associated with earlier onset of regular menstrual cycles , early exposure to hormonal milieu associated with regular ovulatory menstrual cycles might be an important etiologic factor . one case - control study has conducted in brazil , has shown that breastfeeding could not have a protective effect against breast cancer . some researchers have believed that the number of children would not make sense for avoiding breast cancers . but many other studies have revealed that null parity is a great risk for breast cancer and the number of children is a protective factor against breast cancer . another study , which has conducted in nigeria , has shown that parity and breastfeeding are protective against breast cancer . parity and lactation period have reduced the lifetime number of ovulatory cycles , reducing the risk of breast cancer particularly in young mothers . this also possibly has reduced estrogen and increased prolactin production , which might decrease women s cumulative exposure to estrogen , thereby inhibiting the initiation or growth of breast cancer cells . a lower risk of breast cancer in women with high body mass index has reported among premenopausal woman by london et al . ( 1996 ) whereas some studies have found no association . in our study family history could nt have significant effect on bc but in patients group percentage of family history is higher than controls group . in any case , many epidemiologic studies have suggested that a family history of breast cancer increases a woman s risk of developing breast cancer and the extent of risk varies according to the nature of the family history , type of relative affected , age at which relative developed breast cancer the number of relatives affected and might vary according to the age of the individual . there are not any similar studies in iranian populations so further study has suggested to reach a better conclusion . our study has implicated existence of suppressor or problem for producing of gzmh in patients group and levels of estrogen could nt effect on making positive er , pr . our study has implicated existence of suppressor or problem for producing of gzmh in patients group and levels of estrogen could nt effect on making positive er , pr .

backgroundbreast cancer ( bc ) is the most common cancer in iranian women , meanwhile the iranian patients are relatively young . granzyme h ( gzmh ) is a functional cytotoxic serine protease of nk cell granules , which expands the cell death - inducing repertoire of innate immune system . gzmh is constitutively and highly expressed in human nk cells , in order to possess chymotrypsin - like ( chymase ) enzymatic activity . the purpose of this study was to determine gzmh level , in bc and healthy women.methods30 breast cancer patients , and 30 control women in premenopausal status , have participated in this study . gzmh , estrogen levels , and er , pr have been measured in cancer and healthy women subsequently , as using elisa , radioimmunoassay , and immunohistochemistry methods.resultsmean gzmh value was lower in bc than healthy women ( p<0.0001).conclusionour study has implicated existence of suppressor or problem for producing of gzmh in patients group and levels of estrogen could n't effect on making positive er , pr .

<s>[INST]iran , which is located in southwest asia , located in an epidemiologic transition and faces the double burden of diseases . breast cancer is the most common cancer in iranian women ; meanwhile the iranian patients are relatively young . given that iran has a female population of about 38 million , this corresponds to a total number of 8500 new cases of breast cancer annually . breast cancer has more frequently occurred in wealthy countries due to a higher prevalence of bc risk factors , such as aged population , older age at first pregnancy , nulliparity , inappropriate breastfeeding , high - calorie intake , sedentary occupation and steroid hormonal consumption . on the other hand , bc survival would be lower in less affluent countries , and in women with low income , or educational level . based on the report from the ministry of health and medical education ( mohme ) ; cancer is the third cause of death in iran after cardiovascular heart disease , then the injuries [ 3 , 4 ] . experimental data has strongly suggested that estrogens have a role in the development and growth of breast cancer . tumor formation may also result from excessive hormonal stimulation of an organ in which normal growth and function would be under endocrine control . the response of an organ to the proliferative effects of a hormone might be a progression from normal growth , to hyperplasia , then to neoplasia . indirect evidence of this sequence has included the increased risk of breast cancer associated with early menarche , late first full - term pregnancy , and late menopause as well as the reduced risk associated with early menopause . immune surveillance has described the process whereby precancerous and malignant cells have recognized by the immune system as damaged , and then would be consequently targeted for elimination . natural killer ( nk ) cells and cytotoxic t lymphocytes ( ctls ) both have played important roles in the innate and adaptive immunity against intracellular pathogens and tumor cells . granule exocytosis is the main pathway for immune elimination of virus - infected cells and tumor cells by ctls and nk cells . after target - cell recognition , release of the cytotoxic granule contents in to the immunological synapse , have formed between the killer cell and its target induces apoptosis . the perforin / granzyme ( gzm ) pathway is a major mechanism for these cytotoxic lymphocytes to kill their targets . granzyme h ( gzm h ) has regarded as an orphan granzyme with unknown biologic functions in immune defense cells . gzm h , which expands the cell death - inducing repertoire of innate immune system , was a functional cytotoxic serine protease of nk cell granule . several studies have recently shown gzmh to be constitutively and highly expressed in human nk cells and to possess chymotrypsin - like ( chymase ) enzymatic activity . human gzmh triggers rapid cell death of target tumor cells that is characteristic of dna fragmentation and mitochondrial damage and generation of reactive oxygen species [ 8 , 12 ] . the steroid hormones , estradiol , plays an important role in the progression of breast cancer , and a majority of the human breast cancers start out as estrogen dependent and express the estrogen receptor ( er ) . the biological effects of estrogen have mediated by its binding to one of the structurally and functionally distinct ers ( er and er ) . the action of progesterone has mediated through its intracellular cognate receptor , the progesterone receptor ( pr ) , which functions as a transcription factor that regulates gene expression . mutation or aberrant expression of the coregulators might thus affect the normal function of the pr , and hence disrupt the normal development of the mammary gland , which might lead to breast cancer . 30 breast cancer patients who were under study at cancer research center , shahid beheshti university of medical sciences ( crc , sbums ) , and 30 control women in premenopausal status , have participated in this study . a total four ml blood has drawn from patients and control women with a 21-gauge needle by syringe . radioimmunoassay ( ria ) has applied for measurement of serum estrogen ( bio source , kip0629 ) . a sandwich enzyme - linked immunosorbent assay ( elisa ) has applied for measurement of granzyme h in serum ( cusabio , gzmh - e17366h ) . immunohistochemistry ( ihc ) for assaying estrogen and progesterone receptors ( novocastra , product code : rtu - cb11 , rtu - pcr-312 ) result have expressed as meansd of experiments . student 's t - test has used for comparison the means between two groups , logistic regression for bc risk . to assess correlation between granzymeh and estrogen , correlation bivariate test mean of serum levels of granzyme h patients was 71.612.2 and 96.1613.4 in control group ( p<0.0001 ) . mean of serum estrogen in patients group was 107.523.8 and in control group was 90.514.8 ( p<0.003 ) ( table1 ) . there was a weak inverse correlation between gzmh and estrogen levels in patient group ( r=-0.3 p<0.02 ) . spearman correlation analysis between estrogen , er , and pr has indicated a weak positive non - significant correlation in patient group . they are secreted towards a neoplastic target cell subsequent to perforin - dependent delivery to target cell cytosol where they have caused apoptosis in target cell ( tumor ) . according to our finding , experimental data have strongly suggested that estrogens play a great role in development and growth of breast cancer . mean levels of serum estrogen in patients group were statistically higher than controls group ( p<0.003 ) . there was a weak correlation between gzmh and estrogen levels in patient group ( r=-0.3 ) . according to study of jiang x et al . , estrogen has induced increasing levels of granzyme b inhibitor , and caused blocking cell death induced by natural killer cells . so our study has implicated existence of suppressor or problem for producing of gzmh in patients group , but it has seemed to be , that contrary to granzyme b. according to our finding levels of estrogen could nt affect on making positive er , pr . some factors like hormone consumption could increase the risk of bc . logistic regression analysis between hormone consumption with breast cancer , have indicated significant statistically relationship ( p<0.01 , or=32.6 , ci : 1.8 - 57.3 ) ( table 2 ) . epidemiologic data have provided strong evidence for an association between plasma estrogens and breast cancer risk . the 1996 , large meta - analysis of the relationship between oral contraceptive use and breast cancer risk , have shown that a history of recent oral contraceptive use , rather than duration of use , was a better predictor of breast cancer risk . these data have based primarily on older high - dose and moderate - dose oral contraceptive pills and not the recently introduced low - dose pills . it is , therefore , likely that the small increase in breast cancer risk associated with the early formulations of oral contraceptives would diminish with the new low - dose pills . human gzmh triggers rapid cell death of target tumor cells that is characteristic of dna fragmentation and mitochondrial damage and generation of reactive oxygen species .we have observed that decreasing level of granzyme h has increased the risk of breast cancer ( p<0.009,or=0.8,ci:0.8 - 0.9 ) ( table 2 ) . but our study has shown that bmi , number of delivery or breastfeeding , and age at monarch could nt affect on risk of bc . early age at menarche has been found to be one of the important determinants in etiology of breast cancer . many epidemiologic studies have suggested that as younger a woman s age at monarch , would be the higher her risk of breast cancer . since monarch at a young age has associated with earlier onset of regular menstrual cycles , early exposure to hormonal milieu associated with regular ovulatory menstrual cycles might be an important etiologic factor . one case - control study has conducted in brazil , has shown that breastfeeding could not have a protective effect against breast cancer . some researchers have believed that the number of children would not make sense for avoiding breast cancers . but many other studies have revealed that null parity is a great risk for breast cancer and the number of children is a protective factor against breast cancer . another study , which has conducted in nigeria , has shown that parity and breastfeeding are protective against breast cancer . parity and lactation period have reduced the lifetime number of ovulatory cycles , reducing the risk of breast cancer particularly in young mothers . this also possibly has reduced estrogen and increased prolactin production , which might decrease women s cumulative exposure to estrogen , thereby inhibiting the initiation or growth of breast cancer cells . a lower risk of breast cancer in women with high body mass index has reported among premenopausal woman by london et al . ( 1996 ) whereas some studies have found no association . in our study family history could nt have significant effect on bc but in patients group percentage of family history is higher than controls group . in any case , many epidemiologic studies have suggested that a family history of breast cancer increases a woman s risk of developing breast cancer and the extent of risk varies according to the nature of the family history , type of relative affected , age at which relative developed breast cancer the number of relatives affected and might vary according to the age of the individual . there are not any similar studies in iranian populations so further study has suggested to reach a better conclusion . our study has implicated existence of suppressor or problem for producing of gzmh in patients group and levels of estrogen could nt effect on making positive er , pr . our study has implicated existence of suppressor or problem for producing of gzmh in patients group and levels of estrogen could nt effect on making positive er , pr .[/INST]backgroundbreast cancer ( bc ) is the most common cancer in iranian women , meanwhile the iranian patients are relatively young . granzyme h ( gzmh ) is a functional cytotoxic serine protease of nk cell granules , which expands the cell death - inducing repertoire of innate immune system . gzmh is constitutively and highly expressed in human nk cells , in order to possess chymotrypsin - like ( chymase ) enzymatic activity . the purpose of this study was to determine gzmh level , in bc and healthy women.methods30 breast cancer patients , and 30 control women in premenopausal status , have participated in this study . gzmh , estrogen levels , and er , pr have been measured in cancer and healthy women subsequently , as using elisa , radioimmunoassay , and immunohistochemistry methods.resultsmean gzmh value was lower in bc than healthy women ( p<0.0001).conclusionour study has implicated existence of suppressor or problem for producing of gzmh in patients group and levels of estrogen could n't effect on making positive er , pr .</s>

SECTION 1. ESTABLISHMENT OF RESERVATION. Section 1 of the Act entitled ``An Act to establish a reservation for the Confederated Tribes of the Grand Ronde Community of Oregon, and for other purposes,'' approved September 9, 1988 (102 Stat. 1594), is amended as follows: (1) In subsection (a), by adding at the end the following: ``The Secretary may accept title to any additional number of acres of real property located within the boundaries of the original 1857 reservation of the Confederated Tribes of the Grand Ronde Community of Oregon established by Executive Order dated June 30, 1857, comprised of land within the political boundaries of Polk and Yamhill Counties, Oregon, if such real property is conveyed or otherwise transferred to the United States by or on behalf of the Tribe. All applications to take land into trust within the boundaries of the original 1857 reservation shall be treated by the Secretary as an on- reservation trust acquisition. All real property taken into trust within these boundaries, before or after the date of the enactment of this Act shall be part of the Tribe's reservation.''. (2) In subsection (b)-- (A) by modifying the opening paragraph of subsection (c) by striking ``10,311.60'' and inserting ``10,599.66''; (B) by striking the following: ---------------------------------------------------------------------------------------------------------------- ``6 7 8 Tax lot 800 5.55'' ---------------------------------------------------------------------------------------------------------------- (C) by inserting in place of the matter struck under subparagraph (B) the following: ---------------------------------------------------------------------------------------------------------------- ``6 7 7, 8, 17 Former tax lot 800, 5.55''; located within the SE \1/4\, SE \1/4\ of Section 7; the SW \1/4\ of Section 8; and the NW \1/ 4\, NW \1/4\ of Section 17 ---------------------------------------------------------------------------------------------------------------- (D) by striking ``240'' and inserting ``241.06''; and (E) by striking all text in subsection (c) after ---------------------------------------------------------------------------------------------------------------- ``6 7 18 E \1/2\ NE \1/4\ 43.42'' ---------------------------------------------------------------------------------------------------------------- (F) and inserting the following: ------------------------------------------------------------------------ ``6 8 1 W \1/2\, SE 20.6 \1/4\, SE \1/ 4\ and S \1/ 2\, NE \1/4\, SE \1/4\ 6 8 1 N \1/2\, SW \1/ 19.99 4\, SE \1/4\ 6 8 1 SE \1/4\, NE 9.99 \1/4\ 6 8 1 NE \1/4\, SW 10.46 \1/4\ and NW \1/4\, SW \1/ 4\ 6 8 1 NE \1/4\, SW 12.99 \1/4\ and NW \1/4\, SW \1/ 4\ 6 7 6 SW \1/4\, NW 37.99 \1/4\ 6 7 5 NE \1/4\, NW 24.87 \1/4\ 6 7 5, 8 SW \1/4\, SE 109.9 \1/4\ of Section 5 and NE \1/4\, NE \1/4\ NW \1/ 4\, NE \1/4\ NE \1/4\, NW \1/4\ of Section 8 6 8 1 NW \1/4\, SE 31.32 \1/4\ 6 8 1 NE \1/4\, SW 8.89 \1/4\ ----------- ........... Total 10,599.66' '. ------------------------------------------------------------------------

Authorizes the Secretary of the Interior to accept title to any additional number of acres of real property located within the boundaries of the original 1857 reservation of the Confederated Tribes of the Grand Ronde Community of Oregon (comprised of land within the political boundaries of Polk and Yamhill Counties, Oregon), if such real property is conveyed or otherwise transferred to the United States by or on behalf of the Tribe. States that: (1) the Secretary shall treat all applications to take land into trust within the boundaries of the original 1857 reservation as an on-reservation trust acquisition; and (2) all real property taken into trust within these boundaries before or after the date of the enactment of this Act shall be part of the Tribe's reservation.

<s>[INST]SECTION 1. ESTABLISHMENT OF RESERVATION. Section 1 of the Act entitled ``An Act to establish a reservation for the Confederated Tribes of the Grand Ronde Community of Oregon, and for other purposes,'' approved September 9, 1988 (102 Stat. 1594), is amended as follows: (1) In subsection (a), by adding at the end the following: ``The Secretary may accept title to any additional number of acres of real property located within the boundaries of the original 1857 reservation of the Confederated Tribes of the Grand Ronde Community of Oregon established by Executive Order dated June 30, 1857, comprised of land within the political boundaries of Polk and Yamhill Counties, Oregon, if such real property is conveyed or otherwise transferred to the United States by or on behalf of the Tribe. All applications to take land into trust within the boundaries of the original 1857 reservation shall be treated by the Secretary as an on- reservation trust acquisition. All real property taken into trust within these boundaries, before or after the date of the enactment of this Act shall be part of the Tribe's reservation.''. (2) In subsection (b)-- (A) by modifying the opening paragraph of subsection (c) by striking ``10,311.60'' and inserting ``10,599.66''; (B) by striking the following: ---------------------------------------------------------------------------------------------------------------- ``6 7 8 Tax lot 800 5.55'' ---------------------------------------------------------------------------------------------------------------- (C) by inserting in place of the matter struck under subparagraph (B) the following: ---------------------------------------------------------------------------------------------------------------- ``6 7 7, 8, 17 Former tax lot 800, 5.55''; located within the SE \1/4\, SE \1/4\ of Section 7; the SW \1/4\ of Section 8; and the NW \1/ 4\, NW \1/4\ of Section 17 ---------------------------------------------------------------------------------------------------------------- (D) by striking ``240'' and inserting ``241.06''; and (E) by striking all text in subsection (c) after ---------------------------------------------------------------------------------------------------------------- ``6 7 18 E \1/2\ NE \1/4\ 43.42'' ---------------------------------------------------------------------------------------------------------------- (F) and inserting the following: ------------------------------------------------------------------------ ``6 8 1 W \1/2\, SE 20.6 \1/4\, SE \1/ 4\ and S \1/ 2\, NE \1/4\, SE \1/4\ 6 8 1 N \1/2\, SW \1/ 19.99 4\, SE \1/4\ 6 8 1 SE \1/4\, NE 9.99 \1/4\ 6 8 1 NE \1/4\, SW 10.46 \1/4\ and NW \1/4\, SW \1/ 4\ 6 8 1 NE \1/4\, SW 12.99 \1/4\ and NW \1/4\, SW \1/ 4\ 6 7 6 SW \1/4\, NW 37.99 \1/4\ 6 7 5 NE \1/4\, NW 24.87 \1/4\ 6 7 5, 8 SW \1/4\, SE 109.9 \1/4\ of Section 5 and NE \1/4\, NE \1/4\ NW \1/ 4\, NE \1/4\ NE \1/4\, NW \1/4\ of Section 8 6 8 1 NW \1/4\, SE 31.32 \1/4\ 6 8 1 NE \1/4\, SW 8.89 \1/4\ ----------- ........... Total 10,599.66' '. ------------------------------------------------------------------------[/INST]Authorizes the Secretary of the Interior to accept title to any additional number of acres of real property located within the boundaries of the original 1857 reservation of the Confederated Tribes of the Grand Ronde Community of Oregon (comprised of land within the political boundaries of Polk and Yamhill Counties, Oregon), if such real property is conveyed or otherwise transferred to the United States by or on behalf of the Tribe. States that: (1) the Secretary shall treat all applications to take land into trust within the boundaries of the original 1857 reservation as an on-reservation trust acquisition; and (2) all real property taken into trust within these boundaries before or after the date of the enactment of this Act shall be part of the Tribe's reservation.</s>

Libya's first nationwide elections in nearly five decades brought hints Sunday of an Arab Spring precedent: Western-leaning parties making strides over Islamist rivals hoping to follow the same paths to power as in neighbors Egypt and Tunisia. Polling station officials count ballots at a polling station in Tripoli, Libya, Saturday, July 7, 2012. Jubilant Libyans chose a new parliament Saturday in their first nationwide vote in decades, but... (Associated Press) Libyan voters line up at a polling station in Benghazi, Libya Saturday, July 7, 2012. Jubilant Libyans marked a major step toward democracy after decades of erratic one-man rule, voting Saturday in the... (Associated Press) A Libyan man leaves a voting booth to cast his ballot at a polling station in the former loyalist stronghold district of Abu Salim in Tripoli, Libya, Saturday, July 7, 2012. Jubilant Libyans marked a... (Associated Press) Libyans hold up their ink-marked fingers that shows they have voted as they celebrate in Martyrs' Square in Tripoli, Libya, Saturday, July 7, 2012. Jubilant Libyan voters marked a major step toward democracy... (Associated Press) While final results from Saturday's parliamentary election could still be days away under a two-tier selection system, unofficial and partial counts from Libya's biggest cities suggested liberal factions were leading the Muslim Brotherhood and allies in a possible first major setback to their political surge following last year's uprisings. If the Libyan trend holds _ which is still far from certain _ it would challenge the narrative of rising Islamist power since the fall of Western-allied regimes from Tunis to Cairo. It also could display the different political dynamics in Libya, where tribal loyalties run deep and groups such as the Muslim Brotherhood at times cooperated with the rule of Moammar Gadhafi. "Anyone with past ties with old regime is hated, even despised," said Fathi al-Fadhali, a pro-Islamist Libyan political analyst who lived in exile for 30 years. "Any political names associated with the regime are immediately politically burnt by that association." Ultimately, the 200-seat parliament will face the task of forming a government _ which could become tests of strength for Islamists and secular forces over questions such as women's rights, the extent of traditional Islamic law and relations with the U.S. and other Western nations that helped bring down Gadhafi. U.S. President Barack Obama congratulated Libyans on the vote, calling it "another milestone on their extraordinary transition to democracy." U.N. Secretary-General Ban Ki-moon praised the people of Libya and the candidates who "contested the election in a peaceful, democratic spirit," according to his spokesman. Now, the ballots have to be portioned out according to two categories: Eighty seats are set aside for party lists, and the remaining 120 for individual independent candidates. In the first group, a liberal alliance led by the former rebel prime minister Mahmoud Jibril appeared to hold more than half the seats in the capital Tripoli and the revolution stronghold of Benghazi, according to several party representatives. They spoke to The Associated Press on condition of anonymity because they were not authorized to brief media. In western Libya, where Jibril's tribe, the Warfalla, is prominent, his party also was on the top in the early counting, the political officials said. In Libya's third-largest city, Misrata _ which was besieged by Gadhafi forces for weeks _ an upstart faction of local politicians appeared to hold the lead in another possible blow to Islamists. Faisal Krekshi, secretary general of Jibril's Alliance of National Forces, said the results were based on reports by party representatives at ballot counting centers across the vast desert nation of 6 million people. Even officials from rival Islamist parties _ the Muslim Brotherhood's Justice and Construction Party and the Islamist Al-Watan _ described Jibril's alliance as the biggest winner in the race for the 80 party seats. But even if true, that is still a long way from victory. The bulk of the parliament _ 120 seats _ will be decided by the results from the head-to-head races among thousands of candidates, making it nearly impossible to predict. Shortly before the voting, Libya's Grand Mufti issued a religious edict prohibiting Libyans from voting for secularists. Meanwhile, independent candidates are seen as possible wildcards and could punish both the Muslim Brotherhood and Jibril's factions for having former ties to the Gadhafi regime. "We are all waiting and we have nothing to suggest that one party is ahead of others," election commission chief Nouri al-Abar told reporters. He also refused to set a date for announcing complete results. Some observers believe it could take nearly a week. Speaking to reporters, Jibril vowed to "commit ourselves to what the commission will announce officially" and urged for all political factions to work toward "national consensus." Unlike Egypt _ where the Muslim Brotherhood was seen as an alternative to Hosni Mubarak's authoritarian rule _ its brethren in Libya must confront a reputation as compromisers with Gadhafi. A former rebel commander, Fadllah Haroun, called it "their black past." Gadhafi's powerful son, Seif al-Islam, forged deals with the Muslim Brotherhood and allies in efforts to pave the way for his eventual rule. He released more than 150 Islamist political prisoners starting in 2003 and offered others positions in his various media outlets and foundations. Because of such ties, the Muslim Brotherhood boycotted the first Libyan opposition conference in London in 2005 that called for overthrowing Gadhafi's regime at a time Libya was mending its relations with the West. Abdel-Latif Karmous, deputy leader of the Libyan Brotherhood who was among the prisoners released by Gadhafi's son, acknowledged that the group faces perceptions as regime allies. "We didn't immerse ourselves in the regime ... We only kept channels open to achieve political mobilization," said Karmous, a professor at Tripoli University. Since Gadhafi's fall, the Muslim Brotherhood in Libya also has faced questions about its close ties to the wealthy Gulf state of Qatar, which funneled weapons and funds to the anti-Gadhafi forces. Some critics accuse Qatar's rulers of trying to exert influence through Libya's Brotherhood as a bridge between Egypt and Tunisia. In December, influential Egyptian cleric Youssef al-Qaradawi, who is based in Qatar, flew to Libya aboard a Qatari royal jet and was given a feast by a senior Brotherhood leader, Bashir al-Kebti. Later, al-Qaradawi and Tunisian Brotherhood leader Rashid al-Ghannoushi traveled to Tripoli to attend a National Reconciliation conference. But members of the rebel-led National Transition Council withdrew in protest "because they only saw it as a promotion and propaganda for the Brotherhood," said Fathi Baja, head of political committee in the NTC. "Qatar for the Brotherhood is like a shrine," he added. "Twenty-four hour visits, around the clock, members coming and going to Qatar." Libya also is awash with rival Islamist groups, including the ultraconservative Salafis and jihadists inspired by al-Qaida, which could bring future power plays regardless of the election results. Fathi Bin Essa, a prominent political analyst, described the elections as only a "rehearsal" to show "who has the real power in the street." The run-up to the voting, too, showed the political complexities of trying to accommodate all sides in Libya. Jibril's liberal alliance of about 40 groups emphasized the need for a "civil democratic" state, but said that Islamic Sharia law should guide legislation. Jibril also made a point to appear with Muslim clerics in campaign photos even though he is prohibited from running under rules barring NTC members from the ballot. But a religious edict by Libya's Grand Mufti, Sheik Sadek al-Ghariani, accused the liberal factions of using Islam to try to court conservative Libyans. "I advise you to choose the one who will rule by God's religion and God's Sharia," according to an audio clip posted by Libyan activists. Independent candidate and Benghazi city council member Faraj Negm said "the Libyan street doesn't accept anyone to blackmail them." "We are one Muslim nation that doesn't pretend to be politically savvy," Nagm said, "but we learn and we don't want anyone to dictate things on us." ||||| TRIPOLI, Libya — A coalition led by a Western-educated political scientist appeared on Sunday to be beating its Islamist rivals in Libya’s first election after Col. Muammar el-Qaddafi, breaking an Islamist wave that swept across neighboring Egypt, Tunisia and Morocco in the aftermath of the Arab Spring uprisings. The preliminary results, characterized by independent monitors and party representatives who witnessed the vote count for a new national assembly, reflect in part the well-known name and tribal connections of the coalition’s founder, Mahmoud Jibril. He is the former interim prime minister who helped lead the de facto rebel government in Benghazi, and he is also a member of Libya’s most populous tribe, the Warfalla. The apparent success of Mr. Jibril’s party over the Muslim Brotherhood’s bloc makes him perhaps the most important voice in the next stage of Libya’s transition, though he is barred for now from elected office. In a campaign that took place over just two weeks, after a 40-year stretch in which Colonel Qaddafi crushed any dissent or even political organizing, the ideological lines for Libyan voters remained fuzzy, at best. Many voters acknowledged plans to let tribal, family or community ties guide their vote. The Islamists, in contrast, sought to portray Mr. Jibril’s coalition as “liberal” or “secular” — and some who stood with him acknowledged privately that for them those terms were apt. Still, unlike opponents of Islamists in other Arab countries, Mr. Jibril never hurled accusations of extremism against those who called for the application of Islamic law. Like the other major factions here, including the Islamist parties, Mr. Jibril pledged to make Islamic law a main source of legislation, though not the only one. He and his allies publicly echoed a frequent refrain of Libyan voters who were unsure what to make of re-emergent groups like the Muslim Brotherhood: “Do they think they are more Muslim than we are?” A political scientist who earned his doctoral degree at the University of Pittsburgh and taught there as well, Mr. Jibril said in a recent interview on Libyan television that friends and neighbors anywhere he has lived would describe him as someone who “goes to the mosque for Friday prayers, and we see that he prays.” “The Libyan people don’t need either liberalism or secularism, or pretenses in the name of Islam, because Islam, this great religion, cannot be used for political purposes,” he said. “Islam is much bigger than that.” “Jibril is praying five times a day and fasting, so what is the difference?” asked Suleiman Zoubi, a former judge and political independent in the eastern city of Benghazi who appeared set to win a seat in the congress. Ali Tarhouni, the leader of a fledgling party in Mr. Jibril’s coalition and another former minister in the transitional government, called the results evidence of Libyans’ “moderate” character. But he also attributed their success to familiarity. “People trust us,” he said. “Coming out of a war, with a political vacuum and a security vacuum, people were looking for those they knew were tested in the tough times.” Official results will not be released for several days. The votes were counted Saturday night in each polling center in the presence of party and candidate representatives, as well as independent observers. Both Islamists and their opponents said Sunday that Mr. Jibril’s coalition was headed for at least a plurality of the planned congress. It is expected to govern Libya for 18 months and possibly oversee the writing of a constitution. Some leading Islamists had predicted as recently as a few days ago that their parties would win as much as 60 percent of the seats. But on Sunday, Hisham Kreskshi, a leader of the party founded by Libya’s Muslim Brotherhood, said it now expected to win less than a quarter of the 200 seats. He said the Brotherhood’s party was not disappointed by its own results, but it was unhappy with the dominance of Mr. Jibril’s coalition. “We were disappointed that there was nobody else but him and us, disappointed with the other parties we might have had a coalition with.”

– It will be at least a few days before final results from Libya's first election in more than 40 years are in, but early results suggest that a coalition of moderate, Western-leaning groups is ahead of its Islamist rivals. If the alliance led by former rebel prime minister Mahmoud Jibril does manage to defeat the Muslim Brotherhood's bloc, it will mark a shift away from Islamism that stands in contrast to other Arab Spring nations and reflects the different political dynamics in Libya, where the Brotherhood sometimes cooperated with Moammar Gadhafi's regime, the AP notes. "Anyone with past ties with old regime is hated, even despised," a pro-Islamist Libyan political analyst says. "Any political names associated with the regime are immediately politically burnt by that association." Islamists had predicted their parties would win up to 60% of the seats, but after Saturday's vote, the leader of a party founded by the Brotherhood said it expected to win less than a quarter of the 200 seats up for grabs, reports the New York Times.

<s>[INST]Libya's first nationwide elections in nearly five decades brought hints Sunday of an Arab Spring precedent: Western-leaning parties making strides over Islamist rivals hoping to follow the same paths to power as in neighbors Egypt and Tunisia. Polling station officials count ballots at a polling station in Tripoli, Libya, Saturday, July 7, 2012. Jubilant Libyans chose a new parliament Saturday in their first nationwide vote in decades, but... (Associated Press) Libyan voters line up at a polling station in Benghazi, Libya Saturday, July 7, 2012. Jubilant Libyans marked a major step toward democracy after decades of erratic one-man rule, voting Saturday in the... (Associated Press) A Libyan man leaves a voting booth to cast his ballot at a polling station in the former loyalist stronghold district of Abu Salim in Tripoli, Libya, Saturday, July 7, 2012. Jubilant Libyans marked a... (Associated Press) Libyans hold up their ink-marked fingers that shows they have voted as they celebrate in Martyrs' Square in Tripoli, Libya, Saturday, July 7, 2012. Jubilant Libyan voters marked a major step toward democracy... (Associated Press) While final results from Saturday's parliamentary election could still be days away under a two-tier selection system, unofficial and partial counts from Libya's biggest cities suggested liberal factions were leading the Muslim Brotherhood and allies in a possible first major setback to their political surge following last year's uprisings. If the Libyan trend holds _ which is still far from certain _ it would challenge the narrative of rising Islamist power since the fall of Western-allied regimes from Tunis to Cairo. It also could display the different political dynamics in Libya, where tribal loyalties run deep and groups such as the Muslim Brotherhood at times cooperated with the rule of Moammar Gadhafi. "Anyone with past ties with old regime is hated, even despised," said Fathi al-Fadhali, a pro-Islamist Libyan political analyst who lived in exile for 30 years. "Any political names associated with the regime are immediately politically burnt by that association." Ultimately, the 200-seat parliament will face the task of forming a government _ which could become tests of strength for Islamists and secular forces over questions such as women's rights, the extent of traditional Islamic law and relations with the U.S. and other Western nations that helped bring down Gadhafi. U.S. President Barack Obama congratulated Libyans on the vote, calling it "another milestone on their extraordinary transition to democracy." U.N. Secretary-General Ban Ki-moon praised the people of Libya and the candidates who "contested the election in a peaceful, democratic spirit," according to his spokesman. Now, the ballots have to be portioned out according to two categories: Eighty seats are set aside for party lists, and the remaining 120 for individual independent candidates. In the first group, a liberal alliance led by the former rebel prime minister Mahmoud Jibril appeared to hold more than half the seats in the capital Tripoli and the revolution stronghold of Benghazi, according to several party representatives. They spoke to The Associated Press on condition of anonymity because they were not authorized to brief media. In western Libya, where Jibril's tribe, the Warfalla, is prominent, his party also was on the top in the early counting, the political officials said. In Libya's third-largest city, Misrata _ which was besieged by Gadhafi forces for weeks _ an upstart faction of local politicians appeared to hold the lead in another possible blow to Islamists. Faisal Krekshi, secretary general of Jibril's Alliance of National Forces, said the results were based on reports by party representatives at ballot counting centers across the vast desert nation of 6 million people. Even officials from rival Islamist parties _ the Muslim Brotherhood's Justice and Construction Party and the Islamist Al-Watan _ described Jibril's alliance as the biggest winner in the race for the 80 party seats. But even if true, that is still a long way from victory. The bulk of the parliament _ 120 seats _ will be decided by the results from the head-to-head races among thousands of candidates, making it nearly impossible to predict. Shortly before the voting, Libya's Grand Mufti issued a religious edict prohibiting Libyans from voting for secularists. Meanwhile, independent candidates are seen as possible wildcards and could punish both the Muslim Brotherhood and Jibril's factions for having former ties to the Gadhafi regime. "We are all waiting and we have nothing to suggest that one party is ahead of others," election commission chief Nouri al-Abar told reporters. He also refused to set a date for announcing complete results. Some observers believe it could take nearly a week. Speaking to reporters, Jibril vowed to "commit ourselves to what the commission will announce officially" and urged for all political factions to work toward "national consensus." Unlike Egypt _ where the Muslim Brotherhood was seen as an alternative to Hosni Mubarak's authoritarian rule _ its brethren in Libya must confront a reputation as compromisers with Gadhafi. A former rebel commander, Fadllah Haroun, called it "their black past." Gadhafi's powerful son, Seif al-Islam, forged deals with the Muslim Brotherhood and allies in efforts to pave the way for his eventual rule. He released more than 150 Islamist political prisoners starting in 2003 and offered others positions in his various media outlets and foundations. Because of such ties, the Muslim Brotherhood boycotted the first Libyan opposition conference in London in 2005 that called for overthrowing Gadhafi's regime at a time Libya was mending its relations with the West. Abdel-Latif Karmous, deputy leader of the Libyan Brotherhood who was among the prisoners released by Gadhafi's son, acknowledged that the group faces perceptions as regime allies. "We didn't immerse ourselves in the regime ... We only kept channels open to achieve political mobilization," said Karmous, a professor at Tripoli University. Since Gadhafi's fall, the Muslim Brotherhood in Libya also has faced questions about its close ties to the wealthy Gulf state of Qatar, which funneled weapons and funds to the anti-Gadhafi forces. Some critics accuse Qatar's rulers of trying to exert influence through Libya's Brotherhood as a bridge between Egypt and Tunisia. In December, influential Egyptian cleric Youssef al-Qaradawi, who is based in Qatar, flew to Libya aboard a Qatari royal jet and was given a feast by a senior Brotherhood leader, Bashir al-Kebti. Later, al-Qaradawi and Tunisian Brotherhood leader Rashid al-Ghannoushi traveled to Tripoli to attend a National Reconciliation conference. But members of the rebel-led National Transition Council withdrew in protest "because they only saw it as a promotion and propaganda for the Brotherhood," said Fathi Baja, head of political committee in the NTC. "Qatar for the Brotherhood is like a shrine," he added. "Twenty-four hour visits, around the clock, members coming and going to Qatar." Libya also is awash with rival Islamist groups, including the ultraconservative Salafis and jihadists inspired by al-Qaida, which could bring future power plays regardless of the election results. Fathi Bin Essa, a prominent political analyst, described the elections as only a "rehearsal" to show "who has the real power in the street." The run-up to the voting, too, showed the political complexities of trying to accommodate all sides in Libya. Jibril's liberal alliance of about 40 groups emphasized the need for a "civil democratic" state, but said that Islamic Sharia law should guide legislation. Jibril also made a point to appear with Muslim clerics in campaign photos even though he is prohibited from running under rules barring NTC members from the ballot. But a religious edict by Libya's Grand Mufti, Sheik Sadek al-Ghariani, accused the liberal factions of using Islam to try to court conservative Libyans. "I advise you to choose the one who will rule by God's religion and God's Sharia," according to an audio clip posted by Libyan activists. Independent candidate and Benghazi city council member Faraj Negm said "the Libyan street doesn't accept anyone to blackmail them." "We are one Muslim nation that doesn't pretend to be politically savvy," Nagm said, "but we learn and we don't want anyone to dictate things on us." ||||| TRIPOLI, Libya — A coalition led by a Western-educated political scientist appeared on Sunday to be beating its Islamist rivals in Libya’s first election after Col. Muammar el-Qaddafi, breaking an Islamist wave that swept across neighboring Egypt, Tunisia and Morocco in the aftermath of the Arab Spring uprisings. The preliminary results, characterized by independent monitors and party representatives who witnessed the vote count for a new national assembly, reflect in part the well-known name and tribal connections of the coalition’s founder, Mahmoud Jibril. He is the former interim prime minister who helped lead the de facto rebel government in Benghazi, and he is also a member of Libya’s most populous tribe, the Warfalla. The apparent success of Mr. Jibril’s party over the Muslim Brotherhood’s bloc makes him perhaps the most important voice in the next stage of Libya’s transition, though he is barred for now from elected office. In a campaign that took place over just two weeks, after a 40-year stretch in which Colonel Qaddafi crushed any dissent or even political organizing, the ideological lines for Libyan voters remained fuzzy, at best. Many voters acknowledged plans to let tribal, family or community ties guide their vote. The Islamists, in contrast, sought to portray Mr. Jibril’s coalition as “liberal” or “secular” — and some who stood with him acknowledged privately that for them those terms were apt. Still, unlike opponents of Islamists in other Arab countries, Mr. Jibril never hurled accusations of extremism against those who called for the application of Islamic law. Like the other major factions here, including the Islamist parties, Mr. Jibril pledged to make Islamic law a main source of legislation, though not the only one. He and his allies publicly echoed a frequent refrain of Libyan voters who were unsure what to make of re-emergent groups like the Muslim Brotherhood: “Do they think they are more Muslim than we are?” A political scientist who earned his doctoral degree at the University of Pittsburgh and taught there as well, Mr. Jibril said in a recent interview on Libyan television that friends and neighbors anywhere he has lived would describe him as someone who “goes to the mosque for Friday prayers, and we see that he prays.” “The Libyan people don’t need either liberalism or secularism, or pretenses in the name of Islam, because Islam, this great religion, cannot be used for political purposes,” he said. “Islam is much bigger than that.” “Jibril is praying five times a day and fasting, so what is the difference?” asked Suleiman Zoubi, a former judge and political independent in the eastern city of Benghazi who appeared set to win a seat in the congress. Ali Tarhouni, the leader of a fledgling party in Mr. Jibril’s coalition and another former minister in the transitional government, called the results evidence of Libyans’ “moderate” character. But he also attributed their success to familiarity. “People trust us,” he said. “Coming out of a war, with a political vacuum and a security vacuum, people were looking for those they knew were tested in the tough times.” Official results will not be released for several days. The votes were counted Saturday night in each polling center in the presence of party and candidate representatives, as well as independent observers. Both Islamists and their opponents said Sunday that Mr. Jibril’s coalition was headed for at least a plurality of the planned congress. It is expected to govern Libya for 18 months and possibly oversee the writing of a constitution. Some leading Islamists had predicted as recently as a few days ago that their parties would win as much as 60 percent of the seats. But on Sunday, Hisham Kreskshi, a leader of the party founded by Libya’s Muslim Brotherhood, said it now expected to win less than a quarter of the 200 seats. He said the Brotherhood’s party was not disappointed by its own results, but it was unhappy with the dominance of Mr. Jibril’s coalition. “We were disappointed that there was nobody else but him and us, disappointed with the other parties we might have had a coalition with.”[/INST]– It will be at least a few days before final results from Libya's first election in more than 40 years are in, but early results suggest that a coalition of moderate, Western-leaning groups is ahead of its Islamist rivals. If the alliance led by former rebel prime minister Mahmoud Jibril does manage to defeat the Muslim Brotherhood's bloc, it will mark a shift away from Islamism that stands in contrast to other Arab Spring nations and reflects the different political dynamics in Libya, where the Brotherhood sometimes cooperated with Moammar Gadhafi's regime, the AP notes. "Anyone with past ties with old regime is hated, even despised," a pro-Islamist Libyan political analyst says. "Any political names associated with the regime are immediately politically burnt by that association." Islamists had predicted their parties would win up to 60% of the seats, but after Saturday's vote, the leader of a party founded by the Brotherhood said it expected to win less than a quarter of the 200 seats up for grabs, reports the New York Times.</s>

Women's March Floods Washington, Sparking Rallies Worldwide Hide caption Protesters march in Washington, D.C., with the Capitol in the background. Previous Next Joshua Lott/AFP/Getty Images Hide caption Protesters crowd the National Mall during the Women's March on Washington. Previous Next Zach Gibson/AFP/Getty Images Hide caption Protesters march down a D.C. street during the Women's March on Washington. Previous Next Jessica Kourkounis/Getty Images Hide caption Protesters attend the Women's March on Washington in D.C. Previous Next Mario Tama/Getty Images Hide caption Protesters take a selfie with the police as a backdrop outside the U.S. Capitol during the Women's March on Washington. Previous Next Jessica Kourkounis/Getty Images Hide caption Women with bright pink hats and signs gather early on Saturday in Washington, D.C., for the Women's March on Washington. Previous Next Jose Luis Magana/AP Hide caption Demonstrators protest on the National Mall for the Women's March on Washington. Previous Next Andrew Caballero-Reynolds/AFP/Getty Images Hide caption Protesters arrive at the Capitol South Metro station for the Women's March on Washington in Washington, D.C. Previous Next Jessica Kourkounis/Getty Images Hide caption Protesters attend the Women's March on Washington in D.C. Previous Next Jessica Kourkounis/Getty Images Hide caption Marchers gather outside the National Museum of the American Indian, bearing signs protesting President Trump. Previous Next Sarah McCammon/NPR Hide caption Protesters display their signs in Washington, D.C., during the Womens March. Previous Next Joshua Lott/AFP/Getty Images 1 of 11 i View slideshow Updated at 4 p.m. ET The National Mall has flooded with pink, as demonstrators descend on the nation's capital Saturday for the Women's March on Washington. Just one day after President Trump's inauguration, marchers from across the country have gathered in the city to protest his agenda and support for women's rights. The event opened with a rally, to be followed by the march proper — which had a path laid out from a starting position near the U.S. Capitol to its endpoint near the Washington Monument. The city's metro system reported 275,000 rides as of 11 a.m. According to metro officials that's eight times more than a normal Saturday. Reuters adds that the number is also "82,000 more than the 193,000 rides reported at the same point on Friday," the day of Trump's inauguration. toggle caption Becky Harlan/NPR In fact, the number of marchers swelled to the point of prompting reports there would be no space for a formal procession — a claim rebutted by organizers Saturday afternoon in a statement. "We are marching," reads the statement. "We are marching straight ahead toward the Washington Monument to the ellipse of the White House." The event grew from humble origins — a simple Facebook invitation after Election Day — to the much more massive demonstration seen Saturday. By the time marchers hit the streets, the Women's March on Washington developed a broad platform of progressive political positions, a slate of celebrity performers and a series of sister marches planned across the world — on all seven continents. toggle caption Meg Kelly/NPR For protester Amy Jackson, though, the matter was simple: She just wanted to "make her voice heard," she tells NPR's Marisa Penaloza. Jackson, who traveled to D.C. from Chocowinity, N.C., to be part of the march, said, "It was very important to be here today." The Scene On The Ground Among the crowd that gathered for the rally outside the National Museum of the American Indian, NPR's Sarah McCammon reported signs supporting a wide array of causes — from women's rights and LGBTQ rights, to Black Lives Matter and excoriations of xenophobia. One thing seemed to be almost universal, though: The pink knitted caps known as "pussyhats" among the marchers, in protest of Trump's past comments about women. toggle caption Becky Harlan/NPR Popular as they may have been, the pussyhats were not the only costume worn by marchers. Others wore their causes on their sleeves, dressing in attire to call attention to issues like Native rights and environmental fears. In video Sarah recorded a block or two from the main rally, it appears there were marchers in a menagerie of outfits. Meanwhile, at a nearby metro station, NPR's Pam Fessler reported the mood among the demonstrators has been more festive than protests Friday. Most of the demonstrators are women, Pam says, but some men have joined the march, as well — including one man carrying a sign reading: "This is what a feminist looks like." From the main rally stage, musicians and speakers addressed the crowd in an event that lasted some five hours — more than two hours longer than anticipated. The reason for that overflow was partly its smattering of surprise guests. Beyond the planned performances and speeches from figures like Janelle Monáe and Gloria Steinem, others including Madonna and Alicia Keys took the stage. "It was woman that gave you Dr Martin Luther King Jr. It was woman who gave you Malcolm X. And according to the bible, it was a woman who gave you Jesus," Monáe told the crowd, according to The Guardian. The Road To The March What began simply as opposition to Trump has developed a wide-ranging list of demands, which organizers published as a platform prior to the march. toggle caption Becky Harlan/NPR But above all, organizers say, is the principle that "Women's Rights are Human Rights and Human Rights are Women's Rights." That statement is pulled directly from a speech Hillary Clinton delivered more than two decades ago in Beijing. Clinton tweeted her support for the march Saturday, expressing thanks "for standing, speaking & marching for our values." Arriving at that platform was not always a smooth process, though. NPR's Hansi Lo Wang reports there has been disagreement between organizers about how to treat issues of race. "This march was initially put together by white women, and a lot of women of color felt they weren't part of the conversation," Carmen Perez, one of the march's national organizers, told NPR's Hansi Lo Wang. "We can't continue to work in isolation. We can't continue to be one-dimensional. We have to make sure that we look up, that we begin to really coordinate our efforts." toggle caption Sait Serkan Gurbuz/AP Ultimately, more than 200 organizations — ranging from Planned Parenthood and the NAACP, to Amnesty International and the AFL-CIO — partnered with the Women's March on Washington. For Darcy Sawatzki, a demonstrator attending the march with her daughter, Delia, what matters most is showing up. "I think showing up and paying attention is sort of one of the bare minimums of citizenship," Sawatzki told NPR's Brakkton Booker. It's not her first march; she has also participated in Black Lives Matter protests. Enlarge this image toggle caption Meg Kelly/NPR Meg Kelly/NPR She said it's not unease with the new president that inspired her to march. "I'm not here out of anger or fear, I'm out here for determination, for participation and hope that together we can make a difference." ||||| Hundreds of demonstrations around the world are being planned for Jan. 21 in conjunction with the Women’s March on Washington, which is expected to be the largest inauguration-related demonstration in United States history. The March Route in Washington The New York Times | Source: Women’s March Organizers have estimated that 200,000 people could participate in the Washington rally, which will begin at 10 a.m. near the southeast corner of the National Mall. The march is scheduled to start at 1:15 p.m. and will proceed toward the White House. Participants are traveling to Washington from all over the country, with many arriving by bus. Many more are expected to participate in hundreds of sister marches throughout the United States. Women’s Marches Around the Nation WASH. Me. Mont. N.D. N.H. Minn. Vt. Ore. N.Y. Mass. Mich. Wis. S.D. Wyo. Idaho R.I. Conn. Iowa Pa. Neb. N.J. Ill. Nev. Ind. Ohio DEL. Utah W. Va. MD. Colo. Kan. Va. Mo. KY. CaliF. N.C. Tenn. Ark. Okla. Ariz. N.M. S.C. Ga. Miss. Ala. La. Texas ALASKA Fla. HAWAII WASH. Me. N.H. Mont. N.D. Vt. Mich. Minn. Ore. N.Y. Mass. Wis. S.D. Wyo. Idaho R.I. Iowa Conn. Pa. Neb. Ohio Ill. N.J. Nev. Ind. DEL. Utah W. Va. MD. Kan. Va. Colo. Mo. KY. N.C. Tenn. Ark. Okla. Ariz. CaliF. S.C. N.M. Miss. Ga. Ala. La. Texas ALASKA Fla. HAWAII WA NH Me ND Vt Mt Id NY Or Ma Mi Mn Wi SD Wy RI Ia Pa Ct Ne NJ Nv Oh In DE Ut WV MD Il Ks Va Co Mo KY Az Ca NC Tn Ar Ok SC NM Ms Ga Al La Tx Ak HI Fl Me WA NH Mn Mt Vt ND Mi NY Id Or Ma Wi Oh SD Wy RI Ia Pa Ne Ct Nv In NJ Ut WV Il DE Ks Va Co Mo KY MD Tn Ar Ok NC Az Ca Ms NM SC Al Ga La Tx Ak Fl HI March organizers have said the event’s primary focus is to promote equal rights for women and to defend marginalized groups. “The Women’s March on Washington will send a bold message to our new government on their first day in office, and to the world, that women's rights are human rights,” the group’s website says. More than 200 organizations have signed on as partners for the march, including Planned Parenthood, the NAACP, the National Organization for Women and Human Rights Watch. Cher, Katy Perry and Amy Schumer are among the celebrities who have said they will attend. Women’s Marches Around the World Helsinki Vancouver Tokyo Erbil Athens San Jose Nairobi Singapore Rio de Janeiro Sydney Cape Town Helsinki Vancouver Tokyo Erbil Athens San Jose Nairobi Singapore Rio de Janeiro Sydney Cape Town Helsinki Vancouver Tokyo Erbil San Jose Nairobi Singapore Rio de Janeiro Sydney Cape Town Helsinki Erbil Tokyo San Jose Sydney Cape Town Participants outside the United States say they are marching in solidarity with American women and standing up for the rights of women in their own countries. “The recent elections in the United States have shown how real the threat is to our collective rights and liberties,” says the Facebook event page for the Women’s March on Nairobi. The page for the London event, which 23,000 Facebook users have said they will attend, says, “we will march...for the protection of our fundamental rights and for the safeguarding of freedoms threatened by recent political events.” Led by Mrs. Richard Coke Burleson (center, on horseback), suffragists marched on Pennsylvania Avenue on March 3, 1913, the day before President Woodrow Wilson’s inauguration. Library of Congress A previous women’s movement found success in an inauguration-related demonstration. The Women’s Suffrage Parade of 1913, in which an estimated 5,000 to 8,000 suffragists marched on Pennsylvania Avenue the day before President Woodrow Wilson’s inauguration, drew attention to the women’s suffrage movement as thousands of spectators in Washington for the inauguration witnessed the procession. Historians consider the parade a major milestone for the movement to win women the right to vote. It is set to be depicted on the back of a redesigned $10 bill in 2020. ||||| Angela Davis, UCLA professor and political activist, at a news conference in Los Angeles in 1969. (David F. Smith/AP) The Women’s March on Washington just released a big list of speakers for its rally, which includes everyone from civil rights era icon Angela Davis to liberal activist Michael Moore and D.C. Mayor Muriel Bowser. The rally begins at 10 a.m. Saturday at Independence Avenue and Third Street SW, and people will start marching west around 1:15 p.m. [Here’s what you need to know about attending inauguration and other events that weekend.] Here’s the full list of the speakers the march organizers released Wednesday afternoon: Cecile Richards Erika Andiola Ilyasah Shabazz J. Bob Alotta Janet Mock LaDonna Harris Maryum Ali Melanie Campbell Rabbi Sharon Brous Rhea Suh, Sister Simone Campbell Sophie Cruz Zahra Billoo America Ferrera Angela Davis Gloria Steinem Ashley Judd Scarlett Johansson Melissa Harris-Perry Michael Moore Amanda Nguyen Randi Weingarten Van Jones George Gresham Mothers of the Movement (Sybrina Fulton, Lucy McBath, Maria Hamilton, Gwen Carr) Hina Naveed Judith LaBlanc Kristin Rowe-Finkbeiner Aida Hurtado Melissa Mays Raquel Willis Rosyln Brock Sister Ieasha Prime Mayor Muriel Bowser Ai-jen Poo Wendy Carrillo Cynthia Hale March co-chairs Bob Bland, Carmen Perez, Linda Sarsour and Tamika Mallory. March organizers also announced performances by the following artists: ||||| (CNN) The Women's March extended beyond the United States, as similar protests cropped up around the world over women's rights and other issues the marchers fear could be under threat from Donald Trump's presidency. Although the focus of the day was the Women's March on Washington , many people attended the hundreds of "sister marches" that occurred around the US and the globe. Women and men in cities including Sydney, Berlin, London, Paris, Nairobi and Cape Town, marched in solidarity with the marchers in Washington and in opposition to the values they think Trump represents. Near and far A crowd of people gathered near the US Embassy in Mexico City on Saturday, shutting down the street and holding signs. Protesters in Mexico City demonstrated outside the US Embassy. "Say it loud, say it clear, migrants are welcome here," they shouted. Not all of the protesters were Mexican. Some Americans were there, too, in a show of solidarity. One man told CNN, "It's a little strange to have this kind of shame and lack of pride for what direction the United States is heading in." A "pro-peace, pro-environment" march also took place on Antarctica. Twitter user Linda Zunas posted pictures of people there taking part in the global event. #womensMarchAntarctica (still photo from our march video in Paradise Bay this morning) video to come Thursday pic.twitter.com/MfebPcDJsy — linda zunas (@lindazunas) January 21, 2017 "Love rules in Antarctica," read one poster, held by a man bundled up on the snowy landscape in Paradise Bay. "We are allies, not bystanders," read another sign, held by a woman posing in front of a glacier. 'Girl Power vs. Trump Tower' Australia was the scene of the day's first major international march, with thousands joining an anti-Trump demonstration in downtown Sydney. Marchers rally in Sydney in support of women's rights. Organizers said as many as 5,000 people attended the protest at Martin Place; police estimated the number was closer to 3,000. Chants from the crowd included "Women united will never be defeated" and "When women's rights are under attack, what do we do, stand up, fight back." Some carried banners with messages such as "Girl Power vs. Trump Tower" and "Dump the Trump." A small group holds a pro-Trump rally Saturday in Australia's largest city. A separate group of about 30 Trump supporters held a rally in Sydney. The police restrained some of them, blocking them from entering the same area as the Trump protest group. Protest organizers in New Zealand's capital, Wellington, said about 700 people turned out there for a women's march. Marches were also held in Auckland, Christchurch and Dunedin. Protesters also joined together to march in Nairobi, Kenya -- the African nation that was the native country of former President Barack Obama's father. Marchers in Cape Town, South Africa, carried banners with slogans such as "Climate change is a women's issue" and "So over mediocre men running things." Other African nations staging women's marches included Ghana and Malawi. Europe marches Big crowds turned out Saturday in dozens of cities across Europe, with marchers including men, women and children. Protesters who gathered outside one of Rome's most famous structures, the Pantheon, on Saturday morning carried signs reading "Yes we must" and "Women's rights are human rights." Demonstrators also took to the streets of Berlin, Frankfurt, Munich and other cities in Germany. This Pussy Bites Back ! #solidarity #womensmarch #berlin A photo posted by Katy Ray (@raykaty) on Jan 21, 2017 at 2:56am PST Katy Rea, who was at the march in Berlin, told CNN: "There are around 1,000 people. Lots of families, children. Very friendly atmosphere. Some police are present, but it's tame and relaxed." Marches also took place in cities up and down the United Kingdom, from London to Cardiff, Liverpool, Manchester, Belfast and Edinburgh. In London, large crowds joined a two-mile march starting outside the US Embassy and ending with a rally in the city's historic Trafalgar Square. Lots of anti-Trump placards at Womens March in London today but some protesting #Brexit, Workers rights, nuclear weapons, LGBT rights & more pic.twitter.com/LF3bsqcqAh — Nina dos Santos (@NdosSantosCNN) January 21, 2017 Marcher Victoria Dawson told CNN the atmosphere was "positive, inclusive, electric." Women's rights weren't the only issue on the agenda, with placards also bearing slogans to do with Brexit, nuclear weapons, workers' rights and lesbian, gay, bisexual and transgender rights. Speakers at Trafalgar Square told the crowds at least 100,000 people had turned out. London's Metropolitan Police do not provide crowd estimates, but aerial footage showed large numbers of people gathered in the square. London Mayor Sadiq Khan -- who before the US presidential election told CNN that Trump's views of Islam were "ignorant" -- posted a tweet encouraging Londoners to join the march and "show how much we value the rights every woman should have." In Paris, demonstrators gathered near the iconic Eiffel Tower before marching through the streets waving flags and banners. "A woman's place is in the house -- the White House," read one pink poster at the Paris event. Other French cities including Marseille, Toulouse and Bordeaux were also holding events. Protesters march in Marseille, France, in solidarity with women in Washington and around the world. Protesters in Barcelona, Spain, chanted "We will not be silent" and "My body, my choice" as they marched. On Friday night, a crowd of predominantly female protesters gathered in Brussels, Belgium , to denounce sexism and protest against Trump. Marches also took place in Greece, Kosovo, the Czech Republic and Georgia. ||||| Demonstrators take part in the Women's March on London, following the Inauguration of U.S. President Donald Trump, in London, Saturday Jan. 21, 2016. (AP Photo/Tim Ireland) (Associated Press) Demonstrators take part in the Women's March on London, following the Inauguration of U.S. President Donald Trump, in London, Saturday Jan. 21, 2016. (AP Photo/Tim Ireland) (Associated Press) WASHINGTON (AP) — Wearing pink, pointy-eared "pussyhats" to mock the new president, throngs of women descended on the nation's capital and other cities around the globe Saturday for marches and demonstrations aimed at showing Donald Trump they won't be silent over the next four years. They carried signs with messages such as "Women won't back down" and "Less fear more love" and decried Trump's stand on such issues as abortion, diversity and climate change. There were early signs that crowds in Washington could top those that gathered for Trump's inauguration on Friday. City officials said organizers of the Women's March on Washington had more than doubled their turnout estimate to 500,000 as crowds began swelling and subways into the city became clogged with participants. It wasn't just a Washington phenomenon and it wasn't just women: More than 600 "sister marches" were planned across the country and around the world, and plenty of men were part of the tableau. In Washington, Rena Wilson, of Charlotte, North Carolina, said she hopes the women can send Trump a message that they're "not going anywhere." Joy Rodriguez, of Miami, arrived with her husband, William, and their two daughters, ages 12 and 10. "I want to make sure their rights are not infringed on in these years coming up," Joy Rodriguez said. March organizers said women are "hurting and scared" as the new president takes office and want a greater voice for women in political life. "In the spirit of democracy and honoring the champions of human rights, dignity and justice who have come before us, we join in diversity to show our presence in numbers too great to ignore," their mission statement says. Retired teacher Linda Lastella, 69, who came from Metuchen, New Jersey, said she had never marched before but felt the need to speak out when "many nations are experiencing this same kind of pullback and hateful, hateful attitudes." "It just seemed like we needed to make a very firm stand of where we were," she said. Rose Wurm, 64, a retired medical secretary from Bedford, Pennsylvania, boarded a Washington-bound bus in Hagerstown, Maryland, at 7 a.m. carrying two signs: one asking Trump to stop tweeting, and one asking him to fix, not trash, the Obamacare health law. "There are parts of it that do need change. It's something new, something unique that's not going to be perfect right out of the gate," she said. Many arrived wearing hand-knit "pussyhats" — a message of female empowerment aimed squarely at Trump's crude boast about grabbing women's genitals. The march attracted significant support from celebrities. America Ferrara led the artists' contingent, and those scheduled to speak in Washington included Scarlett Johansson, Ashley Judd, Melissa Harris-Perry and Michael Moore. The promised performance lineup included Janelle Monae, Maxwell, Samantha Ronson, the Indigo Girls and Mary Chapin Carpenter. Cher, Katy Perry and Julianne Moore all were expected to attend. Women and other groups were demonstrating across the nation and as far abroad as Myanmar and Australia. In Prague, hundreds gathered in Wenceslas Square in freezing weather, waving portraits of Trump and Russia's Vladimir Putin and holding banners that read "This is just the beginning," ''Kindness" and "Love." "We are worried about the way some politicians talk, especially during the American elections," said organizer Johanna Nejedlova. In Copenhagen, march organizer Lesley-Ann Brown said: "Nationalist, racist and misogynistic trends are growing worldwide and threaten the most marginalized groups in our societies including women, people of color, immigrants, Muslims, the LGBT community and people with disabilities." In Sydney, thousands of Australians marched in solidarity in Hyde Park. One organizer said hatred, bigotry and racism are not only America's problems. The idea for the women's march took off after a number of women posted on social media in the hours after Trump's election about the need to mobilize. Hundreds of groups quickly joined the cause, pushing a wide range of causes, including abortion rights, gun control, climate change and immigrant rights. While the march organizers' "mission and vision" statement never mentions Trump and stresses broad themes, including the message that "women's rights are human rights," the unifying factor among those turning out appeared to be a loathing for the new president and dismay that so much of the country voted for him. Friday's unrest during the inauguration led police to use pepper spray and stun grenades to prevent the chaos from spilling into Trump's formal procession and the evening balls. About a mile from the National Mall, police gave chase to a group of about 100 protesters who smashed the windows of downtown businesses, including a Starbucks, a Bank of America and a McDonald's, as they denounced capitalism and Trump. "They began to destroy property, throw objects at people, through windows. A large percentage of this small group was armed with crowbars and hammers," said the city's interim police chief, Peter Newsham. Six officers suffered minor injuries, he said. ___ Associated Press Writers Alanna Durkin Richer, Brian Witte and David Dishneau in Washington, Karel Janicek in Prague contributed to this report. ||||| Media playback is unsupported on your device Media caption Washington is leading anti-Trump protests around the world Millions of protesters have taken to the streets of cities in the US and around the globe to rally against the new US President Donald Trump. Larger numbers of demonstrators than expected turned out for more than 600 rallies worldwide. The aim was principally to highlight women's rights, which activists believe to be under threat from the new administration. Meanwhile, Mr Trump used his first full day in office to visit the CIA's HQ. He said he was "1,000%" behind the spy agency's employees and also accused the media of being dishonest in its reporting of the size of the crowd at his inauguration. Mr Trump did not refer to Saturday's protests. 'We are the majority' The biggest US rally was in the capital Washington, which city officials estimated to be more than 500,000-strong. This far exceeded the 200,000 that had originally been expected by organisers of the Women's March on Washington. By most estimates, it also surpassed the crowd at Friday's presidential inauguration. The protesters in the nation's capital heard speeches from Scarlett Johansson, Ugly Betty star America Ferrera, Ashley Judd, Gloria Steinem and Michael Moore among others. A planned march to the White House proved impossible as the entire route was filled with demonstrators. Interim DC Police Chief Peter Newsham told Associated Press: "The crowd stretches so far that there's no room left to march." During his speech, Michael Moore ripped up a copy of the Washington Post, saying: "The headline was 'Trump takes power'. I don't think so. Here's the power. Here's the majority of America right here. We are the majority." The singer Madonna also made an appearance, swearing several times in a speech carried live by major US TV networks. "Yes, I am outraged. Yes, I have thought an awful lot about blowing up the White House," she said. America Ferrera told the crowd: "We march today for the moral core of this nation, against which our new president is waging a war." Huge crowds were reported at other US protests. Media playback is unsupported on your device Media caption Women from Kenya, India and Germany explain why they took part in the march So many turned out in Chicago - some 150,000 - that a planned march had to be called off and the event declared a rally. Streets were also overflowing in Los Angeles. Huge crowds were also reported in New York, Seattle, Boston and Miami, some of the venues for about 300 nationwide protests. Many women wore knitted pink "pussy hats" - a reference to a recording that emerged during the election campaign in which Mr Trump talked about groping women. Image copyright Reuters Image caption Washington's transportation system creaked under the strain of travellers Image copyright Reuters Image caption Former secretary of state John Kerry joins the Washington rally Image copyright Reuters Image caption A young Trump supporter gets her message across in Washington Image copyright PA Image caption London joins in the protests that began in Australasia and have swept west to the US 'These are global problems' Organisers of a London rally said between 80,000 and 100,000 people had taken part there. Belfast, Cardiff, Edinburgh, Leeds, Liverpool, Manchester and Bristol were among the other UK cities holding protests. Anti-Trump marches took place earlier in Australia, New Zealand and in several Asian cities. Image copyright Getty Images Image caption Crowds turned out in many European cities, including at the Brandenburg Gate in Berlin Several thousand women and men joined a rally in central Sydney, with a similar number in Melbourne. Women's March Sydney co-founder Mindy Freiband told the crowd: "Hatred, hate speech, bigotry, discrimination, prejudicial policies - these are not American problems, these are global problems." Barcelona, Rome, Amsterdam, Geneva, Budapest, Prague and Berlin were among the European cities that took part. In Paris, protester Francoise Seme Wallon said Mr Trump was "a nasty guy and he's dangerous for the whole world". Website overhaul Mr Trump's first full day in office began with an inter-faith service at Washington National Cathedral. He then visited the CIA's HQ in Langley, Virginia. In a speech there, he told about 400 employees: "There is nobody who feels stronger about the intelligence community and the CIA than me." During the election campaign, Mr Trump had sharply criticised the intelligence agencies over their stance on alleged Russian involvement. Image copyright AFP Image caption Donald Trump attends a multi-faith service in Washington Mr Trump also talked up his yet-to-be-confirmed nominee for CIA chief, Mike Pompeo. "You will be getting a total gem," he told the employees. In one of his first steps, Mr Trump ordered government agencies to ease the "economic burden" of the health law known as Obamacare. His team also quickly overhauled the White House website. The revamp replaces Barack Obama's policies with Mr Trump's new agenda. Media playback is unsupported on your device Media caption 'This American carnage stops right here,' Donald Trump said at his inauguration Media playback is unsupported on your device Media caption Supporters of President Trump give their views on his inauguration speech The new administration lists only six issues on the website - energy, foreign policy, jobs and growth, military, law enforcement and trade deals. Critics complained that it made no mention of civil rights, healthcare, climate change or LGBT rights. ||||| Kate Russell's cardboard placard read "What would Carrie Fisher do." The 26-year-old Londoner said the Star Wars star had been a hero, adding: “She represents what a strong woman is and should be." Other light-hearted placard message included “Free Melania,” “We Shall Overcomb” and “Girls Just Wanna Have Fun… damental Rights.” Topless protester Matilda Bennett, 21, drew cheers from marchers-by on Piccadilly as she and four shirtless friends shouted "free the nipple," waving their hands in the air. The women had journeyed to the capital from Bristol for the march. After allowing fellow demonstrators to march by and cheer them they joined the route. Matilda said:"We're freeing the nipple because women's bodies aren't a sexual object. "We're here because we want fundamental rights and no-one should be able to say what Trump has said and become President. Protesters were seen holding hand-made signs and placards with slogans such as "dump Trump", "reject hate, reclaim politics" and "no to racism, no to Trump". One woman dressed as the Statue of Liberty brandished a torch bearing an image of the new president's face and held a sign which said: "The statue of taking liberties." ||||| Donald Trump is so unpopular that there are even women marching against him in Antarctica. The day after the inauguration of a president who bragged about grabbing women by their genitals, thousands will be marching in Washington and in more than 60 countries around the world, to “stand up for human rights, women’s rights and against hate.” And in Paradise Bay, a remote corner of Antarctica whose population normally comprises gentoo penguins, Weddell seals and the occasional humpback whale, a group of at least 30 women and supportive men will be joining the Women’s March movement. They will march with banners proclaiming 'Penguins for Peace', 'Seals for Science', "Cormorants for Climate', and 'Love from seven continents'. Join Independent Minds For exclusive articles, events and an advertising-free read for just £5.99 €6.99 $9.99 a month Get the best of The Independent With an Independent Minds subscription for just £5.99 €6.99 $9.99 a month Get the best of The Independent Without the ads – for just £5.99 €6.99 $9.99 a month The Antarctic march is being organised by Linda Zunas, 42, a data analytics and market research professional from Oakland, California, who told The Independent she had been motivated by Donald Trump’s apparent intention to reverse the environmental policies of Barack Obama. “I set it up because I wanted to participate in the Women’s March,” she said. “I spent a month after the election mourning the impending damage to the earth that will be done. I felt like I needed to do something to be part of the global movement.” Describing the protesters as "an international group of eco-minded visitors" to Antarctica, Ms Zunas said: "They range in age from 24 to 87, male and female, from over six countries." Because of the environmental sensitivity of the area, she explained, "The actual marching will be short as we have to limit our footprint on land." The shortness of the march, however, would be compensated for by the uniqueness of the spectators. "We hope to have gentoo penguins in the background of our march," said Ms Zunas. Shape Created with Sketch. In pictures: Protests, pomp and Donald Trump Show all 30 left Created with Sketch. right Created with Sketch. Shape Created with Sketch. In pictures: Protests, pomp and Donald Trump 1/30 President-elect Donald Trump acknowledges guests as he arrives on the platform at the US Capitol in Washington DC Getty Images 2/30 Donald Trump is sworn in as the 45th president of the United States by Chief Justice John Roberts as Melania Trump looks on during the 58th Presidential Inauguration at the U.S. Capitol in Washington AP 3/30 President Donald Trump shakes hands with Justice John Roberts after taking the oath at inauguration ceremonies swearing in Trump as the 45th president of the United States Reuters 4/30 President Donald Trump raises his fists after his inauguration on the West Front of the U.S. Capitol Getty 5/30 U.S. President-elect Donald Trump greets outgoing President Barack Obama before Trump is inaugurated during ceremonies on the Capitol in Washington Reuters 6/30 resident-elect Donald Trump arrives on the platform of the US Capitol in Washington DC Getty Images 7/30 Attendees partake in the inauguration ceremonies to swear in Donald Trump as the 45th president of the United States at the U.S. Capitol in Washington DC Reuters 8/30 US President Donald Trump delivers his inaugural address during ceremonies at the US Capitol in Washington DC Getty 9/30 U.S. President Donald Trump waves with wife Melania during the Inaugural Parade in Washington DC Reuters 10/30 Protesters registered their rage against the new president Friday in a chaotic confrontation with police who used pepper spray and stun grenades in a melee just blocks from Donald Trump's inaugural parade route. Scores were arrested for trashing property and attacking officers AP 11/30 Demonstrators protest against US President Donald Trump in Washington DC Getty Images 12/30 A woman holds a sign before the start of the Presidential Inauguration of Donald Trump at Freedom Plaza in Washington DC Getty Images 13/30 Anti-Trump protesters prepare banners for a protest against the inauguration of US President-elect Donald Trump, in Berlin REUTERS 14/30 Demonstrators shout slogans against US President-elect Donald Trump in Washington DC Getty Images 15/30 Demonstrators march, block foot traffic and clash with U.S. Capitol Police at the entry checkpoints for the Inauguration of Donald Trump Alamy Live News 16/30 Demonstrators display a banner as people arrive for US President-elect Donald Trump's inauguration in Washington DC Getty Images 17/30 A man displays a placard as people lineup to get into the National Mall for the inauguration of US President-elect Donald Trump in Washington DC Getty Images 18/30 Protesters demonstrating against U.S. President Donald Trump raise their hands as they are surrounded by police on the sidelines of the inauguration in Washington DC Reuters 19/30 A demonstrator wearing a mask depicting Donald Trump protests outside the US Embassy in London Getty Images 20/30 Demonstrators hold placards as they protest outside the US Embassy in London Getty Images 21/30 Former US President George W. Bush and First Lady Laura Bush arrive for the Presidential Inauguration at the US Capitol Rex 22/30 Michelle Obama and Dr. Jill Biden share an umbrella as President Donald Trump delivers his inaugural address at the inauguration in Washington DC Rex 23/30 Former Democratic presidential nominee Hillary Clinton and former President Bill Clinton arrive on the West Front of the U.S. Capitol in Washington Reuters 24/30 U.S. Vice President Mike Pence takes the oath of office on the West Front of the U.S. Capitol in Washington, DC Getty Images 25/30 Advisors to President-elect Donald Trump, Kellyanne Conway and Steve Bannon depart from services at St. John's Church during the Presidential Inauguration in Washington Reuters 26/30 Protesters demonstrating against U.S. President Donald Trump take cover as they are hit by pepper spray by police on the sidelines of the inauguration in Washington DC Reuters 27/30 An activist demonstrating against U.S. President Donald Trump is helped after being hit by pepper spray on the sidelines of the inauguration in Washington DC Reuters 28/30 A police officer tries to tackle a protester demonstrating against U.S. President Donald Trump Reuters/Adrees Latif 29/30 Police arrest and detain a protester in the street in Washington DC Rex 30/30 A police officer falls to the ground as another shoots pepper spray at protesters demonstrating against U.S. President Donald Trump on the sidelines of the inauguration in Washington DC Reuters 1/30 President-elect Donald Trump acknowledges guests as he arrives on the platform at the US Capitol in Washington DC Getty Images 2/30 Donald Trump is sworn in as the 45th president of the United States by Chief Justice John Roberts as Melania Trump looks on during the 58th Presidential Inauguration at the U.S. Capitol in Washington AP 3/30 President Donald Trump shakes hands with Justice John Roberts after taking the oath at inauguration ceremonies swearing in Trump as the 45th president of the United States Reuters 4/30 President Donald Trump raises his fists after his inauguration on the West Front of the U.S. Capitol Getty 5/30 U.S. President-elect Donald Trump greets outgoing President Barack Obama before Trump is inaugurated during ceremonies on the Capitol in Washington Reuters 6/30 resident-elect Donald Trump arrives on the platform of the US Capitol in Washington DC Getty Images 7/30 Attendees partake in the inauguration ceremonies to swear in Donald Trump as the 45th president of the United States at the U.S. Capitol in Washington DC Reuters 8/30 US President Donald Trump delivers his inaugural address during ceremonies at the US Capitol in Washington DC Getty 9/30 U.S. President Donald Trump waves with wife Melania during the Inaugural Parade in Washington DC Reuters 10/30 Protesters registered their rage against the new president Friday in a chaotic confrontation with police who used pepper spray and stun grenades in a melee just blocks from Donald Trump's inaugural parade route. Scores were arrested for trashing property and attacking officers AP 11/30 Demonstrators protest against US President Donald Trump in Washington DC Getty Images 12/30 A woman holds a sign before the start of the Presidential Inauguration of Donald Trump at Freedom Plaza in Washington DC Getty Images 13/30 Anti-Trump protesters prepare banners for a protest against the inauguration of US President-elect Donald Trump, in Berlin REUTERS 14/30 Demonstrators shout slogans against US President-elect Donald Trump in Washington DC Getty Images 15/30 Demonstrators march, block foot traffic and clash with U.S. Capitol Police at the entry checkpoints for the Inauguration of Donald Trump Alamy Live News 16/30 Demonstrators display a banner as people arrive for US President-elect Donald Trump's inauguration in Washington DC Getty Images 17/30 A man displays a placard as people lineup to get into the National Mall for the inauguration of US President-elect Donald Trump in Washington DC Getty Images 18/30 Protesters demonstrating against U.S. President Donald Trump raise their hands as they are surrounded by police on the sidelines of the inauguration in Washington DC Reuters 19/30 A demonstrator wearing a mask depicting Donald Trump protests outside the US Embassy in London Getty Images 20/30 Demonstrators hold placards as they protest outside the US Embassy in London Getty Images 21/30 Former US President George W. Bush and First Lady Laura Bush arrive for the Presidential Inauguration at the US Capitol Rex 22/30 Michelle Obama and Dr. Jill Biden share an umbrella as President Donald Trump delivers his inaugural address at the inauguration in Washington DC Rex 23/30 Former Democratic presidential nominee Hillary Clinton and former President Bill Clinton arrive on the West Front of the U.S. Capitol in Washington Reuters 24/30 U.S. Vice President Mike Pence takes the oath of office on the West Front of the U.S. Capitol in Washington, DC Getty Images 25/30 Advisors to President-elect Donald Trump, Kellyanne Conway and Steve Bannon depart from services at St. John's Church during the Presidential Inauguration in Washington Reuters 26/30 Protesters demonstrating against U.S. President Donald Trump take cover as they are hit by pepper spray by police on the sidelines of the inauguration in Washington DC Reuters 27/30 An activist demonstrating against U.S. President Donald Trump is helped after being hit by pepper spray on the sidelines of the inauguration in Washington DC Reuters 28/30 A police officer tries to tackle a protester demonstrating against U.S. President Donald Trump Reuters/Adrees Latif 29/30 Police arrest and detain a protester in the street in Washington DC Rex 30/30 A police officer falls to the ground as another shoots pepper spray at protesters demonstrating against U.S. President Donald Trump on the sidelines of the inauguration in Washington DC Reuters “We are not discussing politics at all,” she added, “But you may infer our opinions based on our choice of day and topic.” Ms Zunas' own twitter feed also suggests she is not a fan of Trump. ||||| Massive crowds packed into D.C. Metro stations Saturday night as thousands of participants in the Women's March on Washington headed toward the White House and dispersed from the National Mall. Metro urged people to consider waiting before riding to allow the crowds to ease. Fairfax County police also advised riders to follow police direction. Metrorail has seen more riders on Saturday than it did for former President Barack Obama's second inauguration in 2013, reports News4's Mark Segraves. Stations were packed and more than a dozen parking facilities were full before noon Saturday as hundreds of thousands of participants headed to downtown D.C. for the Women's March on Washington. Trains briefly bypassed the L'Enfant Plaza station due to crowding. They began serving the station again shortly before 1:10 p.m. Officials recommended riders use other stations to get to the march, such as Gallery Place or Metro Center. Posts on social media Saturday showed long lines of people waiting for access to Metro stations. Multiple people shared images and videos of the scene outside the Shady Grove, where Philip Lewis of the Huffington Post reported earlier Saturday that he was hearing riders were waiting an hour to board trains. March organizers said they've increased turnout estimates to 500,000 participants, said D.C. Deputy Mayor for Public Safety and Justice Kevin Donahue. "Be patient & kind!" he posted on Twitter. Metro 'Overwhelmed' by Women's March Attendees Many Metro stations were flooded with travelers trying to get into D.C. for the Women's March. News4's Adam Tuss reports. (Published Saturday, Jan. 21, 2017) It's been a busy day for Metro. Officials said 275,000 rides had been taken as of 11 a.m. "For comparison, that's more than 8 [times] a normal Sat[urday] & even busier than most weekdays," Metro posted on Twitter. As of the same time on Friday, Inauguration Day, 193,000 trips had been taken. Metro station personnel were making adjustments to try to accommodate the large crowds. At the Ballston and Stadium-Armory stations, would-be Metro riders were stopped before the escalators because too many people were already on the platform Saturday morning, reported News4's Adam Tuss, who said it "cannot be overstated how heavy the crowds are." TUSS GREENBELT METRO FOR DIGITAL Metro stations are packed and more than a dozen parking facilities are already full Saturday morning as tens of thousands of participants headed to downtown D.C. for the Women's March on Washington. News4's Adam Tuss reports. (Published Saturday, Jan. 21, 2017) Melissa Zieve of Baltimore said she had to let the first two trains at Tenleytown pass by because they were too full. She was able to board a third train and rode to Union Station. "I've never been on a subway in any city packed quite like that," Zieve said, but added that everyone was respectful and no one was pushing. Parking facilities all stations in Fairfax County and several others are full, according to Metro officials and Fairfax County Police. Those are: Orange, Silver, or Orange/Silver Lines: East Falls Church West Falls Church Dunn Loring Vienna McLean Tysons Corner Greensboro Spring Hill Wiehle-Reston East New Carrollton, lot 2 (lots 1 & 3 have limited capacity) Green Line: Greenbelt Red Line: Forest Glen Fort Totten Glenmont Rhode Island Avenue Rockville Shady Grove, west/south (north has limited capacity) As of 10 a.m., Metro was recommending the following stations with available parking: Branch Avenue, Grosvenor, Prince George's Plaza, Southern Avenue, Suitland, Twinbrook and White Flint. Outside the filled Greenbelt and New Carrollton lots, drivers have been illegally parking on the shoulders of the ramps leading to the Metro stations, according to the Maryland State Highway Administration. Metro had initially planned to keep the Federal Triangle station closed throughout Saturday, but reversed their decision and reopened the station about 9:20 a.m. Riders may also consider exiting at the Federal Center SW or Capitol South stations. Inauguration Weekend in Photos Margaret Warpeha from Minnesota flew in Friday night and described her Metro experience as wonderful Saturday morning. She boarded at Silver Spring about 9 a.m. and said it wasn't too crowded. Warpeha said she wanted to come to D.C. because she was "quite upset" about the election and didn't want to remain silent. Outside Union Station, Lisa Legrand of Minneapolis said she flew into Philadelphia, drove to the Tenleytown station and rode the Metro downtown. "It was really crowded" but had a very positive energy, Legrand said.

– Donald Trump was the target of women's marches worldwide on the first full day of his presidency. As the pre-march rally kicked off in Washington, DC, where numbers might exceed those that turned out of Trump's inauguration, marches were already underway or over in cities including London, Prague, Sydney, and Bangkok. The BBC reports that marches are planned in more than 300 cities in the US and hundreds more worldwide, with marchers highlighting multiple issues, especially the principle that "Women's Rights are Human Rights." A roundup of coverage: March organizers say they want to send a "bold message" to the new government and the world, and they hope to be joined by people of " all genders, ages, races, cultures, political affiliations, and backgrounds ." "In the spirit of democracy and honoring the champions of human rights, dignity and justice who have come before us, we join in diversity to show our presence in numbers too great to ignore," they said in a statement, per the AP. The Washington Post has a full list of speakers and performers at the Washington, DC event. NPR reports that in DC where a rally started at 10am and march will begin at 1:15pm, many women are wearing pink knitted caps nicknamed "pussy hats" in reference to one of Trump's infamous remarks. The New York Times has a guide to marches in the US around the world, and notes that this is expected to be the largest inauguration-related demonstration in history. NBC Washington has travel and parking tips for those in DC, where parking facilities have filled up fast and public transport is crowded. Organizers have increased their estimate of participants to at least 500,000. CNN reports that in one of the first marches to take place, around 5,000 people marched in Sydney, Australia with signs like "Girl Power" vs "Trump Power." A pro-Trump counter-demonstration attracted around 30 people. Some 10,000 people were expected to join the London march, but organizers said at least 80,000 turned up, the Telegraph reports. The Independent reports that a group of around 30 female and male visitors have organized a Women's March in Antarctica, with banners including "Penguins for Peace," and "Love From Seven Continents." To respect wildlife habitats, the amount of actual marching will be kept to a minimum.

<s>[INST]Women's March Floods Washington, Sparking Rallies Worldwide Hide caption Protesters march in Washington, D.C., with the Capitol in the background. Previous Next Joshua Lott/AFP/Getty Images Hide caption Protesters crowd the National Mall during the Women's March on Washington. Previous Next Zach Gibson/AFP/Getty Images Hide caption Protesters march down a D.C. street during the Women's March on Washington. Previous Next Jessica Kourkounis/Getty Images Hide caption Protesters attend the Women's March on Washington in D.C. Previous Next Mario Tama/Getty Images Hide caption Protesters take a selfie with the police as a backdrop outside the U.S. Capitol during the Women's March on Washington. Previous Next Jessica Kourkounis/Getty Images Hide caption Women with bright pink hats and signs gather early on Saturday in Washington, D.C., for the Women's March on Washington. Previous Next Jose Luis Magana/AP Hide caption Demonstrators protest on the National Mall for the Women's March on Washington. Previous Next Andrew Caballero-Reynolds/AFP/Getty Images Hide caption Protesters arrive at the Capitol South Metro station for the Women's March on Washington in Washington, D.C. Previous Next Jessica Kourkounis/Getty Images Hide caption Protesters attend the Women's March on Washington in D.C. Previous Next Jessica Kourkounis/Getty Images Hide caption Marchers gather outside the National Museum of the American Indian, bearing signs protesting President Trump. Previous Next Sarah McCammon/NPR Hide caption Protesters display their signs in Washington, D.C., during the Womens March. Previous Next Joshua Lott/AFP/Getty Images 1 of 11 i View slideshow Updated at 4 p.m. ET The National Mall has flooded with pink, as demonstrators descend on the nation's capital Saturday for the Women's March on Washington. Just one day after President Trump's inauguration, marchers from across the country have gathered in the city to protest his agenda and support for women's rights. The event opened with a rally, to be followed by the march proper — which had a path laid out from a starting position near the U.S. Capitol to its endpoint near the Washington Monument. The city's metro system reported 275,000 rides as of 11 a.m. According to metro officials that's eight times more than a normal Saturday. Reuters adds that the number is also "82,000 more than the 193,000 rides reported at the same point on Friday," the day of Trump's inauguration. toggle caption Becky Harlan/NPR In fact, the number of marchers swelled to the point of prompting reports there would be no space for a formal procession — a claim rebutted by organizers Saturday afternoon in a statement. "We are marching," reads the statement. "We are marching straight ahead toward the Washington Monument to the ellipse of the White House." The event grew from humble origins — a simple Facebook invitation after Election Day — to the much more massive demonstration seen Saturday. By the time marchers hit the streets, the Women's March on Washington developed a broad platform of progressive political positions, a slate of celebrity performers and a series of sister marches planned across the world — on all seven continents. toggle caption Meg Kelly/NPR For protester Amy Jackson, though, the matter was simple: She just wanted to "make her voice heard," she tells NPR's Marisa Penaloza. Jackson, who traveled to D.C. from Chocowinity, N.C., to be part of the march, said, "It was very important to be here today." The Scene On The Ground Among the crowd that gathered for the rally outside the National Museum of the American Indian, NPR's Sarah McCammon reported signs supporting a wide array of causes — from women's rights and LGBTQ rights, to Black Lives Matter and excoriations of xenophobia. One thing seemed to be almost universal, though: The pink knitted caps known as "pussyhats" among the marchers, in protest of Trump's past comments about women. toggle caption Becky Harlan/NPR Popular as they may have been, the pussyhats were not the only costume worn by marchers. Others wore their causes on their sleeves, dressing in attire to call attention to issues like Native rights and environmental fears. In video Sarah recorded a block or two from the main rally, it appears there were marchers in a menagerie of outfits. Meanwhile, at a nearby metro station, NPR's Pam Fessler reported the mood among the demonstrators has been more festive than protests Friday. Most of the demonstrators are women, Pam says, but some men have joined the march, as well — including one man carrying a sign reading: "This is what a feminist looks like." From the main rally stage, musicians and speakers addressed the crowd in an event that lasted some five hours — more than two hours longer than anticipated. The reason for that overflow was partly its smattering of surprise guests. Beyond the planned performances and speeches from figures like Janelle Monáe and Gloria Steinem, others including Madonna and Alicia Keys took the stage. "It was woman that gave you Dr Martin Luther King Jr. It was woman who gave you Malcolm X. And according to the bible, it was a woman who gave you Jesus," Monáe told the crowd, according to The Guardian. The Road To The March What began simply as opposition to Trump has developed a wide-ranging list of demands, which organizers published as a platform prior to the march. toggle caption Becky Harlan/NPR But above all, organizers say, is the principle that "Women's Rights are Human Rights and Human Rights are Women's Rights." That statement is pulled directly from a speech Hillary Clinton delivered more than two decades ago in Beijing. Clinton tweeted her support for the march Saturday, expressing thanks "for standing, speaking & marching for our values." Arriving at that platform was not always a smooth process, though. NPR's Hansi Lo Wang reports there has been disagreement between organizers about how to treat issues of race. "This march was initially put together by white women, and a lot of women of color felt they weren't part of the conversation," Carmen Perez, one of the march's national organizers, told NPR's Hansi Lo Wang. "We can't continue to work in isolation. We can't continue to be one-dimensional. We have to make sure that we look up, that we begin to really coordinate our efforts." toggle caption Sait Serkan Gurbuz/AP Ultimately, more than 200 organizations — ranging from Planned Parenthood and the NAACP, to Amnesty International and the AFL-CIO — partnered with the Women's March on Washington. For Darcy Sawatzki, a demonstrator attending the march with her daughter, Delia, what matters most is showing up. "I think showing up and paying attention is sort of one of the bare minimums of citizenship," Sawatzki told NPR's Brakkton Booker. It's not her first march; she has also participated in Black Lives Matter protests. Enlarge this image toggle caption Meg Kelly/NPR Meg Kelly/NPR She said it's not unease with the new president that inspired her to march. "I'm not here out of anger or fear, I'm out here for determination, for participation and hope that together we can make a difference." ||||| Hundreds of demonstrations around the world are being planned for Jan. 21 in conjunction with the Women’s March on Washington, which is expected to be the largest inauguration-related demonstration in United States history. The March Route in Washington The New York Times | Source: Women’s March Organizers have estimated that 200,000 people could participate in the Washington rally, which will begin at 10 a.m. near the southeast corner of the National Mall. The march is scheduled to start at 1:15 p.m. and will proceed toward the White House. Participants are traveling to Washington from all over the country, with many arriving by bus. Many more are expected to participate in hundreds of sister marches throughout the United States. Women’s Marches Around the Nation WASH. Me. Mont. N.D. N.H. Minn. Vt. Ore. N.Y. Mass. Mich. Wis. S.D. Wyo. Idaho R.I. Conn. Iowa Pa. Neb. N.J. Ill. Nev. Ind. Ohio DEL. Utah W. Va. MD. Colo. Kan. Va. Mo. KY. CaliF. N.C. Tenn. Ark. Okla. Ariz. N.M. S.C. Ga. Miss. Ala. La. Texas ALASKA Fla. HAWAII WASH. Me. N.H. Mont. N.D. Vt. Mich. Minn. Ore. N.Y. Mass. Wis. S.D. Wyo. Idaho R.I. Iowa Conn. Pa. Neb. Ohio Ill. N.J. Nev. Ind. DEL. Utah W. Va. MD. Kan. Va. Colo. Mo. KY. N.C. Tenn. Ark. Okla. Ariz. CaliF. S.C. N.M. Miss. Ga. Ala. La. Texas ALASKA Fla. HAWAII WA NH Me ND Vt Mt Id NY Or Ma Mi Mn Wi SD Wy RI Ia Pa Ct Ne NJ Nv Oh In DE Ut WV MD Il Ks Va Co Mo KY Az Ca NC Tn Ar Ok SC NM Ms Ga Al La Tx Ak HI Fl Me WA NH Mn Mt Vt ND Mi NY Id Or Ma Wi Oh SD Wy RI Ia Pa Ne Ct Nv In NJ Ut WV Il DE Ks Va Co Mo KY MD Tn Ar Ok NC Az Ca Ms NM SC Al Ga La Tx Ak Fl HI March organizers have said the event’s primary focus is to promote equal rights for women and to defend marginalized groups. “The Women’s March on Washington will send a bold message to our new government on their first day in office, and to the world, that women's rights are human rights,” the group’s website says. More than 200 organizations have signed on as partners for the march, including Planned Parenthood, the NAACP, the National Organization for Women and Human Rights Watch. Cher, Katy Perry and Amy Schumer are among the celebrities who have said they will attend. Women’s Marches Around the World Helsinki Vancouver Tokyo Erbil Athens San Jose Nairobi Singapore Rio de Janeiro Sydney Cape Town Helsinki Vancouver Tokyo Erbil Athens San Jose Nairobi Singapore Rio de Janeiro Sydney Cape Town Helsinki Vancouver Tokyo Erbil San Jose Nairobi Singapore Rio de Janeiro Sydney Cape Town Helsinki Erbil Tokyo San Jose Sydney Cape Town Participants outside the United States say they are marching in solidarity with American women and standing up for the rights of women in their own countries. “The recent elections in the United States have shown how real the threat is to our collective rights and liberties,” says the Facebook event page for the Women’s March on Nairobi. The page for the London event, which 23,000 Facebook users have said they will attend, says, “we will march...for the protection of our fundamental rights and for the safeguarding of freedoms threatened by recent political events.” Led by Mrs. Richard Coke Burleson (center, on horseback), suffragists marched on Pennsylvania Avenue on March 3, 1913, the day before President Woodrow Wilson’s inauguration. Library of Congress A previous women’s movement found success in an inauguration-related demonstration. The Women’s Suffrage Parade of 1913, in which an estimated 5,000 to 8,000 suffragists marched on Pennsylvania Avenue the day before President Woodrow Wilson’s inauguration, drew attention to the women’s suffrage movement as thousands of spectators in Washington for the inauguration witnessed the procession. Historians consider the parade a major milestone for the movement to win women the right to vote. It is set to be depicted on the back of a redesigned $10 bill in 2020. ||||| Angela Davis, UCLA professor and political activist, at a news conference in Los Angeles in 1969. (David F. Smith/AP) The Women’s March on Washington just released a big list of speakers for its rally, which includes everyone from civil rights era icon Angela Davis to liberal activist Michael Moore and D.C. Mayor Muriel Bowser. The rally begins at 10 a.m. Saturday at Independence Avenue and Third Street SW, and people will start marching west around 1:15 p.m. [Here’s what you need to know about attending inauguration and other events that weekend.] Here’s the full list of the speakers the march organizers released Wednesday afternoon: Cecile Richards Erika Andiola Ilyasah Shabazz J. Bob Alotta Janet Mock LaDonna Harris Maryum Ali Melanie Campbell Rabbi Sharon Brous Rhea Suh, Sister Simone Campbell Sophie Cruz Zahra Billoo America Ferrera Angela Davis Gloria Steinem Ashley Judd Scarlett Johansson Melissa Harris-Perry Michael Moore Amanda Nguyen Randi Weingarten Van Jones George Gresham Mothers of the Movement (Sybrina Fulton, Lucy McBath, Maria Hamilton, Gwen Carr) Hina Naveed Judith LaBlanc Kristin Rowe-Finkbeiner Aida Hurtado Melissa Mays Raquel Willis Rosyln Brock Sister Ieasha Prime Mayor Muriel Bowser Ai-jen Poo Wendy Carrillo Cynthia Hale March co-chairs Bob Bland, Carmen Perez, Linda Sarsour and Tamika Mallory. March organizers also announced performances by the following artists: ||||| (CNN) The Women's March extended beyond the United States, as similar protests cropped up around the world over women's rights and other issues the marchers fear could be under threat from Donald Trump's presidency. Although the focus of the day was the Women's March on Washington , many people attended the hundreds of "sister marches" that occurred around the US and the globe. Women and men in cities including Sydney, Berlin, London, Paris, Nairobi and Cape Town, marched in solidarity with the marchers in Washington and in opposition to the values they think Trump represents. Near and far A crowd of people gathered near the US Embassy in Mexico City on Saturday, shutting down the street and holding signs. Protesters in Mexico City demonstrated outside the US Embassy. "Say it loud, say it clear, migrants are welcome here," they shouted. Not all of the protesters were Mexican. Some Americans were there, too, in a show of solidarity. One man told CNN, "It's a little strange to have this kind of shame and lack of pride for what direction the United States is heading in." A "pro-peace, pro-environment" march also took place on Antarctica. Twitter user Linda Zunas posted pictures of people there taking part in the global event. #womensMarchAntarctica (still photo from our march video in Paradise Bay this morning) video to come Thursday pic.twitter.com/MfebPcDJsy — linda zunas (@lindazunas) January 21, 2017 "Love rules in Antarctica," read one poster, held by a man bundled up on the snowy landscape in Paradise Bay. "We are allies, not bystanders," read another sign, held by a woman posing in front of a glacier. 'Girl Power vs. Trump Tower' Australia was the scene of the day's first major international march, with thousands joining an anti-Trump demonstration in downtown Sydney. Marchers rally in Sydney in support of women's rights. Organizers said as many as 5,000 people attended the protest at Martin Place; police estimated the number was closer to 3,000. Chants from the crowd included "Women united will never be defeated" and "When women's rights are under attack, what do we do, stand up, fight back." Some carried banners with messages such as "Girl Power vs. Trump Tower" and "Dump the Trump." A small group holds a pro-Trump rally Saturday in Australia's largest city. A separate group of about 30 Trump supporters held a rally in Sydney. The police restrained some of them, blocking them from entering the same area as the Trump protest group. Protest organizers in New Zealand's capital, Wellington, said about 700 people turned out there for a women's march. Marches were also held in Auckland, Christchurch and Dunedin. Protesters also joined together to march in Nairobi, Kenya -- the African nation that was the native country of former President Barack Obama's father. Marchers in Cape Town, South Africa, carried banners with slogans such as "Climate change is a women's issue" and "So over mediocre men running things." Other African nations staging women's marches included Ghana and Malawi. Europe marches Big crowds turned out Saturday in dozens of cities across Europe, with marchers including men, women and children. Protesters who gathered outside one of Rome's most famous structures, the Pantheon, on Saturday morning carried signs reading "Yes we must" and "Women's rights are human rights." Demonstrators also took to the streets of Berlin, Frankfurt, Munich and other cities in Germany. This Pussy Bites Back ! #solidarity #womensmarch #berlin A photo posted by Katy Ray (@raykaty) on Jan 21, 2017 at 2:56am PST Katy Rea, who was at the march in Berlin, told CNN: "There are around 1,000 people. Lots of families, children. Very friendly atmosphere. Some police are present, but it's tame and relaxed." Marches also took place in cities up and down the United Kingdom, from London to Cardiff, Liverpool, Manchester, Belfast and Edinburgh. In London, large crowds joined a two-mile march starting outside the US Embassy and ending with a rally in the city's historic Trafalgar Square. Lots of anti-Trump placards at Womens March in London today but some protesting #Brexit, Workers rights, nuclear weapons, LGBT rights & more pic.twitter.com/LF3bsqcqAh — Nina dos Santos (@NdosSantosCNN) January 21, 2017 Marcher Victoria Dawson told CNN the atmosphere was "positive, inclusive, electric." Women's rights weren't the only issue on the agenda, with placards also bearing slogans to do with Brexit, nuclear weapons, workers' rights and lesbian, gay, bisexual and transgender rights. Speakers at Trafalgar Square told the crowds at least 100,000 people had turned out. London's Metropolitan Police do not provide crowd estimates, but aerial footage showed large numbers of people gathered in the square. London Mayor Sadiq Khan -- who before the US presidential election told CNN that Trump's views of Islam were "ignorant" -- posted a tweet encouraging Londoners to join the march and "show how much we value the rights every woman should have." In Paris, demonstrators gathered near the iconic Eiffel Tower before marching through the streets waving flags and banners. "A woman's place is in the house -- the White House," read one pink poster at the Paris event. Other French cities including Marseille, Toulouse and Bordeaux were also holding events. Protesters march in Marseille, France, in solidarity with women in Washington and around the world. Protesters in Barcelona, Spain, chanted "We will not be silent" and "My body, my choice" as they marched. On Friday night, a crowd of predominantly female protesters gathered in Brussels, Belgium , to denounce sexism and protest against Trump. Marches also took place in Greece, Kosovo, the Czech Republic and Georgia. ||||| Demonstrators take part in the Women's March on London, following the Inauguration of U.S. President Donald Trump, in London, Saturday Jan. 21, 2016. (AP Photo/Tim Ireland) (Associated Press) Demonstrators take part in the Women's March on London, following the Inauguration of U.S. President Donald Trump, in London, Saturday Jan. 21, 2016. (AP Photo/Tim Ireland) (Associated Press) WASHINGTON (AP) — Wearing pink, pointy-eared "pussyhats" to mock the new president, throngs of women descended on the nation's capital and other cities around the globe Saturday for marches and demonstrations aimed at showing Donald Trump they won't be silent over the next four years. They carried signs with messages such as "Women won't back down" and "Less fear more love" and decried Trump's stand on such issues as abortion, diversity and climate change. There were early signs that crowds in Washington could top those that gathered for Trump's inauguration on Friday. City officials said organizers of the Women's March on Washington had more than doubled their turnout estimate to 500,000 as crowds began swelling and subways into the city became clogged with participants. It wasn't just a Washington phenomenon and it wasn't just women: More than 600 "sister marches" were planned across the country and around the world, and plenty of men were part of the tableau. In Washington, Rena Wilson, of Charlotte, North Carolina, said she hopes the women can send Trump a message that they're "not going anywhere." Joy Rodriguez, of Miami, arrived with her husband, William, and their two daughters, ages 12 and 10. "I want to make sure their rights are not infringed on in these years coming up," Joy Rodriguez said. March organizers said women are "hurting and scared" as the new president takes office and want a greater voice for women in political life. "In the spirit of democracy and honoring the champions of human rights, dignity and justice who have come before us, we join in diversity to show our presence in numbers too great to ignore," their mission statement says. Retired teacher Linda Lastella, 69, who came from Metuchen, New Jersey, said she had never marched before but felt the need to speak out when "many nations are experiencing this same kind of pullback and hateful, hateful attitudes." "It just seemed like we needed to make a very firm stand of where we were," she said. Rose Wurm, 64, a retired medical secretary from Bedford, Pennsylvania, boarded a Washington-bound bus in Hagerstown, Maryland, at 7 a.m. carrying two signs: one asking Trump to stop tweeting, and one asking him to fix, not trash, the Obamacare health law. "There are parts of it that do need change. It's something new, something unique that's not going to be perfect right out of the gate," she said. Many arrived wearing hand-knit "pussyhats" — a message of female empowerment aimed squarely at Trump's crude boast about grabbing women's genitals. The march attracted significant support from celebrities. America Ferrara led the artists' contingent, and those scheduled to speak in Washington included Scarlett Johansson, Ashley Judd, Melissa Harris-Perry and Michael Moore. The promised performance lineup included Janelle Monae, Maxwell, Samantha Ronson, the Indigo Girls and Mary Chapin Carpenter. Cher, Katy Perry and Julianne Moore all were expected to attend. Women and other groups were demonstrating across the nation and as far abroad as Myanmar and Australia. In Prague, hundreds gathered in Wenceslas Square in freezing weather, waving portraits of Trump and Russia's Vladimir Putin and holding banners that read "This is just the beginning," ''Kindness" and "Love." "We are worried about the way some politicians talk, especially during the American elections," said organizer Johanna Nejedlova. In Copenhagen, march organizer Lesley-Ann Brown said: "Nationalist, racist and misogynistic trends are growing worldwide and threaten the most marginalized groups in our societies including women, people of color, immigrants, Muslims, the LGBT community and people with disabilities." In Sydney, thousands of Australians marched in solidarity in Hyde Park. One organizer said hatred, bigotry and racism are not only America's problems. The idea for the women's march took off after a number of women posted on social media in the hours after Trump's election about the need to mobilize. Hundreds of groups quickly joined the cause, pushing a wide range of causes, including abortion rights, gun control, climate change and immigrant rights. While the march organizers' "mission and vision" statement never mentions Trump and stresses broad themes, including the message that "women's rights are human rights," the unifying factor among those turning out appeared to be a loathing for the new president and dismay that so much of the country voted for him. Friday's unrest during the inauguration led police to use pepper spray and stun grenades to prevent the chaos from spilling into Trump's formal procession and the evening balls. About a mile from the National Mall, police gave chase to a group of about 100 protesters who smashed the windows of downtown businesses, including a Starbucks, a Bank of America and a McDonald's, as they denounced capitalism and Trump. "They began to destroy property, throw objects at people, through windows. A large percentage of this small group was armed with crowbars and hammers," said the city's interim police chief, Peter Newsham. Six officers suffered minor injuries, he said. ___ Associated Press Writers Alanna Durkin Richer, Brian Witte and David Dishneau in Washington, Karel Janicek in Prague contributed to this report. ||||| Media playback is unsupported on your device Media caption Washington is leading anti-Trump protests around the world Millions of protesters have taken to the streets of cities in the US and around the globe to rally against the new US President Donald Trump. Larger numbers of demonstrators than expected turned out for more than 600 rallies worldwide. The aim was principally to highlight women's rights, which activists believe to be under threat from the new administration. Meanwhile, Mr Trump used his first full day in office to visit the CIA's HQ. He said he was "1,000%" behind the spy agency's employees and also accused the media of being dishonest in its reporting of the size of the crowd at his inauguration. Mr Trump did not refer to Saturday's protests. 'We are the majority' The biggest US rally was in the capital Washington, which city officials estimated to be more than 500,000-strong. This far exceeded the 200,000 that had originally been expected by organisers of the Women's March on Washington. By most estimates, it also surpassed the crowd at Friday's presidential inauguration. The protesters in the nation's capital heard speeches from Scarlett Johansson, Ugly Betty star America Ferrera, Ashley Judd, Gloria Steinem and Michael Moore among others. A planned march to the White House proved impossible as the entire route was filled with demonstrators. Interim DC Police Chief Peter Newsham told Associated Press: "The crowd stretches so far that there's no room left to march." During his speech, Michael Moore ripped up a copy of the Washington Post, saying: "The headline was 'Trump takes power'. I don't think so. Here's the power. Here's the majority of America right here. We are the majority." The singer Madonna also made an appearance, swearing several times in a speech carried live by major US TV networks. "Yes, I am outraged. Yes, I have thought an awful lot about blowing up the White House," she said. America Ferrera told the crowd: "We march today for the moral core of this nation, against which our new president is waging a war." Huge crowds were reported at other US protests. Media playback is unsupported on your device Media caption Women from Kenya, India and Germany explain why they took part in the march So many turned out in Chicago - some 150,000 - that a planned march had to be called off and the event declared a rally. Streets were also overflowing in Los Angeles. Huge crowds were also reported in New York, Seattle, Boston and Miami, some of the venues for about 300 nationwide protests. Many women wore knitted pink "pussy hats" - a reference to a recording that emerged during the election campaign in which Mr Trump talked about groping women. Image copyright Reuters Image caption Washington's transportation system creaked under the strain of travellers Image copyright Reuters Image caption Former secretary of state John Kerry joins the Washington rally Image copyright Reuters Image caption A young Trump supporter gets her message across in Washington Image copyright PA Image caption London joins in the protests that began in Australasia and have swept west to the US 'These are global problems' Organisers of a London rally said between 80,000 and 100,000 people had taken part there. Belfast, Cardiff, Edinburgh, Leeds, Liverpool, Manchester and Bristol were among the other UK cities holding protests. Anti-Trump marches took place earlier in Australia, New Zealand and in several Asian cities. Image copyright Getty Images Image caption Crowds turned out in many European cities, including at the Brandenburg Gate in Berlin Several thousand women and men joined a rally in central Sydney, with a similar number in Melbourne. Women's March Sydney co-founder Mindy Freiband told the crowd: "Hatred, hate speech, bigotry, discrimination, prejudicial policies - these are not American problems, these are global problems." Barcelona, Rome, Amsterdam, Geneva, Budapest, Prague and Berlin were among the European cities that took part. In Paris, protester Francoise Seme Wallon said Mr Trump was "a nasty guy and he's dangerous for the whole world". Website overhaul Mr Trump's first full day in office began with an inter-faith service at Washington National Cathedral. He then visited the CIA's HQ in Langley, Virginia. In a speech there, he told about 400 employees: "There is nobody who feels stronger about the intelligence community and the CIA than me." During the election campaign, Mr Trump had sharply criticised the intelligence agencies over their stance on alleged Russian involvement. Image copyright AFP Image caption Donald Trump attends a multi-faith service in Washington Mr Trump also talked up his yet-to-be-confirmed nominee for CIA chief, Mike Pompeo. "You will be getting a total gem," he told the employees. In one of his first steps, Mr Trump ordered government agencies to ease the "economic burden" of the health law known as Obamacare. His team also quickly overhauled the White House website. The revamp replaces Barack Obama's policies with Mr Trump's new agenda. Media playback is unsupported on your device Media caption 'This American carnage stops right here,' Donald Trump said at his inauguration Media playback is unsupported on your device Media caption Supporters of President Trump give their views on his inauguration speech The new administration lists only six issues on the website - energy, foreign policy, jobs and growth, military, law enforcement and trade deals. Critics complained that it made no mention of civil rights, healthcare, climate change or LGBT rights. ||||| Kate Russell's cardboard placard read "What would Carrie Fisher do." The 26-year-old Londoner said the Star Wars star had been a hero, adding: “She represents what a strong woman is and should be." Other light-hearted placard message included “Free Melania,” “We Shall Overcomb” and “Girls Just Wanna Have Fun… damental Rights.” Topless protester Matilda Bennett, 21, drew cheers from marchers-by on Piccadilly as she and four shirtless friends shouted "free the nipple," waving their hands in the air. The women had journeyed to the capital from Bristol for the march. After allowing fellow demonstrators to march by and cheer them they joined the route. Matilda said:"We're freeing the nipple because women's bodies aren't a sexual object. "We're here because we want fundamental rights and no-one should be able to say what Trump has said and become President. Protesters were seen holding hand-made signs and placards with slogans such as "dump Trump", "reject hate, reclaim politics" and "no to racism, no to Trump". One woman dressed as the Statue of Liberty brandished a torch bearing an image of the new president's face and held a sign which said: "The statue of taking liberties." ||||| Donald Trump is so unpopular that there are even women marching against him in Antarctica. The day after the inauguration of a president who bragged about grabbing women by their genitals, thousands will be marching in Washington and in more than 60 countries around the world, to “stand up for human rights, women’s rights and against hate.” And in Paradise Bay, a remote corner of Antarctica whose population normally comprises gentoo penguins, Weddell seals and the occasional humpback whale, a group of at least 30 women and supportive men will be joining the Women’s March movement. They will march with banners proclaiming 'Penguins for Peace', 'Seals for Science', "Cormorants for Climate', and 'Love from seven continents'. Join Independent Minds For exclusive articles, events and an advertising-free read for just £5.99 €6.99 $9.99 a month Get the best of The Independent With an Independent Minds subscription for just £5.99 €6.99 $9.99 a month Get the best of The Independent Without the ads – for just £5.99 €6.99 $9.99 a month The Antarctic march is being organised by Linda Zunas, 42, a data analytics and market research professional from Oakland, California, who told The Independent she had been motivated by Donald Trump’s apparent intention to reverse the environmental policies of Barack Obama. “I set it up because I wanted to participate in the Women’s March,” she said. “I spent a month after the election mourning the impending damage to the earth that will be done. I felt like I needed to do something to be part of the global movement.” Describing the protesters as "an international group of eco-minded visitors" to Antarctica, Ms Zunas said: "They range in age from 24 to 87, male and female, from over six countries." Because of the environmental sensitivity of the area, she explained, "The actual marching will be short as we have to limit our footprint on land." The shortness of the march, however, would be compensated for by the uniqueness of the spectators. "We hope to have gentoo penguins in the background of our march," said Ms Zunas. Shape Created with Sketch. In pictures: Protests, pomp and Donald Trump Show all 30 left Created with Sketch. right Created with Sketch. Shape Created with Sketch. In pictures: Protests, pomp and Donald Trump 1/30 President-elect Donald Trump acknowledges guests as he arrives on the platform at the US Capitol in Washington DC Getty Images 2/30 Donald Trump is sworn in as the 45th president of the United States by Chief Justice John Roberts as Melania Trump looks on during the 58th Presidential Inauguration at the U.S. Capitol in Washington AP 3/30 President Donald Trump shakes hands with Justice John Roberts after taking the oath at inauguration ceremonies swearing in Trump as the 45th president of the United States Reuters 4/30 President Donald Trump raises his fists after his inauguration on the West Front of the U.S. Capitol Getty 5/30 U.S. President-elect Donald Trump greets outgoing President Barack Obama before Trump is inaugurated during ceremonies on the Capitol in Washington Reuters 6/30 resident-elect Donald Trump arrives on the platform of the US Capitol in Washington DC Getty Images 7/30 Attendees partake in the inauguration ceremonies to swear in Donald Trump as the 45th president of the United States at the U.S. Capitol in Washington DC Reuters 8/30 US President Donald Trump delivers his inaugural address during ceremonies at the US Capitol in Washington DC Getty 9/30 U.S. President Donald Trump waves with wife Melania during the Inaugural Parade in Washington DC Reuters 10/30 Protesters registered their rage against the new president Friday in a chaotic confrontation with police who used pepper spray and stun grenades in a melee just blocks from Donald Trump's inaugural parade route. Scores were arrested for trashing property and attacking officers AP 11/30 Demonstrators protest against US President Donald Trump in Washington DC Getty Images 12/30 A woman holds a sign before the start of the Presidential Inauguration of Donald Trump at Freedom Plaza in Washington DC Getty Images 13/30 Anti-Trump protesters prepare banners for a protest against the inauguration of US President-elect Donald Trump, in Berlin REUTERS 14/30 Demonstrators shout slogans against US President-elect Donald Trump in Washington DC Getty Images 15/30 Demonstrators march, block foot traffic and clash with U.S. Capitol Police at the entry checkpoints for the Inauguration of Donald Trump Alamy Live News 16/30 Demonstrators display a banner as people arrive for US President-elect Donald Trump's inauguration in Washington DC Getty Images 17/30 A man displays a placard as people lineup to get into the National Mall for the inauguration of US President-elect Donald Trump in Washington DC Getty Images 18/30 Protesters demonstrating against U.S. President Donald Trump raise their hands as they are surrounded by police on the sidelines of the inauguration in Washington DC Reuters 19/30 A demonstrator wearing a mask depicting Donald Trump protests outside the US Embassy in London Getty Images 20/30 Demonstrators hold placards as they protest outside the US Embassy in London Getty Images 21/30 Former US President George W. Bush and First Lady Laura Bush arrive for the Presidential Inauguration at the US Capitol Rex 22/30 Michelle Obama and Dr. Jill Biden share an umbrella as President Donald Trump delivers his inaugural address at the inauguration in Washington DC Rex 23/30 Former Democratic presidential nominee Hillary Clinton and former President Bill Clinton arrive on the West Front of the U.S. Capitol in Washington Reuters 24/30 U.S. Vice President Mike Pence takes the oath of office on the West Front of the U.S. Capitol in Washington, DC Getty Images 25/30 Advisors to President-elect Donald Trump, Kellyanne Conway and Steve Bannon depart from services at St. John's Church during the Presidential Inauguration in Washington Reuters 26/30 Protesters demonstrating against U.S. President Donald Trump take cover as they are hit by pepper spray by police on the sidelines of the inauguration in Washington DC Reuters 27/30 An activist demonstrating against U.S. President Donald Trump is helped after being hit by pepper spray on the sidelines of the inauguration in Washington DC Reuters 28/30 A police officer tries to tackle a protester demonstrating against U.S. President Donald Trump Reuters/Adrees Latif 29/30 Police arrest and detain a protester in the street in Washington DC Rex 30/30 A police officer falls to the ground as another shoots pepper spray at protesters demonstrating against U.S. President Donald Trump on the sidelines of the inauguration in Washington DC Reuters 1/30 President-elect Donald Trump acknowledges guests as he arrives on the platform at the US Capitol in Washington DC Getty Images 2/30 Donald Trump is sworn in as the 45th president of the United States by Chief Justice John Roberts as Melania Trump looks on during the 58th Presidential Inauguration at the U.S. Capitol in Washington AP 3/30 President Donald Trump shakes hands with Justice John Roberts after taking the oath at inauguration ceremonies swearing in Trump as the 45th president of the United States Reuters 4/30 President Donald Trump raises his fists after his inauguration on the West Front of the U.S. Capitol Getty 5/30 U.S. President-elect Donald Trump greets outgoing President Barack Obama before Trump is inaugurated during ceremonies on the Capitol in Washington Reuters 6/30 resident-elect Donald Trump arrives on the platform of the US Capitol in Washington DC Getty Images 7/30 Attendees partake in the inauguration ceremonies to swear in Donald Trump as the 45th president of the United States at the U.S. Capitol in Washington DC Reuters 8/30 US President Donald Trump delivers his inaugural address during ceremonies at the US Capitol in Washington DC Getty 9/30 U.S. President Donald Trump waves with wife Melania during the Inaugural Parade in Washington DC Reuters 10/30 Protesters registered their rage against the new president Friday in a chaotic confrontation with police who used pepper spray and stun grenades in a melee just blocks from Donald Trump's inaugural parade route. Scores were arrested for trashing property and attacking officers AP 11/30 Demonstrators protest against US President Donald Trump in Washington DC Getty Images 12/30 A woman holds a sign before the start of the Presidential Inauguration of Donald Trump at Freedom Plaza in Washington DC Getty Images 13/30 Anti-Trump protesters prepare banners for a protest against the inauguration of US President-elect Donald Trump, in Berlin REUTERS 14/30 Demonstrators shout slogans against US President-elect Donald Trump in Washington DC Getty Images 15/30 Demonstrators march, block foot traffic and clash with U.S. Capitol Police at the entry checkpoints for the Inauguration of Donald Trump Alamy Live News 16/30 Demonstrators display a banner as people arrive for US President-elect Donald Trump's inauguration in Washington DC Getty Images 17/30 A man displays a placard as people lineup to get into the National Mall for the inauguration of US President-elect Donald Trump in Washington DC Getty Images 18/30 Protesters demonstrating against U.S. President Donald Trump raise their hands as they are surrounded by police on the sidelines of the inauguration in Washington DC Reuters 19/30 A demonstrator wearing a mask depicting Donald Trump protests outside the US Embassy in London Getty Images 20/30 Demonstrators hold placards as they protest outside the US Embassy in London Getty Images 21/30 Former US President George W. Bush and First Lady Laura Bush arrive for the Presidential Inauguration at the US Capitol Rex 22/30 Michelle Obama and Dr. Jill Biden share an umbrella as President Donald Trump delivers his inaugural address at the inauguration in Washington DC Rex 23/30 Former Democratic presidential nominee Hillary Clinton and former President Bill Clinton arrive on the West Front of the U.S. Capitol in Washington Reuters 24/30 U.S. Vice President Mike Pence takes the oath of office on the West Front of the U.S. Capitol in Washington, DC Getty Images 25/30 Advisors to President-elect Donald Trump, Kellyanne Conway and Steve Bannon depart from services at St. John's Church during the Presidential Inauguration in Washington Reuters 26/30 Protesters demonstrating against U.S. President Donald Trump take cover as they are hit by pepper spray by police on the sidelines of the inauguration in Washington DC Reuters 27/30 An activist demonstrating against U.S. President Donald Trump is helped after being hit by pepper spray on the sidelines of the inauguration in Washington DC Reuters 28/30 A police officer tries to tackle a protester demonstrating against U.S. President Donald Trump Reuters/Adrees Latif 29/30 Police arrest and detain a protester in the street in Washington DC Rex 30/30 A police officer falls to the ground as another shoots pepper spray at protesters demonstrating against U.S. President Donald Trump on the sidelines of the inauguration in Washington DC Reuters “We are not discussing politics at all,” she added, “But you may infer our opinions based on our choice of day and topic.” Ms Zunas' own twitter feed also suggests she is not a fan of Trump. ||||| Massive crowds packed into D.C. Metro stations Saturday night as thousands of participants in the Women's March on Washington headed toward the White House and dispersed from the National Mall. Metro urged people to consider waiting before riding to allow the crowds to ease. Fairfax County police also advised riders to follow police direction. Metrorail has seen more riders on Saturday than it did for former President Barack Obama's second inauguration in 2013, reports News4's Mark Segraves. Stations were packed and more than a dozen parking facilities were full before noon Saturday as hundreds of thousands of participants headed to downtown D.C. for the Women's March on Washington. Trains briefly bypassed the L'Enfant Plaza station due to crowding. They began serving the station again shortly before 1:10 p.m. Officials recommended riders use other stations to get to the march, such as Gallery Place or Metro Center. Posts on social media Saturday showed long lines of people waiting for access to Metro stations. Multiple people shared images and videos of the scene outside the Shady Grove, where Philip Lewis of the Huffington Post reported earlier Saturday that he was hearing riders were waiting an hour to board trains. March organizers said they've increased turnout estimates to 500,000 participants, said D.C. Deputy Mayor for Public Safety and Justice Kevin Donahue. "Be patient & kind!" he posted on Twitter. Metro 'Overwhelmed' by Women's March Attendees Many Metro stations were flooded with travelers trying to get into D.C. for the Women's March. News4's Adam Tuss reports. (Published Saturday, Jan. 21, 2017) It's been a busy day for Metro. Officials said 275,000 rides had been taken as of 11 a.m. "For comparison, that's more than 8 [times] a normal Sat[urday] & even busier than most weekdays," Metro posted on Twitter. As of the same time on Friday, Inauguration Day, 193,000 trips had been taken. Metro station personnel were making adjustments to try to accommodate the large crowds. At the Ballston and Stadium-Armory stations, would-be Metro riders were stopped before the escalators because too many people were already on the platform Saturday morning, reported News4's Adam Tuss, who said it "cannot be overstated how heavy the crowds are." TUSS GREENBELT METRO FOR DIGITAL Metro stations are packed and more than a dozen parking facilities are already full Saturday morning as tens of thousands of participants headed to downtown D.C. for the Women's March on Washington. News4's Adam Tuss reports. (Published Saturday, Jan. 21, 2017) Melissa Zieve of Baltimore said she had to let the first two trains at Tenleytown pass by because they were too full. She was able to board a third train and rode to Union Station. "I've never been on a subway in any city packed quite like that," Zieve said, but added that everyone was respectful and no one was pushing. Parking facilities all stations in Fairfax County and several others are full, according to Metro officials and Fairfax County Police. Those are: Orange, Silver, or Orange/Silver Lines: East Falls Church West Falls Church Dunn Loring Vienna McLean Tysons Corner Greensboro Spring Hill Wiehle-Reston East New Carrollton, lot 2 (lots 1 & 3 have limited capacity) Green Line: Greenbelt Red Line: Forest Glen Fort Totten Glenmont Rhode Island Avenue Rockville Shady Grove, west/south (north has limited capacity) As of 10 a.m., Metro was recommending the following stations with available parking: Branch Avenue, Grosvenor, Prince George's Plaza, Southern Avenue, Suitland, Twinbrook and White Flint. Outside the filled Greenbelt and New Carrollton lots, drivers have been illegally parking on the shoulders of the ramps leading to the Metro stations, according to the Maryland State Highway Administration. Metro had initially planned to keep the Federal Triangle station closed throughout Saturday, but reversed their decision and reopened the station about 9:20 a.m. Riders may also consider exiting at the Federal Center SW or Capitol South stations. Inauguration Weekend in Photos Margaret Warpeha from Minnesota flew in Friday night and described her Metro experience as wonderful Saturday morning. She boarded at Silver Spring about 9 a.m. and said it wasn't too crowded. Warpeha said she wanted to come to D.C. because she was "quite upset" about the election and didn't want to remain silent. Outside Union Station, Lisa Legrand of Minneapolis said she flew into Philadelphia, drove to the Tenleytown station and rode the Metro downtown. "It was really crowded" but had a very positive energy, Legrand said.[/INST]– Donald Trump was the target of women's marches worldwide on the first full day of his presidency. As the pre-march rally kicked off in Washington, DC, where numbers might exceed those that turned out of Trump's inauguration, marches were already underway or over in cities including London, Prague, Sydney, and Bangkok. The BBC reports that marches are planned in more than 300 cities in the US and hundreds more worldwide, with marchers highlighting multiple issues, especially the principle that "Women's Rights are Human Rights." A roundup of coverage: March organizers say they want to send a "bold message" to the new government and the world, and they hope to be joined by people of " all genders, ages, races, cultures, political affiliations, and backgrounds ." "In the spirit of democracy and honoring the champions of human rights, dignity and justice who have come before us, we join in diversity to show our presence in numbers too great to ignore," they said in a statement, per the AP. The Washington Post has a full list of speakers and performers at the Washington, DC event. NPR reports that in DC where a rally started at 10am and march will begin at 1:15pm, many women are wearing pink knitted caps nicknamed "pussy hats" in reference to one of Trump's infamous remarks. The New York Times has a guide to marches in the US around the world, and notes that this is expected to be the largest inauguration-related demonstration in history. NBC Washington has travel and parking tips for those in DC, where parking facilities have filled up fast and public transport is crowded. Organizers have increased their estimate of participants to at least 500,000. CNN reports that in one of the first marches to take place, around 5,000 people marched in Sydney, Australia with signs like "Girl Power" vs "Trump Power." A pro-Trump counter-demonstration attracted around 30 people. Some 10,000 people were expected to join the London march, but organizers said at least 80,000 turned up, the Telegraph reports. The Independent reports that a group of around 30 female and male visitors have organized a Women's March in Antarctica, with banners including "Penguins for Peace," and "Love From Seven Continents." To respect wildlife habitats, the amount of actual marching will be kept to a minimum.</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Health Insurance Equity Act of 2000''. SEC. 2. CERTAIN GRANTS BY PRIVATE FOUNDATIONS TO QUALIFIED HEALTH BENEFIT PURCHASING COALITIONS. (a) In General.--Section 4942 of the Internal Revenue Code of 1986 (relating to taxes on failure to distribute income) is amended by adding at the end the following: ``(k) Certain Qualified Health Benefit Purchasing Coalition Distributions.-- ``(1) In general.--For purposes of subsection (g) and section 4945(d)(5), a qualified health benefit purchasing coalition distribution by a private foundation shall be considered to be a distribution for a charitable purpose. ``(2) Qualified health benefit purchasing coalition distribution.--For purposes of paragraph (1)-- ``(A) In general.--The term `qualified health benefit purchasing coalition distribution' means any amount paid by a private foundation to or on behalf of a qualified health benefit purchasing coalition (as defined in section 9841) for purposes of payment or reimbursement of start-up costs paid or incurred in connection with the establishment and maintenance of such coalition. ``(B) Exclusions.--Such term shall not include any amount used by a qualified health benefit purchasing coalition (as so defined)-- ``(i) for the purchase of real property, ``(ii) as payment to, or for the benefit of, members (or employees or affiliates of such members) of such coalition, or ``(iii) for start-up costs paid or incurred more than 24 months after the date of establishment of such coalition. ``(3) Termination.--This subsection shall not apply-- ``(A) to qualified health benefit purchasing coalition distributions paid or incurred after December 31, 2008, and ``(B) with respect to start-up costs of a coalition which are paid or incurred after December 31, 2010.''. (b) Effective Date.--The amendment made by this subsection shall apply to qualified health benefit purchasing coalition distributions, as defined in section 4942(k)(2) of the Internal Revenue Code of 1986, as added by subsection (a), paid in taxable years beginning after December 31, 2000. SEC. 3. SMALL BUSINESS HEALTH PLAN TAX CREDIT. (a) In General.--Subpart D of part IV of subchapter A of chapter 1 of the Internal Revenue Code of 1986 (relating to business-related credits) is amended by adding at the end the following: ``SEC. 45D. EMPLOYEE HEALTH INSURANCE EXPENSES. ``(a) General Rule.--For purposes of section 38, in the case of a small employer (as defined in section 4980D(d)(2)), the employee health insurance expenses credit determined under this section for the taxable year is an amount equal to the applicable percentage of the amount paid by the taxpayer during the taxable year for qualified employee health insurance expenses. ``(b) Applicable Percentage.--For purposes of subsection (a), the applicable percentage is-- ``(1) in the case of insurance purchased as a member of a qualified health benefit purchasing coalition (as defined in section 9841), 25 percent, and ``(2) in the case of insurance not described in paragraph (1), 20 percent. ``(c) Per Employee Dollar Limitation.-- ``(1) In general.--The amount of qualified employee health insurance expenses taken into account under subsection (a) with respect to any qualified employee for any taxable year shall not exceed the sum of the monthly limitations for coverage months of such employee during such taxable year. ``(2) Monthly limitation.--The monthly limitation for each coverage month during the taxable year is equal to \1/12\ of-- ``(A) $2,000 in the case of self-only coverage, and ``(B) $5,000 in the case of family coverage. ``(3) Coverage month.--For purposes of this subsection, the term `coverage month' means, with respect to an individual, any month if-- ``(A) as of the first day of such month such individual is covered by the taxpayer's new health plan, and ``(B) the premium for coverage under such plan for such month is paid by the taxpayer. ``(d) Definitions.--For purposes of this section-- ``(1) Qualified employee.-- ``(A) In general.--The term `qualified employee' means, with respect to any period, an employee of an employer if-- ``(i) the total amount of wages paid or incurred by such employer with respect to such employee for the taxable year exceeds $10,000, and ``(ii) the employee is not a highly compensated employee. ``(B) Treatment of certain employees.--For purposes of subparagraph (A), the term `employee' shall include-- ``(i) an employee within the meaning of section 401(c)(1), and ``(ii) a leased employee within the meaning of section 414(n). ``(C) Exclusion of certain employees.-- ``(i) In general.--If a plan-- ``(I) prescribes minimum age and service requirements as a condition of coverage, and ``(II) excludes all employees not meeting such requirements from coverage, then such employees shall be excluded from consideration for purposes of this paragraph. ``(ii) Collective bargaining agreement.-- For purposes of this paragraph, there shall be excluded from consideration employees who are included in a unit of employees covered by an agreement between employee representatives and one or more employers, if there is evidence that health insurance benefits were the subject of good faith bargaining between such employee representatives and such employer. ``(iii) Limits on minimum requirements.-- Rules similar to the rules of section 410(a) shall apply with respect to minimum age and service requirements under clause (i). ``(D) Wages.--The term `wages'-- ``(i) has the meaning given such term by section 3121(a) (determined without regard to any dollar limitation contained in such section), and ``(ii) in the case of an employee described in subparagraph (B)(i), includes the net earnings from self-employment (as defined in section 1402(a) and as so determined). ``(2) Qualified employee health insurance expenses.-- ``(A) In general.--The term `qualified employee health insurance expenses' means any amount paid or incurred by an employer during the applicable period for health insurance coverage provided under a new health plan to the extent such amount is attributable to coverage provided to any employee who is not a highly compensated employee. ``(B) Exception for amounts paid under salary reduction arrangements.--No amount paid or incurred for health insurance coverage pursuant to a salary reduction arrangement shall be taken into account under subparagraph (A). ``(C) Health insurance coverage.--The term `health insurance coverage' has the meaning given such term by section 9832(b)(1). ``(D) New health plan.--For purposes of this paragraph, the term `new health plan' means any arrangement of the employer which provides health insurance coverage to employees if-- ``(i) such employer (or predecessor employer) did not establish or maintain such arrangement (or any similar arrangement) at any time during the 2 taxable years ending prior to the taxable year in which the credit under this section is first allowed, and ``(ii) such arrangement covers at least 70 percent of the qualified employees of such employer who are not otherwise covered by health insurance. ``(E) Applicable period.--For purposes of subparagraph (A), the applicable period with respect to an employer shall be the 4-year period beginning on the date such employer establishes a new health plan. ``(3) Highly compensated employee.--The term `highly compensated employee' means an employee who for the preceding year had compensation from the employer in excess of $75,000. ``(e) Certain rules made applicable.--For purposes of this section, rules similar to the rules of section 52 shall apply. ``(f) Disallowance of Deduction.--No deduction shall be allowed for that portion of the qualified employee health insurance expenses for the taxable year which is equal to the amount of the credit determined under subsection (a). ``(g) Termination.--This section shall not apply to expenses paid or incurred by an employer with respect to any arrangement established on or after January 1, 2009.''. (b) Credit To Be Part of General Business Credit.--Section 38(b) of the Internal Revenue Code of 1986 (relating to current year business credit) is amended by striking ``plus'' at the end of paragraph (11), by striking the period at the end of paragraph (12) and inserting ``, plus'', and by adding at the end the following: ``(13) the employee health insurance expenses credit determined under section 45D.'' (c) No Carrybacks.--Subsection (d) of section 39 of the Internal Revenue Code of 1986 (relating to carryback and carryforward of unused credits) is amended by adding at the end the following: ``(9) No carryback of section 45d credit before effective date.--No portion of the unused business credit for any taxable year which is attributable to the employee health insurance expenses credit determined under section 45D may be carried back to a taxable year ending before the date of the enactment of section 45D.'' (d) Clerical Amendment.--The table of sections for subpart D of part IV of subchapter A of chapter 1 of the Internal Revenue Code of 1986 is amended by adding at the end the following: ``Sec. 45D. Employee health insurance expenses.'' (e) Effective Date.--The amendments made by this section shall apply to amounts paid or incurred in taxable years beginning after December 31, 2000, for arrangements established after the date of the enactment of this Act. SEC. 4. QUALIFIED HEALTH BENEFIT PURCHASING COALITION. (a) In General.--Chapter 100 of the Internal Revenue Code of 1986 (relating to group health plan requirements) is amended by adding at the end the following new subchapter: ``Subchapter D--Qualified Health Benefit Purchasing Coalition ``Sec. 9841. Qualified health benefit purchasing coalition. ``SEC. 9841. QUALIFIED HEALTH BENEFIT PURCHASING COALITION. ``(a) In General.--A qualified health benefit purchasing coalition is a private not-for-profit corporation which-- ``(1) is licensed to provide health insurance in the State in which the employers to which such coalition is providing insurance is located, and ``(2) establishes to the Secretary, under State certification procedures or other procedures as the Secretary may provide by regulation, that such coalition meets the requirements of this section. ``(b) Board of Directors.-- ``(1) In general.--Each purchasing coalition under this section shall be governed by a Board of Directors. ``(2) Election.--The Secretary shall establish procedures governing election of such Board. ``(3) Membership.--The Board of Directors shall-- ``(A) be composed of small employers and employee representatives of such employers, but ``(B) not include other interested parties, such as service providers, health insurers, or insurance agents or brokers which may have a conflict of interest with the purposes of the coalition. ``(c) Membership of Coalition.-- ``(1) In general.--A purchasing coalition-- ``(A) shall accept all small employers residing within the area served by the coalition as members if such employers request such membership, and ``(B) may accept any other employers residing with such area. ``(2) Voting.--Members of a purchasing coalition shall have voting rights consistent with the rules established by the State. ``(d) Duties of Purchasing Coalitions.--Each purchasing coalition shall-- ``(1) enter into agreements with employers to provide health insurance benefits to employees of such employers, ``(2) enter into agreements with 3 or more unaffiliated, qualified licensed health plans, to offer benefits to members, ``(3) offer to members at least 1 open enrollment period per calendar year, ``(4) serve a significant geographical area, and ``(5) carry out other functions provided for under this section. ``(e) Limitation on Activities.--A purchasing coalition shall not-- ``(1) perform any activity (including certification or enforcement) relating to compliance or licensing of health plans, ``(2) assume insurance or financial risk in relation to any health plan, or ``(3) perform other activities identified by the State as being inconsistent with the performance of its duties under this section. ``(f) Additional Requirements For Purchasing Coalitions.--As provided by the Secretary in regulations, a purchasing coalition shall be subject to requirements similar to the requirements of a group health plan under this chapter. ``(g) Definition of Small Employer.--The term `small employer' has the meaning given such term by section 4980D(d)(2).''. (b) Conforming Amendment.--The table of subchapters for chapter 100 of the Internal Revenue Code of 1986 is amended by adding at the end the following item: ``Subchapter D. Qualified health benefit purchasing coalition.''.

Provides for the establishment of qualified health benefit purchasing coalitions which shall enter into agreements with small business employers to provide health benefits to employees of such employers.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Health Insurance Equity Act of 2000''. SEC. 2. CERTAIN GRANTS BY PRIVATE FOUNDATIONS TO QUALIFIED HEALTH BENEFIT PURCHASING COALITIONS. (a) In General.--Section 4942 of the Internal Revenue Code of 1986 (relating to taxes on failure to distribute income) is amended by adding at the end the following: ``(k) Certain Qualified Health Benefit Purchasing Coalition Distributions.-- ``(1) In general.--For purposes of subsection (g) and section 4945(d)(5), a qualified health benefit purchasing coalition distribution by a private foundation shall be considered to be a distribution for a charitable purpose. ``(2) Qualified health benefit purchasing coalition distribution.--For purposes of paragraph (1)-- ``(A) In general.--The term `qualified health benefit purchasing coalition distribution' means any amount paid by a private foundation to or on behalf of a qualified health benefit purchasing coalition (as defined in section 9841) for purposes of payment or reimbursement of start-up costs paid or incurred in connection with the establishment and maintenance of such coalition. ``(B) Exclusions.--Such term shall not include any amount used by a qualified health benefit purchasing coalition (as so defined)-- ``(i) for the purchase of real property, ``(ii) as payment to, or for the benefit of, members (or employees or affiliates of such members) of such coalition, or ``(iii) for start-up costs paid or incurred more than 24 months after the date of establishment of such coalition. ``(3) Termination.--This subsection shall not apply-- ``(A) to qualified health benefit purchasing coalition distributions paid or incurred after December 31, 2008, and ``(B) with respect to start-up costs of a coalition which are paid or incurred after December 31, 2010.''. (b) Effective Date.--The amendment made by this subsection shall apply to qualified health benefit purchasing coalition distributions, as defined in section 4942(k)(2) of the Internal Revenue Code of 1986, as added by subsection (a), paid in taxable years beginning after December 31, 2000. SEC. 3. SMALL BUSINESS HEALTH PLAN TAX CREDIT. (a) In General.--Subpart D of part IV of subchapter A of chapter 1 of the Internal Revenue Code of 1986 (relating to business-related credits) is amended by adding at the end the following: ``SEC. 45D. EMPLOYEE HEALTH INSURANCE EXPENSES. ``(a) General Rule.--For purposes of section 38, in the case of a small employer (as defined in section 4980D(d)(2)), the employee health insurance expenses credit determined under this section for the taxable year is an amount equal to the applicable percentage of the amount paid by the taxpayer during the taxable year for qualified employee health insurance expenses. ``(b) Applicable Percentage.--For purposes of subsection (a), the applicable percentage is-- ``(1) in the case of insurance purchased as a member of a qualified health benefit purchasing coalition (as defined in section 9841), 25 percent, and ``(2) in the case of insurance not described in paragraph (1), 20 percent. ``(c) Per Employee Dollar Limitation.-- ``(1) In general.--The amount of qualified employee health insurance expenses taken into account under subsection (a) with respect to any qualified employee for any taxable year shall not exceed the sum of the monthly limitations for coverage months of such employee during such taxable year. ``(2) Monthly limitation.--The monthly limitation for each coverage month during the taxable year is equal to \1/12\ of-- ``(A) $2,000 in the case of self-only coverage, and ``(B) $5,000 in the case of family coverage. ``(3) Coverage month.--For purposes of this subsection, the term `coverage month' means, with respect to an individual, any month if-- ``(A) as of the first day of such month such individual is covered by the taxpayer's new health plan, and ``(B) the premium for coverage under such plan for such month is paid by the taxpayer. ``(d) Definitions.--For purposes of this section-- ``(1) Qualified employee.-- ``(A) In general.--The term `qualified employee' means, with respect to any period, an employee of an employer if-- ``(i) the total amount of wages paid or incurred by such employer with respect to such employee for the taxable year exceeds $10,000, and ``(ii) the employee is not a highly compensated employee. ``(B) Treatment of certain employees.--For purposes of subparagraph (A), the term `employee' shall include-- ``(i) an employee within the meaning of section 401(c)(1), and ``(ii) a leased employee within the meaning of section 414(n). ``(C) Exclusion of certain employees.-- ``(i) In general.--If a plan-- ``(I) prescribes minimum age and service requirements as a condition of coverage, and ``(II) excludes all employees not meeting such requirements from coverage, then such employees shall be excluded from consideration for purposes of this paragraph. ``(ii) Collective bargaining agreement.-- For purposes of this paragraph, there shall be excluded from consideration employees who are included in a unit of employees covered by an agreement between employee representatives and one or more employers, if there is evidence that health insurance benefits were the subject of good faith bargaining between such employee representatives and such employer. ``(iii) Limits on minimum requirements.-- Rules similar to the rules of section 410(a) shall apply with respect to minimum age and service requirements under clause (i). ``(D) Wages.--The term `wages'-- ``(i) has the meaning given such term by section 3121(a) (determined without regard to any dollar limitation contained in such section), and ``(ii) in the case of an employee described in subparagraph (B)(i), includes the net earnings from self-employment (as defined in section 1402(a) and as so determined). ``(2) Qualified employee health insurance expenses.-- ``(A) In general.--The term `qualified employee health insurance expenses' means any amount paid or incurred by an employer during the applicable period for health insurance coverage provided under a new health plan to the extent such amount is attributable to coverage provided to any employee who is not a highly compensated employee. ``(B) Exception for amounts paid under salary reduction arrangements.--No amount paid or incurred for health insurance coverage pursuant to a salary reduction arrangement shall be taken into account under subparagraph (A). ``(C) Health insurance coverage.--The term `health insurance coverage' has the meaning given such term by section 9832(b)(1). ``(D) New health plan.--For purposes of this paragraph, the term `new health plan' means any arrangement of the employer which provides health insurance coverage to employees if-- ``(i) such employer (or predecessor employer) did not establish or maintain such arrangement (or any similar arrangement) at any time during the 2 taxable years ending prior to the taxable year in which the credit under this section is first allowed, and ``(ii) such arrangement covers at least 70 percent of the qualified employees of such employer who are not otherwise covered by health insurance. ``(E) Applicable period.--For purposes of subparagraph (A), the applicable period with respect to an employer shall be the 4-year period beginning on the date such employer establishes a new health plan. ``(3) Highly compensated employee.--The term `highly compensated employee' means an employee who for the preceding year had compensation from the employer in excess of $75,000. ``(e) Certain rules made applicable.--For purposes of this section, rules similar to the rules of section 52 shall apply. ``(f) Disallowance of Deduction.--No deduction shall be allowed for that portion of the qualified employee health insurance expenses for the taxable year which is equal to the amount of the credit determined under subsection (a). ``(g) Termination.--This section shall not apply to expenses paid or incurred by an employer with respect to any arrangement established on or after January 1, 2009.''. (b) Credit To Be Part of General Business Credit.--Section 38(b) of the Internal Revenue Code of 1986 (relating to current year business credit) is amended by striking ``plus'' at the end of paragraph (11), by striking the period at the end of paragraph (12) and inserting ``, plus'', and by adding at the end the following: ``(13) the employee health insurance expenses credit determined under section 45D.'' (c) No Carrybacks.--Subsection (d) of section 39 of the Internal Revenue Code of 1986 (relating to carryback and carryforward of unused credits) is amended by adding at the end the following: ``(9) No carryback of section 45d credit before effective date.--No portion of the unused business credit for any taxable year which is attributable to the employee health insurance expenses credit determined under section 45D may be carried back to a taxable year ending before the date of the enactment of section 45D.'' (d) Clerical Amendment.--The table of sections for subpart D of part IV of subchapter A of chapter 1 of the Internal Revenue Code of 1986 is amended by adding at the end the following: ``Sec. 45D. Employee health insurance expenses.'' (e) Effective Date.--The amendments made by this section shall apply to amounts paid or incurred in taxable years beginning after December 31, 2000, for arrangements established after the date of the enactment of this Act. SEC. 4. QUALIFIED HEALTH BENEFIT PURCHASING COALITION. (a) In General.--Chapter 100 of the Internal Revenue Code of 1986 (relating to group health plan requirements) is amended by adding at the end the following new subchapter: ``Subchapter D--Qualified Health Benefit Purchasing Coalition ``Sec. 9841. Qualified health benefit purchasing coalition. ``SEC. 9841. QUALIFIED HEALTH BENEFIT PURCHASING COALITION. ``(a) In General.--A qualified health benefit purchasing coalition is a private not-for-profit corporation which-- ``(1) is licensed to provide health insurance in the State in which the employers to which such coalition is providing insurance is located, and ``(2) establishes to the Secretary, under State certification procedures or other procedures as the Secretary may provide by regulation, that such coalition meets the requirements of this section. ``(b) Board of Directors.-- ``(1) In general.--Each purchasing coalition under this section shall be governed by a Board of Directors. ``(2) Election.--The Secretary shall establish procedures governing election of such Board. ``(3) Membership.--The Board of Directors shall-- ``(A) be composed of small employers and employee representatives of such employers, but ``(B) not include other interested parties, such as service providers, health insurers, or insurance agents or brokers which may have a conflict of interest with the purposes of the coalition. ``(c) Membership of Coalition.-- ``(1) In general.--A purchasing coalition-- ``(A) shall accept all small employers residing within the area served by the coalition as members if such employers request such membership, and ``(B) may accept any other employers residing with such area. ``(2) Voting.--Members of a purchasing coalition shall have voting rights consistent with the rules established by the State. ``(d) Duties of Purchasing Coalitions.--Each purchasing coalition shall-- ``(1) enter into agreements with employers to provide health insurance benefits to employees of such employers, ``(2) enter into agreements with 3 or more unaffiliated, qualified licensed health plans, to offer benefits to members, ``(3) offer to members at least 1 open enrollment period per calendar year, ``(4) serve a significant geographical area, and ``(5) carry out other functions provided for under this section. ``(e) Limitation on Activities.--A purchasing coalition shall not-- ``(1) perform any activity (including certification or enforcement) relating to compliance or licensing of health plans, ``(2) assume insurance or financial risk in relation to any health plan, or ``(3) perform other activities identified by the State as being inconsistent with the performance of its duties under this section. ``(f) Additional Requirements For Purchasing Coalitions.--As provided by the Secretary in regulations, a purchasing coalition shall be subject to requirements similar to the requirements of a group health plan under this chapter. ``(g) Definition of Small Employer.--The term `small employer' has the meaning given such term by section 4980D(d)(2).''. (b) Conforming Amendment.--The table of subchapters for chapter 100 of the Internal Revenue Code of 1986 is amended by adding at the end the following item: ``Subchapter D. Qualified health benefit purchasing coalition.''.[/INST]Provides for the establishment of qualified health benefit purchasing coalitions which shall enter into agreements with small business employers to provide health benefits to employees of such employers.</s>

as a common malignant tumor in the digestive tract , colorectal cancer occurs in both the colon and rectum . nearly 1.5 million people are diagnosed with colorectal carcinoma each year , making it the second most common cancer in industrial countries . the incidence of colorectal cancer in china is higher in urban than non - urban areas , possibly due to lifestyle transitions . in urban areas , the incidence and mortality of colorectal cancer it is estimated that with economic development and change of lifestyles , the incidence rate will continue to rise . multiple factors underlie the occurrence of colorectal cancer , including genetic influences , over - intake of fatty acids or calories , and lack of exercise . recent studies have revealed a correlation between colorectal cancer and diabetes , which is a metabolic disorder featuring hyperglycemia , and can be caused by the interaction of genetic and environmental factors . recently , the incidence of type 2 diabetes mellitus ( t2db ) , complicated with malignant tumors , especially the digestive tract cancers , has been increasing . surveys have proved that about 12~20% of diabetic patients are at risk of colorectal cancer , and the incidence rate is more than twice as much as that in other populations . these results suggest that certain unique biological molecules in diabetic patients might facilitate the occurrence of colorectal cancer . evidence has demonstrated a close correlation between insulin - like growth factor system ( igfs ) and colorectal cancer pathogenesis and progression , as suggested by abnormal expression of igfs proteins in diabetic patients blood samples . igfs include igf - i , igf - ii , relevant receptors igf - ir and igf - iir , and igf - binding proteins ( igfbps ) , all of which exert crucial roles in anti - apoptosis and facilitating cell proliferation . we thus performed a case - control study to investigate the difference of colorectal cancer incidence between diabetic and non - diabetic people . the expression levels of igfs - related genes were further tested and the role of igfs in pathogenesis of colorectal cancer was investigated . a total of 206 individuals who had undergone primary screening for colorectal cancer from january 2013 to december 2013 were recruited in the first hospital of hebei medical university . of these 206 , 85 were diagnosed with diabetes , while the other 121 people were non - diabetics recruited as the control group . the diagnostic criteria for diabetes were : ( 1 ) clinical symptoms of diabetes mellitus ; ( 2 ) fasted blood glucose 7.0 mmol / l or normal blood glucose 11.1 we collected 5-ml peripheral blood samples for separation of plasma by cold centrifugation . among the 85 diabetic patients , 11 were diagnosed with colorectal cancer ; 5 patients eventually had surgical resection of tumors . this study was approved by the ethics committee of the first hospital of hebei medical university . total rna was extracted from plasma samples using an extraction kit ( invitrogen , usa ) , following the manufacturer s instructions . in brief , 0.5 ml of plasma was mixed with an equal volume of 2 solution buffer . after iced incubation for 5 min , phenol - chloroform was added to extract rna , which included vortex ( 1 min ) , room temperature incubation ( 5 min ) , and centrifugation ( 12 000 g , 10 min ) . the upper aqueous phase was transferred to a new tube containing 1 ml of absolute ethanol . the mixture was loaded onto the column , followed by 12 000 g centrifugation to precipitate rna . the total system was 20 l , containing rna , buffer 2 mix , and reverse transcriptase . in vitro reverse transcription was performed with incubation at 65c for 5 min , followed by 37c for 15 min and 98c denaturing ( 5 min ) . a real - time pcr system containing cdna , specific primers ( sequence as table 1 ) , sybr green mixture ( toyobo , japan ) , and sterilized water , was performed in a pcr cycler ( model viia7 , abi , usa ) . reaction conditions were : 95c for 5 min , followed by 40 cycles of 95c denature for 15 s , 60c annealing for 45 s , and 72c elongation for 15 s. relative dna level was determined by 2 method . about 1 g of tumor or adjacent tissues was homogenized on ice , along with 1 ml ripa and proteinase inhibitor . the mixture was incubated on ice for 30 min and centrifuged at 12 000 g for 10 min . proteins were then separated by sds - page and were transferred to nc membrane under 300-ma electrical fields . the membrane was first blocked in 5% defatted milk powder for 2 h , and then rinsed in pbst buffer . primary antibodies against igf - i , igf - ir , igfbp-5 , and -actin ( abcam , usa ) were applied at 1:1000 dilution for overnight incubation . on the next day , secondary antibody was added at 1:10 000 for 1-h incubation . after rinsing in pbst 3 times , the membrane was mixed with chromogenic substrates for exposure in the dark ( 90 s ) . the optical density ( od ) values of each protein band were recorded using the gis-2020d system ( tanon , china ) for calculating relative expression levels of proteins . the spss 16.0 software package ( ibm , us ) was used to process all collected data , and quantitative results are presented as mean standard deviation ( sd ) . the t test or analysis of variance ( anova ) was used to compare means between groups , as appropriate . enumeration data are presented as percentages and were analyzed by the chi - square test . a total of 206 individuals who had undergone primary screening for colorectal cancer from january 2013 to december 2013 were recruited in the first hospital of hebei medical university . of these 206 , 85 were diagnosed with diabetes , while the other 121 people were non - diabetics recruited as the control group . the diagnostic criteria for diabetes were : ( 1 ) clinical symptoms of diabetes mellitus ; ( 2 ) fasted blood glucose 7.0 mmol / l or normal blood glucose 11.1 we collected 5-ml peripheral blood samples for separation of plasma by cold centrifugation . among the 85 diabetic patients , 11 were diagnosed with colorectal cancer ; 5 patients eventually had surgical resection of tumors . this study was approved by the ethics committee of the first hospital of hebei medical university . total rna was extracted from plasma samples using an extraction kit ( invitrogen , usa ) , following the manufacturer s instructions . in brief , 0.5 ml of plasma was mixed with an equal volume of 2 solution buffer . after iced incubation for 5 min , phenol - chloroform was added to extract rna , which included vortex ( 1 min ) , room temperature incubation ( 5 min ) , and centrifugation ( 12 000 g , 10 min ) . the upper aqueous phase was transferred to a new tube containing 1 ml of absolute ethanol . the mixture was loaded onto the column , followed by 12 000 g centrifugation to precipitate rna . the total system was 20 l , containing rna , buffer 2 mix , and reverse transcriptase . in vitro reverse transcription was performed with incubation at 65c for 5 min , followed by 37c for 15 min and 98c denaturing ( 5 min ) . a real - time pcr system containing cdna , specific primers ( sequence as table 1 ) , sybr green mixture ( toyobo , japan ) , and sterilized water , was performed in a pcr cycler ( model viia7 , abi , usa ) . reaction conditions were : 95c for 5 min , followed by 40 cycles of 95c denature for 15 s , 60c annealing for 45 s , and 72c elongation for 15 s. relative dna level was determined by 2 method . about 1 g of tumor or adjacent tissues was homogenized on ice , along with 1 ml ripa and proteinase inhibitor . the mixture was incubated on ice for 30 min and centrifuged at 12 000 g for 10 min . proteins were then separated by sds - page and were transferred to nc membrane under 300-ma electrical fields . the membrane was first blocked in 5% defatted milk powder for 2 h , and then rinsed in pbst buffer . primary antibodies against igf - i , igf - ir , igfbp-5 , and -actin ( abcam , usa ) were applied at 1:1000 dilution for overnight incubation . on the next day after rinsing in pbst 3 times , the membrane was mixed with chromogenic substrates for exposure in the dark ( 90 s ) . the optical density ( od ) values of each protein band were recorded using the gis-2020d system ( tanon , china ) for calculating relative expression levels of proteins . the spss 16.0 software package ( ibm , us ) was used to process all collected data , and quantitative results are presented as mean standard deviation ( sd ) . the t test or analysis of variance ( anova ) was used to compare means between groups , as appropriate . enumeration data are presented as percentages and were analyzed by the chi - square test . in a total of 206 individuals recruited , there were 85 diabetic patients ( 47 males and 38 females , average age=57.2 years ) and 121 non - diabetic controls ( 67 males and 54 females , average age=59.3 years ) . no significant difference was identified in the age or sex ratio between these 2 groups ( t test or chi - square test , both p>0.05 , table 2 ) , suggesting the comparability and homogeneity of the 2 groups . in the diabetes group , a total of 11 colorectal cancer patients were discovered , while only 5 people in the control group were found to have cancer . the incidence of colorectal carcinoma was significantly higher in diabetics ( chi - square test , p<0.05 ) . we also found that the diabetic group had higher body weight ( p<0.05 , table 2 ) . real - time pcr was used to test the expression of igfs in patient plasma . as shown in figure 1 , the level of igf - i in plasma was elevated to 2.06-fold in the diabetic group compared to that in the control group ( figure 1a ) . igf - ii , igf - ir , and igf - iir levels increased by 46% , 75% , and 38% , respectively ( figure 2b2d ) , but igfbp-2 and igfbp-6 decreased to only 72% and 58% of the control level ( figure 2e , 2f ) . in all 10 patients who had undergone surgical resection for colorectal carcinoma ( 5 from the diabetic group and 5 from the control group ) , we studied the expression of igf - i , igf - ir , and igfbp-6 in tumors and adjacent tissues . as shown in figure 2 , the mrna expressions of igf - i and igf - ir increased by 1.61-fold and 1.15-fold in tumor tissues compared to adjacent tissues ( figure 2a , 2b ) , while igfbp-6 level decreased by 48% ( figure 2c ) . we further compared the expression level of these 3 proteins between diabetic and control groups , finding that igf - i and igf - ir were up regulated by 71% and 57% , respectively ( figure 2d , 2e ) while igfbp-6 was down regulated by 39% ( figure 2f ) . western blot analysis obtained consistent results , showing that igf - i and igf - ir were up - regulated in tumor tissues , while igfbp-6 was down - regulated ( figure 3 ) . these results collectively suggest a correlation between igfs - related protein expression and the occurrence of colorectal carcinoma . to investigate the role of igfs in pathogenesis of colorectal cancer , we tested the levels of igfs - related factors in plasma in patients to analyze their correlation . as shown in figure 4 , there was a positive correlation between igf - i and igf - ir level ( r=0.626 , p<0.05 , figure 4a ) , while igfbp-6 was negatively correlated with both igf - i and igf - ir ( r=0.656 and 0.688 , p<0.05 , figure 4b , 4c ) . based on previous studies , igfs - related proteins expressions were closely correlated with the occurrence of colorectal cancer , and the cancer incidence in diabetic patients was significantly higher than that in non - diabetic individuals . to further prove the correlation between plasma igfs expression and occurrence of colorectal cancer , we investigated levels of igf - i , igf - ir , and igfbp-6 in blood of all 16 patients ( 11 from the diabetic group and 5 from the control group ) . results showed that , compared to non - diabetic people , diabetic patients with colorectal carcinoma had higher igf - i and igf - ir levels in plasma , and reduced igfbp-6 levels ( p<0.05 in all cases , table 3 ) . in a total of 206 individuals recruited , there were 85 diabetic patients ( 47 males and 38 females , average age=57.2 years ) and 121 non - diabetic controls ( 67 males and 54 females , average age=59.3 years ) . no significant difference was identified in the age or sex ratio between these 2 groups ( t test or chi - square test , both p>0.05 , table 2 ) , suggesting the comparability and homogeneity of the 2 groups . in the diabetes group , a total of 11 colorectal cancer patients were discovered , while only 5 people in the control group were found to have cancer . the incidence of colorectal carcinoma was significantly higher in diabetics ( chi - square test , p<0.05 ) . we also found that the diabetic group had higher body weight ( p<0.05 , table 2 ) . real - time pcr was used to test the expression of igfs in patient plasma . as shown in figure 1 , the level of igf - i in plasma was elevated to 2.06-fold in the diabetic group compared to that in the control group ( figure 1a ) . igf - ii , igf - ir , and igf - iir levels increased by 46% , 75% , and 38% , respectively ( figure 2b2d ) , but igfbp-2 and igfbp-6 decreased to only 72% and 58% of the control level ( figure 2e , 2f ) . in all 10 patients who had undergone surgical resection for colorectal carcinoma ( 5 from the diabetic group and 5 from the control group ) , we studied the expression of igf - i , igf - ir , and igfbp-6 in tumors and adjacent tissues . as shown in figure 2 , the mrna expressions of igf - i and igf - ir increased by 1.61-fold and 1.15-fold in tumor tissues compared to adjacent tissues ( figure 2a , 2b ) , while igfbp-6 level decreased by 48% ( figure 2c ) . we further compared the expression level of these 3 proteins between diabetic and control groups , finding that igf - i and igf - ir were up regulated by 71% and 57% , respectively ( figure 2d , 2e ) while igfbp-6 was down regulated by 39% ( figure 2f ) . western blot analysis obtained consistent results , showing that igf - i and igf - ir were up - regulated in tumor tissues , while igfbp-6 was down - regulated ( figure 3 ) . these results collectively suggest a correlation between igfs - related protein expression and the occurrence of colorectal carcinoma . to investigate the role of igfs in pathogenesis of colorectal cancer , we tested the levels of igfs - related factors in plasma in patients to analyze their correlation . as shown in figure 4 , there was a positive correlation between igf - i and igf - ir level ( r=0.626 , p<0.05 , figure 4a ) , while igfbp-6 was negatively correlated with both igf - i and igf - ir ( r=0.656 and 0.688 , p<0.05 , figure 4b , 4c ) . based on previous studies , igfs - related proteins expressions were closely correlated with the occurrence of colorectal cancer , and the cancer incidence in diabetic patients was significantly higher than that in non - diabetic individuals . to further prove the correlation between plasma igfs expression and occurrence of colorectal cancer , we investigated levels of igf - i , igf - ir , and igfbp-6 in blood of all 16 patients ( 11 from the diabetic group and 5 from the control group ) . results showed that , compared to non - diabetic people , diabetic patients with colorectal carcinoma had higher igf - i and igf - ir levels in plasma , and reduced igfbp-6 levels ( p<0.05 in all cases , table 3 ) . our study illustrates the higher incidence of colorectal cancer in diabetes patients and shows the critical role of alternation of igfs in occurrence of colorectal tumors among the diabetes group . as the most common malignant tumor in the digestive tract , previous surveys showed a regional difference of tumor incidence , as industrial countries and more developed regions had higher incidence of colorectal cancer compared to developing countries and under - developed regions . in china , tumor incidence is higher in urban than in rural areas . with economic development and lifestyle transition , current knowledge of pathogenesis mechanism underlying colorectal cancer mainly includes economic conditions , environmental pollution , lifestyle and diet . studies have revealed that about 12% to 20% of diabetic patients are at risk of colorectal cancer , but the underlying reason remains unclear . some studies suggested the possible involvement of unhealthy lifestyle - induced compensatory insulinemia and t2 dm in occurrence of colorectal cancer . igfs include igf - i , igf - ii , igf - ir , igf - iir , and igfbps , all of which exert critical roles in anti - apoptosis and facilitating cell proliferation . igf - i and igf - ii are polypeptides containing 70 or 67 amino acid residues , and are modulated by igf - ir and igfbps . via specific binding onto membranes , glycosylated proteins , igf - ir , and igf - i can activate multiple intracellular pathways mediating cell growth , proliferation , and apoptosis . previous studies have shown the up - regulation of igf - i in multiple tumors , including hepatocyte carcinoma , pancreatic cancer , and colorectal cancer . it can also inhibit the expression of fas / fasl gene and induce anti - apoptotic gene bcl-2 expression , thus favoring tumor growth . our retrospective study found no statistically significant difference in sex and age between the diabetic and control groups , suggesting their comparability and homogeneity . the incidence of colorectal cancer was higher in diabetic patients compared to controls , in agreement with a previous study . further study of tumor tissues also found elevated igf - i and igf - ir , and decreased igfbp-6 compared to adjacent tissues . consistent patterns also occurred in colorectal cancer complicated with diabetes in comparison to cancer patients without diabetes , indicating an important role of igfs in the transformation from normal tissues into tumors . based on these data , we further analyzed the relationship between those factors and found a positive correlation between igf - i and igf - ir , and a negative relationship between igfbp-6 and igf - i or igf - ir . we thus postulated that igf - i and igf - ir might exert a synergistic effect to facilitate the tumor growth in colorectal tissues , while igfbp-6 can antagonize such favorable effects . it has been demonstrated that active rho gtpase cdc42 can greatly enhance colorectal cancer cell sw480 metastasis , migration , and invasion showing a contributory role in colorectal cancer metastasis . similarly , early research has shown that the fas / fasl or bcl-2 pathway are activated in colorectal carcinoma cells by igf - i / igf - ir axis , indicating the regulatory role in the transcription and translation of related genes , and demonstrating its involvement in inhibiting cell apoptosis and affecting tumor growth . it is thus possible to prevent or treat colorectal cancer by modulating the intracellular expression of igf - i , igf - ir , and igfbp-6 . the alteration of igfs expressions in diabetic patients increases the risk of the occurrence of colorectal cancer . our finding highlights the importance of early diagnosis for the prevention of colorectal cancer in diabetic patients and may provide evidence useful in the development of anti - colorectal cancer drugs , by using rnai or chemical synthesis ways , which aim to target such igfs .

backgrounddiabetes mellitus a common metabolic disorder with hyperglycemia , is caused by the interaction of genetic and environmental factors . approximately 12~20% of diabetic patients have risk of colorectal cancer . recent studies revealed that the insulin - like growth factor system ( igfs ) plays an important role in tumor occurrence . this study thus investigated the relationship between igfs - related proteins in diabetic patients and the incidence of colorectal carcinoma.material/methodsa retrospective study was performed in a total of 206 individuals , including 85 diagnosed with diabetes . the incidence of colorectal cancer was tracked , along with the detection of igfs expression in serum . during the surgical resection , tumor tissues and adjacent tissues were collected and quantified for igfs expression level.resultswe found no significant difference in age or sex between the diabetic and control groups . diabetic patients , however , had elevated body weight and higher incidence of colorectal cancer compared to non - diabetic controls ( p<0.05 ) . the diabetic group also had higher igf - i and igf - ir mrna levels in serum , while igfbp-6 expression was down - regulated . in comparison to adjacent healthy tissues , tumor tissue had higher levels of igf - i and igf - ir but lower levels of igfbp-6 ( p<0.05).conclusionsour study showed higher incidence of colorectal cancer in diabetics compared to non - diabetics . the occurrence of colorectal cancer in diabetic patients may be associated with elevated igfs - related protein expression level .

<s>[INST]as a common malignant tumor in the digestive tract , colorectal cancer occurs in both the colon and rectum . nearly 1.5 million people are diagnosed with colorectal carcinoma each year , making it the second most common cancer in industrial countries . the incidence of colorectal cancer in china is higher in urban than non - urban areas , possibly due to lifestyle transitions . in urban areas , the incidence and mortality of colorectal cancer it is estimated that with economic development and change of lifestyles , the incidence rate will continue to rise . multiple factors underlie the occurrence of colorectal cancer , including genetic influences , over - intake of fatty acids or calories , and lack of exercise . recent studies have revealed a correlation between colorectal cancer and diabetes , which is a metabolic disorder featuring hyperglycemia , and can be caused by the interaction of genetic and environmental factors . recently , the incidence of type 2 diabetes mellitus ( t2db ) , complicated with malignant tumors , especially the digestive tract cancers , has been increasing . surveys have proved that about 12~20% of diabetic patients are at risk of colorectal cancer , and the incidence rate is more than twice as much as that in other populations . these results suggest that certain unique biological molecules in diabetic patients might facilitate the occurrence of colorectal cancer . evidence has demonstrated a close correlation between insulin - like growth factor system ( igfs ) and colorectal cancer pathogenesis and progression , as suggested by abnormal expression of igfs proteins in diabetic patients blood samples . igfs include igf - i , igf - ii , relevant receptors igf - ir and igf - iir , and igf - binding proteins ( igfbps ) , all of which exert crucial roles in anti - apoptosis and facilitating cell proliferation . we thus performed a case - control study to investigate the difference of colorectal cancer incidence between diabetic and non - diabetic people . the expression levels of igfs - related genes were further tested and the role of igfs in pathogenesis of colorectal cancer was investigated . a total of 206 individuals who had undergone primary screening for colorectal cancer from january 2013 to december 2013 were recruited in the first hospital of hebei medical university . of these 206 , 85 were diagnosed with diabetes , while the other 121 people were non - diabetics recruited as the control group . the diagnostic criteria for diabetes were : ( 1 ) clinical symptoms of diabetes mellitus ; ( 2 ) fasted blood glucose 7.0 mmol / l or normal blood glucose 11.1 we collected 5-ml peripheral blood samples for separation of plasma by cold centrifugation . among the 85 diabetic patients , 11 were diagnosed with colorectal cancer ; 5 patients eventually had surgical resection of tumors . this study was approved by the ethics committee of the first hospital of hebei medical university . total rna was extracted from plasma samples using an extraction kit ( invitrogen , usa ) , following the manufacturer s instructions . in brief , 0.5 ml of plasma was mixed with an equal volume of 2 solution buffer . after iced incubation for 5 min , phenol - chloroform was added to extract rna , which included vortex ( 1 min ) , room temperature incubation ( 5 min ) , and centrifugation ( 12 000 g , 10 min ) . the upper aqueous phase was transferred to a new tube containing 1 ml of absolute ethanol . the mixture was loaded onto the column , followed by 12 000 g centrifugation to precipitate rna . the total system was 20 l , containing rna , buffer 2 mix , and reverse transcriptase . in vitro reverse transcription was performed with incubation at 65c for 5 min , followed by 37c for 15 min and 98c denaturing ( 5 min ) . a real - time pcr system containing cdna , specific primers ( sequence as table 1 ) , sybr green mixture ( toyobo , japan ) , and sterilized water , was performed in a pcr cycler ( model viia7 , abi , usa ) . reaction conditions were : 95c for 5 min , followed by 40 cycles of 95c denature for 15 s , 60c annealing for 45 s , and 72c elongation for 15 s. relative dna level was determined by 2 method . about 1 g of tumor or adjacent tissues was homogenized on ice , along with 1 ml ripa and proteinase inhibitor . the mixture was incubated on ice for 30 min and centrifuged at 12 000 g for 10 min . proteins were then separated by sds - page and were transferred to nc membrane under 300-ma electrical fields . the membrane was first blocked in 5% defatted milk powder for 2 h , and then rinsed in pbst buffer . primary antibodies against igf - i , igf - ir , igfbp-5 , and -actin ( abcam , usa ) were applied at 1:1000 dilution for overnight incubation . on the next day , secondary antibody was added at 1:10 000 for 1-h incubation . after rinsing in pbst 3 times , the membrane was mixed with chromogenic substrates for exposure in the dark ( 90 s ) . the optical density ( od ) values of each protein band were recorded using the gis-2020d system ( tanon , china ) for calculating relative expression levels of proteins . the spss 16.0 software package ( ibm , us ) was used to process all collected data , and quantitative results are presented as mean standard deviation ( sd ) . the t test or analysis of variance ( anova ) was used to compare means between groups , as appropriate . enumeration data are presented as percentages and were analyzed by the chi - square test . a total of 206 individuals who had undergone primary screening for colorectal cancer from january 2013 to december 2013 were recruited in the first hospital of hebei medical university . of these 206 , 85 were diagnosed with diabetes , while the other 121 people were non - diabetics recruited as the control group . the diagnostic criteria for diabetes were : ( 1 ) clinical symptoms of diabetes mellitus ; ( 2 ) fasted blood glucose 7.0 mmol / l or normal blood glucose 11.1 we collected 5-ml peripheral blood samples for separation of plasma by cold centrifugation . among the 85 diabetic patients , 11 were diagnosed with colorectal cancer ; 5 patients eventually had surgical resection of tumors . this study was approved by the ethics committee of the first hospital of hebei medical university . total rna was extracted from plasma samples using an extraction kit ( invitrogen , usa ) , following the manufacturer s instructions . in brief , 0.5 ml of plasma was mixed with an equal volume of 2 solution buffer . after iced incubation for 5 min , phenol - chloroform was added to extract rna , which included vortex ( 1 min ) , room temperature incubation ( 5 min ) , and centrifugation ( 12 000 g , 10 min ) . the upper aqueous phase was transferred to a new tube containing 1 ml of absolute ethanol . the mixture was loaded onto the column , followed by 12 000 g centrifugation to precipitate rna . the total system was 20 l , containing rna , buffer 2 mix , and reverse transcriptase . in vitro reverse transcription was performed with incubation at 65c for 5 min , followed by 37c for 15 min and 98c denaturing ( 5 min ) . a real - time pcr system containing cdna , specific primers ( sequence as table 1 ) , sybr green mixture ( toyobo , japan ) , and sterilized water , was performed in a pcr cycler ( model viia7 , abi , usa ) . reaction conditions were : 95c for 5 min , followed by 40 cycles of 95c denature for 15 s , 60c annealing for 45 s , and 72c elongation for 15 s. relative dna level was determined by 2 method . about 1 g of tumor or adjacent tissues was homogenized on ice , along with 1 ml ripa and proteinase inhibitor . the mixture was incubated on ice for 30 min and centrifuged at 12 000 g for 10 min . proteins were then separated by sds - page and were transferred to nc membrane under 300-ma electrical fields . the membrane was first blocked in 5% defatted milk powder for 2 h , and then rinsed in pbst buffer . primary antibodies against igf - i , igf - ir , igfbp-5 , and -actin ( abcam , usa ) were applied at 1:1000 dilution for overnight incubation . on the next day after rinsing in pbst 3 times , the membrane was mixed with chromogenic substrates for exposure in the dark ( 90 s ) . the optical density ( od ) values of each protein band were recorded using the gis-2020d system ( tanon , china ) for calculating relative expression levels of proteins . the spss 16.0 software package ( ibm , us ) was used to process all collected data , and quantitative results are presented as mean standard deviation ( sd ) . the t test or analysis of variance ( anova ) was used to compare means between groups , as appropriate . enumeration data are presented as percentages and were analyzed by the chi - square test . in a total of 206 individuals recruited , there were 85 diabetic patients ( 47 males and 38 females , average age=57.2 years ) and 121 non - diabetic controls ( 67 males and 54 females , average age=59.3 years ) . no significant difference was identified in the age or sex ratio between these 2 groups ( t test or chi - square test , both p>0.05 , table 2 ) , suggesting the comparability and homogeneity of the 2 groups . in the diabetes group , a total of 11 colorectal cancer patients were discovered , while only 5 people in the control group were found to have cancer . the incidence of colorectal carcinoma was significantly higher in diabetics ( chi - square test , p<0.05 ) . we also found that the diabetic group had higher body weight ( p<0.05 , table 2 ) . real - time pcr was used to test the expression of igfs in patient plasma . as shown in figure 1 , the level of igf - i in plasma was elevated to 2.06-fold in the diabetic group compared to that in the control group ( figure 1a ) . igf - ii , igf - ir , and igf - iir levels increased by 46% , 75% , and 38% , respectively ( figure 2b2d ) , but igfbp-2 and igfbp-6 decreased to only 72% and 58% of the control level ( figure 2e , 2f ) . in all 10 patients who had undergone surgical resection for colorectal carcinoma ( 5 from the diabetic group and 5 from the control group ) , we studied the expression of igf - i , igf - ir , and igfbp-6 in tumors and adjacent tissues . as shown in figure 2 , the mrna expressions of igf - i and igf - ir increased by 1.61-fold and 1.15-fold in tumor tissues compared to adjacent tissues ( figure 2a , 2b ) , while igfbp-6 level decreased by 48% ( figure 2c ) . we further compared the expression level of these 3 proteins between diabetic and control groups , finding that igf - i and igf - ir were up regulated by 71% and 57% , respectively ( figure 2d , 2e ) while igfbp-6 was down regulated by 39% ( figure 2f ) . western blot analysis obtained consistent results , showing that igf - i and igf - ir were up - regulated in tumor tissues , while igfbp-6 was down - regulated ( figure 3 ) . these results collectively suggest a correlation between igfs - related protein expression and the occurrence of colorectal carcinoma . to investigate the role of igfs in pathogenesis of colorectal cancer , we tested the levels of igfs - related factors in plasma in patients to analyze their correlation . as shown in figure 4 , there was a positive correlation between igf - i and igf - ir level ( r=0.626 , p<0.05 , figure 4a ) , while igfbp-6 was negatively correlated with both igf - i and igf - ir ( r=0.656 and 0.688 , p<0.05 , figure 4b , 4c ) . based on previous studies , igfs - related proteins expressions were closely correlated with the occurrence of colorectal cancer , and the cancer incidence in diabetic patients was significantly higher than that in non - diabetic individuals . to further prove the correlation between plasma igfs expression and occurrence of colorectal cancer , we investigated levels of igf - i , igf - ir , and igfbp-6 in blood of all 16 patients ( 11 from the diabetic group and 5 from the control group ) . results showed that , compared to non - diabetic people , diabetic patients with colorectal carcinoma had higher igf - i and igf - ir levels in plasma , and reduced igfbp-6 levels ( p<0.05 in all cases , table 3 ) . in a total of 206 individuals recruited , there were 85 diabetic patients ( 47 males and 38 females , average age=57.2 years ) and 121 non - diabetic controls ( 67 males and 54 females , average age=59.3 years ) . no significant difference was identified in the age or sex ratio between these 2 groups ( t test or chi - square test , both p>0.05 , table 2 ) , suggesting the comparability and homogeneity of the 2 groups . in the diabetes group , a total of 11 colorectal cancer patients were discovered , while only 5 people in the control group were found to have cancer . the incidence of colorectal carcinoma was significantly higher in diabetics ( chi - square test , p<0.05 ) . we also found that the diabetic group had higher body weight ( p<0.05 , table 2 ) . real - time pcr was used to test the expression of igfs in patient plasma . as shown in figure 1 , the level of igf - i in plasma was elevated to 2.06-fold in the diabetic group compared to that in the control group ( figure 1a ) . igf - ii , igf - ir , and igf - iir levels increased by 46% , 75% , and 38% , respectively ( figure 2b2d ) , but igfbp-2 and igfbp-6 decreased to only 72% and 58% of the control level ( figure 2e , 2f ) . in all 10 patients who had undergone surgical resection for colorectal carcinoma ( 5 from the diabetic group and 5 from the control group ) , we studied the expression of igf - i , igf - ir , and igfbp-6 in tumors and adjacent tissues . as shown in figure 2 , the mrna expressions of igf - i and igf - ir increased by 1.61-fold and 1.15-fold in tumor tissues compared to adjacent tissues ( figure 2a , 2b ) , while igfbp-6 level decreased by 48% ( figure 2c ) . we further compared the expression level of these 3 proteins between diabetic and control groups , finding that igf - i and igf - ir were up regulated by 71% and 57% , respectively ( figure 2d , 2e ) while igfbp-6 was down regulated by 39% ( figure 2f ) . western blot analysis obtained consistent results , showing that igf - i and igf - ir were up - regulated in tumor tissues , while igfbp-6 was down - regulated ( figure 3 ) . these results collectively suggest a correlation between igfs - related protein expression and the occurrence of colorectal carcinoma . to investigate the role of igfs in pathogenesis of colorectal cancer , we tested the levels of igfs - related factors in plasma in patients to analyze their correlation . as shown in figure 4 , there was a positive correlation between igf - i and igf - ir level ( r=0.626 , p<0.05 , figure 4a ) , while igfbp-6 was negatively correlated with both igf - i and igf - ir ( r=0.656 and 0.688 , p<0.05 , figure 4b , 4c ) . based on previous studies , igfs - related proteins expressions were closely correlated with the occurrence of colorectal cancer , and the cancer incidence in diabetic patients was significantly higher than that in non - diabetic individuals . to further prove the correlation between plasma igfs expression and occurrence of colorectal cancer , we investigated levels of igf - i , igf - ir , and igfbp-6 in blood of all 16 patients ( 11 from the diabetic group and 5 from the control group ) . results showed that , compared to non - diabetic people , diabetic patients with colorectal carcinoma had higher igf - i and igf - ir levels in plasma , and reduced igfbp-6 levels ( p<0.05 in all cases , table 3 ) . our study illustrates the higher incidence of colorectal cancer in diabetes patients and shows the critical role of alternation of igfs in occurrence of colorectal tumors among the diabetes group . as the most common malignant tumor in the digestive tract , previous surveys showed a regional difference of tumor incidence , as industrial countries and more developed regions had higher incidence of colorectal cancer compared to developing countries and under - developed regions . in china , tumor incidence is higher in urban than in rural areas . with economic development and lifestyle transition , current knowledge of pathogenesis mechanism underlying colorectal cancer mainly includes economic conditions , environmental pollution , lifestyle and diet . studies have revealed that about 12% to 20% of diabetic patients are at risk of colorectal cancer , but the underlying reason remains unclear . some studies suggested the possible involvement of unhealthy lifestyle - induced compensatory insulinemia and t2 dm in occurrence of colorectal cancer . igfs include igf - i , igf - ii , igf - ir , igf - iir , and igfbps , all of which exert critical roles in anti - apoptosis and facilitating cell proliferation . igf - i and igf - ii are polypeptides containing 70 or 67 amino acid residues , and are modulated by igf - ir and igfbps . via specific binding onto membranes , glycosylated proteins , igf - ir , and igf - i can activate multiple intracellular pathways mediating cell growth , proliferation , and apoptosis . previous studies have shown the up - regulation of igf - i in multiple tumors , including hepatocyte carcinoma , pancreatic cancer , and colorectal cancer . it can also inhibit the expression of fas / fasl gene and induce anti - apoptotic gene bcl-2 expression , thus favoring tumor growth . our retrospective study found no statistically significant difference in sex and age between the diabetic and control groups , suggesting their comparability and homogeneity . the incidence of colorectal cancer was higher in diabetic patients compared to controls , in agreement with a previous study . further study of tumor tissues also found elevated igf - i and igf - ir , and decreased igfbp-6 compared to adjacent tissues . consistent patterns also occurred in colorectal cancer complicated with diabetes in comparison to cancer patients without diabetes , indicating an important role of igfs in the transformation from normal tissues into tumors . based on these data , we further analyzed the relationship between those factors and found a positive correlation between igf - i and igf - ir , and a negative relationship between igfbp-6 and igf - i or igf - ir . we thus postulated that igf - i and igf - ir might exert a synergistic effect to facilitate the tumor growth in colorectal tissues , while igfbp-6 can antagonize such favorable effects . it has been demonstrated that active rho gtpase cdc42 can greatly enhance colorectal cancer cell sw480 metastasis , migration , and invasion showing a contributory role in colorectal cancer metastasis . similarly , early research has shown that the fas / fasl or bcl-2 pathway are activated in colorectal carcinoma cells by igf - i / igf - ir axis , indicating the regulatory role in the transcription and translation of related genes , and demonstrating its involvement in inhibiting cell apoptosis and affecting tumor growth . it is thus possible to prevent or treat colorectal cancer by modulating the intracellular expression of igf - i , igf - ir , and igfbp-6 . the alteration of igfs expressions in diabetic patients increases the risk of the occurrence of colorectal cancer . our finding highlights the importance of early diagnosis for the prevention of colorectal cancer in diabetic patients and may provide evidence useful in the development of anti - colorectal cancer drugs , by using rnai or chemical synthesis ways , which aim to target such igfs .[/INST]backgrounddiabetes mellitus a common metabolic disorder with hyperglycemia , is caused by the interaction of genetic and environmental factors . approximately 12~20% of diabetic patients have risk of colorectal cancer . recent studies revealed that the insulin - like growth factor system ( igfs ) plays an important role in tumor occurrence . this study thus investigated the relationship between igfs - related proteins in diabetic patients and the incidence of colorectal carcinoma.material/methodsa retrospective study was performed in a total of 206 individuals , including 85 diagnosed with diabetes . the incidence of colorectal cancer was tracked , along with the detection of igfs expression in serum . during the surgical resection , tumor tissues and adjacent tissues were collected and quantified for igfs expression level.resultswe found no significant difference in age or sex between the diabetic and control groups . diabetic patients , however , had elevated body weight and higher incidence of colorectal cancer compared to non - diabetic controls ( p<0.05 ) . the diabetic group also had higher igf - i and igf - ir mrna levels in serum , while igfbp-6 expression was down - regulated . in comparison to adjacent healthy tissues , tumor tissue had higher levels of igf - i and igf - ir but lower levels of igfbp-6 ( p<0.05).conclusionsour study showed higher incidence of colorectal cancer in diabetics compared to non - diabetics . the occurrence of colorectal cancer in diabetic patients may be associated with elevated igfs - related protein expression level .</s>

pregnancy in the early reproductive life in modern times has been discouraged because of possible harm to the physical , emotional , and social health of adolescents and because of potential adverse consequences for children s health . however , depending on the teenager s social context , pregnancy can be seen as normal event , accepted within their society and customs.1 pregnancy leads to changes that impact on women s lives , and these changes can be endocrine , somatic , or psychological . when these changes occur in adolescence , they may become more intense because of the synergy of crises common in both these life phases.2,3 although the magnitude of teenage pregnancy has been reducing in countries around the world , this situation is still worrying in africa , where teenage pregnancies represent 35%77% of total births.5 angola has a young population of approximately 17 million inhabitants . wealth is concentrated in certain population groups , and the country is still rated at very low levels in most global socioeconomic development and health measures . angola is divided into 18 provinces , 164 districts , and 557 comunidades.6 the availability of data on health , official or published in scientific articles , is very limited . the mother and infant and reproductive health indicators are the worst in sub - saharan africa . world health organization ( who ) research reported in 2009 showed an infant mortality of 154/1000 live births and a fertility rate of 6.7 births per woman . however , substantial improvements were recorded in 2013 , when who estimated a fertility rate of 6.4 births per woman and an infant mortality rate of 116/1000 live births.7 underreporting of births does occur in angola s health information system , since most births occur outside the hospital environment , often without assistance of health professionals . considering these data , we chose to describe the mode of delivery , vaginal or cesarean , of the adolescents studied . the aim of this study was to establish a profile of teenage pregnancy and describe factors associated with the type of delivery , vaginal or cesarean , at a referral hospital in huambo , angola , from february to august 2010 . the sample consisted of 381 adolescent mothers , aged 1019 years , who gave birth in the maternity ward of huambo central hospital , huambo , angola . the study hospital is in the capital city of the huambo province , which has a population of approximately 2,225,000 inhabitants . at - risk pregnancies are referred to huambo central hospital , and the tertiary hospital is unique in the region . its maternity unit performs an average of 36 births a day and has 17 predelivery beds and 7 postpartum beds . medical professionals are responsible for cesarean sections and normal deliveries with some level of complication , while low - risk hospital births are attended by nurses . data were obtained through interviews in the postpartum period , using a structured questionnaire validated by the national school of public health ( ensp)fiocruz in a study of assistance to teenage pregnancy in rio de janeiro . some adaptations were made for use in africa , mainly in regard to cultural and traditional differences . a pilot study was performed with a sample of 20 mothers to evaluate the applicability of the questionnaire as well as the conditions , duration and uniformity of the interviews . data collection was performed by trained staff in a reserved space to preserve the anonymity and privacy of the mothers . the interviews took place with the written informed consent of the legal guardians of the adolescents . the independent variables were as follows : age postpartum , categorized into two age groups , 1416 years , called early , and 1719 years , called late adolescence ; area of residence , urban or rural ; paternal employment ; and teenager s enrollment in study when she became pregnant . we defined the two age groups because , in our sample , we did not have any mothers under 14 years . social and obstetric data were also analyzed , including whether the postpartum woman lived with the infant s father , the father s literacy status , if the father has another family ( as it is common in angola for some men to have more than one family at the same time ) , whether prenatal visits were attended , number of visits , < 6 or 6 , if prenatal care started in the first , second , or third trimester of pregnancy , morbidity during pregnancy ( malaria , urinary tract infection , hypertensive syndrome , anemia , bleeding , heart disease , and hiv ) , and whether prenatal care extended until the end of pregnancy . postpartum mothers aged between 10 and 19 years were considered adolescents according to the who guidelines.4 however , as mentioned earlier , the youngest mother to present during our study period was aged 14 years . bivariate analyses using chi - squared tests with a 5% significance level were performed to compare the adolescent mothers grouped by sociodemographic and psychosocial variables , which were collated according to maternal age and marital status . data were processed and analyzed using the software epi info version 6.04b from the centers for disease control and prevention . the project was reviewed and approved by the research ethics committee of the ministry of health of angola and was authorized by the huambo central hospital . the sample consisted of 381 adolescent mothers , aged 1019 years , who gave birth in the maternity ward of huambo central hospital , huambo , angola . the study hospital is in the capital city of the huambo province , which has a population of approximately 2,225,000 inhabitants . at - risk pregnancies are referred to huambo central hospital , and the tertiary hospital is unique in the region . its maternity unit performs an average of 36 births a day and has 17 predelivery beds and 7 postpartum beds . medical professionals are responsible for cesarean sections and normal deliveries with some level of complication , while low - risk hospital births are attended by nurses . data were obtained through interviews in the postpartum period , using a structured questionnaire validated by the national school of public health ( ensp)fiocruz in a study of assistance to teenage pregnancy in rio de janeiro . some adaptations were made for use in africa , mainly in regard to cultural and traditional differences . a pilot study was performed with a sample of 20 mothers to evaluate the applicability of the questionnaire as well as the conditions , duration and uniformity of the interviews . data collection was performed by trained staff in a reserved space to preserve the anonymity and privacy of the mothers . the interviews took place with the written informed consent of the legal guardians of the adolescents . the independent variables were as follows : age postpartum , categorized into two age groups , 1416 years , called early , and 1719 years , called late adolescence ; area of residence , urban or rural ; paternal employment ; and teenager s enrollment in study when she became pregnant . we defined the two age groups because , in our sample , we did not have any mothers under 14 years . social and obstetric data were also analyzed , including whether the postpartum woman lived with the infant s father , the father s literacy status , if the father has another family ( as it is common in angola for some men to have more than one family at the same time ) , whether prenatal visits were attended , number of visits , < 6 or 6 , if prenatal care started in the first , second , or third trimester of pregnancy , morbidity during pregnancy ( malaria , urinary tract infection , hypertensive syndrome , anemia , bleeding , heart disease , and hiv ) , and whether prenatal care extended until the end of pregnancy . postpartum mothers aged between 10 and 19 years were considered adolescents according to the who guidelines.4 however , as mentioned earlier , the youngest mother to present during our study period was aged 14 years . bivariate analyses using chi - squared tests with a 5% significance level were performed to compare the adolescent mothers grouped by sociodemographic and psychosocial variables , which were collated according to maternal age and marital status . data were processed and analyzed using the software epi info version 6.04b from the centers for disease control and prevention . the project was reviewed and approved by the research ethics committee of the ministry of health of angola and was authorized by the huambo central hospital . for this study , 381 subjects were interviewed , with 147 ( 38.6% ) aged between 10 and 16 years and 234 ( 61.4% ) between 17 and 19 years . in table 1 , we can see that the proportion of mothers who lived in rural areas was high in both groups , 78.2% in the early adolescent group and 70.5% in the late adolescent group . a higher percentage of the mothers in the early group had unemployed parents , 47.3% , compared to 38.0% in the older group . unemployment of the baby s father was also more common among the younger mothers . with regard to marital status , the early adolescent group had a higher proportion not living with the child s father , 70.7% , versus 38.5% of the older group . in the older group , just 32.1% of the subjects had been enrolled in education when they became pregnant . in both groups , few respondents saw teenage pregnancy as a hindrance to their lives , only 11.6% in the younger group and 15.0% in the older group . in both groups the father having another family was more common among the younger group . as shown in table 2 , the difference between the groups in terms of the reported use of contraceptive methods was not statistically significant . there was also no significant difference between groups in the number of prenatal visits , with more than 80% of subjects having fewer than six visits . use of alcohol and smoking during pregnancy was almost zero in the early group , and use of alcohol and smoking was 3.8% and 0.9% , respectively , in the late adolescence group . reports of previous abortion were also low , although higher in the late adolescence group at 4.7% . regarding the type of delivery , there was a high proportion of cesarean sections , reaching 46.2% in the older group . the late adolescent group also reported more morbidity during pregnancy , with 43.6% reporting one of the above - listed conditions , compared to 25.2% in the early group . of the younger group , 78.9% did not wish to become pregnant , compared to 41.9% in the older group . with regard to family support during pregnancy , 35.4% of the group of 1016 years and 21.8% of the group of 1719 years had family support . the younger group also reported higher frequency of negative reaction of the baby s father and family regarding the pregnancy , lack of support from the baby s father , and dissatisfaction with pregnancy . reports of worsened quality of life and of physical violence during pregnancy were uncommon but more frequent in the older group . tables 4 and 5 present social , demographic , and obstetric variables according to the type of birth , vaginal or cesarean . although the majority of deliveries among adolescents in the study were vaginal , incidence of cesarean section was high , 27.9% in the early teens and 46.2% in late . living in an urban versus suburban / rural area was significantly associated with the type of delivery . although there were a higher proportion of unemployed parents in the vaginal delivery group , this finding was not statistically significant . in relation to educational status , we identified that those who were in school had more vaginal deliveries , compared to those who were already out of school . among those who lived with the infant s father , 78.4% delivered vaginally , and for those who did not live with the infant s father , this value was substantially lower , at 42.8% . proportions of each delivery type are also shown in table 4 for pregnancies in which the baby s father could read and write , and among those in which the father had another family . the description of sociodemographic variables according to age of the mothers shows a less favorable situation for younger mothers , a situation repeated in several studies conducted in brazil.1,911 in recent decades , teenage pregnancy has been much discussed , particularly the negative effects experienced in this age group , although satisfaction and positive gestational outcome are identified in most cases.12,13 the prevalence of births among adolescents in huambo hospital was 19.3% recorded during the study is higher than that found in brazil in the same year ( 2010).14 although official figures are not available for huambo or even angola , it is believed that the rate of teen pregnancy found in this study may be slightly overestimated , since the data analyzed in this study are from a reference hospital for high - risk pregnancies . on other continents , especially in developed countries , teenage pregnancy rates are around 1%5% , with some variations : the netherlands ( 0.9% ) , israel ( 2.3% ) , usa ( 12.8% ) , and russia ( 13.0%).15,16 on the other hand , in some african countries , such as mozambique , zimbabwe , malawi , south africa , and swaziland , these values are much higher than those found in this study , reaching rates of around 65% of births in adolescent women.17 more than a third of adolescent mothers who gave birth in the maternity ward of central hospital , huambo , angola , were in the age group 1016 years . despite the magnitude , this figure is also lower than that found in some african countries , including mozambique , zimbabwe , malawi , south africa , and swaziland.17 the difference in pregnancy rates in adolescence among african people can be related to a sociocultural bias . according to altuna , although most of the african peoples are of bantu origin and retain many traditional aspects of their cultures , angolans are considered more moderate than the people who live in the northeast of africa , whose population has a higher rate of teenage pregnancy.18 other factors also seem to affect pregnancy rates in adolescence , such as polygamy , early marriages dictated by the appearance of menarche , arranged marriages according to family wishes , and social interests.18 a study by sabroza et al evaluated 1228 adolescent mothers whose deliveries occurred in the city of rio de janeiro from 1999 to 2001 , in public and private hospitals , and found that less than a third of the teens were younger than 17 years.18 it is thought that fluctuations in the rates of pregnancy in early or late adolescence vary by region due to the migration of young people , especially the poor who are in search of places with better living conditions . one survey found that most adolescent mothers interviewed lived in suburban areas , suggesting that the event may be related to the degree of urbanization of a city . in those areas , marriages are often made as early as possible , due to the prevalence of early marriage as a traditional and cultural practice , low levels of education , poverty , and low social status.1,18 in brazil , duarte et al19 conducted an cross - sectional study of adolescents who had infant while living in santo andr , sp , concluding that the sexual and reproductive patterns vary according to different factors , including the place of residence , pointing out that the phenomenon is more checked in rural areas . studies by necchi1 and bennett et al20 also found that the higher incidence of teenage pregnancy is checked in rural areas . probably in these areas , in relation to africa , people have less education , little access to information , and are more conservative , although there are many stories of teenage pregnancy in their predecessors.11 also , a bibliographic review by vitalle and amancio9 confirmed that in rural areas , home to more disadvantaged populations , the prevalence of teenage pregnancy is higher than in urban areas . similarly , chalem et al10 observed concordant results when studying teenage pregnancy in a population on the outskirts of sao paulo , brazil . in this study , there was a higher proportion of unemployment in the baby s parents among adolescents under 17 years of age . probably this was because they are young and still enrolled in education , in accordance with the demands of their parents . similar results were found by sabroza et al,8 in an evaluation of some emotional repercussions of early pregnancy in adolescents in rio de janeiro ; high unemployment rates were found among the fathers of babies born to mothers aged under 17 years . however , the proportion of the teen mothers whose parents were without paid work was very low , which may be linked to the need to support the family , even if it is in the informal market . however , a contrary situation was found when analyzing whether the father of the infant lived with the teen mother , with a higher proportion of younger adolescents not living with their parents . a study by gama et al21 in the city of rio de janeiro , brazil , investigating the experience of pregnancy in adolescence , associated factors , and perinatal outcomes among low - income mothers , found that a third of adolescents were not living with the infant s father . training is seen as a mean to achieve professional fulfillment , which is considered the gateway to changing one s quality of life.11,22,23 age did not influence involvement in education , with a distribution with no statistical difference between the two groups . this is most likely because both age groups experienced the same need to attend to present survival above future goals , so most needed to work in the informal market , in the fields or with livestock . although both groups of adolescents in this study included high proportions of mothers who were not studying , this was less so in the younger group , demonstrating that studying is a characteristic of this age in angola , where the parents require their children to study . this is in contrast to the results found by sabroza et al,8 in which more than half of the study group was not studying at the time of pregnancy . for a pregnant adolescent , living with the baby s father or not influences legal status , as well as pregnancy outcome , perception , emotional status , and the perceptions of family and friends . in this study this is similar to the results of a study by chalem et al,10 who evaluated teenage pregnancy by sociodemographic and behavioral profiles in a population on the outskirts of sao paulo , brazil . the study found that more than half of the teenage parents lived in common - law marriages.10 probably in these areas , people marry early and highly value the woman who lives with her partner . seeing pregnancy as a hindrance was not much reported in either group in this study . however , almost all subjects showed great interest in working , which seems to be a manifestation of seeking to improve the quality of life in order to take better care of one s descendents . their availability is limited , the amount of training and education is low , and accessibility is limited.22 in many countries , basic forms of the contraceptive on methods are distributed by the health services in the basic units , but the teenagers almost often do not use these methods.8 similarly , carvalho assessed the socioeconomic aspects of the teenage pregnancy in gois , brazil , and found that half of those studied reported using some method of contraception . in africa , the use of contraception is low , as shown by gabi , 6% in angola , 14% in malawi , and 12% in mozambique in 2013.24 it is recommended that prenatal care should include psychological assistance , preparation for motherhood , and instruction regarding childbirth , childcare , postpartum nutrition , use of drugs , and other matters relevant to the fetus or newborn . pregnant teenagers commonly attend fewer prenatal consultations.22 who recommends attending at least six prenatal visits during gestation.25 in this survey , most of the teenagers had fewer than six , regardless of age , probably because many have changed their lifestyle and are living in rural areas with limited access to health services due to the distance between their homes and the unit . this result is similar to those of gama in rio de janeiro.22,25 there is no significant statistical difference between the two groups because 89.1% of the younger group ( 1016 ) and 84.6% of the older group had less than six consultations . we found low use of alcoholic beverages and tobacco among our study group , which is a good thing because they disrupt fetal growth and development , contribute to preterm labor , and premature separation of the membranes , chronic inflammation , and cardiovascular diseases.26 analyzing the history of abortion in our sample , we found that it was reported in a very small proportion of cases , even lower in the younger group . these data show that teenagers access to information about contraception is subject to religious influences . in an epidemiological study with adolescents , conducted in the city of rio de janeiro , vieira et al27 observed that one of the attitudes that early adolescents adopt when faced with unplanned pregnancies is to seek out an abortion , which increased the proportion of abortion in this age group in that study . diniz28 notes that although it is considered as a crime , abortion is common in the brazilian population . interviews of women hospitalized for complications of abortion show that most are young , poor , and already have children . although studies show the growth of cesarean sections without medical indication in several countries,29 it is assumed that , in africa , this type of delivery is being done due to risk in the pregnancy . a hospital study includes a higher proportion of at - risk births , because most births occur outside the hospital . there was a high rate of cesarean births , supported by the literature and justified by body immaturity in adolescence.30 the high rate of cesarean births may also be linked to the fact that many angolan women go to the hospital later during labor . high rates of cesarean sections have also been observed in pregnant women with few prenatal consultations , according to results found in studies by scholl , diallo , and michelazo.3133 of all deliveries in brazil , almost half are by cesarean section,34 which is high when compared to other countries . for example , the united states recorded 23.5% of births by cesarean in adults and 13.8% among adolescents ; in hong kong , these rates were 12.6% and 4.1% , respectively.15 the occurrence of diseases during pregnancy was higher in the older group , although it was expected that we would find more morbidity in the younger group . mothers in the younger group more frequently reported that they had not desired their pregnancies and that they were dissatisfied with pregnancy . this was probably because these younger teenagers had not expected to become pregnant , and because they often did not live with the child s father , their lives became more difficult . similar results were found by abreu , when assessing the obstetric , sociodemographic , and psychosocial profiles of adolescent mothers assisted by the health care system in the city of muria , mata mineira , brazil , where dissatisfaction was observed mostly in the early adolescent groups and among those who were not living with the baby s father.35 in this research , the support of family and the father of the baby were registered in more than half of adolescents . those results are similar to those of lima , who assessed perceptions and practices of pregnant adolescents and families related to pregnancy in recife , brazil , and concluded that more than half of adolescents reported having support from family.36 less than half of respondents in this study reported lack of support during pregnancy , which is explained by the fact that is seen as a phase in angola pregnancy in which women need more help . in particular , angolan culture believes that older , experienced women should provide unconditional support to pregnant women , as reported by altuna18 and necchi.1 regarding the emotional and psychological states of the adolescents , few reported worsening of life as the result of pregnancy , characteristic of adolescents with many plans for the future . in africa , the infant is seen as an important reason to stay at home and is often reported to be the main reason for getting married.1,37 regarding the reaction of parents and partners of adolescents , in the early group , there was a higher proportion of negative reaction , most likely due to the fact that at this age parents do not expect their children to be getting pregnant , because they think that they lack maturity . in the study group , high rates of cesarean section are showed in both age groups , being above the 15% recommended by the who . however , this is still below 56.7% found by bruzadeli and tavares,38 when researching expectations about delivery and cesareans among adolescents and adult women . it was expected that the majority of cesareans would be observed in the early group ; however , in this study , higher rates were reported in the group of late teens . in campinas , so paulo , the incidence rate of cesarean section among the adolescents in a referral hospital was 36.2%.39 the employment status of the parents of the teens did not influence the type of delivery . it is assumed that adolescents who were studying had more vaginal births because they had more access to information and prenatal care , reducing risks of a surgical delivery . this study identifies the main factors related to adolescent pregnancy as nonuse of contraceptives and cultural and traditional influences . the consequences of adolescent pregnancy were found to be abandonment of education , resulting difficulty in professional advancement , family conflicts , and lost dreams , pointing to the need to change this reality in the country .

this study aims to establish a profile of teenage pregnancy ( < 20 years ) at a hospital in huambo , angola . subjects were categorized into two age groups , 1016 and 1719 years . we interviewed 381 mothers in the postpartum maternity ward of the central hospital of huambo . statistical analysis then followed two stages , a descriptive analysis of the study population and analysis through a bivariate 2 2 table , using a chi - squared test to evaluate the hypothesis of homogeneity of proportions with a significance level of 5% . comparing the two groups revealed a more frequent occurrence of problems among mothers under 17 years of age , including a higher frequency of involvement with unemployed parents , more often not living with parents , and fewer prenatal consultations .

<s>[INST]pregnancy in the early reproductive life in modern times has been discouraged because of possible harm to the physical , emotional , and social health of adolescents and because of potential adverse consequences for children s health . however , depending on the teenager s social context , pregnancy can be seen as normal event , accepted within their society and customs.1 pregnancy leads to changes that impact on women s lives , and these changes can be endocrine , somatic , or psychological . when these changes occur in adolescence , they may become more intense because of the synergy of crises common in both these life phases.2,3 although the magnitude of teenage pregnancy has been reducing in countries around the world , this situation is still worrying in africa , where teenage pregnancies represent 35%77% of total births.5 angola has a young population of approximately 17 million inhabitants . wealth is concentrated in certain population groups , and the country is still rated at very low levels in most global socioeconomic development and health measures . angola is divided into 18 provinces , 164 districts , and 557 comunidades.6 the availability of data on health , official or published in scientific articles , is very limited . the mother and infant and reproductive health indicators are the worst in sub - saharan africa . world health organization ( who ) research reported in 2009 showed an infant mortality of 154/1000 live births and a fertility rate of 6.7 births per woman . however , substantial improvements were recorded in 2013 , when who estimated a fertility rate of 6.4 births per woman and an infant mortality rate of 116/1000 live births.7 underreporting of births does occur in angola s health information system , since most births occur outside the hospital environment , often without assistance of health professionals . considering these data , we chose to describe the mode of delivery , vaginal or cesarean , of the adolescents studied . the aim of this study was to establish a profile of teenage pregnancy and describe factors associated with the type of delivery , vaginal or cesarean , at a referral hospital in huambo , angola , from february to august 2010 . the sample consisted of 381 adolescent mothers , aged 1019 years , who gave birth in the maternity ward of huambo central hospital , huambo , angola . the study hospital is in the capital city of the huambo province , which has a population of approximately 2,225,000 inhabitants . at - risk pregnancies are referred to huambo central hospital , and the tertiary hospital is unique in the region . its maternity unit performs an average of 36 births a day and has 17 predelivery beds and 7 postpartum beds . medical professionals are responsible for cesarean sections and normal deliveries with some level of complication , while low - risk hospital births are attended by nurses . data were obtained through interviews in the postpartum period , using a structured questionnaire validated by the national school of public health ( ensp)fiocruz in a study of assistance to teenage pregnancy in rio de janeiro . some adaptations were made for use in africa , mainly in regard to cultural and traditional differences . a pilot study was performed with a sample of 20 mothers to evaluate the applicability of the questionnaire as well as the conditions , duration and uniformity of the interviews . data collection was performed by trained staff in a reserved space to preserve the anonymity and privacy of the mothers . the interviews took place with the written informed consent of the legal guardians of the adolescents . the independent variables were as follows : age postpartum , categorized into two age groups , 1416 years , called early , and 1719 years , called late adolescence ; area of residence , urban or rural ; paternal employment ; and teenager s enrollment in study when she became pregnant . we defined the two age groups because , in our sample , we did not have any mothers under 14 years . social and obstetric data were also analyzed , including whether the postpartum woman lived with the infant s father , the father s literacy status , if the father has another family ( as it is common in angola for some men to have more than one family at the same time ) , whether prenatal visits were attended , number of visits , < 6 or 6 , if prenatal care started in the first , second , or third trimester of pregnancy , morbidity during pregnancy ( malaria , urinary tract infection , hypertensive syndrome , anemia , bleeding , heart disease , and hiv ) , and whether prenatal care extended until the end of pregnancy . postpartum mothers aged between 10 and 19 years were considered adolescents according to the who guidelines.4 however , as mentioned earlier , the youngest mother to present during our study period was aged 14 years . bivariate analyses using chi - squared tests with a 5% significance level were performed to compare the adolescent mothers grouped by sociodemographic and psychosocial variables , which were collated according to maternal age and marital status . data were processed and analyzed using the software epi info version 6.04b from the centers for disease control and prevention . the project was reviewed and approved by the research ethics committee of the ministry of health of angola and was authorized by the huambo central hospital . the sample consisted of 381 adolescent mothers , aged 1019 years , who gave birth in the maternity ward of huambo central hospital , huambo , angola . the study hospital is in the capital city of the huambo province , which has a population of approximately 2,225,000 inhabitants . at - risk pregnancies are referred to huambo central hospital , and the tertiary hospital is unique in the region . its maternity unit performs an average of 36 births a day and has 17 predelivery beds and 7 postpartum beds . medical professionals are responsible for cesarean sections and normal deliveries with some level of complication , while low - risk hospital births are attended by nurses . data were obtained through interviews in the postpartum period , using a structured questionnaire validated by the national school of public health ( ensp)fiocruz in a study of assistance to teenage pregnancy in rio de janeiro . some adaptations were made for use in africa , mainly in regard to cultural and traditional differences . a pilot study was performed with a sample of 20 mothers to evaluate the applicability of the questionnaire as well as the conditions , duration and uniformity of the interviews . data collection was performed by trained staff in a reserved space to preserve the anonymity and privacy of the mothers . the interviews took place with the written informed consent of the legal guardians of the adolescents . the independent variables were as follows : age postpartum , categorized into two age groups , 1416 years , called early , and 1719 years , called late adolescence ; area of residence , urban or rural ; paternal employment ; and teenager s enrollment in study when she became pregnant . we defined the two age groups because , in our sample , we did not have any mothers under 14 years . social and obstetric data were also analyzed , including whether the postpartum woman lived with the infant s father , the father s literacy status , if the father has another family ( as it is common in angola for some men to have more than one family at the same time ) , whether prenatal visits were attended , number of visits , < 6 or 6 , if prenatal care started in the first , second , or third trimester of pregnancy , morbidity during pregnancy ( malaria , urinary tract infection , hypertensive syndrome , anemia , bleeding , heart disease , and hiv ) , and whether prenatal care extended until the end of pregnancy . postpartum mothers aged between 10 and 19 years were considered adolescents according to the who guidelines.4 however , as mentioned earlier , the youngest mother to present during our study period was aged 14 years . bivariate analyses using chi - squared tests with a 5% significance level were performed to compare the adolescent mothers grouped by sociodemographic and psychosocial variables , which were collated according to maternal age and marital status . data were processed and analyzed using the software epi info version 6.04b from the centers for disease control and prevention . the project was reviewed and approved by the research ethics committee of the ministry of health of angola and was authorized by the huambo central hospital . for this study , 381 subjects were interviewed , with 147 ( 38.6% ) aged between 10 and 16 years and 234 ( 61.4% ) between 17 and 19 years . in table 1 , we can see that the proportion of mothers who lived in rural areas was high in both groups , 78.2% in the early adolescent group and 70.5% in the late adolescent group . a higher percentage of the mothers in the early group had unemployed parents , 47.3% , compared to 38.0% in the older group . unemployment of the baby s father was also more common among the younger mothers . with regard to marital status , the early adolescent group had a higher proportion not living with the child s father , 70.7% , versus 38.5% of the older group . in the older group , just 32.1% of the subjects had been enrolled in education when they became pregnant . in both groups , few respondents saw teenage pregnancy as a hindrance to their lives , only 11.6% in the younger group and 15.0% in the older group . in both groups the father having another family was more common among the younger group . as shown in table 2 , the difference between the groups in terms of the reported use of contraceptive methods was not statistically significant . there was also no significant difference between groups in the number of prenatal visits , with more than 80% of subjects having fewer than six visits . use of alcohol and smoking during pregnancy was almost zero in the early group , and use of alcohol and smoking was 3.8% and 0.9% , respectively , in the late adolescence group . reports of previous abortion were also low , although higher in the late adolescence group at 4.7% . regarding the type of delivery , there was a high proportion of cesarean sections , reaching 46.2% in the older group . the late adolescent group also reported more morbidity during pregnancy , with 43.6% reporting one of the above - listed conditions , compared to 25.2% in the early group . of the younger group , 78.9% did not wish to become pregnant , compared to 41.9% in the older group . with regard to family support during pregnancy , 35.4% of the group of 1016 years and 21.8% of the group of 1719 years had family support . the younger group also reported higher frequency of negative reaction of the baby s father and family regarding the pregnancy , lack of support from the baby s father , and dissatisfaction with pregnancy . reports of worsened quality of life and of physical violence during pregnancy were uncommon but more frequent in the older group . tables 4 and 5 present social , demographic , and obstetric variables according to the type of birth , vaginal or cesarean . although the majority of deliveries among adolescents in the study were vaginal , incidence of cesarean section was high , 27.9% in the early teens and 46.2% in late . living in an urban versus suburban / rural area was significantly associated with the type of delivery . although there were a higher proportion of unemployed parents in the vaginal delivery group , this finding was not statistically significant . in relation to educational status , we identified that those who were in school had more vaginal deliveries , compared to those who were already out of school . among those who lived with the infant s father , 78.4% delivered vaginally , and for those who did not live with the infant s father , this value was substantially lower , at 42.8% . proportions of each delivery type are also shown in table 4 for pregnancies in which the baby s father could read and write , and among those in which the father had another family . the description of sociodemographic variables according to age of the mothers shows a less favorable situation for younger mothers , a situation repeated in several studies conducted in brazil.1,911 in recent decades , teenage pregnancy has been much discussed , particularly the negative effects experienced in this age group , although satisfaction and positive gestational outcome are identified in most cases.12,13 the prevalence of births among adolescents in huambo hospital was 19.3% recorded during the study is higher than that found in brazil in the same year ( 2010).14 although official figures are not available for huambo or even angola , it is believed that the rate of teen pregnancy found in this study may be slightly overestimated , since the data analyzed in this study are from a reference hospital for high - risk pregnancies . on other continents , especially in developed countries , teenage pregnancy rates are around 1%5% , with some variations : the netherlands ( 0.9% ) , israel ( 2.3% ) , usa ( 12.8% ) , and russia ( 13.0%).15,16 on the other hand , in some african countries , such as mozambique , zimbabwe , malawi , south africa , and swaziland , these values are much higher than those found in this study , reaching rates of around 65% of births in adolescent women.17 more than a third of adolescent mothers who gave birth in the maternity ward of central hospital , huambo , angola , were in the age group 1016 years . despite the magnitude , this figure is also lower than that found in some african countries , including mozambique , zimbabwe , malawi , south africa , and swaziland.17 the difference in pregnancy rates in adolescence among african people can be related to a sociocultural bias . according to altuna , although most of the african peoples are of bantu origin and retain many traditional aspects of their cultures , angolans are considered more moderate than the people who live in the northeast of africa , whose population has a higher rate of teenage pregnancy.18 other factors also seem to affect pregnancy rates in adolescence , such as polygamy , early marriages dictated by the appearance of menarche , arranged marriages according to family wishes , and social interests.18 a study by sabroza et al evaluated 1228 adolescent mothers whose deliveries occurred in the city of rio de janeiro from 1999 to 2001 , in public and private hospitals , and found that less than a third of the teens were younger than 17 years.18 it is thought that fluctuations in the rates of pregnancy in early or late adolescence vary by region due to the migration of young people , especially the poor who are in search of places with better living conditions . one survey found that most adolescent mothers interviewed lived in suburban areas , suggesting that the event may be related to the degree of urbanization of a city . in those areas , marriages are often made as early as possible , due to the prevalence of early marriage as a traditional and cultural practice , low levels of education , poverty , and low social status.1,18 in brazil , duarte et al19 conducted an cross - sectional study of adolescents who had infant while living in santo andr , sp , concluding that the sexual and reproductive patterns vary according to different factors , including the place of residence , pointing out that the phenomenon is more checked in rural areas . studies by necchi1 and bennett et al20 also found that the higher incidence of teenage pregnancy is checked in rural areas . probably in these areas , in relation to africa , people have less education , little access to information , and are more conservative , although there are many stories of teenage pregnancy in their predecessors.11 also , a bibliographic review by vitalle and amancio9 confirmed that in rural areas , home to more disadvantaged populations , the prevalence of teenage pregnancy is higher than in urban areas . similarly , chalem et al10 observed concordant results when studying teenage pregnancy in a population on the outskirts of sao paulo , brazil . in this study , there was a higher proportion of unemployment in the baby s parents among adolescents under 17 years of age . probably this was because they are young and still enrolled in education , in accordance with the demands of their parents . similar results were found by sabroza et al,8 in an evaluation of some emotional repercussions of early pregnancy in adolescents in rio de janeiro ; high unemployment rates were found among the fathers of babies born to mothers aged under 17 years . however , the proportion of the teen mothers whose parents were without paid work was very low , which may be linked to the need to support the family , even if it is in the informal market . however , a contrary situation was found when analyzing whether the father of the infant lived with the teen mother , with a higher proportion of younger adolescents not living with their parents . a study by gama et al21 in the city of rio de janeiro , brazil , investigating the experience of pregnancy in adolescence , associated factors , and perinatal outcomes among low - income mothers , found that a third of adolescents were not living with the infant s father . training is seen as a mean to achieve professional fulfillment , which is considered the gateway to changing one s quality of life.11,22,23 age did not influence involvement in education , with a distribution with no statistical difference between the two groups . this is most likely because both age groups experienced the same need to attend to present survival above future goals , so most needed to work in the informal market , in the fields or with livestock . although both groups of adolescents in this study included high proportions of mothers who were not studying , this was less so in the younger group , demonstrating that studying is a characteristic of this age in angola , where the parents require their children to study . this is in contrast to the results found by sabroza et al,8 in which more than half of the study group was not studying at the time of pregnancy . for a pregnant adolescent , living with the baby s father or not influences legal status , as well as pregnancy outcome , perception , emotional status , and the perceptions of family and friends . in this study this is similar to the results of a study by chalem et al,10 who evaluated teenage pregnancy by sociodemographic and behavioral profiles in a population on the outskirts of sao paulo , brazil . the study found that more than half of the teenage parents lived in common - law marriages.10 probably in these areas , people marry early and highly value the woman who lives with her partner . seeing pregnancy as a hindrance was not much reported in either group in this study . however , almost all subjects showed great interest in working , which seems to be a manifestation of seeking to improve the quality of life in order to take better care of one s descendents . their availability is limited , the amount of training and education is low , and accessibility is limited.22 in many countries , basic forms of the contraceptive on methods are distributed by the health services in the basic units , but the teenagers almost often do not use these methods.8 similarly , carvalho assessed the socioeconomic aspects of the teenage pregnancy in gois , brazil , and found that half of those studied reported using some method of contraception . in africa , the use of contraception is low , as shown by gabi , 6% in angola , 14% in malawi , and 12% in mozambique in 2013.24 it is recommended that prenatal care should include psychological assistance , preparation for motherhood , and instruction regarding childbirth , childcare , postpartum nutrition , use of drugs , and other matters relevant to the fetus or newborn . pregnant teenagers commonly attend fewer prenatal consultations.22 who recommends attending at least six prenatal visits during gestation.25 in this survey , most of the teenagers had fewer than six , regardless of age , probably because many have changed their lifestyle and are living in rural areas with limited access to health services due to the distance between their homes and the unit . this result is similar to those of gama in rio de janeiro.22,25 there is no significant statistical difference between the two groups because 89.1% of the younger group ( 1016 ) and 84.6% of the older group had less than six consultations . we found low use of alcoholic beverages and tobacco among our study group , which is a good thing because they disrupt fetal growth and development , contribute to preterm labor , and premature separation of the membranes , chronic inflammation , and cardiovascular diseases.26 analyzing the history of abortion in our sample , we found that it was reported in a very small proportion of cases , even lower in the younger group . these data show that teenagers access to information about contraception is subject to religious influences . in an epidemiological study with adolescents , conducted in the city of rio de janeiro , vieira et al27 observed that one of the attitudes that early adolescents adopt when faced with unplanned pregnancies is to seek out an abortion , which increased the proportion of abortion in this age group in that study . diniz28 notes that although it is considered as a crime , abortion is common in the brazilian population . interviews of women hospitalized for complications of abortion show that most are young , poor , and already have children . although studies show the growth of cesarean sections without medical indication in several countries,29 it is assumed that , in africa , this type of delivery is being done due to risk in the pregnancy . a hospital study includes a higher proportion of at - risk births , because most births occur outside the hospital . there was a high rate of cesarean births , supported by the literature and justified by body immaturity in adolescence.30 the high rate of cesarean births may also be linked to the fact that many angolan women go to the hospital later during labor . high rates of cesarean sections have also been observed in pregnant women with few prenatal consultations , according to results found in studies by scholl , diallo , and michelazo.3133 of all deliveries in brazil , almost half are by cesarean section,34 which is high when compared to other countries . for example , the united states recorded 23.5% of births by cesarean in adults and 13.8% among adolescents ; in hong kong , these rates were 12.6% and 4.1% , respectively.15 the occurrence of diseases during pregnancy was higher in the older group , although it was expected that we would find more morbidity in the younger group . mothers in the younger group more frequently reported that they had not desired their pregnancies and that they were dissatisfied with pregnancy . this was probably because these younger teenagers had not expected to become pregnant , and because they often did not live with the child s father , their lives became more difficult . similar results were found by abreu , when assessing the obstetric , sociodemographic , and psychosocial profiles of adolescent mothers assisted by the health care system in the city of muria , mata mineira , brazil , where dissatisfaction was observed mostly in the early adolescent groups and among those who were not living with the baby s father.35 in this research , the support of family and the father of the baby were registered in more than half of adolescents . those results are similar to those of lima , who assessed perceptions and practices of pregnant adolescents and families related to pregnancy in recife , brazil , and concluded that more than half of adolescents reported having support from family.36 less than half of respondents in this study reported lack of support during pregnancy , which is explained by the fact that is seen as a phase in angola pregnancy in which women need more help . in particular , angolan culture believes that older , experienced women should provide unconditional support to pregnant women , as reported by altuna18 and necchi.1 regarding the emotional and psychological states of the adolescents , few reported worsening of life as the result of pregnancy , characteristic of adolescents with many plans for the future . in africa , the infant is seen as an important reason to stay at home and is often reported to be the main reason for getting married.1,37 regarding the reaction of parents and partners of adolescents , in the early group , there was a higher proportion of negative reaction , most likely due to the fact that at this age parents do not expect their children to be getting pregnant , because they think that they lack maturity . in the study group , high rates of cesarean section are showed in both age groups , being above the 15% recommended by the who . however , this is still below 56.7% found by bruzadeli and tavares,38 when researching expectations about delivery and cesareans among adolescents and adult women . it was expected that the majority of cesareans would be observed in the early group ; however , in this study , higher rates were reported in the group of late teens . in campinas , so paulo , the incidence rate of cesarean section among the adolescents in a referral hospital was 36.2%.39 the employment status of the parents of the teens did not influence the type of delivery . it is assumed that adolescents who were studying had more vaginal births because they had more access to information and prenatal care , reducing risks of a surgical delivery . this study identifies the main factors related to adolescent pregnancy as nonuse of contraceptives and cultural and traditional influences . the consequences of adolescent pregnancy were found to be abandonment of education , resulting difficulty in professional advancement , family conflicts , and lost dreams , pointing to the need to change this reality in the country .[/INST]this study aims to establish a profile of teenage pregnancy ( < 20 years ) at a hospital in huambo , angola . subjects were categorized into two age groups , 1016 and 1719 years . we interviewed 381 mothers in the postpartum maternity ward of the central hospital of huambo . statistical analysis then followed two stages , a descriptive analysis of the study population and analysis through a bivariate 2 2 table , using a chi - squared test to evaluate the hypothesis of homogeneity of proportions with a significance level of 5% . comparing the two groups revealed a more frequent occurrence of problems among mothers under 17 years of age , including a higher frequency of involvement with unemployed parents , more often not living with parents , and fewer prenatal consultations .</s>

SECTION 1. ELIMINATING BARRIERS TO JOBS FOR LOAN ORIGINATORS. (a) In General.--The S.A.F.E. Mortgage Licensing Act of 2008 (12 U.S.C. 5101 et seq.) is amended by adding at the end the following: ``SEC. 1518. EMPLOYMENT TRANSITION OF LOAN ORIGINATORS. ``(a) Temporary Authority To Originate Loans for Loan Originators Moving From a Depository Institution to a Non-Depository Institution.-- ``(1) In general.--Upon employment by a State-licensed mortgage company, an individual who is a registered loan originator shall be deemed to have temporary authority to act as a loan originator in an application State for the period described in paragraph (2) if the individual-- ``(A) has not had an application for a loan originator license denied, or had such a license revoked or suspended in any governmental jurisdiction; ``(B) has not been subject to or served with a cease and desist order in any governmental jurisdiction or as described in section 1514(c); ``(C) has not been convicted of a felony that would preclude licensure under the law of the application State; ``(D) has submitted an application to be a State- licensed loan originator in the application State; and ``(E) was registered in the Nationwide Mortgage Licensing System and Registry as a loan originator during the 12-month period preceding the date of submission of the information required under section 1505(a). ``(2) Period.--The period described in paragraph (1) shall begin on the date that the individual submits the information required under section 1505(a) and shall end on the earliest of-- ``(A) the date that the individual withdraws the application to be a State-licensed loan originator in the application State; ``(B) the date that the application State denies, or issues a notice of intent to deny, the application; ``(C) the date that the application State grants a State license; or ``(D) the date that is 120 days after the date on which the individual submits the application, if the application is listed on the Nationwide Mortgage Licensing System and Registry as incomplete. ``(b) Temporary Authority To Originate Loans for State-Licensed Loan Originators Moving Interstate.-- ``(1) In general.--A State-licensed loan originator shall be deemed to have temporary authority to act as a loan originator in an application State for the period described in paragraph (2) if the State-licensed loan originator-- ``(A) meets the requirements of subparagraphs (A), (B), (C), and (D) of subsection (a)(1); ``(B) is employed by a State-licensed mortgage company in the application State; and ``(C) was licensed in a State that is not the application State during the 30-day period preceding the date of submission of the information required under section 1505(a) in connection with the application submitted to the application State. ``(2) Period.--The period described in paragraph (1) shall begin on the date that the State-licensed loan originator submits the information required under section 1505(a) in connection with the application submitted to the application State and end on the earliest of-- ``(A) the date that the State-licensed loan originator withdraws the application to be a State- licensed loan originator in the application State; ``(B) the date that the application State denies, or issues a notice of intent to deny, the application; ``(C) the date that the application State grants a State license; or ``(D) the date that is 120 days after the date on which the State-licensed loan originator submits the application, if the application is listed on the Nationwide Mortgage Licensing System and Registry as incomplete. ``(c) Applicability.-- ``(1) Any person employing an individual who is deemed to have temporary authority to act as a loan originator in an application State pursuant to this section shall be subject to the requirements of this title and to applicable State law to the same extent as if such individual was a State-licensed loan originator licensed by the application State. ``(2) Any individual who is deemed to have temporary authority to act as a loan originator in an application State pursuant to this section and who engages in residential mortgage loan origination activities shall be subject to the requirements of this title and to applicable State law to the same extent as if such individual was a State-licensed loan originator licensed by the application State. ``(d) Definitions.--In this section, the following definitions shall apply: ``(1) State-licensed mortgage company.--The term `State- licensed mortgage company' means an entity licensed or registered under the law of any State to engage in residential mortgage loan origination and processing activities. ``(2) Application state.--The term `application State' means a State in which a registered loan originator or a State- licensed loan originator seeks to be licensed.''. (b) Table of Contents Amendment.--The table of contents in section 1(b) of the Housing and Economic Recovery Act of 2008 (42 U.S.C. 4501 note) is amended by inserting after the item relating to section 1517 the following: ``Sec. 1518. Employment transition of loan originators.''. SEC. 2. AMENDMENT TO CIVIL LIABILITY OF THE BUREAU AND OTHER OFFICIALS. Section 1513 of the S.A.F.E. Mortgage Licensing Act of 2008 (12 U.S.C. 5112) is amended by striking ``are loan originators or are applying for licensing or registration as loan originators.'' and inserting ``have applied, are applying, or are currently licensed or registered through the Nationwide Mortgage Licensing System and Registry. The previous sentence shall only apply to persons in an industry with respect to which persons were licensed or registered through the Nationwide Mortgage Licensing System and Registry on the date of the enactment of this sentence.''. SEC. 3. EFFECTIVE DATE. This Act and the amendments made by this Act shall take effect on the date that is 18 months after the date of the enactment of this Act.

. (Sec. 1) This bill amends the S.A.F.E. Mortgage Licensing Act of 2008 to temporarily allow loan originators that meet specified requirements to continue to originate loans after moving: (1)&nbsp;from one state to another, or (2) from a depository institution to a non-depository institution. (Sec. 2) The bill revises the Act's civil liability immunity provisions.

<s>[INST]SECTION 1. ELIMINATING BARRIERS TO JOBS FOR LOAN ORIGINATORS. (a) In General.--The S.A.F.E. Mortgage Licensing Act of 2008 (12 U.S.C. 5101 et seq.) is amended by adding at the end the following: ``SEC. 1518. EMPLOYMENT TRANSITION OF LOAN ORIGINATORS. ``(a) Temporary Authority To Originate Loans for Loan Originators Moving From a Depository Institution to a Non-Depository Institution.-- ``(1) In general.--Upon employment by a State-licensed mortgage company, an individual who is a registered loan originator shall be deemed to have temporary authority to act as a loan originator in an application State for the period described in paragraph (2) if the individual-- ``(A) has not had an application for a loan originator license denied, or had such a license revoked or suspended in any governmental jurisdiction; ``(B) has not been subject to or served with a cease and desist order in any governmental jurisdiction or as described in section 1514(c); ``(C) has not been convicted of a felony that would preclude licensure under the law of the application State; ``(D) has submitted an application to be a State- licensed loan originator in the application State; and ``(E) was registered in the Nationwide Mortgage Licensing System and Registry as a loan originator during the 12-month period preceding the date of submission of the information required under section 1505(a). ``(2) Period.--The period described in paragraph (1) shall begin on the date that the individual submits the information required under section 1505(a) and shall end on the earliest of-- ``(A) the date that the individual withdraws the application to be a State-licensed loan originator in the application State; ``(B) the date that the application State denies, or issues a notice of intent to deny, the application; ``(C) the date that the application State grants a State license; or ``(D) the date that is 120 days after the date on which the individual submits the application, if the application is listed on the Nationwide Mortgage Licensing System and Registry as incomplete. ``(b) Temporary Authority To Originate Loans for State-Licensed Loan Originators Moving Interstate.-- ``(1) In general.--A State-licensed loan originator shall be deemed to have temporary authority to act as a loan originator in an application State for the period described in paragraph (2) if the State-licensed loan originator-- ``(A) meets the requirements of subparagraphs (A), (B), (C), and (D) of subsection (a)(1); ``(B) is employed by a State-licensed mortgage company in the application State; and ``(C) was licensed in a State that is not the application State during the 30-day period preceding the date of submission of the information required under section 1505(a) in connection with the application submitted to the application State. ``(2) Period.--The period described in paragraph (1) shall begin on the date that the State-licensed loan originator submits the information required under section 1505(a) in connection with the application submitted to the application State and end on the earliest of-- ``(A) the date that the State-licensed loan originator withdraws the application to be a State- licensed loan originator in the application State; ``(B) the date that the application State denies, or issues a notice of intent to deny, the application; ``(C) the date that the application State grants a State license; or ``(D) the date that is 120 days after the date on which the State-licensed loan originator submits the application, if the application is listed on the Nationwide Mortgage Licensing System and Registry as incomplete. ``(c) Applicability.-- ``(1) Any person employing an individual who is deemed to have temporary authority to act as a loan originator in an application State pursuant to this section shall be subject to the requirements of this title and to applicable State law to the same extent as if such individual was a State-licensed loan originator licensed by the application State. ``(2) Any individual who is deemed to have temporary authority to act as a loan originator in an application State pursuant to this section and who engages in residential mortgage loan origination activities shall be subject to the requirements of this title and to applicable State law to the same extent as if such individual was a State-licensed loan originator licensed by the application State. ``(d) Definitions.--In this section, the following definitions shall apply: ``(1) State-licensed mortgage company.--The term `State- licensed mortgage company' means an entity licensed or registered under the law of any State to engage in residential mortgage loan origination and processing activities. ``(2) Application state.--The term `application State' means a State in which a registered loan originator or a State- licensed loan originator seeks to be licensed.''. (b) Table of Contents Amendment.--The table of contents in section 1(b) of the Housing and Economic Recovery Act of 2008 (42 U.S.C. 4501 note) is amended by inserting after the item relating to section 1517 the following: ``Sec. 1518. Employment transition of loan originators.''. SEC. 2. AMENDMENT TO CIVIL LIABILITY OF THE BUREAU AND OTHER OFFICIALS. Section 1513 of the S.A.F.E. Mortgage Licensing Act of 2008 (12 U.S.C. 5112) is amended by striking ``are loan originators or are applying for licensing or registration as loan originators.'' and inserting ``have applied, are applying, or are currently licensed or registered through the Nationwide Mortgage Licensing System and Registry. The previous sentence shall only apply to persons in an industry with respect to which persons were licensed or registered through the Nationwide Mortgage Licensing System and Registry on the date of the enactment of this sentence.''. SEC. 3. EFFECTIVE DATE. This Act and the amendments made by this Act shall take effect on the date that is 18 months after the date of the enactment of this Act.[/INST]. (Sec. 1) This bill amends the S.A.F.E. Mortgage Licensing Act of 2008 to temporarily allow loan originators that meet specified requirements to continue to originate loans after moving: (1)&nbsp;from one state to another, or (2) from a depository institution to a non-depository institution. (Sec. 2) The bill revises the Act's civil liability immunity provisions. </s>

events with a region of rapidity space devoid of particles ( rapidity gaps ) were first observed in cosmic ray data @xcite . the idea of diffractive dissociation of projectile and target to produce such events soon followed @xcite . later the interpretation of total , elastic and diffractive cross sections in terms of the exchange of an object with the quantum numbers of the vacuum , called the pomeron , proved very useful @xcite . f. low and s. nussinov suggested that the pomeron corresponds to the interchange of two gluons @xcite . in a latter development ingelman and schlein ( is ) proposed that high @xmath4 jets could be diffractively produced via pomeron exchange and that this might probe the partonic structure of the pomeron @xcite . events containing rapidity gaps and jets were first observed by ua8 @xcite , giving rise to the field of hard diffraction . this area of interest has expanded considerably in the last decade , with the availability of high energy colliding beams . jet production with rapidity gaps have been observed at the tevatron @xcite and at hera @xcite . cdf and d have studied dijet + rapidity gap events using data from the 1992 - 1996 tevatron @xmath0 collider run ( run i ) at center - of - mass energy ( ) = 1.8 tev , with a short run at 630 gev during that period . because of the large center of mass energy and large integrated luminosity , the new cdf and d results can give further insight into diffractive processes . the d detector is described elsewhere @xcite . jets are found in the uranium - liquid argon calorimeters using a cone algorithm with radius @xmath5 in the @xmath6 plane @xcite . particle multiplicity is determined in the central region ( @xmath7 ) using the number of towers ( @xmath8 in @xmath9 ) with transverse energy ( @xmath3 ) above 200 mev in the central electromagnetic calorimeter and the number of tracks in the central drift chamber . in the forward region this multiplicity is measured by the number of towers with ( @xmath3 ) above 125 mev in the electromagnetic end cap calorimeter ( 2.1 @xmath10 ) and 500 mev in the hadronic end cap calorimeter ( 3.2 @xmath11 ) . because the last layer of the hadronic calorimeter ( at the limit of the forward acceptance ) is composed of stainless steel and produces less noise than the uranium sections , the threshold for particle detection was reduced to 50 mev in this layer . in addition , in the forward region we also use an array of scintillator hodoscopes , called l detector , to tag the presence of charged particles in the region 2.3 @xmath12 . the cdf detector , described in ref . @xcite , consists of a large central detector with tracking in a solenoidal field and calorimetry over @xmath13 . to measure particle multiplicities , cdf uses the central tracker ( @xmath14 mev ) , the central calorimeter ( @xmath15 mev corrected ) , and forward calorimeters ( 2.2 @xmath16 ) . for the last two months of the collider run , cdf installed three roman pot detectors to trigger on quasi - elastically scatted antiprotons . nearly all the pot triggers have @xmath17 , where @xmath18 = @xmath19 is the fraction of momentum lost by the antiproton and carried by the pomeron . two jets separated by a rapidity gap has been proposed as the signature of color singlet exchange ( cse ) carrying a high @xmath20 @xcite . rapidity gaps between jets have been observed both at the tevatron @xcite and at the desy @xmath21 collider ( hera ) @xcite . the measured rates of @xmath22 at the tevatron and @xmath23 at hera are too large to be accounted for by electroweak boson exchange and indicate a strong interaction process . d and cdf have made recent studies of dijet data with central rapidity gaps . both experiments measure the color singlet fraction ( ) at of 630 gev and 1.8 tev . the observed color singlet fraction includes the probability that the rapidity gap is not contaminated by particles from spectator interactions . this survival probability ( @xmath24 at 1.8 tev ) is assumed to be independent of bjorken @xmath25 and the flavor of the initial partons in the hard scattering @xcite but depends on @xmath26 @xcite . cdf measures the fraction of colorless exchange to all opposite side dijets from the tracking distribution . results are listed in table [ table : cse_fs ] . the ratio of the cdf fractions from the measurements at the two center of mass energies is @xmath27 . no @xmath3 dependence of the signal is observed . = 3.5 in .kinematic cuts for color singlet exchange . [ cols="^,<,^,<,^,^ " , ] d has recently published results for dijet + central gap events@xcite . ( see table [ table : cse_kin ] for kinematic cuts . ) single interaction events are required . the particle multiplicity in the central rapidity region is approximated by the multiplicity , @xmath28 , of transverse energy above 200 mev in the electromagnetic calorimeter , and by the track multiplicity in the central tracking chamber , @xmath29 . figure 1 ( a ) shows the d multiplicity distribution for @xmath28 versus @xmath29 . to calculate the fraction due to color singlet exchange , the leading edge of each @xmath28 distribution is fitted using a single negative binomial distribution ( nbd ) . the fraction of rapidity gap events ( ) is calculated from the excess of events over the fit in the first two bins ( @xmath30 or 1 ) divided by the total number of entries . figure 1 ( b ) shows the @xmath28 distribution and the nbd fit for the high @xmath3 sample . see table [ table : cse_fs ] for values of . the d value of the ratio of the rapidity gap fractions at 630 and 1800 gev is @xmath31 . measuring the color - singlet fraction as a function of @xmath3 , @xmath2 and probes the nature of the color - singlet exchange and its coupling to quarks and gluons . if the color - singlet dynamics are similar to single gluon exchange except for different coupling factors to quarks and gluons , the color - singlet fraction would depend only on parton distribution functions via @xmath32 . thus for a color - singlet that couples more strongly to gluons than quarks , the color - singlet fraction would fall as a function of increasing @xmath25 , since the gluon distribution becomes suppressed relative to the quark distribution as @xmath25 increases . this implies a decreasing color singlet fraction with increasing jet @xmath3 and @xmath33 or decreasing . to measure the color - singlet fraction as a function of @xmath3 and @xmath2 , duses the two - dimensional multiplicity , ( @xmath34 ) which gives improved signal - to - background ratios compared to the nbd method . this is useful for smaller statistics samples and avoids large uncertainties in the color - exchange background subtraction . the `` 2d '' color - singlet fraction @xmath35 is defined as the fraction of events with @xmath36 . the results are shown in figure [ fig : d0_cse_et _ ] . the systematic errors include effects from background estimation . the measured color - singlet fraction shows a slight rise as a function of dijet @xmath3 and @xmath33 . to compare the experimental color singlet fractions to models , d uses herwig 5.9 @xcite , which includes a two - gluon exchange with bfkl dynamics @xcite , and uses cteq2 m parton distribution functions . in addition , d uses the @xmath37-channel photon exchange process in herwig to investigate models in which the color singlet couples only to quarks with a massless photon - like singlet . in the soft - color rearrangement model@xcite , initial state quarks have fewer color combinations and thus , a higher probability of being rearranged into a colorless state , than initial state gluons , i.e. @xmath38 , where the `` @xmath39s '' are the effective color factors representing the couplings to different initial state partons . a reasonable choice of color factors is @xmath40 , @xmath41 and @xmath42 . predictions of these models are simultaneously fit to the experimental @xmath3 and @xmath33 dependence of at = 1.8 tev , letting the normalization float . the results are shown in figure [ fig : d0_cse_et _ ] . the data favour color - singlet models that couple more strongly to quarks than gluons , but a single - gluon model ( no dependence ) can not be excluded . in the is picture of hard single diffraction , a pomeron ( color singlet object ) is emitted from the incident @xmath43 ( @xmath44 ) and undergoes a hard scattering with the @xmath44 ( @xmath43 ) , leaving a rapidity gap in the direction of the parent particle . the signature is two jets produced on the same side and a forward rapidity gap along the direction of one of initial beam particles . data was taken by the cdf detector at the end of run i using a trigger which requires tagging the recoil @xmath44 with `` roman pot '' detectors . the typical acceptance for these detectors is @xmath45 and @xmath46 , where @xmath18 is the fractional momentum lost by the antiproton and @xmath37 its four momentum squared . after applying several cuts to select events with a good reconstructed track in the roman pots , cdf extracted the momentum fraction of the interacting parton in the pomeron , @xmath47 , for dijet events with @xmath48 , using the following expression : @xmath49 the @xmath47 distribution for the pomeron was obtained by subtracting several background contributions in the data , of which the most importants are 1 ) non - diffractive dijet events accidentally overlapped with a roman pot hit , 2 ) meson exchange background and 3 ) double diffraction background . after subtracting these contributions from the data , then unfolding the detector acceptance by using simulations with a flat gluon distribution , the data was divided by monte carlo simulations based on pompyt@xcite using a flat gluon distribution and the standard donnachie and landshoff flux parametrization@xcite . the comparison , shown in figure [ cdf_hsd ] , shows agreement in shape for @xmath50 , but there is a discrepancy in the normalization by about a factor of 6 , as well as an enhancement for the low @xmath47 region . = 4.0 in the d data were obtained using an inclusive jet trigger or a forward two jet trigger . events are selected with two jets with @xmath3 @xmath51 12 gev and @xmath521.6 . the number of end cap calorimeter towers ( @xmath28 ) above threshold is measured opposite to the leading two jets . the @xmath28 distribution for the forward trigger sample at center of mass energies of 1800 and 630 gev is shown in figure [ fig : d0_hds_mult _ ] . a clear peak is seen in the @xmath53 ( zero multiplicity ) bin as expected for a diffractive signal . a two - dimensional fit on the @xmath54 distribution , where data and background are fit simultaneously , allows the direct extraction of the fraction of events containing a rapidity gap at both energies . this gap fraction , including statistical and systematic uncertainties , is determined to be @xmath55 for the 1800 gev data and @xmath56 for the 630 gev data . work is in progress for the extraction of the pomeron parton distributions . central dijet events containing two rapidity gaps or a rapidity gap on the opposite side of a quasi - elastically scattered anti - proton have been studied by d and cdf respectively . this event topology is consistent with double pomeron exchange ( dpe ) . the data can be used to give more information about the hypothesized pomeron . cdf took data at 1800 gev center of mass energy using the roman pot trigger to tag antiprotons . a sample of 27,000 events with a tagged @xmath44 and at least two jets with @xmath57 gev is obtained . low multiplicity events are selected by requiring @xmath58 in the 16 element beam - beam counters ( bbc ) on the same side as the pots . this gives 22,304 pjj ( pot - jet - jet ) events . a sample of minimum bias events , with the same dijet selection , is used for comparison . figure [ fig : cdf_dpe_lego ] ( a ) shows the calorimeter tower multiplicity in the east side ( opposite to the pot track ) , @xmath59 , versus the number of hits in the bbc . in order to understand the shape of this distribution , monte carlo events were generated using a version of pompyt modified to include double pomeron exchange , where the incoming proton and antiproton emit pomerons with a standard flux ( donnachie and landshoff form @xcite with parameters as measured by cdf @xcite ) . the pomeron - pomeron interaction is treated like a hadron hadron collision which produces jets . a flat @xmath47 distribution of partons inside the pomeron was assumed . diffractive deep inelastic scattering data from hera suggest such a hard structure with a rather flat @xmath47-distribution @xcite . the simulated events are shown in figure [ fig : cdf_dpe_lego ] ( b ) . the strong signal in the ( 0,0 ) bin only contains 24 % of the dpe events with @xmath60 for 7 gev dijets . by extrapolating linearly into the @xmath61 bin along the diagonal axis , cdf obtained the ratio of dijet gap to dijet no - gap events to be : @xmath62\%$ ] where g means gap ( no detected particles for @xmath63 ) , jj means two jets with @xmath57 gev and p means a pot track with @xmath17 . when the discrepancy factor , d=18% , found in previous analyses of diffraction in @xmath64 and @xmath21 collisions @xcite , is applied ( squared ) , the ratio from simulation is in good agreement with the data . d has taken inclusive jet data with a special trigger and searched for dijet events with two forward rapidity gaps along the direction of the proton and antiproton . events were selected having two jets with @xmath65 12 gev , @xmath66 and a rapidity gap in the region @xmath67 the multiplicity distribution of calorimeter towers and level hits ( @xmath68 ) , on the opposite side to the rapidity gap , for data taken at 630 gev center of mass energy is shown in figure [ fig : d0_dpe_lego_et ] ( a ) . a clear peak at low multiplicity is observed above a fairly flat background in qualitative agreement with that expected for double pomeron exchange . figure [ fig : d0_dpe_lego_et ] ( b ) shows the @xmath3 spectra for the two leading jets in an inclusive sample with two central @xmath69 gev jets , a single forward gap sample and the double gap sample at 630 gev . all three spectra are in good agreement where data are available , implying that the dynamics of leading jets produced in rapidity gap events appear similar to those of inclusive qcd production . similar results are seen by d in data taken at 1800 gev . recent studies of hard diffraction at the tevatron have given new information about rates of diffraction and dependencies on @xmath3 , @xmath2 and . the fraction of dijet events produced via hard color singlet exchange is about 1% at 1.8 tev and is larger by a factor of 2 to 3 at = 630 gev . d has compared the @xmath3 and @xmath33 dependence of the fraction of hard color singlet events to several models . the data favor a soft - color rearrangement model preferring initial quark states over two - gluon color - singlet models . cdf has preliminary results on the momentum distribution of partons in the pomeron using `` roman pot '' detectors to measure quasi - elastic scattered @xmath70 in hard single diffractive events . d has studied hard single diffraction in forward dijet events and new results on pomeron parton distributions will soon be available . both cdf and d have preliminary evidence for events with a hard double pomeron exchange topology . cdf has measured the fraction of pot dijet gap events to be 0.36% of the pot dijet events at = 1.8 tev . d has studied gap - dijet - gap events at = 630 gev and 1.8 tev . the @xmath3 distribution of the leading jets in double pomeron exchange type events is similar to other processes producing jets . the pseudorapidity , @xmath2 is defined as @xmath71 . the polar angle , @xmath72 , is defined relative the the proton beam direction , @xmath73 is the azimuthal angle , and @xmath3 is the energy measured transverse to the beam .

hard diffraction in events with dijets and rapidity gaps has been studied by d and cdf for three processes : hard color singlet exchange , hard single diffraction , and hard double pomeron exchange , using tevatron @xmath0 data at @xmath1 = 630 gev and 1.8 tev . measurements of rates , @xmath2 , @xmath3 and @xmath1 dependencies are presented and comparisons made with predictions of several models . # 1#2#3#4#1 * # 2 * , # 3 ( # 4 )

<s>[INST]events with a region of rapidity space devoid of particles ( rapidity gaps ) were first observed in cosmic ray data @xcite . the idea of diffractive dissociation of projectile and target to produce such events soon followed @xcite . later the interpretation of total , elastic and diffractive cross sections in terms of the exchange of an object with the quantum numbers of the vacuum , called the pomeron , proved very useful @xcite . f. low and s. nussinov suggested that the pomeron corresponds to the interchange of two gluons @xcite . in a latter development ingelman and schlein ( is ) proposed that high @xmath4 jets could be diffractively produced via pomeron exchange and that this might probe the partonic structure of the pomeron @xcite . events containing rapidity gaps and jets were first observed by ua8 @xcite , giving rise to the field of hard diffraction . this area of interest has expanded considerably in the last decade , with the availability of high energy colliding beams . jet production with rapidity gaps have been observed at the tevatron @xcite and at hera @xcite . cdf and d have studied dijet + rapidity gap events using data from the 1992 - 1996 tevatron @xmath0 collider run ( run i ) at center - of - mass energy ( ) = 1.8 tev , with a short run at 630 gev during that period . because of the large center of mass energy and large integrated luminosity , the new cdf and d results can give further insight into diffractive processes . the d detector is described elsewhere @xcite . jets are found in the uranium - liquid argon calorimeters using a cone algorithm with radius @xmath5 in the @xmath6 plane @xcite . particle multiplicity is determined in the central region ( @xmath7 ) using the number of towers ( @xmath8 in @xmath9 ) with transverse energy ( @xmath3 ) above 200 mev in the central electromagnetic calorimeter and the number of tracks in the central drift chamber . in the forward region this multiplicity is measured by the number of towers with ( @xmath3 ) above 125 mev in the electromagnetic end cap calorimeter ( 2.1 @xmath10 ) and 500 mev in the hadronic end cap calorimeter ( 3.2 @xmath11 ) . because the last layer of the hadronic calorimeter ( at the limit of the forward acceptance ) is composed of stainless steel and produces less noise than the uranium sections , the threshold for particle detection was reduced to 50 mev in this layer . in addition , in the forward region we also use an array of scintillator hodoscopes , called l detector , to tag the presence of charged particles in the region 2.3 @xmath12 . the cdf detector , described in ref . @xcite , consists of a large central detector with tracking in a solenoidal field and calorimetry over @xmath13 . to measure particle multiplicities , cdf uses the central tracker ( @xmath14 mev ) , the central calorimeter ( @xmath15 mev corrected ) , and forward calorimeters ( 2.2 @xmath16 ) . for the last two months of the collider run , cdf installed three roman pot detectors to trigger on quasi - elastically scatted antiprotons . nearly all the pot triggers have @xmath17 , where @xmath18 = @xmath19 is the fraction of momentum lost by the antiproton and carried by the pomeron . two jets separated by a rapidity gap has been proposed as the signature of color singlet exchange ( cse ) carrying a high @xmath20 @xcite . rapidity gaps between jets have been observed both at the tevatron @xcite and at the desy @xmath21 collider ( hera ) @xcite . the measured rates of @xmath22 at the tevatron and @xmath23 at hera are too large to be accounted for by electroweak boson exchange and indicate a strong interaction process . d and cdf have made recent studies of dijet data with central rapidity gaps . both experiments measure the color singlet fraction ( ) at of 630 gev and 1.8 tev . the observed color singlet fraction includes the probability that the rapidity gap is not contaminated by particles from spectator interactions . this survival probability ( @xmath24 at 1.8 tev ) is assumed to be independent of bjorken @xmath25 and the flavor of the initial partons in the hard scattering @xcite but depends on @xmath26 @xcite . cdf measures the fraction of colorless exchange to all opposite side dijets from the tracking distribution . results are listed in table [ table : cse_fs ] . the ratio of the cdf fractions from the measurements at the two center of mass energies is @xmath27 . no @xmath3 dependence of the signal is observed . = 3.5 in .kinematic cuts for color singlet exchange . [ cols="^,<,^,<,^,^ " , ] d has recently published results for dijet + central gap events@xcite . ( see table [ table : cse_kin ] for kinematic cuts . ) single interaction events are required . the particle multiplicity in the central rapidity region is approximated by the multiplicity , @xmath28 , of transverse energy above 200 mev in the electromagnetic calorimeter , and by the track multiplicity in the central tracking chamber , @xmath29 . figure 1 ( a ) shows the d multiplicity distribution for @xmath28 versus @xmath29 . to calculate the fraction due to color singlet exchange , the leading edge of each @xmath28 distribution is fitted using a single negative binomial distribution ( nbd ) . the fraction of rapidity gap events ( ) is calculated from the excess of events over the fit in the first two bins ( @xmath30 or 1 ) divided by the total number of entries . figure 1 ( b ) shows the @xmath28 distribution and the nbd fit for the high @xmath3 sample . see table [ table : cse_fs ] for values of . the d value of the ratio of the rapidity gap fractions at 630 and 1800 gev is @xmath31 . measuring the color - singlet fraction as a function of @xmath3 , @xmath2 and probes the nature of the color - singlet exchange and its coupling to quarks and gluons . if the color - singlet dynamics are similar to single gluon exchange except for different coupling factors to quarks and gluons , the color - singlet fraction would depend only on parton distribution functions via @xmath32 . thus for a color - singlet that couples more strongly to gluons than quarks , the color - singlet fraction would fall as a function of increasing @xmath25 , since the gluon distribution becomes suppressed relative to the quark distribution as @xmath25 increases . this implies a decreasing color singlet fraction with increasing jet @xmath3 and @xmath33 or decreasing . to measure the color - singlet fraction as a function of @xmath3 and @xmath2 , duses the two - dimensional multiplicity , ( @xmath34 ) which gives improved signal - to - background ratios compared to the nbd method . this is useful for smaller statistics samples and avoids large uncertainties in the color - exchange background subtraction . the `` 2d '' color - singlet fraction @xmath35 is defined as the fraction of events with @xmath36 . the results are shown in figure [ fig : d0_cse_et _ ] . the systematic errors include effects from background estimation . the measured color - singlet fraction shows a slight rise as a function of dijet @xmath3 and @xmath33 . to compare the experimental color singlet fractions to models , d uses herwig 5.9 @xcite , which includes a two - gluon exchange with bfkl dynamics @xcite , and uses cteq2 m parton distribution functions . in addition , d uses the @xmath37-channel photon exchange process in herwig to investigate models in which the color singlet couples only to quarks with a massless photon - like singlet . in the soft - color rearrangement model@xcite , initial state quarks have fewer color combinations and thus , a higher probability of being rearranged into a colorless state , than initial state gluons , i.e. @xmath38 , where the `` @xmath39s '' are the effective color factors representing the couplings to different initial state partons . a reasonable choice of color factors is @xmath40 , @xmath41 and @xmath42 . predictions of these models are simultaneously fit to the experimental @xmath3 and @xmath33 dependence of at = 1.8 tev , letting the normalization float . the results are shown in figure [ fig : d0_cse_et _ ] . the data favour color - singlet models that couple more strongly to quarks than gluons , but a single - gluon model ( no dependence ) can not be excluded . in the is picture of hard single diffraction , a pomeron ( color singlet object ) is emitted from the incident @xmath43 ( @xmath44 ) and undergoes a hard scattering with the @xmath44 ( @xmath43 ) , leaving a rapidity gap in the direction of the parent particle . the signature is two jets produced on the same side and a forward rapidity gap along the direction of one of initial beam particles . data was taken by the cdf detector at the end of run i using a trigger which requires tagging the recoil @xmath44 with `` roman pot '' detectors . the typical acceptance for these detectors is @xmath45 and @xmath46 , where @xmath18 is the fractional momentum lost by the antiproton and @xmath37 its four momentum squared . after applying several cuts to select events with a good reconstructed track in the roman pots , cdf extracted the momentum fraction of the interacting parton in the pomeron , @xmath47 , for dijet events with @xmath48 , using the following expression : @xmath49 the @xmath47 distribution for the pomeron was obtained by subtracting several background contributions in the data , of which the most importants are 1 ) non - diffractive dijet events accidentally overlapped with a roman pot hit , 2 ) meson exchange background and 3 ) double diffraction background . after subtracting these contributions from the data , then unfolding the detector acceptance by using simulations with a flat gluon distribution , the data was divided by monte carlo simulations based on pompyt@xcite using a flat gluon distribution and the standard donnachie and landshoff flux parametrization@xcite . the comparison , shown in figure [ cdf_hsd ] , shows agreement in shape for @xmath50 , but there is a discrepancy in the normalization by about a factor of 6 , as well as an enhancement for the low @xmath47 region . = 4.0 in the d data were obtained using an inclusive jet trigger or a forward two jet trigger . events are selected with two jets with @xmath3 @xmath51 12 gev and @xmath521.6 . the number of end cap calorimeter towers ( @xmath28 ) above threshold is measured opposite to the leading two jets . the @xmath28 distribution for the forward trigger sample at center of mass energies of 1800 and 630 gev is shown in figure [ fig : d0_hds_mult _ ] . a clear peak is seen in the @xmath53 ( zero multiplicity ) bin as expected for a diffractive signal . a two - dimensional fit on the @xmath54 distribution , where data and background are fit simultaneously , allows the direct extraction of the fraction of events containing a rapidity gap at both energies . this gap fraction , including statistical and systematic uncertainties , is determined to be @xmath55 for the 1800 gev data and @xmath56 for the 630 gev data . work is in progress for the extraction of the pomeron parton distributions . central dijet events containing two rapidity gaps or a rapidity gap on the opposite side of a quasi - elastically scattered anti - proton have been studied by d and cdf respectively . this event topology is consistent with double pomeron exchange ( dpe ) . the data can be used to give more information about the hypothesized pomeron . cdf took data at 1800 gev center of mass energy using the roman pot trigger to tag antiprotons . a sample of 27,000 events with a tagged @xmath44 and at least two jets with @xmath57 gev is obtained . low multiplicity events are selected by requiring @xmath58 in the 16 element beam - beam counters ( bbc ) on the same side as the pots . this gives 22,304 pjj ( pot - jet - jet ) events . a sample of minimum bias events , with the same dijet selection , is used for comparison . figure [ fig : cdf_dpe_lego ] ( a ) shows the calorimeter tower multiplicity in the east side ( opposite to the pot track ) , @xmath59 , versus the number of hits in the bbc . in order to understand the shape of this distribution , monte carlo events were generated using a version of pompyt modified to include double pomeron exchange , where the incoming proton and antiproton emit pomerons with a standard flux ( donnachie and landshoff form @xcite with parameters as measured by cdf @xcite ) . the pomeron - pomeron interaction is treated like a hadron hadron collision which produces jets . a flat @xmath47 distribution of partons inside the pomeron was assumed . diffractive deep inelastic scattering data from hera suggest such a hard structure with a rather flat @xmath47-distribution @xcite . the simulated events are shown in figure [ fig : cdf_dpe_lego ] ( b ) . the strong signal in the ( 0,0 ) bin only contains 24 % of the dpe events with @xmath60 for 7 gev dijets . by extrapolating linearly into the @xmath61 bin along the diagonal axis , cdf obtained the ratio of dijet gap to dijet no - gap events to be : @xmath62\%$ ] where g means gap ( no detected particles for @xmath63 ) , jj means two jets with @xmath57 gev and p means a pot track with @xmath17 . when the discrepancy factor , d=18% , found in previous analyses of diffraction in @xmath64 and @xmath21 collisions @xcite , is applied ( squared ) , the ratio from simulation is in good agreement with the data . d has taken inclusive jet data with a special trigger and searched for dijet events with two forward rapidity gaps along the direction of the proton and antiproton . events were selected having two jets with @xmath65 12 gev , @xmath66 and a rapidity gap in the region @xmath67 the multiplicity distribution of calorimeter towers and level hits ( @xmath68 ) , on the opposite side to the rapidity gap , for data taken at 630 gev center of mass energy is shown in figure [ fig : d0_dpe_lego_et ] ( a ) . a clear peak at low multiplicity is observed above a fairly flat background in qualitative agreement with that expected for double pomeron exchange . figure [ fig : d0_dpe_lego_et ] ( b ) shows the @xmath3 spectra for the two leading jets in an inclusive sample with two central @xmath69 gev jets , a single forward gap sample and the double gap sample at 630 gev . all three spectra are in good agreement where data are available , implying that the dynamics of leading jets produced in rapidity gap events appear similar to those of inclusive qcd production . similar results are seen by d in data taken at 1800 gev . recent studies of hard diffraction at the tevatron have given new information about rates of diffraction and dependencies on @xmath3 , @xmath2 and . the fraction of dijet events produced via hard color singlet exchange is about 1% at 1.8 tev and is larger by a factor of 2 to 3 at = 630 gev . d has compared the @xmath3 and @xmath33 dependence of the fraction of hard color singlet events to several models . the data favor a soft - color rearrangement model preferring initial quark states over two - gluon color - singlet models . cdf has preliminary results on the momentum distribution of partons in the pomeron using `` roman pot '' detectors to measure quasi - elastic scattered @xmath70 in hard single diffractive events . d has studied hard single diffraction in forward dijet events and new results on pomeron parton distributions will soon be available . both cdf and d have preliminary evidence for events with a hard double pomeron exchange topology . cdf has measured the fraction of pot dijet gap events to be 0.36% of the pot dijet events at = 1.8 tev . d has studied gap - dijet - gap events at = 630 gev and 1.8 tev . the @xmath3 distribution of the leading jets in double pomeron exchange type events is similar to other processes producing jets . the pseudorapidity , @xmath2 is defined as @xmath71 . the polar angle , @xmath72 , is defined relative the the proton beam direction , @xmath73 is the azimuthal angle , and @xmath3 is the energy measured transverse to the beam .[/INST] hard diffraction in events with dijets and rapidity gaps has been studied by d and cdf for three processes : hard color singlet exchange , hard single diffraction , and hard double pomeron exchange , using tevatron @xmath0 data at @xmath1 = 630 gev and 1.8 tev . measurements of rates , @xmath2 , @xmath3 and @xmath1 dependencies are presented and comparisons made with predictions of several models . # 1#2#3#4#1 * # 2 * , # 3 ( # 4 ) </s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Economic Conversion Clearinghouse Act''. SEC. 2. OFFICE. (a) Establishment.--There is established, within the Department of Commerce, the Office of Economic Conversion Information (hereinafter referred to as ``Office''). (b) Purpose.--It is the purpose of the Office-- (1) to serve as a central information clearinghouse on matters relating to economic adjustment and defense conversion programs and activities of the Federal and State governments, including political subdivisions of the States; and (2) to help potential and actual applicants for economic adjustment and defense conversion assistance under Federal, State and local laws in locating and applying for such assistance, including financial and technical assistance. (c) Director.--The Office shall be headed by a Director. The Secretary of Commerce shall appoint and fix the compensation of the Director. (d) Staff.--The Director may appoint such personnel as may be necessary to enable the Office to perform its duties. SEC. 3. FUNCTIONS. (a) Information Databases.-- (1) Uses.--The Office shall develop information databases for use by Federal departments and agencies, State and local governmental agencies, public and private entities, and individuals to assist such agencies, entities, and individuals in the process of identifying and applying for assistance and resources under economic adjustment and defense conversion programs and activities of the Federal, State, and local governments. (2) Federal agencies and programs.--The databases established pursuant to paragraph (1) shall include a comprehensive compilation of all relevant information concerning available economic adjustment and defense conversion-related programs of the Federal Government. The compilation shall identify the administering department, office, or agency, which administers such programs, and key contact people; and descriptions of the application process, eligibility requirements and criteria, selection, and followup procedures. Such compilation shall also include data as to the expenditure of funds under such programs, projects supported by such programs, and the types and amounts of funding available for assistance under such programs. (3) Range of programs.--The range of programs covered by the database shall include: worker adjustment assistance for private sector employees and Federal civilian and military personnel; community adjustment assistance (planning and implementation), including the so-called ``bricks and mortar'' programs, such as infrastructure rebuilding, and airport improvement; technology development and deployment programs administered through the Advanced Research Projects Agency, Department of Defense, coordinated Technology Reinvestment Project; other relevant technology research and development programs administered by the Department of Commerce, National Aeronautics and Space Administration, Department of Energy, the Environmental Protection Agency, Department of Transportation, and the National Institutes of Health and other technology agencies; small business assistance (financial, technical, marketing); defense facility environmental restoration; available tax credits and incentives, relevant regulatory information (environmental, occupational health and safety, and intellectual property rights) affecting application procedures and the implementation of federally supported projects involving economic adjustment and defense conversion. (4) Available assistance.--In developing such database, the Office shall survey all Federal departments and agencies in order to identify all relevant assistance and resources that may be available to assist defense-dependent communities, businesses, and workers in their adjustment and conversion efforts, especially the Department of Defense, the Department of Commerce, the Department of Labor, the Small Business Administration, the Department of Housing and Urban Development, the Department of Health and Human Services, the Department of Education, the Department of Transportation, the National Science Foundation, the National Aeronautics and Space Administration, and the Environmental Protection Agency. (5) Database of major state and local programs.--The Office shall establish a database containing State and local governmental economic adjustment and defense conversion assistance programs. Such database shall include a current listing of appropriate offices, officers, and contact personnel connected with, or involved in, such programs. (6) Defense cutback early warning database.--The Office, working with the Secretary of Defense, shall establish and keep current a database containing a listing of available defense contracts, and information listing military bases and installations expected to be closed, cut back, or realigned, or which are in the process of being closed, cut back, or realigned, including a current listing of States, communities, industries, firms, and employment likely to be most adversely affected as a result thereof. (7) Database of conversion efforts and successes.--The Office shall establish a database of listings and descriptions of defense conversion efforts, their successes and failures, as well as a current listing of ongoing conversion and assistance efforts by communities, contractors, and small- and mid-sized businesses, and labor organizations. (8) Reference lists and bibliographies.--The Office shall establish a database which shall include a listing of published works (books, reports, articles, videos, and tapes) related to all facets of defense economic adjustment and defense conversion. Such listing shall further include manuals relating to economic adjustment and defense conversion developed by the National Governors Association, the National League of Cities, public interest groups, labor unions, business associations, and similar organizations, and a listing of contact organizations and people for obtaining such references. The Office shall also maintain in electronic form the full texts of selected references and make such references available to the public through online services. (9) Alternative product bank for industries and firms.--The Office shall establish a databank of potentially commercializable technologies and products matched to the capabilities of defense-dependent industries and firms. Such databank shall include a short overview of market potential and shall identify potential programs in Federal, State and local governments that may be available to support technology development, deployment, and commercialization in these specific areas. (b) Multiple Points of Public Access to Databases.-- (1) Easy access.--The Office shall establish several mechanisms to assure easy access by the public and others to such databases, and to assure that the databases be as accessible, user-friendly, culturally neutral, and affordable as possible. In addition, the Office shall conduct an extensive outreach to States and communities, especially in the most defense-dependent regions of the Nation, and to a wide range of constituencies, including State and local government officials, chambers of commerce, industrial organizations, labor unions, and community organizations, to publicize the existence of databanks and other assistance and services provided by this Act, and how to acquire such assistance and services, and access such databanks. (2) 1-800-toll free number.--The Office shall establish a toll free 1-800 number to provide a first point of entry into the Office information database system. An individual calling such number shall receive information on how to use the Office databases, how to receive printed materials, and how to contact appropriate people in other governmental agencies for information about specific programs, and answer other requests regarding services of the Office. (3) Online electronic access through network.--Databases established by the Office shall be easily accessible through existing computer networks and publicly available computer database access facilities, such as at repository libraries and by direct call-in via modem, and shall be menu-driven and highly user-friendly. (4) Printed manuals and orientation materials.--The Office shall develop and make available to the public and others a printed manual, and other printed material, reviewing the major Federal agencies and programs engaged in economic adjustment, defense conversion, and technology investments. It shall also serve as a guide to using the databases and services of the Office, list State and local contacts and resources, and include a bibliography of major reference materials. (5) Orientation workshops.--The Office shall offer periodic workshops (1-2 weeks long) available to selected representatives from defense-dependent communities, businesses, and occupational groups, to orient and train them in using the Office and the services of the Office. (6) Information specialists.--The Office shall maintain on- call economic adjustment and conversion information specialists to address special problems requiring person-to-person assistance, as needed. (c) Program Evaluation.-- (1) Review.--The Office shall conduct a regular review of the various agencies and programs in the Federal system involving economic adjustment and defense conversion. Such review shall evaluate the procedures of these agencies and programs, and the success of their activities. Such reviews shall be based on periodic surveys of both Federal officials and recipients of assistance pursuant to this Act. The Office shall identify problems with the programs and barriers to entry, for inclusion in the databases established pursuant to this Act. Such review shall include recommendations for improving such programs. (2) Community roundtables.--The Office shall conduct, on an annual basis, consultative meetings and briefings with defense- impacted constituencies drawn from local and State governments, business, labor, community and public interest organizations and academic institutions. Such meetings and briefings shall be held in all major defense-dependent regions of the United States, both to introduce its programs and receive comments and recommendations concerning its services and how to expand and improve them. SEC. 4. INTERAGENCY COORDINATING COMMITTEE. (a) Establishment.--There is established the Interagency Economic Conversion Information Coordinating Committee (referred to in this section as the ``Committee''). (b) Members.--The members of the Committee are as follows: (1) Director of the Office, who shall serve as Chairperson of the Committee. (2) Director of the Economic Development Administration. (3) Director of the Office of Economic Adjustment, Department of Defense. (4) One member appointed by the Secretary of Labor. (5) Director of the Advanced Research Projects Agency, Department of Defense. (6) Director of the National Institute for Standards and Technology. (7) Director of the Small Business Administration. (8) One member appointed by the Director of the National Economic Council. (c) Functions.--It shall be the function of the Committee-- (1) to advise and make recommendations to the Office in carrying out the purposes of this Act; (2) to coordinate and facilitate the information gathering and monitoring activities of the Office among Federal departments and agencies; (3) to help the Office prepare and present information in a manner that is publicly accessible, affordable, and user- friendly; and (4) to assist the Office in making technical assistance personnel available as needed. (d) Compensation of Members.--All members of the Committee shall serve without compensation in addition to that received for their services as officers or employees of the United States. (e) Travel Expenses.--The members of the Committee shall be allowed travel expenses, including per diem in lieu of subsistence, at rates authorized for employees of agencies under subchapter I of chapter 57 of title 5, United States Code, while away from their homes or regular places of business in the performance of services for the Committee. (f) Staff.--The Chairman of the Committee may request any Federal department or agency to detail such employees to the Committee as may be necessary to enable the Committee to perform its duties. (g) Detail of Government Employees.--Any Federal Government employee may be detailed to the Committee without reimbursement, and such detail shall be without interruption or loss of civil service status or privilege. (h) Procurement of Temporary and Intermittent Services.--The Chairman of the Committee may procure temporary and intermittent services under section 3109(b) of title 5, United States Code, at rates for individuals which do not exceed the daily equivalent of the annual rate of basic pay prescribed for level V of the Executive Schedule under section 5316 of such title. SEC. 5. AUTHORIZATION. (a) Startup and Operating Expenses.--For fiscal year 1994, there are authorized to be appropriated such amounts as may be necessary to carry out the provisions of this Act. (b) Operating Expenses.--For fiscal year 1995, and each fiscal year thereafter, there are authorized to be appropriated such amounts as may be necessary to carry out the provisions of this Act.

Economic Conversion Clearinghouse Act - Establishes within the Department of Commerce the Office of Economic Conversion Information to: (1) serve as a central information clearinghouse on matters relating to economic adjustment and defense conversion programs and activities of the Federal and State governments; and (2) aid persons in applying for economic adjustment and defense conversion assistance under Federal, State, and local laws. Outlines further Office functions, including: (1) the development of information data bases for use in identifying and applying for such assistance; (2) the establishment of mechanisms to assure easy access to such information data bases, as well as their user-friendliness (including establishing a toll-free number); and (3) the conduct of a regular review of the various agencies and programs in the Federal system involving economic adjustment and defense conversion. Establishes the Interagency Economic Conversion Information Coordinating Committee to: (1) advise and make appropriate recommendations to the Office; (2) coordinate and facilitate the information gathering and monitoring activities of the Office among Federal departments and agencies; (3) aid the Office in preparing and presenting information in an accessible, user-friendly manner; and (4) assist the Office in making technical assistance personnel available as needed. Authorizes appropriations.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Economic Conversion Clearinghouse Act''. SEC. 2. OFFICE. (a) Establishment.--There is established, within the Department of Commerce, the Office of Economic Conversion Information (hereinafter referred to as ``Office''). (b) Purpose.--It is the purpose of the Office-- (1) to serve as a central information clearinghouse on matters relating to economic adjustment and defense conversion programs and activities of the Federal and State governments, including political subdivisions of the States; and (2) to help potential and actual applicants for economic adjustment and defense conversion assistance under Federal, State and local laws in locating and applying for such assistance, including financial and technical assistance. (c) Director.--The Office shall be headed by a Director. The Secretary of Commerce shall appoint and fix the compensation of the Director. (d) Staff.--The Director may appoint such personnel as may be necessary to enable the Office to perform its duties. SEC. 3. FUNCTIONS. (a) Information Databases.-- (1) Uses.--The Office shall develop information databases for use by Federal departments and agencies, State and local governmental agencies, public and private entities, and individuals to assist such agencies, entities, and individuals in the process of identifying and applying for assistance and resources under economic adjustment and defense conversion programs and activities of the Federal, State, and local governments. (2) Federal agencies and programs.--The databases established pursuant to paragraph (1) shall include a comprehensive compilation of all relevant information concerning available economic adjustment and defense conversion-related programs of the Federal Government. The compilation shall identify the administering department, office, or agency, which administers such programs, and key contact people; and descriptions of the application process, eligibility requirements and criteria, selection, and followup procedures. Such compilation shall also include data as to the expenditure of funds under such programs, projects supported by such programs, and the types and amounts of funding available for assistance under such programs. (3) Range of programs.--The range of programs covered by the database shall include: worker adjustment assistance for private sector employees and Federal civilian and military personnel; community adjustment assistance (planning and implementation), including the so-called ``bricks and mortar'' programs, such as infrastructure rebuilding, and airport improvement; technology development and deployment programs administered through the Advanced Research Projects Agency, Department of Defense, coordinated Technology Reinvestment Project; other relevant technology research and development programs administered by the Department of Commerce, National Aeronautics and Space Administration, Department of Energy, the Environmental Protection Agency, Department of Transportation, and the National Institutes of Health and other technology agencies; small business assistance (financial, technical, marketing); defense facility environmental restoration; available tax credits and incentives, relevant regulatory information (environmental, occupational health and safety, and intellectual property rights) affecting application procedures and the implementation of federally supported projects involving economic adjustment and defense conversion. (4) Available assistance.--In developing such database, the Office shall survey all Federal departments and agencies in order to identify all relevant assistance and resources that may be available to assist defense-dependent communities, businesses, and workers in their adjustment and conversion efforts, especially the Department of Defense, the Department of Commerce, the Department of Labor, the Small Business Administration, the Department of Housing and Urban Development, the Department of Health and Human Services, the Department of Education, the Department of Transportation, the National Science Foundation, the National Aeronautics and Space Administration, and the Environmental Protection Agency. (5) Database of major state and local programs.--The Office shall establish a database containing State and local governmental economic adjustment and defense conversion assistance programs. Such database shall include a current listing of appropriate offices, officers, and contact personnel connected with, or involved in, such programs. (6) Defense cutback early warning database.--The Office, working with the Secretary of Defense, shall establish and keep current a database containing a listing of available defense contracts, and information listing military bases and installations expected to be closed, cut back, or realigned, or which are in the process of being closed, cut back, or realigned, including a current listing of States, communities, industries, firms, and employment likely to be most adversely affected as a result thereof. (7) Database of conversion efforts and successes.--The Office shall establish a database of listings and descriptions of defense conversion efforts, their successes and failures, as well as a current listing of ongoing conversion and assistance efforts by communities, contractors, and small- and mid-sized businesses, and labor organizations. (8) Reference lists and bibliographies.--The Office shall establish a database which shall include a listing of published works (books, reports, articles, videos, and tapes) related to all facets of defense economic adjustment and defense conversion. Such listing shall further include manuals relating to economic adjustment and defense conversion developed by the National Governors Association, the National League of Cities, public interest groups, labor unions, business associations, and similar organizations, and a listing of contact organizations and people for obtaining such references. The Office shall also maintain in electronic form the full texts of selected references and make such references available to the public through online services. (9) Alternative product bank for industries and firms.--The Office shall establish a databank of potentially commercializable technologies and products matched to the capabilities of defense-dependent industries and firms. Such databank shall include a short overview of market potential and shall identify potential programs in Federal, State and local governments that may be available to support technology development, deployment, and commercialization in these specific areas. (b) Multiple Points of Public Access to Databases.-- (1) Easy access.--The Office shall establish several mechanisms to assure easy access by the public and others to such databases, and to assure that the databases be as accessible, user-friendly, culturally neutral, and affordable as possible. In addition, the Office shall conduct an extensive outreach to States and communities, especially in the most defense-dependent regions of the Nation, and to a wide range of constituencies, including State and local government officials, chambers of commerce, industrial organizations, labor unions, and community organizations, to publicize the existence of databanks and other assistance and services provided by this Act, and how to acquire such assistance and services, and access such databanks. (2) 1-800-toll free number.--The Office shall establish a toll free 1-800 number to provide a first point of entry into the Office information database system. An individual calling such number shall receive information on how to use the Office databases, how to receive printed materials, and how to contact appropriate people in other governmental agencies for information about specific programs, and answer other requests regarding services of the Office. (3) Online electronic access through network.--Databases established by the Office shall be easily accessible through existing computer networks and publicly available computer database access facilities, such as at repository libraries and by direct call-in via modem, and shall be menu-driven and highly user-friendly. (4) Printed manuals and orientation materials.--The Office shall develop and make available to the public and others a printed manual, and other printed material, reviewing the major Federal agencies and programs engaged in economic adjustment, defense conversion, and technology investments. It shall also serve as a guide to using the databases and services of the Office, list State and local contacts and resources, and include a bibliography of major reference materials. (5) Orientation workshops.--The Office shall offer periodic workshops (1-2 weeks long) available to selected representatives from defense-dependent communities, businesses, and occupational groups, to orient and train them in using the Office and the services of the Office. (6) Information specialists.--The Office shall maintain on- call economic adjustment and conversion information specialists to address special problems requiring person-to-person assistance, as needed. (c) Program Evaluation.-- (1) Review.--The Office shall conduct a regular review of the various agencies and programs in the Federal system involving economic adjustment and defense conversion. Such review shall evaluate the procedures of these agencies and programs, and the success of their activities. Such reviews shall be based on periodic surveys of both Federal officials and recipients of assistance pursuant to this Act. The Office shall identify problems with the programs and barriers to entry, for inclusion in the databases established pursuant to this Act. Such review shall include recommendations for improving such programs. (2) Community roundtables.--The Office shall conduct, on an annual basis, consultative meetings and briefings with defense- impacted constituencies drawn from local and State governments, business, labor, community and public interest organizations and academic institutions. Such meetings and briefings shall be held in all major defense-dependent regions of the United States, both to introduce its programs and receive comments and recommendations concerning its services and how to expand and improve them. SEC. 4. INTERAGENCY COORDINATING COMMITTEE. (a) Establishment.--There is established the Interagency Economic Conversion Information Coordinating Committee (referred to in this section as the ``Committee''). (b) Members.--The members of the Committee are as follows: (1) Director of the Office, who shall serve as Chairperson of the Committee. (2) Director of the Economic Development Administration. (3) Director of the Office of Economic Adjustment, Department of Defense. (4) One member appointed by the Secretary of Labor. (5) Director of the Advanced Research Projects Agency, Department of Defense. (6) Director of the National Institute for Standards and Technology. (7) Director of the Small Business Administration. (8) One member appointed by the Director of the National Economic Council. (c) Functions.--It shall be the function of the Committee-- (1) to advise and make recommendations to the Office in carrying out the purposes of this Act; (2) to coordinate and facilitate the information gathering and monitoring activities of the Office among Federal departments and agencies; (3) to help the Office prepare and present information in a manner that is publicly accessible, affordable, and user- friendly; and (4) to assist the Office in making technical assistance personnel available as needed. (d) Compensation of Members.--All members of the Committee shall serve without compensation in addition to that received for their services as officers or employees of the United States. (e) Travel Expenses.--The members of the Committee shall be allowed travel expenses, including per diem in lieu of subsistence, at rates authorized for employees of agencies under subchapter I of chapter 57 of title 5, United States Code, while away from their homes or regular places of business in the performance of services for the Committee. (f) Staff.--The Chairman of the Committee may request any Federal department or agency to detail such employees to the Committee as may be necessary to enable the Committee to perform its duties. (g) Detail of Government Employees.--Any Federal Government employee may be detailed to the Committee without reimbursement, and such detail shall be without interruption or loss of civil service status or privilege. (h) Procurement of Temporary and Intermittent Services.--The Chairman of the Committee may procure temporary and intermittent services under section 3109(b) of title 5, United States Code, at rates for individuals which do not exceed the daily equivalent of the annual rate of basic pay prescribed for level V of the Executive Schedule under section 5316 of such title. SEC. 5. AUTHORIZATION. (a) Startup and Operating Expenses.--For fiscal year 1994, there are authorized to be appropriated such amounts as may be necessary to carry out the provisions of this Act. (b) Operating Expenses.--For fiscal year 1995, and each fiscal year thereafter, there are authorized to be appropriated such amounts as may be necessary to carry out the provisions of this Act.[/INST]Economic Conversion Clearinghouse Act - Establishes within the Department of Commerce the Office of Economic Conversion Information to: (1) serve as a central information clearinghouse on matters relating to economic adjustment and defense conversion programs and activities of the Federal and State governments; and (2) aid persons in applying for economic adjustment and defense conversion assistance under Federal, State, and local laws. Outlines further Office functions, including: (1) the development of information data bases for use in identifying and applying for such assistance; (2) the establishment of mechanisms to assure easy access to such information data bases, as well as their user-friendliness (including establishing a toll-free number); and (3) the conduct of a regular review of the various agencies and programs in the Federal system involving economic adjustment and defense conversion. Establishes the Interagency Economic Conversion Information Coordinating Committee to: (1) advise and make appropriate recommendations to the Office; (2) coordinate and facilitate the information gathering and monitoring activities of the Office among Federal departments and agencies; (3) aid the Office in preparing and presenting information in an accessible, user-friendly manner; and (4) assist the Office in making technical assistance personnel available as needed. Authorizes appropriations.</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Gold Star Families Equality Act''. SEC. 2. LAPEL BUTTON FOR NEXT OF KIN OF DECEASED MEMBERS OF THE ARMED FORCES. (a) Service-Wide Adoption of Next of Kin Lapel Button.--Section 1126 of title 10, United States Code, is amended-- (1) by striking subsection (b); (2) by redesignating subsections (c) and (d) as subsections (d) and (e), respectively; and (3) by inserting after subsection (a) the following new subsections: ``(b) A lapel button, to be known as the lapel button for next of kin of deceased members of the armed forces, shall be designed, as approved by the Secretary of Defense, to identify widows, parents, and next of kin of members of the armed forces who die, under circumstances not prescribed by subsection (a), while serving on active duty or while assigned to a reserve component in a drill status. ``(c) Under regulations to be prescribed by the Secretary of Defense, the Secretary concerned, upon application to the Secretary, shall furnish-- ``(1) one gold star lapel button without cost to the widow and to each parent and next of kin of a member who lost or loses his or her life under any circumstances prescribed in subsection (a); and ``(2) one lapel button for next of kin of deceased members to the widow and to each parent and next of kin of a member who lost or loses his or her life under the circumstances prescribed in subsection (b).''. (b) Conforming Amendments.--Subsection (d) of section 1126 of title 10, United States Code, as redesignated by subsection (a)(2), is amended by inserting ``or lapel button for next of kin of deceased members'' after ``gold star lapel button'' both places it appears. (c) Use of Existing Design.--The design of the lapel button for the next of kin of deceased members of the Armed Forces required by subsection (b) of section 1126 of title 10, United States Code, as added by subsection (a)(3), shall be based on the design of such a lapel button provided by the Secretary of the Army to certain survivors of deceased members of the Army, including the Army Reserve and the Army National Guard, pursuant to Army regulation 600-6-18, as in effect on the date of the enactment of this Act. (d) Retroactive Availability.--The lapel button for the next of kin of deceased members of the Armed Forces required by subsection (b) of section 1126 of title 10, United States Code, as added by subsection (a)(3), shall be available to provide appropriate recognition for the survivors of members of the Armed Forces who have died since September 10, 2001. SEC. 3. GOLD STAR INSTALLATION ACCESS CARD. (a) Service-Wide Adoption of Access Card.--The Secretary of each military department and the Secretary of the Department in which the Coast Guard is operating (in this section referred to as the ``Secretary concerned'') shall provide for the issuance of a Gold Star Installation Access Card to Gold Star family members who are the survivors of deceased members of the Armed Forces under the jurisdiction of the Secretary concerned to expedite the ability of a Gold Star family member to gain unescorted access to military installations for the purpose of obtaining the on-base services and benefits for which the Gold Star family member is entitled or eligible. (b) Service-Wide Acceptance of Access Card.--The Secretaries concerned shall work jointly to ensure that a Gold Star Installation Access Card issued to a Gold Star family member by one Armed Force is accepted for access to military installations of another Armed Force. (c) Protection of Installation Security.--In developing, issuing, and accepting the Gold Star Installation Access Card, the Secretary concerned may take such measures as the Secretary concerned considers necessary-- (1) to prevent fraud in the procurement or use of the Gold Star Installation Access Card; (2) to limit installation access to those areas that provide the services and benefits for which the Gold Star family member is entitled or eligible; and (3) to ensure that the availability and use of the Gold Star Installation Access Card does not adversely affect military installation security. (d) Implementation.--Not later than 180 days after the date of the enactment of this Act, the Secretaries concerned shall complete implementation of this section. (e) Gold Star Family Member Defined.--In this section, the term ``Gold Star family member'' means a person who has received a Gold Star Lapel Button or a Lapel Button for the Next of Kin of Deceased Members of the Armed Forces under section 1126 of title 10, United States Code. SEC. 4. USE OF COMMISSARY STORES AND MWR RETAIL FACILITIES BY PARENTS OF DECEASED MEMBERS OF THE ARMED FORCES. (a) Use Authorized.--The Secretary of each military department and the Secretary of the Department in which the Coast Guard is operating shall prescribe such regulations as may be necessary to ensure that a parent of a deceased member of the Armed Forces who receives a Gold Star Lapel Button or a Lapel Button for the Next of Kin of Deceased Members of the Armed Forces under section 1126 of title 10, United States Code, is permitted to use commissary stores and MWR retail facilities on the same basis as any surviving spouse or child of the member. (b) Definitions.--In this section: (1) The term ``MWR retail facilities'' means exchange stores and other revenue generating facilities operated by nonappropriated fund activities of the Department of Defense or the department in which the Coast Guard is operating for the morale, welfare, and recreation of members of the Armed Forces. (2) The term ``parent'' includes mother, father, stepmother, stepfather, mother through adoption, father through adoption, or foster parent who stood in loco parentis.

Gold Star Families Equality Act - Requires a lapel button to be designed to identify widows, parents, and next of kin of members of the Armed Forces who die, under circumstances not already prescribed for under existing eligibility standards for a gold star lapel button, while serving on active duty or while assigned to a reserve component in a drill status. Makes such next of kin button available retroactively to survivors of members of the Armed Forces who have died since September 10, 2001. Directs the Secretary of each military department and the Secretary of the department in which the Coast Guard is operating to provide for the issuance of a Gold Star Installation Access Card to family members with gold or next of kin buttons to expedite their ability to gain unescorted access to military installations for the purpose of obtaining on-base services and benefits. Requires regulations to be prescribed to permit parents (including stepparents, parents though adoption, or foster parents who stood in loco parentis) with such buttons to use commissary stores and other military retail facilities on the same basis as surviving spouses or children.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Gold Star Families Equality Act''. SEC. 2. LAPEL BUTTON FOR NEXT OF KIN OF DECEASED MEMBERS OF THE ARMED FORCES. (a) Service-Wide Adoption of Next of Kin Lapel Button.--Section 1126 of title 10, United States Code, is amended-- (1) by striking subsection (b); (2) by redesignating subsections (c) and (d) as subsections (d) and (e), respectively; and (3) by inserting after subsection (a) the following new subsections: ``(b) A lapel button, to be known as the lapel button for next of kin of deceased members of the armed forces, shall be designed, as approved by the Secretary of Defense, to identify widows, parents, and next of kin of members of the armed forces who die, under circumstances not prescribed by subsection (a), while serving on active duty or while assigned to a reserve component in a drill status. ``(c) Under regulations to be prescribed by the Secretary of Defense, the Secretary concerned, upon application to the Secretary, shall furnish-- ``(1) one gold star lapel button without cost to the widow and to each parent and next of kin of a member who lost or loses his or her life under any circumstances prescribed in subsection (a); and ``(2) one lapel button for next of kin of deceased members to the widow and to each parent and next of kin of a member who lost or loses his or her life under the circumstances prescribed in subsection (b).''. (b) Conforming Amendments.--Subsection (d) of section 1126 of title 10, United States Code, as redesignated by subsection (a)(2), is amended by inserting ``or lapel button for next of kin of deceased members'' after ``gold star lapel button'' both places it appears. (c) Use of Existing Design.--The design of the lapel button for the next of kin of deceased members of the Armed Forces required by subsection (b) of section 1126 of title 10, United States Code, as added by subsection (a)(3), shall be based on the design of such a lapel button provided by the Secretary of the Army to certain survivors of deceased members of the Army, including the Army Reserve and the Army National Guard, pursuant to Army regulation 600-6-18, as in effect on the date of the enactment of this Act. (d) Retroactive Availability.--The lapel button for the next of kin of deceased members of the Armed Forces required by subsection (b) of section 1126 of title 10, United States Code, as added by subsection (a)(3), shall be available to provide appropriate recognition for the survivors of members of the Armed Forces who have died since September 10, 2001. SEC. 3. GOLD STAR INSTALLATION ACCESS CARD. (a) Service-Wide Adoption of Access Card.--The Secretary of each military department and the Secretary of the Department in which the Coast Guard is operating (in this section referred to as the ``Secretary concerned'') shall provide for the issuance of a Gold Star Installation Access Card to Gold Star family members who are the survivors of deceased members of the Armed Forces under the jurisdiction of the Secretary concerned to expedite the ability of a Gold Star family member to gain unescorted access to military installations for the purpose of obtaining the on-base services and benefits for which the Gold Star family member is entitled or eligible. (b) Service-Wide Acceptance of Access Card.--The Secretaries concerned shall work jointly to ensure that a Gold Star Installation Access Card issued to a Gold Star family member by one Armed Force is accepted for access to military installations of another Armed Force. (c) Protection of Installation Security.--In developing, issuing, and accepting the Gold Star Installation Access Card, the Secretary concerned may take such measures as the Secretary concerned considers necessary-- (1) to prevent fraud in the procurement or use of the Gold Star Installation Access Card; (2) to limit installation access to those areas that provide the services and benefits for which the Gold Star family member is entitled or eligible; and (3) to ensure that the availability and use of the Gold Star Installation Access Card does not adversely affect military installation security. (d) Implementation.--Not later than 180 days after the date of the enactment of this Act, the Secretaries concerned shall complete implementation of this section. (e) Gold Star Family Member Defined.--In this section, the term ``Gold Star family member'' means a person who has received a Gold Star Lapel Button or a Lapel Button for the Next of Kin of Deceased Members of the Armed Forces under section 1126 of title 10, United States Code. SEC. 4. USE OF COMMISSARY STORES AND MWR RETAIL FACILITIES BY PARENTS OF DECEASED MEMBERS OF THE ARMED FORCES. (a) Use Authorized.--The Secretary of each military department and the Secretary of the Department in which the Coast Guard is operating shall prescribe such regulations as may be necessary to ensure that a parent of a deceased member of the Armed Forces who receives a Gold Star Lapel Button or a Lapel Button for the Next of Kin of Deceased Members of the Armed Forces under section 1126 of title 10, United States Code, is permitted to use commissary stores and MWR retail facilities on the same basis as any surviving spouse or child of the member. (b) Definitions.--In this section: (1) The term ``MWR retail facilities'' means exchange stores and other revenue generating facilities operated by nonappropriated fund activities of the Department of Defense or the department in which the Coast Guard is operating for the morale, welfare, and recreation of members of the Armed Forces. (2) The term ``parent'' includes mother, father, stepmother, stepfather, mother through adoption, father through adoption, or foster parent who stood in loco parentis.[/INST]Gold Star Families Equality Act - Requires a lapel button to be designed to identify widows, parents, and next of kin of members of the Armed Forces who die, under circumstances not already prescribed for under existing eligibility standards for a gold star lapel button, while serving on active duty or while assigned to a reserve component in a drill status. Makes such next of kin button available retroactively to survivors of members of the Armed Forces who have died since September 10, 2001. Directs the Secretary of each military department and the Secretary of the department in which the Coast Guard is operating to provide for the issuance of a Gold Star Installation Access Card to family members with gold or next of kin buttons to expedite their ability to gain unescorted access to military installations for the purpose of obtaining on-base services and benefits. Requires regulations to be prescribed to permit parents (including stepparents, parents though adoption, or foster parents who stood in loco parentis) with such buttons to use commissary stores and other military retail facilities on the same basis as surviving spouses or children.</s>

many improved actions have been proposed and studied which may allow us much more reliable simulations near the continuum limit within the limited computer resources existing nowadays . one way to obtain such improved actions is to find the renormalized trajectory ( rt ) , any point on which serves as a `` perfect action '' @xcite . here we will consider the simplest case , i.e. , actions in two coupling @xmath0 space , which for practical purposes are preferable than actions with a larger number of operators . in this contribution , we evaluate the rg flow and study whether the performance of such actions improves when they approach the renormalized trajectory . we adapt swendsen s blocking transformation scheme @xcite , which is defined as @xmath2 under this transformation the lattice spacing is doubled . repeating this blocking transformation , we can get an action near the rt . after each transformation we generate a blocked configuration , the couplings on which can be determined via the schwinger - dyson equation : where @xmath3 are the `` staples '' corresponding to the link @xmath4 . solving these equations , we can calculate the coefficients of operators corresponding to the blocked action . in this paper we will neglect truncation errors and assume that the resulting blocked actions also have only two couplings , @xmath5 and @xmath6 . figure [ fig.flow ] shows the blocking transformation flow in two - coupling space . the rt can be calculated within the strong coupling expansion . the string tension is obtained from the expectation value of wilson loops . to leading order , @xmath7 imposing that in the strong coupling limit , the lattice spacing goes to infinity , one easily derives the following relation @xmath8 as this equation tells us , in this limit , the rt is a parabola which is presented in figure [ fig.flow ] to compare with the rt obtained by solving the s - d equations as indicated above . one could as well solve the s - d equations with coefficients calculated by the strong coupling expansion . this is work in progress and the results will be reported elsewhere . here we report on the scaling analysis of several improved actions . we study the violation of rotational symmetry as well as @xmath9 . first we define the following quantity which represents the violation of rotational symmetry @xmath10 ^ 2 } { v(r)^2\delta v(r)^2}\left(\sum_{\mbox{off}}\frac{1}{\delta v(r)^2 } \right)^{-1}\ ] ] where @xmath11 is the static quark potential and @xmath12 its error . @xmath13 is a fitting function from only on - axis data , and @xmath14 implies summation over only off - axis data . we calculate this quantity with various improved actions . we write @xmath15 , and impose the condition , @xmath16 . the wilson action corresponds @xmath17 . for symanzik(tree ) , iwasaki and dbw2 actions , @xmath18 , respectively @xcite . dbw2 ( double blocked from wilson action in 2 coupling space ) is defined in ref . results are summarized in figure [ fig.dv ] . simulations have been performed on a lattice of size @xmath19 . thermalization is 5000 sweeps , while the interval between wilson loop measurements is 500 sweeps . we used 100 configurations . here we study the scaling behavior of @xmath9 for dbw2 . the critical temperature is defined by @xmath20 where @xmath21 is the temporal extension of the lattice , and @xmath22 is the lattice spacing at critical coupling @xmath23 . in order to extract @xmath23 , we calculate the polyakov loop susceptibility on @xmath24 lattices . then @xmath25 in the infinite volume limit are obtained by using finite size scaling ( of @xmath26 ) . the results of @xmath23 for dbw2 are presented below . + + [ cols="^,^,^",options="header " , ] + + where we used the ansatz @xmath27 . for this action @xmath9 is @xmath28 and @xmath29 at @xmath26 and @xmath30 respectively - see fig . [ fig.scale ] for a comparison with other actions in two - coupling space . we have studied the non - perturbative rt of su(3 ) gauge theory in two - coupling space . we find an improvement of rotational invariance as the improved action becomes closer to the rt . wilson , in _ recent developments in gauge theories _ g. thooft ( plenum press , new york , 1980 ) p.363 . y. iwasaki , university of tsukuba preprint , uthep-118 , 1983 . p. hasenfratz , f. niedermayer , nucl . b414 ( 1994 ) 785 . qcdtaro collaboration , phys . lett . , ( 1993 ) 71 , 3963 . a. gonzlez - arroyo and m. okawa , phys . d35 ( 1987 ) 672 ; phys . b35 ( 1987 ) 2108 . swendsen , phys . 42 ( 1979 ) 859 . k. symanzik , nucl . b226 ( 1983 ) 187 , 205 t. takaishi , phys . d54 ( 1996 ) 1050 . y. iwasaki and k. kanaya , k. kaneko , t.yoshi , phys.rev.d 56 ( 1997 ) 151 . b. beinlich , f. karsch , e. laermann and a. peikert hep - lat/9707023

we have explored the behaviour of some improved actions based on a nonperturbative renormalization group ( rg ) analysis in coupling space . we calculate the rg flow in two - coupling space @xmath0 and examine the restoration of rotational invariance and the scaling of physical quantities @xmath1 .

<s>[INST]many improved actions have been proposed and studied which may allow us much more reliable simulations near the continuum limit within the limited computer resources existing nowadays . one way to obtain such improved actions is to find the renormalized trajectory ( rt ) , any point on which serves as a `` perfect action '' @xcite . here we will consider the simplest case , i.e. , actions in two coupling @xmath0 space , which for practical purposes are preferable than actions with a larger number of operators . in this contribution , we evaluate the rg flow and study whether the performance of such actions improves when they approach the renormalized trajectory . we adapt swendsen s blocking transformation scheme @xcite , which is defined as @xmath2 under this transformation the lattice spacing is doubled . repeating this blocking transformation , we can get an action near the rt . after each transformation we generate a blocked configuration , the couplings on which can be determined via the schwinger - dyson equation : where @xmath3 are the `` staples '' corresponding to the link @xmath4 . solving these equations , we can calculate the coefficients of operators corresponding to the blocked action . in this paper we will neglect truncation errors and assume that the resulting blocked actions also have only two couplings , @xmath5 and @xmath6 . figure [ fig.flow ] shows the blocking transformation flow in two - coupling space . the rt can be calculated within the strong coupling expansion . the string tension is obtained from the expectation value of wilson loops . to leading order , @xmath7 imposing that in the strong coupling limit , the lattice spacing goes to infinity , one easily derives the following relation @xmath8 as this equation tells us , in this limit , the rt is a parabola which is presented in figure [ fig.flow ] to compare with the rt obtained by solving the s - d equations as indicated above . one could as well solve the s - d equations with coefficients calculated by the strong coupling expansion . this is work in progress and the results will be reported elsewhere . here we report on the scaling analysis of several improved actions . we study the violation of rotational symmetry as well as @xmath9 . first we define the following quantity which represents the violation of rotational symmetry @xmath10 ^ 2 } { v(r)^2\delta v(r)^2}\left(\sum_{\mbox{off}}\frac{1}{\delta v(r)^2 } \right)^{-1}\ ] ] where @xmath11 is the static quark potential and @xmath12 its error . @xmath13 is a fitting function from only on - axis data , and @xmath14 implies summation over only off - axis data . we calculate this quantity with various improved actions . we write @xmath15 , and impose the condition , @xmath16 . the wilson action corresponds @xmath17 . for symanzik(tree ) , iwasaki and dbw2 actions , @xmath18 , respectively @xcite . dbw2 ( double blocked from wilson action in 2 coupling space ) is defined in ref . results are summarized in figure [ fig.dv ] . simulations have been performed on a lattice of size @xmath19 . thermalization is 5000 sweeps , while the interval between wilson loop measurements is 500 sweeps . we used 100 configurations . here we study the scaling behavior of @xmath9 for dbw2 . the critical temperature is defined by @xmath20 where @xmath21 is the temporal extension of the lattice , and @xmath22 is the lattice spacing at critical coupling @xmath23 . in order to extract @xmath23 , we calculate the polyakov loop susceptibility on @xmath24 lattices . then @xmath25 in the infinite volume limit are obtained by using finite size scaling ( of @xmath26 ) . the results of @xmath23 for dbw2 are presented below . + + [ cols="^,^,^",options="header " , ] + + where we used the ansatz @xmath27 . for this action @xmath9 is @xmath28 and @xmath29 at @xmath26 and @xmath30 respectively - see fig . [ fig.scale ] for a comparison with other actions in two - coupling space . we have studied the non - perturbative rt of su(3 ) gauge theory in two - coupling space . we find an improvement of rotational invariance as the improved action becomes closer to the rt . wilson , in _ recent developments in gauge theories _ g. thooft ( plenum press , new york , 1980 ) p.363 . y. iwasaki , university of tsukuba preprint , uthep-118 , 1983 . p. hasenfratz , f. niedermayer , nucl . b414 ( 1994 ) 785 . qcdtaro collaboration , phys . lett . , ( 1993 ) 71 , 3963 . a. gonzlez - arroyo and m. okawa , phys . d35 ( 1987 ) 672 ; phys . b35 ( 1987 ) 2108 . swendsen , phys . 42 ( 1979 ) 859 . k. symanzik , nucl . b226 ( 1983 ) 187 , 205 t. takaishi , phys . d54 ( 1996 ) 1050 . y. iwasaki and k. kanaya , k. kaneko , t.yoshi , phys.rev.d 56 ( 1997 ) 151 . b. beinlich , f. karsch , e. laermann and a. peikert hep - lat/9707023[/INST] we have explored the behaviour of some improved actions based on a nonperturbative renormalization group ( rg ) analysis in coupling space . we calculate the rg flow in two - coupling space @xmath0 and examine the restoration of rotational invariance and the scaling of physical quantities @xmath1 . </s>

care of individuals with multimorbidity defined as the coexistence of two or more chronic conditions is an emerging area of research . existing studies have reported negative effects of multimorbidity on a variety of health outcomes such as disability , functional status , health - related quality of life , healthcare expenditures , and survival [ 112 ] . multimorbidity is also associated with healthcare utilization specifically an increased number of hospital admissions and prescription medications among individuals with multiple chronic conditions [ 13 , 14 ] . in a us study of the elderly , it was found that an overwhelming majority ( 73% ) with three or more chronic conditions were using 5 or more prescription drugs . in an australian study of multimorbidity across all age groups , it was reported that those with multimorbidity were 7 times to 22 times as likely to use four or more prescription medications as those without multimorbidity . multiple medications use often results in harmful drug - drug interactions . a study by nolan and o'malley suggested that individuals taking 10 or more medications had over a 90% probability of experiencing one or more clinically significant drug interactions . there have been many studies on polypharmacy among the elderly ; however , studies with specific focus on the association between polypharmacy generally defined as concurrent use of multiple medications and multimorbidity are very limited . one italian study of hospitalized elderly patients reported significant associations between specific clusters of diseases and polypharmacy . in this study , elderly patients with diabetes and coronary heart disease and cerebrovascular diseases had greater likelihood of polypharmacy compared to those without diabetes and cerebrovascular diseases . the adjusted odds ratio ( aor ) was 9.8 with 95% confidence interval of 1.372.2 , suggesting that coronary heart disease may increase the likelihood of polypharmacy . additionally , polypharmacy issues have only been examined in the elderly populations while an australian study documented that multimorbidity was prevalent ( 4.4% for 2039 years of age and 15.0% for 4059 years of age ) in the younger adults as well . therefore , it is necessary to examine the relationship between polypharmacy and multimorbidity across all age groups . the primary objective of the current study was to estimate rates of polypharmacy among individuals living in the community with specific clusters of chronic conditions , using a nationally representative sample of households in the united states . we also examined the independent relationship between specific clusters of chronic conditions and polypharmacy within a multivariate framework after controlling for demographic , socioeconomic , access to care , health status , lifestyle risk factors , and outpatient visits that may be associated with polypharmacy . we hypothesize that the rates of polypharmacy will depend on the specific chronic condition cluster and multiple conditions may not necessarily lead to greater rates of polypharmacy compared to those with single clusters . data were extracted from the agency for healthcare research and quality- ( ahrq- ) sponsored medical expenditure panel survey ( meps ) which is a nationally representative household survey of the united states noninstitutionalized civilian population . the meps household component ( hc ) collected information on demographic and socioeconomic characteristics of household members , medical conditions , and treatments for these conditions including prescription drug use over five interview rounds . a sample of medical providers were contacted to gather information on dates of visit , diagnosis and procedure codes , charges , and payments and were typically used as an imputation source to supplement / replace the data on household reported expenditures . ( 1 ) a disease condition may be reported in the priority condition enumeration section in which persons are asked if they have been diagnosed with specific conditions ; ( 2 ) a disease condition may be reported by the respondent when they had a particular medical event ( hospital stay , outpatient visit , emergency room visit , home health episode , prescribed medication purchase , or medical provider visit ) ; ( 3 ) a disease condition may be reported as the reason for one or more episodes of disability days ; ( 4 ) a disease condition may be reported by the household level respondent as a condition bothering the person during the reference period . on sensitivity of household reported medical conditions in the meps found that household reports tend to be accurate for many conditions . information on medical conditions was recorded verbatim and verbatim text was translated into international classification of diseases , 9th edition , clinical modification ( icd-9-cm ) codes by experienced and professional coders ( http://meps.ahrq.gov/mepsweb/data_stats/download_data/pufs/h128/h128doc.pdf ) . for privacy reasons meps provided the crosswalk between icd-9-cm and clinical condition classification codes . for purposes of our study , data were drawn from multiple files of meps ( 2009 survey ) such as household , medical conditions , prescribed medicines , and office - based medical provider visits and outpatients visits . our study sample comprised living individuals over 21 years of age as of the end of 2009 , reported having had at least one chronic physical condition in the following clusters : cardiometabolic ( consisting of diabetes or heart disease or hypertension ) , musculoskeletal ( consisting of arthritis or osteoporosis ) , and respiratory ( consisting of copd or asthma ) . our analytical sample consisted of 10,528 individuals representing approximately 102 million individuals of the united states civilian noninstitutionalized population . however , a systematic review of the literature stated use of six or more concomitant medications as one of the most cited definitions of polypharmacy . accordingly we classified polypharmacy variable into two categories : ( 1 ) 0 to 5 drugs and ( 2 ) polypharmacy ( 6 drugs ) . meps prescription medications file contains information on therapeutic classes of medications through linkage of multum lexicon database ( http://www.multum.com/lexicon.htm ) . the unique therapeutic class codes were used to identify the maximum number of classes of medications taken by individuals in any one of the five interview rounds . we defined polypharmacy as using at least six prescribed medications in any one of the five rounds of interviews during year 2009 . such clustering of disease conditions based on synergism in treatment patterns and self - management approaches have been used in our prior study . using a similar approach , we grouped three clinically meaningful disease clusters among diabetes , heart disease , hypertension , copd , asthma , arthritis , and osteoporosis . these conditions were chosen due to their high prevalence , cost , morbidity , and mortality ( http://meps.ahrq.gov/mepsweb/data_files/publications/st167/stat167.shtml ) . the specific clusters were ( 1 ) cardiometabolic ( diabetes or heart disease or hypertension ) , ( 2 ) musculoskeletal ( arthritis or osteoporosis ) , and ( 3 ) respiratory ( asthma or copd ) . these clusters were pooled together to form the following seven mutually exclusive categories of multimorbidity : ( 1 ) cardiometabolic conditions only ; ( 2 ) musculoskeletal conditions only , ( 3 ) respiratory conditions only , ( 4 ) cardiometabolic and musculoskeletal conditions , ( 5 ) cardiometabolic and respiratory conditions , ( 6 ) musculoskeletal and respiratory conditions , and ( 7 ) cardiometabolic , musculoskeletal , and respiratory conditions . demographic variables consisted of gender ( women , men ) , race / ethnicity ( white , african american , latino , other ) , age ( 2239 , 4049 , 5064 , 6569 , 7074 , and 75 and older ) , and marital status ( married , widowed , separated / divorced , never married ) . socioeconomic variables consisted of education ( less than high school , high school , above high school ) , area of residence ( metro , nonmetro ) , and poverty status ( poor , near poor , middle income , high income ) . access to care was assessed using health insurance coverage ( private , public , uninsured ) and usual source of care ( yes , no ) . health status was measured with variables such as perceived physical and mental health status ( excellent / very good , good , fair / poor ) . lifestyle risk factors comprised of body mass index ( bmi ) ( underweight / normal weight , overweight , obese ) , current smoking ( yes / no ) , and physical activity ( vigorous activity 3 days a week / other ) . we also included total number of visits to either office - based provider or outpatient hospital clinics as a measure of contact with the healthcare system . chi - square tests were used to assess significant differences between the multimorbidity categories and polypharmacy . unadjusted and multivariate logistic regressions were used to analyze the association between polypharmacy and multimorbidity categories and other independent variables . for example , we compared the aors of polypharmacy between cardiometabolic and musculoskeletal clusters and cardiometabolic and respiratory clusters . in all these regressions , all analyses used primary sampling unit , strata , and weights provided in the meps to control for clustering and unequal probability design and were conducted in survey procedures using sas 9.2 to handle study weights and clustering . table 1 characterizes the study sample by multimorbidity categories in our study sample above 21 years of age , alive , with at least one of the cardiometabolic , musculoskeletal , and respiratory conditions in year 2009 . thirty - four percent of our study sample had cardiometabolic conditions and 25% had both cardiometabolic and musculoskeletal disease clusters ; 4% had both cardiometabolic and respiratory disease clusters . however , only 7% of the study sample had all the three , cardiometabolic , musculoskeletal , and respiratory disease clusters . table 2 summarizes number and weighted percentages of individuals with polypharmacy by selected characteristics . women compared to men were significantly more likely to be on polypharmacy ( or = 1.41 , 95% ci = 1.271.56 ) . individuals in older age groups 4049 , 5064 , 6569 , 7074 , and 75 and older were also significantly more likely to be on polypharmacy compared to individuals in the age group 2239 . there was also a positive and significant association between total outpatient visit quartiles and polypharmacy . individuals who had visits in the upper quartile ( 4th quartile ) were 17 times as likely as those with visits in the 1st quartile ( or = 16.77 ; 95% ci = 12.522.4 ) . we present weighted percentage of individuals with polypharmacy among different multimorbidity categories in the left panel of table 3 . as seen from table 3 , the highest rates ( 64.1% ) of polypharmacy were found in sample individuals with all three ( cardiometabolic and respiratory and musculoskeletal ) disease clusters . the next highest rates ( 41.2% and 41.8% ) were observed among those with cardiometabolic and musculoskeletal disease clusters and among those with cardiometabolic and respiratory disease clusters . the lowest rates were found in those with only musculoskeletal ( 7.9% ) and only respiratory clusters ( 7.2% ) . unadjusted logistic regressions and multivariable logistic regressions were used to examine the association between chronic condition clusters and polypharmacy . odds ratios ( or ) and aors with their 95% confidence intervals for polypharmacy are presented in table 3 . compared to individuals with all the three disease clusters ( cardiometabolic , musculoskeletal , and respiratory ) , those with either one or two disease clusters were significantly less likely to receive polypharmacy . the unadjusted odds ratios ranged from 0.04 among those with respiratory conditions only to 0.40 among those with cardiometabolic and respiratory disease clusters . we also examined the differences in the likelihood of polypharmacy between different single condition clusters . compared to individuals with cardiometabolic disease cluster only , those with musculoskeletal cluster only and respiratory cluster only had lower odds ratios of reporting polypharmacy ( or = 0.38 and or = 0.35 , resp . ) . on the other hand , there were no significant differences in ors between individuals with musculoskeletal conditions only and respiratory conditions only ( or = 0.91 , 95% ci = ( 0.59 , 1.39 ) ) . when examining the differences in the likelihood of polypharmacy by two disease clusters , we found that individuals with both cardiometabolic and musculoskeletal clusters were more likely to report polypharmacy compared to those with both musculoskeletal and respiratory clusters ( or = 1.77 ) . similarly , individuals with both cardiometabolic and respiratory clusters were more likely to report polypharmacy ( or = 1.82 ) as compared to those with both musculoskeletal and respiratory clusters . individuals with cardiometabolic and respiratory clusters did not significantly differ in the or of polypharmacy from those with cardiometabolic and musculoskeletal clusters ( or = 1.03 , 95% ci = 0.80 , 1.32 ) . multivariable logistic regressions to assess the association between multimorbidity and polypharmacy that controlled for gender , age , race / ethnicity , marital status , education , poverty status , health insurance , usual source of care , perceived physical and mental health , smoking status , bmi , and exercise revealed similar findings . for example , compared to individuals with cardiometabolic disease cluster only , those with musculoskeletal cluster only ( aor = 0.38 ; 95% ci = 0.300.49 ) and respiratory cluster only had lower likelihood ( aor = 0.62 ; 95% ci = 0.400.96 ) of polypharmacy . however , individuals with respiratory conditions had higher likelihood of receiving polypharmacy as compared to individuals with musculoskeletal conditions only ( aor = 1.62 , 95% ci = 1.012.60 ) . our study estimated the rates of polypharmacy by multimorbidity categories among individuals with specific disease clusters such as cardiometabolic , musculoskeletal , and respiratory conditions . in our sample multimorbidity was highly prevalent with 39% of our sample having two or more disease clusters . in our sample , of all living adults over age 21 , the prevalence of polypharmacy was 26% . while this rate is within the reported range from 5% to 78% of polypharmacy among the elderly , we are not able to find other studies in individuals across all age groups supporting the prevalence rates from our study . we found that multimorbidity was associated with polypharmacy and rates of polypharmacy varied across multimorbidity categories . when examined by two disease clusters , those with cardiometabolic conditions had higher rates of polypharmacy as compared to those without cardiometabolic conditions . even when examined by single disease clusters , those with cardiometabolic conditions were more likely to have polypharmacy compared those with other single clusters . this finding is consistent with an italian study of hospitalized elderly patients . in the us , during office visits cardiovascular medication classes were a consistent part of polypharmacy between 1990 and 2000 . high rates of polypharmacy among individuals with cardiometabolic conditions are not surprising because of the use of many therapeutic categories such as beta - blockers , angiotensin converting enzyme inhibitors , calcium channel antagonists , antiarrhythmics , and lipid lowering drugs [ 2830 ] for synergistic management of these conditions . indeed , the mean number of prescribed medications was above 7 for those with diabetes and/or heart disease . on the other hand , for example , in copd , on average an individual used only 3.5 medications . our study findings suggest that providers need to routinely monitor individuals with cardiometabolic conditions for adverse drug events and drug - drug interactions . in addition , a new drug classification system based on pharmacokinetic profiles and interaction potential that is currently proposed to combat the harmful effects of multiple medications use [ 16 , 32 ] may go a long way in reducing adverse outcomes due to drug interactions in this group . although highest rates of polypharmacy were found among elderly over 65 years of age , younger individuals between 50 and 64 years of age were also significantly more likely to report polypharmacy as compared to individuals in the age group 2239 years . the prevalence of multimorbidity ( i.e. , the presence of all three disease clusters ) was similar between 65 and older ( 9.0% ) and adults in the 5064 age group ( 8.2% ) . these two findings taken together suggest that multimorbidity in 5064 age group was similar to those of elderly and the relationship between multimorbidity and polypharmacy is similar across the two groups . again our findings are consistent with the australian study by taylor et al . , which reported that multimorbidity was associated with polypharmacy in all the adult age groups . an interesting study finding was the association between greater number of visits and presence of polypharmacy , suggesting that ambulatory care visits increased the likelihood of polypharmacy . this finding is supported by existing literature . in a literature review on polypharmacy in the elderly , it was reported that [ 19 , 28 ] five or more visits to a primary care physician increased the risk of polypharmacy by fifteen times . approximately 75% of all the visits to primary care physicians end with a written prescription . it is also plausible that the risk of polypharmacy could be increased to treat the high symptom burden among those with multiple conditions . however , a prospective randomized study at a single urban general practice in ireland suggested that a ten - minute review of medications by general practitioners showed that 70% of the patients had stopped at least one medication after review . this finding suggests that a routine medication review by primary care physicians can be incorporated to reduce the risk of polypharmacy among those with multiple chronic conditions . individuals with multimorbidity often see multiple providers to manage their chronic conditions and also may have the increased likelihood of hospitalization . although managed care organizations in the united states attempt to provide coordinated care , the financial incentives of the fee - for - service system in the country do not encourage integrated and coordinated care between providers , specifically between primary and specialized care providers [ 35 , 36 ] and care sites ( hospital and outpatient settings ) . care from different providers without coordination often involves handoff of care among healthcare providers and changes to the medication regimens [ 37 , 38 ] , ultimately resulting in polypharmacy . reducing polypharmacy will require coordinated efforts by physicians , nurses , and pharmacists . our study has several advantages such as use of nationally representative sample of adults and a large sample size , which allowed examination of polypharmacy across all adult age groups . our definition of multimorbidity was based on synergism in treatment patterns and self - management approaches among different disease clusters . our study also included a comprehensive list of independent variables that may be associated with polypharmacy . some limitations of our study need to be taken into account while interpreting the findings . all measures in the study we also did not measure severity of chronic conditions which may necessitate multiple medications use . polypharmacy was broadly defined as number of therapeutic classes and in many of the chronic conditions combination therapies have become the norm rather than an exception . despite these limitations , our study added to the existing literature by defining multimorbidity in term of disease clusters rather than count of conditions and also highlighting the variation in polypharmacy across different types of disease clusters . future research needs to examine specific drugs in those with polypharmacy and identify potential drug combinations that may cause adverse drug events and adverse health outcomes . in addition , our study highlighted the need for routine surveillance to monitor polypharmacy and its adverse consequences among individuals with cardiometabolic conditions .

objective . the primary objective of the study was to estimate the rates of polypharmacy among individuals with multimorbidity defined as chronic condition clusters and examine their associations with polypharmacy . methods . cross - sectional analysis of 10,528 individuals of age above 21 , with at least one physical condition in cardiometabolic ( diabetes or heart disease or hypertension ) , musculoskeletal ( arthritis or osteoporosis ) , and respiratory ( chronic obstructive pulmonary disease ( copd ) or asthma ) clusters from the 2009 medical expenditure panel survey . chi - square tests and logistic regressions were performed to analyze the association between polypharmacy and multimorbidity . results . polypharmacy rates varied from a low of 7.2% among those with respiratory cluster to a high of 64.1% among those with all three disease clusters . among those with two or more disease clusters , the rates varied from 28.3% for musculoskeletal and respiratory clusters to 41.8% for those with cardiometabolic and respiratory clusters . individual with cardiometabolic conditions alone or in combination with other disease clusters were more likely to have polypharmacy . compared to those with musculoskeletal and respiratory conditions , those with cardiometabolic and respiratory conditions had 1.68 times higher likelihood of polypharmacy . conclusions . rates of polypharmacy differed by specific disease clusters . individuals with cardiometabolic condition were particularly at high risk of polypharmacy , suggesting greater surveillance for adverse drug interaction in this group .

<s>[INST]care of individuals with multimorbidity defined as the coexistence of two or more chronic conditions is an emerging area of research . existing studies have reported negative effects of multimorbidity on a variety of health outcomes such as disability , functional status , health - related quality of life , healthcare expenditures , and survival [ 112 ] . multimorbidity is also associated with healthcare utilization specifically an increased number of hospital admissions and prescription medications among individuals with multiple chronic conditions [ 13 , 14 ] . in a us study of the elderly , it was found that an overwhelming majority ( 73% ) with three or more chronic conditions were using 5 or more prescription drugs . in an australian study of multimorbidity across all age groups , it was reported that those with multimorbidity were 7 times to 22 times as likely to use four or more prescription medications as those without multimorbidity . multiple medications use often results in harmful drug - drug interactions . a study by nolan and o'malley suggested that individuals taking 10 or more medications had over a 90% probability of experiencing one or more clinically significant drug interactions . there have been many studies on polypharmacy among the elderly ; however , studies with specific focus on the association between polypharmacy generally defined as concurrent use of multiple medications and multimorbidity are very limited . one italian study of hospitalized elderly patients reported significant associations between specific clusters of diseases and polypharmacy . in this study , elderly patients with diabetes and coronary heart disease and cerebrovascular diseases had greater likelihood of polypharmacy compared to those without diabetes and cerebrovascular diseases . the adjusted odds ratio ( aor ) was 9.8 with 95% confidence interval of 1.372.2 , suggesting that coronary heart disease may increase the likelihood of polypharmacy . additionally , polypharmacy issues have only been examined in the elderly populations while an australian study documented that multimorbidity was prevalent ( 4.4% for 2039 years of age and 15.0% for 4059 years of age ) in the younger adults as well . therefore , it is necessary to examine the relationship between polypharmacy and multimorbidity across all age groups . the primary objective of the current study was to estimate rates of polypharmacy among individuals living in the community with specific clusters of chronic conditions , using a nationally representative sample of households in the united states . we also examined the independent relationship between specific clusters of chronic conditions and polypharmacy within a multivariate framework after controlling for demographic , socioeconomic , access to care , health status , lifestyle risk factors , and outpatient visits that may be associated with polypharmacy . we hypothesize that the rates of polypharmacy will depend on the specific chronic condition cluster and multiple conditions may not necessarily lead to greater rates of polypharmacy compared to those with single clusters . data were extracted from the agency for healthcare research and quality- ( ahrq- ) sponsored medical expenditure panel survey ( meps ) which is a nationally representative household survey of the united states noninstitutionalized civilian population . the meps household component ( hc ) collected information on demographic and socioeconomic characteristics of household members , medical conditions , and treatments for these conditions including prescription drug use over five interview rounds . a sample of medical providers were contacted to gather information on dates of visit , diagnosis and procedure codes , charges , and payments and were typically used as an imputation source to supplement / replace the data on household reported expenditures . ( 1 ) a disease condition may be reported in the priority condition enumeration section in which persons are asked if they have been diagnosed with specific conditions ; ( 2 ) a disease condition may be reported by the respondent when they had a particular medical event ( hospital stay , outpatient visit , emergency room visit , home health episode , prescribed medication purchase , or medical provider visit ) ; ( 3 ) a disease condition may be reported as the reason for one or more episodes of disability days ; ( 4 ) a disease condition may be reported by the household level respondent as a condition bothering the person during the reference period . on sensitivity of household reported medical conditions in the meps found that household reports tend to be accurate for many conditions . information on medical conditions was recorded verbatim and verbatim text was translated into international classification of diseases , 9th edition , clinical modification ( icd-9-cm ) codes by experienced and professional coders ( http://meps.ahrq.gov/mepsweb/data_stats/download_data/pufs/h128/h128doc.pdf ) . for privacy reasons meps provided the crosswalk between icd-9-cm and clinical condition classification codes . for purposes of our study , data were drawn from multiple files of meps ( 2009 survey ) such as household , medical conditions , prescribed medicines , and office - based medical provider visits and outpatients visits . our study sample comprised living individuals over 21 years of age as of the end of 2009 , reported having had at least one chronic physical condition in the following clusters : cardiometabolic ( consisting of diabetes or heart disease or hypertension ) , musculoskeletal ( consisting of arthritis or osteoporosis ) , and respiratory ( consisting of copd or asthma ) . our analytical sample consisted of 10,528 individuals representing approximately 102 million individuals of the united states civilian noninstitutionalized population . however , a systematic review of the literature stated use of six or more concomitant medications as one of the most cited definitions of polypharmacy . accordingly we classified polypharmacy variable into two categories : ( 1 ) 0 to 5 drugs and ( 2 ) polypharmacy ( 6 drugs ) . meps prescription medications file contains information on therapeutic classes of medications through linkage of multum lexicon database ( http://www.multum.com/lexicon.htm ) . the unique therapeutic class codes were used to identify the maximum number of classes of medications taken by individuals in any one of the five interview rounds . we defined polypharmacy as using at least six prescribed medications in any one of the five rounds of interviews during year 2009 . such clustering of disease conditions based on synergism in treatment patterns and self - management approaches have been used in our prior study . using a similar approach , we grouped three clinically meaningful disease clusters among diabetes , heart disease , hypertension , copd , asthma , arthritis , and osteoporosis . these conditions were chosen due to their high prevalence , cost , morbidity , and mortality ( http://meps.ahrq.gov/mepsweb/data_files/publications/st167/stat167.shtml ) . the specific clusters were ( 1 ) cardiometabolic ( diabetes or heart disease or hypertension ) , ( 2 ) musculoskeletal ( arthritis or osteoporosis ) , and ( 3 ) respiratory ( asthma or copd ) . these clusters were pooled together to form the following seven mutually exclusive categories of multimorbidity : ( 1 ) cardiometabolic conditions only ; ( 2 ) musculoskeletal conditions only , ( 3 ) respiratory conditions only , ( 4 ) cardiometabolic and musculoskeletal conditions , ( 5 ) cardiometabolic and respiratory conditions , ( 6 ) musculoskeletal and respiratory conditions , and ( 7 ) cardiometabolic , musculoskeletal , and respiratory conditions . demographic variables consisted of gender ( women , men ) , race / ethnicity ( white , african american , latino , other ) , age ( 2239 , 4049 , 5064 , 6569 , 7074 , and 75 and older ) , and marital status ( married , widowed , separated / divorced , never married ) . socioeconomic variables consisted of education ( less than high school , high school , above high school ) , area of residence ( metro , nonmetro ) , and poverty status ( poor , near poor , middle income , high income ) . access to care was assessed using health insurance coverage ( private , public , uninsured ) and usual source of care ( yes , no ) . health status was measured with variables such as perceived physical and mental health status ( excellent / very good , good , fair / poor ) . lifestyle risk factors comprised of body mass index ( bmi ) ( underweight / normal weight , overweight , obese ) , current smoking ( yes / no ) , and physical activity ( vigorous activity 3 days a week / other ) . we also included total number of visits to either office - based provider or outpatient hospital clinics as a measure of contact with the healthcare system . chi - square tests were used to assess significant differences between the multimorbidity categories and polypharmacy . unadjusted and multivariate logistic regressions were used to analyze the association between polypharmacy and multimorbidity categories and other independent variables . for example , we compared the aors of polypharmacy between cardiometabolic and musculoskeletal clusters and cardiometabolic and respiratory clusters . in all these regressions , all analyses used primary sampling unit , strata , and weights provided in the meps to control for clustering and unequal probability design and were conducted in survey procedures using sas 9.2 to handle study weights and clustering . table 1 characterizes the study sample by multimorbidity categories in our study sample above 21 years of age , alive , with at least one of the cardiometabolic , musculoskeletal , and respiratory conditions in year 2009 . thirty - four percent of our study sample had cardiometabolic conditions and 25% had both cardiometabolic and musculoskeletal disease clusters ; 4% had both cardiometabolic and respiratory disease clusters . however , only 7% of the study sample had all the three , cardiometabolic , musculoskeletal , and respiratory disease clusters . table 2 summarizes number and weighted percentages of individuals with polypharmacy by selected characteristics . women compared to men were significantly more likely to be on polypharmacy ( or = 1.41 , 95% ci = 1.271.56 ) . individuals in older age groups 4049 , 5064 , 6569 , 7074 , and 75 and older were also significantly more likely to be on polypharmacy compared to individuals in the age group 2239 . there was also a positive and significant association between total outpatient visit quartiles and polypharmacy . individuals who had visits in the upper quartile ( 4th quartile ) were 17 times as likely as those with visits in the 1st quartile ( or = 16.77 ; 95% ci = 12.522.4 ) . we present weighted percentage of individuals with polypharmacy among different multimorbidity categories in the left panel of table 3 . as seen from table 3 , the highest rates ( 64.1% ) of polypharmacy were found in sample individuals with all three ( cardiometabolic and respiratory and musculoskeletal ) disease clusters . the next highest rates ( 41.2% and 41.8% ) were observed among those with cardiometabolic and musculoskeletal disease clusters and among those with cardiometabolic and respiratory disease clusters . the lowest rates were found in those with only musculoskeletal ( 7.9% ) and only respiratory clusters ( 7.2% ) . unadjusted logistic regressions and multivariable logistic regressions were used to examine the association between chronic condition clusters and polypharmacy . odds ratios ( or ) and aors with their 95% confidence intervals for polypharmacy are presented in table 3 . compared to individuals with all the three disease clusters ( cardiometabolic , musculoskeletal , and respiratory ) , those with either one or two disease clusters were significantly less likely to receive polypharmacy . the unadjusted odds ratios ranged from 0.04 among those with respiratory conditions only to 0.40 among those with cardiometabolic and respiratory disease clusters . we also examined the differences in the likelihood of polypharmacy between different single condition clusters . compared to individuals with cardiometabolic disease cluster only , those with musculoskeletal cluster only and respiratory cluster only had lower odds ratios of reporting polypharmacy ( or = 0.38 and or = 0.35 , resp . ) . on the other hand , there were no significant differences in ors between individuals with musculoskeletal conditions only and respiratory conditions only ( or = 0.91 , 95% ci = ( 0.59 , 1.39 ) ) . when examining the differences in the likelihood of polypharmacy by two disease clusters , we found that individuals with both cardiometabolic and musculoskeletal clusters were more likely to report polypharmacy compared to those with both musculoskeletal and respiratory clusters ( or = 1.77 ) . similarly , individuals with both cardiometabolic and respiratory clusters were more likely to report polypharmacy ( or = 1.82 ) as compared to those with both musculoskeletal and respiratory clusters . individuals with cardiometabolic and respiratory clusters did not significantly differ in the or of polypharmacy from those with cardiometabolic and musculoskeletal clusters ( or = 1.03 , 95% ci = 0.80 , 1.32 ) . multivariable logistic regressions to assess the association between multimorbidity and polypharmacy that controlled for gender , age , race / ethnicity , marital status , education , poverty status , health insurance , usual source of care , perceived physical and mental health , smoking status , bmi , and exercise revealed similar findings . for example , compared to individuals with cardiometabolic disease cluster only , those with musculoskeletal cluster only ( aor = 0.38 ; 95% ci = 0.300.49 ) and respiratory cluster only had lower likelihood ( aor = 0.62 ; 95% ci = 0.400.96 ) of polypharmacy . however , individuals with respiratory conditions had higher likelihood of receiving polypharmacy as compared to individuals with musculoskeletal conditions only ( aor = 1.62 , 95% ci = 1.012.60 ) . our study estimated the rates of polypharmacy by multimorbidity categories among individuals with specific disease clusters such as cardiometabolic , musculoskeletal , and respiratory conditions . in our sample multimorbidity was highly prevalent with 39% of our sample having two or more disease clusters . in our sample , of all living adults over age 21 , the prevalence of polypharmacy was 26% . while this rate is within the reported range from 5% to 78% of polypharmacy among the elderly , we are not able to find other studies in individuals across all age groups supporting the prevalence rates from our study . we found that multimorbidity was associated with polypharmacy and rates of polypharmacy varied across multimorbidity categories . when examined by two disease clusters , those with cardiometabolic conditions had higher rates of polypharmacy as compared to those without cardiometabolic conditions . even when examined by single disease clusters , those with cardiometabolic conditions were more likely to have polypharmacy compared those with other single clusters . this finding is consistent with an italian study of hospitalized elderly patients . in the us , during office visits cardiovascular medication classes were a consistent part of polypharmacy between 1990 and 2000 . high rates of polypharmacy among individuals with cardiometabolic conditions are not surprising because of the use of many therapeutic categories such as beta - blockers , angiotensin converting enzyme inhibitors , calcium channel antagonists , antiarrhythmics , and lipid lowering drugs [ 2830 ] for synergistic management of these conditions . indeed , the mean number of prescribed medications was above 7 for those with diabetes and/or heart disease . on the other hand , for example , in copd , on average an individual used only 3.5 medications . our study findings suggest that providers need to routinely monitor individuals with cardiometabolic conditions for adverse drug events and drug - drug interactions . in addition , a new drug classification system based on pharmacokinetic profiles and interaction potential that is currently proposed to combat the harmful effects of multiple medications use [ 16 , 32 ] may go a long way in reducing adverse outcomes due to drug interactions in this group . although highest rates of polypharmacy were found among elderly over 65 years of age , younger individuals between 50 and 64 years of age were also significantly more likely to report polypharmacy as compared to individuals in the age group 2239 years . the prevalence of multimorbidity ( i.e. , the presence of all three disease clusters ) was similar between 65 and older ( 9.0% ) and adults in the 5064 age group ( 8.2% ) . these two findings taken together suggest that multimorbidity in 5064 age group was similar to those of elderly and the relationship between multimorbidity and polypharmacy is similar across the two groups . again our findings are consistent with the australian study by taylor et al . , which reported that multimorbidity was associated with polypharmacy in all the adult age groups . an interesting study finding was the association between greater number of visits and presence of polypharmacy , suggesting that ambulatory care visits increased the likelihood of polypharmacy . this finding is supported by existing literature . in a literature review on polypharmacy in the elderly , it was reported that [ 19 , 28 ] five or more visits to a primary care physician increased the risk of polypharmacy by fifteen times . approximately 75% of all the visits to primary care physicians end with a written prescription . it is also plausible that the risk of polypharmacy could be increased to treat the high symptom burden among those with multiple conditions . however , a prospective randomized study at a single urban general practice in ireland suggested that a ten - minute review of medications by general practitioners showed that 70% of the patients had stopped at least one medication after review . this finding suggests that a routine medication review by primary care physicians can be incorporated to reduce the risk of polypharmacy among those with multiple chronic conditions . individuals with multimorbidity often see multiple providers to manage their chronic conditions and also may have the increased likelihood of hospitalization . although managed care organizations in the united states attempt to provide coordinated care , the financial incentives of the fee - for - service system in the country do not encourage integrated and coordinated care between providers , specifically between primary and specialized care providers [ 35 , 36 ] and care sites ( hospital and outpatient settings ) . care from different providers without coordination often involves handoff of care among healthcare providers and changes to the medication regimens [ 37 , 38 ] , ultimately resulting in polypharmacy . reducing polypharmacy will require coordinated efforts by physicians , nurses , and pharmacists . our study has several advantages such as use of nationally representative sample of adults and a large sample size , which allowed examination of polypharmacy across all adult age groups . our definition of multimorbidity was based on synergism in treatment patterns and self - management approaches among different disease clusters . our study also included a comprehensive list of independent variables that may be associated with polypharmacy . some limitations of our study need to be taken into account while interpreting the findings . all measures in the study we also did not measure severity of chronic conditions which may necessitate multiple medications use . polypharmacy was broadly defined as number of therapeutic classes and in many of the chronic conditions combination therapies have become the norm rather than an exception . despite these limitations , our study added to the existing literature by defining multimorbidity in term of disease clusters rather than count of conditions and also highlighting the variation in polypharmacy across different types of disease clusters . future research needs to examine specific drugs in those with polypharmacy and identify potential drug combinations that may cause adverse drug events and adverse health outcomes . in addition , our study highlighted the need for routine surveillance to monitor polypharmacy and its adverse consequences among individuals with cardiometabolic conditions .[/INST]objective . the primary objective of the study was to estimate the rates of polypharmacy among individuals with multimorbidity defined as chronic condition clusters and examine their associations with polypharmacy . methods . cross - sectional analysis of 10,528 individuals of age above 21 , with at least one physical condition in cardiometabolic ( diabetes or heart disease or hypertension ) , musculoskeletal ( arthritis or osteoporosis ) , and respiratory ( chronic obstructive pulmonary disease ( copd ) or asthma ) clusters from the 2009 medical expenditure panel survey . chi - square tests and logistic regressions were performed to analyze the association between polypharmacy and multimorbidity . results . polypharmacy rates varied from a low of 7.2% among those with respiratory cluster to a high of 64.1% among those with all three disease clusters . among those with two or more disease clusters , the rates varied from 28.3% for musculoskeletal and respiratory clusters to 41.8% for those with cardiometabolic and respiratory clusters . individual with cardiometabolic conditions alone or in combination with other disease clusters were more likely to have polypharmacy . compared to those with musculoskeletal and respiratory conditions , those with cardiometabolic and respiratory conditions had 1.68 times higher likelihood of polypharmacy . conclusions . rates of polypharmacy differed by specific disease clusters . individuals with cardiometabolic condition were particularly at high risk of polypharmacy , suggesting greater surveillance for adverse drug interaction in this group .</s>

rhabdomyolysis is a clinical syndrome characterized by muscle necrosis and the release of intracellular muscle constituents into the circulation . it can be caused by burns , shock , acidosis , infections , crush trauma , immobility , malignancy , toxins , drugs , and muscle diseases1 ) . among the various types of rhabdomyolysis , non - traumatic exertional rhabdomyolysis ( exrml ) occurs in individuals with normal muscles and appears when the energy supplied to the muscle is insufficient23 ) . exrml related to military training , marathon running , weight training , and other forms of strenuous exercise have been reported4 ) . spinning is a group indoor cycling exercise , which has become popular recently over the past few years . this stationary cycling program is composed of five core movements and riders may synchronize their pedaling to the rhythm of the music while they are exercising5 ) . we observed that recently there has been an increasing number of patients who were diagnosed with exrml at cha bundang medical center after attending a spinning class . here , we introduced the clinical cases of spinning induced rhabdomyolysis and review the related literature . we found 11 cases of exrml patients who were admitted to cha bundang medical center between july 1 , 2014 and march 31 , 2015 . their mean body mass index ( bmi ) was 23.92.6 kg / m ( ranged from 19.6 to 28.0 ) . two to three days prior to the presentation , the patients had attended a spinning class for the first time . nine of the patients had brown - colored urine within two days and another two patients noticed that their urine had become darker three days after their first spinning class . none of the patients had any significant past medical history and were not on any medication . their thighs were moderately firm and warm to the touch , with reduced range of movement and strength . complete blood - count , urea , creatinine , and electrolyte values were within normal ranges at the initial blood analysis . however , their serum creatinine phosphokinase ( cpk ) level was over 11,000 u / l ( normal range : 38 - 160 ) . additionally , other serum levels of muscle enzymes ( creatine kinase - mb type , lactate dehydrogenase , alanine aminotransferase , aspartate aminotransferase , and myoglobin ) were significantly elevated ( table 1 ) . serum bun and creatinine levels stayed within the normal range and no acute kidney injury ( aki ) had developed during treatment . dipstick testing of the urine was positive ( 3 + ) for blood ; however , subsequent microscopy revealed less than four red blood cells under high power field ( hpf ) microscopy . a bone scan study showed diffuse type of soft tissue uptakes in the damaged muscles including rectus femoris , sartorius , vastus medialis , vastus lateralis , and pectineus ( fig . a diagnosis of rhabdomyolysis was made and the patients were treated with a combination of bed rest and aggressive intravenous fluid ( normal saline ) to maintain a urine output of 200 to 300ml / hour . when the urine ph was less than 6.0 , sodium bicarbonate ( mixed with 5% dextrose water ) was used for urine akalinization . although eight of the patients had mild hypocalcemia , calcium supplementation was unnecessary because no hypocalcemic symptoms were observed ( table 1 ) . in a span of 6 - 12 days , one patient ( number 1 ) was hospitalized for an additional 4 days after her cpk level was markedly reduced ( 4,820 u / l ) on the 8 day along with her complaints of thigh myalgia . exrml has been defined by a combination of findings , including exercise - associated muscle pain , swelling , dark urine , and increased cpk level to at least five times the upper limit of normal , and myoglobinuria6 ) . it should be noted that our patients had cpk levels of nearly 70 times the upper limit of normal ( table 1 ) . also , a urine dipstick that is positive for blood but shows few red blood cells is suggestive of myoglobinuria7 ) . in the pathogenesis of exercise - induced rhabdomyolysis , calcium(ca ) has been suggested as an important key factor3 ) . during exercise , a decreased amount of adenosine triphosphate ( atp ) could cause dysfunction of na - k atpase and an increased level of na in the cells , resulting in the reverse activation of na - ca exchanger mode3 ) . consequently , the increased intracellular calcium leads to the activation of proteases , skeletal muscle cell contraction , mitochondrial dysfunction , reactive oxygen species production , and eventual skeletal muscle cell death23 ) . treatment of rhabdomyolysis involves stopping the continued breakdown of the muscle fibers and preventing the development of aki . the rapid and aggressive infusion of intravenous crystalloid is used to obtain a urinary output of 200 - 300ml / hour . myoglobin is toxic in acidic urine , and most experts advocate the use of intravenous sodium bicarbonate to maintain a urinary ph of 6.5 or greater67 ) . loop diuretics may be given to patients who develop volume overload complications such as pulmonary edema . the initiation of renal replacement therapy in clinical practice depends on the status of renal impairment , with complications such as life - threatening hyperkalemia , anuria , metabolic acidosis , or hyperhydration without response to diuretic therapy89 ) . it is reported that both continuous venovenous hemofiltration with a high permeability membrane and high cutoff membrane hemodiafiltration are effective in removing serum myoglobin ( 17kda)1011 ) . although successful treatment with plasmapheresis to remove serum myoglobin in statin - induced rhabdomyolysis have been reported , its use seems still controversial9 ) . most of the related articles mentioned that the majority of spinning - induced rhabdomyolysis patients were discharged without any complication when they were treated early and aggressively with intravenous fluids7 ) . however , in rare cases , some patients demonstrated severe complications , such as compartment syndrome and aki4 ) . aki in rhabdomyolysis may occur due to renal vasoconstriction , formation of intratubular casts , and direct myoglobin toxicity caused by accumulation of myoglobin in the renal tubules19 ) . compartment syndrome may occur in the leg or forearm due to the edema caused by muscle injury and tissue damage4 ) . cardiac dysrhythmias via electrolyte abnormalities and disseminated intravascular coagulopathy are other possible complications of exrml4 ) . known risk factors of exrml are the exercise experience , intensities or types of exercises37 ) . other possible causes were hyperthermal environments , electrolyte imbalance , malnutrition , creatine supplements and alcohol drinking3 ) . influenza virus infection and genetic deficiency of metabolic factors can be risk factors as well3 ) . it has been reported that men are vulnerable to exrml because estrogen plays a protective role1213 ) . interestingly , all 11 spinning - induced rhabdomyolysis cases in this article occurred in females . it is unclear whether they were malnourished by their diet plan or had little exercise experience and thus were at higher risk of spinning induced rhabdomyolysis . third , exercise should be modified or abstained in the presence of evitable risk factors such as influenza . all 11 patients were treated early and properly without any complication , except a mild non - symptomatic hypocalcemia . however , considering the possibility of severe complications of exrml as aforementioned , and the medical expenses of hospital stay , information and guidelines for preventing spinning - induced rhabdomyolysis have to be provided prior to starting the exercise .

non - traumatic exertional rhabdomyolysis ( exrml ) occurs in individuals with normal muscles when the energy supplied to the muscle is insufficient . here , we report 11 cases of spinning - induced rhabdomyolysis and review related literature . spinning is a kind of indoor bicycle sport . the 11 patients who were diagnosed with exrml and admitted to cha bundang medical center were female and their ages ranged from 15 to 46 years . two to three days prior to the presentation , the patients had attended a spinning class for the first time . all the patients had been otherwise healthy without any known medical illnesses . they were successfully treated without any complications , except mild non - symptomatic hypocalcemia . however , in the literature , severe complications such as compartment syndrome or acute kidney injury had been reported in relation to exrml including spinning - induced rhabdomyolysis . this spinning exercise needs prior guidelines and specific warnings to prevent exertional rhabdomyolysis .

<s>[INST]rhabdomyolysis is a clinical syndrome characterized by muscle necrosis and the release of intracellular muscle constituents into the circulation . it can be caused by burns , shock , acidosis , infections , crush trauma , immobility , malignancy , toxins , drugs , and muscle diseases1 ) . among the various types of rhabdomyolysis , non - traumatic exertional rhabdomyolysis ( exrml ) occurs in individuals with normal muscles and appears when the energy supplied to the muscle is insufficient23 ) . exrml related to military training , marathon running , weight training , and other forms of strenuous exercise have been reported4 ) . spinning is a group indoor cycling exercise , which has become popular recently over the past few years . this stationary cycling program is composed of five core movements and riders may synchronize their pedaling to the rhythm of the music while they are exercising5 ) . we observed that recently there has been an increasing number of patients who were diagnosed with exrml at cha bundang medical center after attending a spinning class . here , we introduced the clinical cases of spinning induced rhabdomyolysis and review the related literature . we found 11 cases of exrml patients who were admitted to cha bundang medical center between july 1 , 2014 and march 31 , 2015 . their mean body mass index ( bmi ) was 23.92.6 kg / m ( ranged from 19.6 to 28.0 ) . two to three days prior to the presentation , the patients had attended a spinning class for the first time . nine of the patients had brown - colored urine within two days and another two patients noticed that their urine had become darker three days after their first spinning class . none of the patients had any significant past medical history and were not on any medication . their thighs were moderately firm and warm to the touch , with reduced range of movement and strength . complete blood - count , urea , creatinine , and electrolyte values were within normal ranges at the initial blood analysis . however , their serum creatinine phosphokinase ( cpk ) level was over 11,000 u / l ( normal range : 38 - 160 ) . additionally , other serum levels of muscle enzymes ( creatine kinase - mb type , lactate dehydrogenase , alanine aminotransferase , aspartate aminotransferase , and myoglobin ) were significantly elevated ( table 1 ) . serum bun and creatinine levels stayed within the normal range and no acute kidney injury ( aki ) had developed during treatment . dipstick testing of the urine was positive ( 3 + ) for blood ; however , subsequent microscopy revealed less than four red blood cells under high power field ( hpf ) microscopy . a bone scan study showed diffuse type of soft tissue uptakes in the damaged muscles including rectus femoris , sartorius , vastus medialis , vastus lateralis , and pectineus ( fig . a diagnosis of rhabdomyolysis was made and the patients were treated with a combination of bed rest and aggressive intravenous fluid ( normal saline ) to maintain a urine output of 200 to 300ml / hour . when the urine ph was less than 6.0 , sodium bicarbonate ( mixed with 5% dextrose water ) was used for urine akalinization . although eight of the patients had mild hypocalcemia , calcium supplementation was unnecessary because no hypocalcemic symptoms were observed ( table 1 ) . in a span of 6 - 12 days , one patient ( number 1 ) was hospitalized for an additional 4 days after her cpk level was markedly reduced ( 4,820 u / l ) on the 8 day along with her complaints of thigh myalgia . exrml has been defined by a combination of findings , including exercise - associated muscle pain , swelling , dark urine , and increased cpk level to at least five times the upper limit of normal , and myoglobinuria6 ) . it should be noted that our patients had cpk levels of nearly 70 times the upper limit of normal ( table 1 ) . also , a urine dipstick that is positive for blood but shows few red blood cells is suggestive of myoglobinuria7 ) . in the pathogenesis of exercise - induced rhabdomyolysis , calcium(ca ) has been suggested as an important key factor3 ) . during exercise , a decreased amount of adenosine triphosphate ( atp ) could cause dysfunction of na - k atpase and an increased level of na in the cells , resulting in the reverse activation of na - ca exchanger mode3 ) . consequently , the increased intracellular calcium leads to the activation of proteases , skeletal muscle cell contraction , mitochondrial dysfunction , reactive oxygen species production , and eventual skeletal muscle cell death23 ) . treatment of rhabdomyolysis involves stopping the continued breakdown of the muscle fibers and preventing the development of aki . the rapid and aggressive infusion of intravenous crystalloid is used to obtain a urinary output of 200 - 300ml / hour . myoglobin is toxic in acidic urine , and most experts advocate the use of intravenous sodium bicarbonate to maintain a urinary ph of 6.5 or greater67 ) . loop diuretics may be given to patients who develop volume overload complications such as pulmonary edema . the initiation of renal replacement therapy in clinical practice depends on the status of renal impairment , with complications such as life - threatening hyperkalemia , anuria , metabolic acidosis , or hyperhydration without response to diuretic therapy89 ) . it is reported that both continuous venovenous hemofiltration with a high permeability membrane and high cutoff membrane hemodiafiltration are effective in removing serum myoglobin ( 17kda)1011 ) . although successful treatment with plasmapheresis to remove serum myoglobin in statin - induced rhabdomyolysis have been reported , its use seems still controversial9 ) . most of the related articles mentioned that the majority of spinning - induced rhabdomyolysis patients were discharged without any complication when they were treated early and aggressively with intravenous fluids7 ) . however , in rare cases , some patients demonstrated severe complications , such as compartment syndrome and aki4 ) . aki in rhabdomyolysis may occur due to renal vasoconstriction , formation of intratubular casts , and direct myoglobin toxicity caused by accumulation of myoglobin in the renal tubules19 ) . compartment syndrome may occur in the leg or forearm due to the edema caused by muscle injury and tissue damage4 ) . cardiac dysrhythmias via electrolyte abnormalities and disseminated intravascular coagulopathy are other possible complications of exrml4 ) . known risk factors of exrml are the exercise experience , intensities or types of exercises37 ) . other possible causes were hyperthermal environments , electrolyte imbalance , malnutrition , creatine supplements and alcohol drinking3 ) . influenza virus infection and genetic deficiency of metabolic factors can be risk factors as well3 ) . it has been reported that men are vulnerable to exrml because estrogen plays a protective role1213 ) . interestingly , all 11 spinning - induced rhabdomyolysis cases in this article occurred in females . it is unclear whether they were malnourished by their diet plan or had little exercise experience and thus were at higher risk of spinning induced rhabdomyolysis . third , exercise should be modified or abstained in the presence of evitable risk factors such as influenza . all 11 patients were treated early and properly without any complication , except a mild non - symptomatic hypocalcemia . however , considering the possibility of severe complications of exrml as aforementioned , and the medical expenses of hospital stay , information and guidelines for preventing spinning - induced rhabdomyolysis have to be provided prior to starting the exercise .[/INST]non - traumatic exertional rhabdomyolysis ( exrml ) occurs in individuals with normal muscles when the energy supplied to the muscle is insufficient . here , we report 11 cases of spinning - induced rhabdomyolysis and review related literature . spinning is a kind of indoor bicycle sport . the 11 patients who were diagnosed with exrml and admitted to cha bundang medical center were female and their ages ranged from 15 to 46 years . two to three days prior to the presentation , the patients had attended a spinning class for the first time . all the patients had been otherwise healthy without any known medical illnesses . they were successfully treated without any complications , except mild non - symptomatic hypocalcemia . however , in the literature , severe complications such as compartment syndrome or acute kidney injury had been reported in relation to exrml including spinning - induced rhabdomyolysis . this spinning exercise needs prior guidelines and specific warnings to prevent exertional rhabdomyolysis .</s>

the problem of dynamic resource allocation in constrained queueing networks is fundamental to modern communication networks . this has long been the subject of significant research , where the @xcite of tassiulas and ephremides proposed the mw ( maximum weight ) scheduling algorithm of throughput - optimality . it has been also a powerful paradigm in cross - layer control and resource allocation @xcite . however , the algorithm can not be implemented in practice due to its high algorithmic complexity . been made since then for developing algorithms of lower complexity while maintaining the same performance guarantee . examples of such algorithms include greedy algorithms @xcite and random access algorithms @xcite . recently , there have been exciting progresses for the topic that even fully distributed random access algorithms based on csma ( carrier sense multiple access ) can achieve the desired high performance , i.e. , throughput - optimality , in wireless interference network models , e.g. , see @xcite . the main intuition underlying these results is that nodes in a network can adjust their csma parameters dynamically using local information such as queue - length so that they can simulate the mw algorithm asymptotically for throughput - optimality . however , it is known that the queue - based csma algorithms suffer from very poor delay performance . there have been also significant efforts formally addressing the limitation in the delay performance of the queue - based csma algorithms @xcite as well as designing better alternatives in delay under certain scenarios @xcite . in addition , another issue is that the throughput - optimality proof in @xcite is very sensitive to the underlying wireless network model . namely , it is not an easy task to design similar csma - like throughput - optimal algorithms in other network models since one has to reproduce painful , long and routine proof - arguments for throughput - optimality in each different model . the main goal of this paper is to resolve these issues of the recent queue - based csma algorithms by developing a general framework that can produce a variety of throughput - optimal and low - complexity scheduling algorithms , not to the underlying network models . design and analysis of resource allocation algorithms in constrained queueing networks have been of great interest for last four decades across various research communities , where the contention resolution protocols in multiple - access broadcast channels have been studied since the mid-1970s @xcite . the broadcast channels induce a special constraint in resources usages among queues ( i.e. , every queue contend with all other queues ) , and simple distributed contention resolution protocols gained much attention in the ages . it is the year 1992 that the seminal work by tassiulas and ephremides proposed a throughput - optimal algorithm , referred to as mw , for general resource constraints . its main appeal is that it does require only information on the current queue lengths ( and instantaneous service rates ) and does not rely on the knowledge of underlying system parameters . however , as we mentioned earlier , the mw algorithm suffers from the high implementation complexity , and a huge array of subsequent research has been made to develop algorithms with high performance guarantees and low - complexity . maximal scheduling or longest - queue - first algorithm are low - complexity alternatives to mw , but they achieve only some fraction of the maximal throughput region . parallel iterative matching @xcite and islip @xcite were shown to be 50% throughput - optimal @xcite . on the other hand , kumar et al . @xcite and dimakis and walrand @xcite identified sufficient conditions on the network topology for throughput - optimality . those conditions were further analyzed to obtain fractional throughput results about a class of wireless networks by joo et al . @xcite and leconte et al . these algorithms are generally not throughput - optimal and require multiple rounds of message exchanges between nodes . simpler or distributed implementations of mw has been also extensively studied in the literature . tassiulas @xcite provides linear - complexity versions of mw , called ` pick - and - compare ' , but it is known that they suffer from the bad delay performance . the works on this line also include a variant of mw by giaccone , prabhakar and shah @xcite and a gossip - based algorithm by modiano , shah and zussman @xcite . however , these algorithms are specific to certain network models and still require high information ( or message ) exchanges for each new scheduling decision . a few years ago , it was proven that even fully distributed queue - based random access algorithms based on csma with very little message passing can simulate the mw algorithm asymptotically and hence achieve throughput - optimality in wireless interference network models @xcite . however , the csma algorithms are known to suffer from the following two issues : the bad delay performance and the limited applicability to other network models . for the delay issue , bouman et al . @xcite formally established explicit lower bounds on the delay of queue - based random access algorithms . on the other hand , significant efforts have also been made to design csma algorithms with better delay performance , e.g. , see @xcite . the limited applicability issue is rather technical : it is a technically tedious task to design similar csma - like throughput - optimal algorithms in other network models since one has to reproduce painful , long and routine proof - arguments for analyzing ` time - varying ' markov chains in each different model , e.g. , see the buffered circuit switched network model @xcite . the main motivation of this paper is for resolving these issues and goes beyond csma - like algorithms for achieving high performance guarantees and low implementation complexity , not sensitive to the underlying network models . we develop a generic framework for designing throughput - optimal and low - complexity scheduling algorithms , where queue - based csma algorithms belong to it as special cases . under the framework , an algorithm updates current schedules via an interaction with a given oracle system that can generate a solution of a certain discrete optimization problem in a finite number of interactive queries . specifically , an algorithm maintains three parameters , ` schedule ' , ` weight ' and ` advice ' , at each time instance . the schedule and advice are kept being updated under interactions with the oracle system and the weight is decided by some function of current queue - size , which we call ` queue - length - function ' . therefore , the scheduling algorithm design is determined by ` which oracle is used ' and ` which queue - length - function is chosen ' . the oracle system can be designed through iterative optimization methods including the naive exhaustive search algorithm , the markov chain monte carlo ( e.g. , the glauber dynamics @xcite ) , the message - passing inference algorithms ( e.g. , the belief propagation @xcite ) and the linear / integer programming ( e.g. , the cutting - plane method @xcite ) . in this paper , we describe three oracle examples , the exhaustive search ( es ) , the markov chain monte carlo ( mcmc ) and the belief propagation ( bp ) in section [ sec : exam ] . in particular , the ` pick - and - compare ' algorithms @xcite and queue - based csma algorithms can be understood as such algorithms ( with minor modifications ) using es and mcmc oracles , respectively ( see section [ sec : exam ] ) . the scheduling complexity is decided by the number of operations required for an oracle processing a single query , which is typically very small , e.g. , es , mcmc and bp . we prove that given any oracle system , there exists a queue - length - function such that an algorithm using the oracle is throughput - optimal under general constrained queueing network models , which includes wireless network models , input - queued switch models , the buffered circuit switched network model , etc . in particular , we first show there exists a queue - length - function such that its value does not change too often ( i.e. , remains fixed for a long time ) and hence the mw optimization problem can be solved through ( enough ) interactions to the oracle , i.e. , the algorithm simulates mw and is throughput - optimal . this proof strategy is similar to those of @xcite in spirit . the main difference is that we force the queue - length - function value being ` rarely - varying ' in integers , while the authors in @xcite do it being ` slowly - varying ' in real numbers . due to such a difference , now we do not need to analyze ` time - varying ' algorithms ( e.g. , markov chains ) , i.e. , analysis when algorithm parameters are fixed is enough . this makes the proof much simpler and not sensitive to the given oracle and underlying network model . our strong theoretical statement provides a quite powerful paradigm for developing a variety of low - complexity scheduling algorithms of high performance . for example , our experimental results show that the delay performance of such an algorithm using the bp oracle is close to that of the mw algorithm , and it significantly outperforms csma algorithms ( see section [ sec : exp ] ) . moreover , one can also easily design other types of throughput - optimal algorithms , via designing various oracle systems , under a quite broad class of constrained queueing network models , without suffering from repeating tedious proofs sensitive to the underlying assumptions and setups . at a high level , we use the interactive oracle concept to provide a ` black - box ' tool for designing scheduling algorithms of high performance and low - complexity . this establishes a rigorous connection between iterative optimization methods and low - complexity scheduling algorithms , which we believe provides various future directions and new insights in both areas . in section [ sec : pre ] , we describe the constrained queueing network model of our interest and the performance metric ( i.e. , throughput - optimality ) for scheduling algorithms . section [ sec : main ] provides the main result of this paper , i.e. , our generic framework for designing a throughput - optimal and low - complexity scheduling algorithm which decides its current schedule via an interaction with an oracle system . in section [ sec : exam ] , we provide several examples of scheduling algorithms under the framework . section [ sec : pfmainthm ] provides the formal proof of the main result , and our experimental results are presented in section [ sec : exp ] . we consider a stochastic network of @xmath0 queues represented by @xmath1 with @xmath2 , and time is discrete indexed by @xmath3 . external packets ( or jobs ) arrive at each queue as per an exogenous stochastic process , where we let @xmath4 denote the number of packets arriving at queue @xmath5 during the time interval @xmath6 . we assume that @xmath7 are independent bernoulli random variables with @xmath8=\lambda_i\ ] ] for some @xmath9 $ ] , called the _ arrival rate _ for queue @xmath5 . packets in queues are served at unit rate subject to scheduling constraints . formally , a schedule is denoted by @xmath10\in \{0,1\}^n$ ] , where @xmath11 means queue @xmath5 is transmitting ( or active ) and @xmath12 otherwise . we let @xmath13 be a set of all available schedules and let @xmath14 be the schedule during @xmath6 for @xmath15 . to describe the dynamics in the network , we let @xmath16 denote the number of packets in @xmath5-th queue at time @xmath17 ( i.e. , _ length of queue _ ) and let @xmath18 $ ] be the vector of queue lengths . then the queueing dynamics for queue @xmath5 can be described as @xmath19 where @xmath15 and @xmath20 for given @xmath1 and @xmath21 , our goal is to develop low - complexity and high - performance scheduling algorithms which determine @xmath22 for each time instance @xmath15 . a scheduling algorithm is required to choose @xmath14 at each time instance @xmath15 . we say an algorithm is throughput - optimal if it keeps queues finite for as large a set of arrival rates @xmath23 $ ] as possible . to describe it formally , we define the capacity region as follows : @xmath24 where it is the convex hull of the feasible scheduling set @xmath21 . since @xmath14 , the effective ` service ' rate induced by any algorithm over time is essentially in @xmath25 . therefore , if arrival rates @xmath26 can be served by any algorithm , then there exists @xmath27 such that @xmath28 component - wise . we say @xmath26 is _ ( strictly ) admissible _ if @xmath29 is ( strictly ) less than @xmath30 for some @xmath31 . let @xmath32 and @xmath33 be the set of all admissible and strictly admissible rates , respectively : @xmath34 a throughput - optimal algorithm keeps queues finite for any @xmath35 , where there can be many different ways to argue the finiteness of queues . in this paper , we use the following popular definition of throughput - optimality . [ def : throughput - optimality ] a scheduling algorithm is called _ throughput - optimal _ if for any @xmath35 the ( appropriately defined ) network markov chain is positive recurrent . if the state of the network markov chain includes queue - sizes , then its positive recurrence implies that the queues remain finite with probability 1 , which motivates the above definition . we recall the definition of the positive recurrence of a markov chain @xmath36 on a countable state space @xmath37 . a state @xmath38 is said to be _ recurrent _ if @xmath39=1 $ ] , where @xmath40 . if @xmath41<\infty$ ] , a recurrent state @xmath42 is called _ positive recurrent_. if a markov chain is irreducible and it has a positive recurrent state , all states are positive recurrent . in this case , we call such a markov chain positive recurrent . one way to show the positive recurrence of a markov chain is using the following lyapunov - foster criteria . a function @xmath43 is called a ` lyapunov function ' if @xmath44 . the following theorem provides a criteria about the positive recurrence using a lyapunov function , e.g. , see @xcite . [ thm : lyapunov ] consider a lyapunov function @xmath45 such that @xmath46 is finite for any @xmath47 . suppose there exist functions @xmath48 such that @xmath49\leq -\kappa({\mathsf{x}}),~\forall x\in\omega,\ ] ] and they satisfy the following conditions : 1 . 2 . @xmath51 . @xmath52 for all @xmath47 . 4 . @xmath53 . then , @xmath54 is positive recurrent . this section presents our main result , throughput - optimal and low - complexity scheduling algorithms . we first describe the generic concept of our algorithms utilizing certain oracle systems . the oracle systems are motivated by ( randomized or deterministic ) iterative algorithms which find an approximate optimal solution to the following optimization problem : @xmath55 typically , in an iterative algorithm , the output at each iteration depends only on information from the previous iteration ( and weight @xmath56 ) . we call such information ` advice ' . one can understand an iteration of the algorithm as an interaction to an oracle system , where a query consisting of advice and weight is sent to an interactive oracle system , and the oracle returns a schedule together with an updated advice for the next iteration . this naturally suggests the following scheduling algorithm : at each time instance @xmath17 , ( a ) it sends a query consisting of the advice @xmath57 produced in the previous step and weight @xmath58 decided by current queue lengths to the oracle system , and then ( b ) the oracle returns a schedule to use at the next time instance @xmath59 . hence , the complexity of the scheduling algorithm is that of the oracle system processing a query ( equivalently , that of one iteration of an iterative algorithm ) , which is typically very small as we provide examples in section [ sec : exam ] . in the following sections , we provide the formal descriptions of oracle systems of interest and scheduling algorithms utilizing them . and weight @xmath58 is sent to the oracle . the oracle returns the schedule @xmath60 to use at the next time instance and updated advice @xmath61 . , width=288 ] we consider a network model introduced in section [ subsec : network_model ] with set of queues @xmath1 with @xmath2 and available schedules @xmath62 . then the oracle system we are interested in has an advice space @xmath63 with the following input and output : * it takes inputs @xmath64 and @xmath65 $ ] , * it outputs ( or returns ) @xmath66 and @xmath67 , where @xmath56 , @xmath68 , and @xmath69 are called ` weights ' on queues , ` advice ' , and ` updated advice ' , respectively . formally , let the outputs @xmath70 and @xmath71 , where the oracle can generate random outputs in general . we assume that the oracle system satisfies the following properties : 1 . for any @xmath72 , if @xmath73 is large enough , then there exists @xmath74 such that for any @xmath75 and advice @xmath64 , @xmath76 where @xmath77 is the function composing @xmath78 ` @xmath17 times ' , i.e. , @xmath79 . 2 . for any @xmath56 , @xmath80 the first assumption * a1 * implies that the schedule @xmath30 generated by the oracle system after @xmath81 interactions is an approximate solution to the optimization problem . the second assumption * a2 * is merely for a technical purpose : it provides the countability of the underlying space of the network markov chain which we define in the following section . in this section , we describe our scheduling algorithm given an oracle system . to this end , we let @xmath82 be positive - real - valued functions and @xmath83 where @xmath84 . the algorithm maintains parameters @xmath85 . it updates the schedule @xmath22 and parameters @xmath86 under an interaction with the oracle system as follows : ' '' '' * @xmath87 , * @xmath88 , * @xmath89 is the closest integer to @xmath90 if @xmath91 and @xmath92 otherwise . ' '' '' figure [ fig : oracle ] illustrates the above scheduling algorithm using an interactive oracle system . for each time @xmath93 , we let @xmath94 then , @xmath95 becomes a markov chain on the following state space @xmath37 : @xmath96 then , @xmath37 is countable due to the assumption * a2 * of the oracle system . now we are ready to state the main result in this paper , where its proof is presented in section [ sec : pfmainthm ] . [ thm : mainresult ] the above scheduling algorithm is throughput - optimal , i.e. , @xmath54 is positive recurrent for any @xmath35 , if functions @xmath97 satisfy the assumptions * a1-a2 * and the following conditions : 1 . @xmath98 and @xmath99 are increasing , differentiable and concave . 2 . @xmath100 and @xmath101 . 3 . @xmath102 . 5 . for any fixed @xmath104 , @xmath105 6 . there exists @xmath106 such that , for any fixed @xmath104 , @xmath107 in the following section , we provide several specific examples of throughput - optimal and low - complexity scheduling algorithms under theorem [ thm : mainresult ] . in this section , we show the wide - applicability of our framework by designing several throughput - optimal and low - complexity scheduling algorithms under it . in particular , we provide examples of low - complexity oracle systems with corresponding explicit functions @xmath97 so that they satisfy the assumptions * a1-a2 * and the conditions * c1-c6 * of theorem [ thm : mainresult ] . the first oracle system we introduce utilizes an exhaustive search ( es ) algorithm to find a maximum weight schedule @xmath66 , i.e. , it maximizes @xmath108 over @xmath66 for given @xmath1 with @xmath2 , @xmath62 , and @xmath109 . an es algorithm keeps a search - index @xmath110 which may not be in @xmath21 , and current maximum schedule @xmath66 . at each iteration , if @xmath111 is in @xmath21 and its weight is greater than the weight of @xmath30 , replace @xmath30 by @xmath111 . in addition , it updates the search index @xmath111 by @xmath112 where @xmath113 can be considered as a non - negative integer less than @xmath114 and @xmath112 is naturally defined under the interpretation . * es oracle system . * formally , the es oracle system has an advice space @xmath115 . for an advice @xmath116 and weights @xmath117 , the oracle outputs @xmath118 and @xmath119 are decided as follows : ' '' '' * set @xmath120 * set @xmath121 . ' '' '' since it compares all schedules in @xmath21 exhaustively , after @xmath114 interactions with the oracle system , it returns a schedule @xmath66 whose weight is maximum . thus we have , for all @xmath64 and @xmath122 , @xmath123 which implies that we can take @xmath124 for the the assumption * a1 * , i.e. , @xmath81 is a constant function with respect to @xmath125 . in addition , the assumption * a2 * holds obviously . using these facts and theorem [ thm : mainresult ] , the following corollary can be derived . [ cor : es ] the scheduling algorithm described in section [ sec : algorithm_description ] using the es oracle system is throughput - optimal if @xmath126 it is elementary to check the conditions * c1 * -*c5 * of theorem [ thm : mainresult ] , where @xmath124 . the condition * c6 * of theorem [ thm : mainresult ] can be derived as follows : for @xmath127 , @xmath128 this completes the proof of corollary [ cor : es ] . the second oracle system we introduce is the markov chain monte carlo ( mcmc ) algorithm . for a detailed description of the oracle , we consider a special setup of available schedules @xmath21 . [ fig : wireless ] queues in grid interference topology . available schedules are @xmath129 , @xmath130 , @xmath131 , @xmath132 , @xmath133 , @xmath134 , etc.,title="fig:",width=240 ] * wireless network model . * we consider an undirected graph @xmath135 and the set of available schedules @xmath21 is defined as : @xmath136 the above scheduling constraint has been popularly used for modeling interference in wireless networks @xcite , i.e. , two queues @xmath5 and @xmath137 can not transmit simultaneously if they share an edge in the ` interference ' graph @xmath138 . we let @xmath139 denote the set of interfering neighbors of queue @xmath5 . * mcmc oracle system . * in the mcmc oracle system , the advice space is @xmath140 and for an advice @xmath141 , the oracle outputs @xmath118 and @xmath142 are decided randomly as follows : ' '' '' 1 . choose a queue @xmath5 uniformly at random , and set @xmath143 2 . if @xmath144 for some @xmath145 , then set @xmath146 . otherwise , set @xmath147 @xmath148 where @xmath149 . 4 . for each @xmath150 , * if @xmath11 , then set @xmath151 * else if @xmath152 for all @xmath145 , then set @xmath153 * otherwise , set @xmath154 . ' '' '' then , using known results on the mixing time of mcmc , one can prove that the assumption * a1 * holds with @xmath155 where @xmath156 are some ( ` @xmath0-dependent ' ) constants independent of @xmath157 . the proof of is a direct consequence of lemma 3 and lemma 7 in @xcite , and we omit the details due to space constraints . the assumption * a2 * also holds obviously again . using these facts and theorem [ thm : mainresult ] , the following corollary can be derived . [ cor : mcmc ] the scheduling algorithm described in section [ sec : algorithm_description ] using the mcmc oracle system is throughput - optimal if @xmath158 it is elementary to check the conditions * c1 * -*c4 * of theorem [ thm : mainresult ] . the condition * c5 * is from and @xmath159 : @xmath160 furthermore , the condition * c6 * can be derived as follows : this completes the proof of corollary [ cor : mcmc ] . [ cor : mcmc ] the scheduling algorithm described in section [ sec : algorithm_description ] using the mcmc oracle system is throughput - optimal if @xmath161 where @xmath162 . it is elementary to check the conditions * c1 * -*c4 * of theorem [ thm : mainresult ] . for the condition * c5 * , @xmath163 which comes from and @xmath164 . then @xmath165 and it implies the condition * c5*. the condition * c6 * can be derived as follows : for large enough @xmath166 , @xmath167 . combining this with , we have that @xmath168 it completes the proof of corollary [ cor : mcmc ] . we note that the scheduling algorithm described in section [ sec : algorithm_description ] using the mcmc oracle system is the discrete - time version of the csma algorithm in @xcite . the third oracle system we introduce is the belief propagation ( bp ) algorithm , where bp is a popular heuristic iterative algorithm for solving inference problems arising in graphical models @xcite . for the provable throughput - optimality of the scheduling algorithm using the bp oracle system , we consider a special setup of available schedules @xmath21 which is described in what follows . * input - queued switch model . * we consider the undirected complete bipartite graph of left - vertices @xmath169 , right - vertices @xmath170 , and edges @xmath171 , where @xmath172 then , the set of queues is @xmath173 of @xmath174 queues and @xmath175 where this is a popular model for input - queued switches @xcite , and also a special case of the wireless network model described in the previous section . input ports and @xmath176 output ports , there are @xmath177 queues . available schedules are @xmath178 , @xmath179 , @xmath132 , @xmath133 , @xmath180 , and @xmath181.,width=240 ] * bp oracle system . * in the bp oracle system , the advice space is @xmath182 and for an advice @xmath183 , where @xmath184 $ ] , the oracle outputs @xmath118 and @xmath185 are decided as follows : ' '' '' * for each @xmath186 , set @xmath187 where @xmath188 * if @xmath189 , reset @xmath190 . ' '' '' in the above , one can set @xmath191\in [ 0,1]^{|\mathcal e|}$ ] such that @xmath192 is unique , and @xmath193 for some constant @xmath194 , e.g. , let @xmath195 be a random number in the interval @xmath196 $ ] . then , from the works by bayati et al . @xcite or sanghavi et al . @xcite , it follows that the assumption * a1 * holds with @xmath197 for the assumption * a2 * , one can observe that @xmath198 which is obviously a finite set given @xmath56 . using these facts and theorem [ thm : mainresult ] , the following corollary can be derived . in the bp oracle system , the advice space is @xmath199 and for an advice @xmath200\in \mathbb a$ ] , the oracle outputs @xmath118 and @xmath201 are decided as follows : * for each @xmath202 , set @xmath203 where @xmath204 * if @xmath189 , reset @xmath205 by an arbitrary schedule in @xmath21 . in the above , we carefully design @xmath206 so that ( a ) @xmath192 is unique , ( b ) @xmath207 and ( c ) @xmath208 . then , from the work by bayati et al . @xcite , it follows that the assumption * a1 * holds with @xmath209 for the assumption * a2 * , one can observe that @xmath210 which is obviously a finite set given @xmath56 . using these facts and theorem [ thm : mainresult ] , the following corollary follows . the ( max - product ) bp is an iterative , message - passing algorithm for finding @xmath66 which maximizes @xmath108 . the algorithm maintains messages @xmath211 at the @xmath17-th iteration , and they are updated as : @xmath212 where @xmath213 is @xmath166 if @xmath214 and @xmath215 otherwise . after enough iterations , the algorithm outputs @xmath216 if @xmath217 , and @xmath218 otherwise . bayati et al . @xcite establish the following result . * if the desired maximizer @xmath219 is unique , the bp algorithm outputs it for all @xmath220 , where @xmath221 is the difference between the weights of the maximum weight schedule and the second maximum weight schedule , i.e. , @xmath222 . the unique condition in the above theorem can be removed by adding small noises to weights . for example , for integer weight @xmath56 , by adding @xmath223 for the @xmath5-th weight , we guarantee unique maximizer . in our model , for @xmath224 and @xmath225 , we add @xmath226 to @xmath227 weight and we get the following conclusion : * for integer weight @xmath56 , the bp algorithm outputs @xmath219 for all @xmath228 . now we explain how the bp algorithm can be understood as an oracle system . an advice is represented by @xmath229 and , with input @xmath68 , the oracle system outputs following @xmath230 and @xmath231 : @xmath232 namely , the iterative bp mechanism can be thought as an interactive oracle system , where messages corresponds to advices . due to * bp2 * , we have @xmath233 and by theorem [ thm : mainresult ] , the following corollary follows . [ cor : bp ] the scheduling algorithm described in section [ sec : algorithm_description ] using the bp oracle system is throughput - optimal if @xmath234 it is elementary to check the conditions * c1 * -*c5 * of theorem [ thm : mainresult ] , where @xmath235 . the condition * c6 * of theorem [ thm : mainresult ] can be derived as follows : for @xmath236 , @xmath237 where @xmath238 is some constant depending on @xmath239 and the last equality is from @xmath240 and @xmath241 . this completes the proof of corollary [ cor : bp ] . we note that there are many different ways to design the bp oracle , for example , one can consider the following variant . ' '' '' * for each @xmath186 , set @xmath242 * choose @xmath186 so that @xmath243 is the largest one among those which @xmath244 after resetting @xmath245 . * reset @xmath245 and keep this procedure until no more edge is found in the step 2 . ' '' '' the scheduling algorithm described in section [ sec : algorithm_description ] using the above second bp oracle system is also throughput - optimal for the same set of functions @xmath246 in theorem [ cor : bp ] , where its proof is identical to that of the first bp oracle system . the main difference in the second bp oracle is that it decides the schedule @xmath247 greedily based on the ` belief ' @xmath248 $ ] , while the first one simply checks whether @xmath243 is positive or not . a similar version of the scheduling algorithm using the second oracle system was actually studied in @xcite heuristically , where by carefully choosing queue - length functions , theorem [ thm : mainresult ] provides its formal throughput - optimality proof which is missing in @xcite . in this section , we introduce the fourth oracle system combining two mechanisms , bp and es , in the wireless interference network model described in section [ sec : mcmc_wireless ] . we call it the bp - es oracle system . * bp - es oracle system . * in the oracle system , the advice space is @xmath249 , and for an advice @xmath250 where @xmath251 $ ] , the oracle outputs @xmath118 and @xmath252 are decided as follows : ' '' '' * for each edge @xmath186 , set @xmath253 * choose a queue @xmath5 uniformly at random , and set @xmath254 * set @xmath255 where @xmath256 $ ] is defined as @xmath257 ' '' '' as in section [ sec : mcmc_wireless ] , we consider an undirecteted graph @xmath258 and let @xmath259 the first algorithm we utilize for this model is exhaustive search ( es ) which is introduced in section [ sec : es ] and for fixed weight @xmath56 , it find a maximum weight scheduling in @xmath114 iterations . another algorithm is belief propagation ( bp ) for maximum weight independent set . in this algorithm , at every iteration @xmath17 , each node @xmath5 sends a message @xmath260 to each neighbor @xmath145 . each node also maintains a belief @xmath261 . the message and belief updates are as follows : * initially , set @xmath262 for all @xmath263 . * update messages : @xmath264 * for each @xmath150 , @xmath265 * output @xmath22 as @xmath266 bp algorithm for wireless networks sometimes finds a maximum weight schedule but it does not always converge . so , we combine two algorithms and call it es+bp . in the above , the second and third steps can be implementable in distributed fashions using poisson clocks @xcite and gossip algorithms for distributed averaging @xcite . the bp - es oracle system outputs schedule @xmath205 as the maximum weight one among three schedules @xmath30 , @xmath111 and @xmath267 , where @xmath30 is the current maximum schedule , @xmath111 is the es search index and @xmath267 is decided by the bp mechanism . since the search index @xmath111 is decided randomly , the bp - es oracle finds an maximum weight schedule with probability @xmath268 after @xmath269 interactions for the the assumption * a1*. the assumption * a2 * holds with similar reasons as before . using these facts and theorem [ thm : mainresult ] , the following corollary can be derived . [ cor : esbp ] the scheduling algorithm described in section [ sec : algorithm_description ] with the bp - es oracle system is throughput - optimal if @xmath270 the proof of corollary [ cor : esbp ] is almost identical to that of corollary [ cor : es ] . this section provides the proof of theorem [ thm : mainresult ] , i.e. , we show that @xmath36 described in section [ sec : algorithm_description ] is positive recurrent , as long as @xmath271 and @xmath97 satisfy the assumptions * a1-a2 * and the conditions * c1 * -*c6 * stated in theorem [ thm : mainresult ] . towards this , we shall construct a lyapunov function @xmath169 and auxiliary functions @xmath272 , @xmath273 so that they satisfy the conditions of theorem [ thm : lyapunov ] . first , note that the state space @xmath37 is countably infinite from the assumption * a2 * of the oracle system . for @xmath274 , we consider the following function : @xmath275 where @xmath276 . since @xmath277 from the condition * c2 * , we have @xmath278 as @xmath279 . thus , @xmath280 and @xmath43 is a lyapunov function . with an abuse of notation , we use @xmath281 to denote @xmath282 . now , given @xmath271 , there exists @xmath283 and @xmath284\in [ 0,1]^{|s|}$ ] so that @xmath285 for a state @xmath274 , we consider the following functions @xmath272 and @xmath273 : @xmath286 where @xmath287 is a constant in the condition * c6 * , @xmath288 is the largest integer not greater than @xmath166 , and @xmath289 are some constants satisfying @xmath290 for example , one can choose @xmath291 . using the above functions , we shall establish the following lemma . [ lemma : negative_drift ] for every initial state @xmath38 with large enough @xmath292 and every arrival rate @xmath35 , it follows that @xmath293\,|\,{\boldsymbol{x}}(0)={\mathsf{x}}]\leq -\kappa({\mathsf{x}}).\label{eq : negative_drift}\ ] ] the proof of the above lemma is presented in section [ sec : pf : lemma : negative_drift ] . in the remainder of this section , we check that @xmath272 and @xmath273 satisfy the desired conditions * l1-l4 * of theorem [ thm : lyapunov ] , which leads to the positive recurrence of the markov chain @xmath95 . first , it is easy to check that @xmath294 is finite . without loss of generality , we can also assume that holds for every @xmath38 by letting @xmath295 if @xmath292 is not large enough . from the conditions * c2 * and * c4 * , we have @xmath296 as @xmath297 . since @xmath98 is an unbounded increasing function due to * c1 * and * c2 * , we have @xmath298 as @xmath297 . thus , the first two conditions * l1 * and * l2 * are satisfied . by the definition of function @xmath272 , it is not hard to check that @xmath272 increases as @xmath299 does . therefore , it follows that @xmath300 which implies the condition * l3*. finally , as @xmath278 ( i.e. , @xmath297 ) , @xmath301^{-1}\to 0,\end{aligned}\ ] ] which implies the condition * l4*. this completes the proof of theorem [ thm : mainresult ] . to begin with , we describe the main steps to prove lemma [ lemma : negative_drift ] at a high level : 1 . for given initial state @xmath42 with large enough @xmath299 , @xmath58 does not change many times in @xmath302 $ ] , which is formally stated in lemma [ lemma : stopping_time ] . the schedule @xmath22 is close to a max - weight one with respect to @xmath303 ` mostly ' in the time interval @xmath304 $ ] , which is formally stated in lemma [ lemma : bernoulli_main ] . the first step plays a key role for establishing the second step : since @xmath58 does not change often , the interactive oracle system can find a max - weight schedule with respect to @xmath305 . the max - weight property in the second step will lead to the negative drift property in lemma [ lemma : negative_drift ] . now we proceed toward proving lemma [ lemma : negative_drift ] formally . let @xmath306 is the time at which the @xmath307-th change of @xmath58 occurs , i.e. , @xmath58 remains fixed during the time interval @xmath308 . formally , let @xmath309 and for @xmath310 , iteratively define @xmath311 in the following lemma , for initial state @xmath42 with large enough @xmath299 , we show that @xmath58 can be changed at most @xmath0 times in time interval @xmath302 $ ] , i.e. , @xmath312 . [ lemma : stopping_time ] for any initial state @xmath313 with large enough @xmath299 , the following event occurs with probability @xmath314 : @xmath312 and @xmath315,\label{eq : bound_of_q_max}\end{aligned}\ ] ] where @xmath287 is the constant in the condition * c6 * of theorem [ thm : mainresult ] . since @xmath58 remains fixed for @xmath316 , the assumption * a1 * implies that that with high probability , @xmath22 is close to the max - weight schedule with respect to @xmath58 for @xmath317 using this observation with lemma [ lemma : stopping_time ] , we obtain the following lemma that with high probability , the schedule @xmath22 is closed to a max - weight one with respect to @xmath303 ` mostly ' in the time interval @xmath304 $ ] . [ lemma : bernoulli_main ] for any @xmath318 and initial state @xmath274 with large enough @xmath299 , it follows that @xmath319~\geq~1-\beta,\ ] ] where @xmath320\,:\\ & { \boldsymbol{\sigma}}(t)\cdot f({\boldsymbol{q}}(t))\geq ( 1-\eta)\max_{{\boldsymbol{\rho}}\in s}{\boldsymbol{\rho}}\cdot f({\boldsymbol{q}}(t))\bigg\}. \end{aligned}\ ] ] in the remainder of this section , we shall establish the proof of lemma [ lemma : negative_drift ] using lemma [ lemma : stopping_time ] and lemma [ lemma : bernoulli_main ] . to this end , we first recall that @xmath321 from the conditions * c1 * and * c4 * , we have @xmath322 where @xmath323 $ ] . in addition , from , we have an upper bound on the expectation of the first term in : @xmath324 } \nonumber \\ & = & { \mathbb e}[{\boldsymbol{a}}(t)]\cdot { \mathbb e}[f({\boldsymbol{q}}(t))\;|\ ; { \boldsymbol{x}}(0)={\mathsf{x } } ] \nonumber \\ & \leq & \sum_{{\boldsymbol{\rho}}\in s } \alpha_{{\boldsymbol{\rho}}}{\boldsymbol{\rho}}\cdot { \mathbb e}[f({\boldsymbol{q}}(t))\;|\ ; { \boldsymbol{x}}(0)={\mathsf{x } } ] \nonumber \\ & \leq & ( 1-\varepsilon ) { \mathbb e}[\max_{{\boldsymbol{\rho}}\in s}{\boldsymbol{\rho}}\cdot f({\boldsymbol{q}}(t))\;|\ ; { \boldsymbol{x}}(0)={\mathsf{x } } ] . \label{eq : arrival_bound}\end{aligned}\ ] ] by combining and , it follows that @xmath325\,|\,{\boldsymbol{x}}(0)={\mathsf{x}}]}\\ & = & { \mathbb e}\left[\sum_{t=0}^{\tau({\mathsf{x}})-1}l(t+1)-l(t)\,\bigg|\,{\boldsymbol{x}}(0)={\mathsf{x}}\right]\\ & \leq & \sum_{t=0}^{\tau({\mathsf{x}})-1}{\mathbb e}\left [ { \boldsymbol{a}}(t)\cdot f({\boldsymbol{q}}(t))\,|\,{\boldsymbol{x}}(0)={\mathsf{x}}\right]\\ & & \mbox { } -\sum_{t=0}^{\tau({\mathsf{x}})-1}{\mathbb e}\left[{\boldsymbol{\sigma}}(t)\cdot f({\boldsymbol{q}}(t))\,|\,{\boldsymbol{x}}(0)={\mathsf{x}}\right ] + n f'(0)\tau({\mathsf{x}})\\ & = & { \mathbb e}\left[\sum_{t=0}^{\tau({\mathsf{x}})-1}\delta(t)\;\bigg|\ ; { \boldsymbol{x}}(0)={\mathsf{x}}\right],\end{aligned}\ ] ] where @xmath326 now we will bound @xmath327 . from lemma [ lemma : bernoulli_main ] with @xmath328 , where @xmath329 is defined in , it follows that for @xmath330 , @xmath331 where the last inequality is from lemma [ lemma : stopping_time ] . on the other hand , for any @xmath332 $ ] , we know that @xmath333 using these facts with lemma [ lemma : bernoulli_main ] , we further have that @xmath325\,|\,{\boldsymbol{x}}(0)={\mathsf{x}}]}\\ & \leq & { \mathbb e}\left[\sum_{t=0}^{\tau({\mathsf{x}})-1}\delta(t)\;\bigg|\ ; { \boldsymbol{x}}(0)={\mathsf{x}}\right]\\ & = & \pr [ \mathcal a^c]\cdot { \mathbb e}\left[\sum_{t=0}^{\tau({\mathsf{x}})-1}\delta(t)\;\bigg|\ ; { \boldsymbol{x}}(0)={\mathsf{x}},\mathcal a^c\right]\\ & & \qquad + ~\pr[\mathcal a]\cdot { \mathbb e}\left[\sum_{t=0}^{\tau({\mathsf{x}})-1}\delta(t)\;\bigg|\ ; { \boldsymbol{x}}(0)={\mathsf{x}},\mathcal a\right]\\ & \leq & \beta\,n\,f((1+c)q_{\max})\tau({\mathsf{x } } ) + n\,f'(0)\tau({\mathsf{x}})\\ & & \qquad + ( 1-\beta)\,n\,f((1+c)q_{\max})\alpha\,\tau({\mathsf{x}})\\ & & \qquad + \left(1-\beta\right)\left(-\frac{\varepsilon}{2 } f((1-c)q_{\max})\right)(1-\alpha)\tau({\mathsf{x}})\\ & \leq & \left ( -\frac{\varepsilon}{2}(1-\beta)(1-\alpha)+\frac{2n(\beta+(1-\beta)\alpha)}{1-c}\right)\times\\ & & \qquad f((1-c)q_{\max})\tau({\mathsf{x } } ) + n\,f'(0)\tau({\mathsf{x}})\\ & = & -\kappa({\mathsf{x}}),\end{aligned}\ ] ] where @xmath334 denotes the event that @xmath335 and in the last inequality , we use the following property for concave function @xmath98 : @xmath336 this completes the proof of lemma [ lemma : negative_drift ] . we first proceed toward proving in lemma [ lemma : stopping_time ] . it follows from the following observations : @xmath337 where the first inequality is from our modeling assumption that @xmath338 and @xmath339 , and the second inequality is from the definition of @xmath272 . hence , for @xmath340 $ ] , @xmath341 does not change more than @xmath342 from its initial value @xmath343 , which completes the proof of . now , we aim for proving @xmath312 . it suffices to show that , for given initial state @xmath42 with large enough @xmath299 , @xmath344,\ ] ] i.e. , @xmath345 does not change more than @xmath314 , and hence @xmath346 can be updated at most once for each @xmath150 . to prove , it is enough to show the following inequality : @xmath347 since using the definition of @xmath272 , @xmath348 to this end , for @xmath340 $ ] , consider following cases : 1 . if @xmath349 , then from the definition @xmath350 the amount of change @xmath351 is bounded by @xmath352 where we use and the condition * c1 * , i.e. , @xmath353 is decreasing . 2 . otherwise , it is bounded by @xmath354 where we use and the conditions * c1-c2 * , i.e. , @xmath353 is decreasing , @xmath355 and @xmath356 for large enough @xmath166 . this completes the proof of and hence that of lemma [ lemma : stopping_time ] . without loss of generality , assume that @xmath357 and let @xmath358 to simplify notation , we will use @xmath359 instead of @xmath360 . from conditions * c1 * -*c6 * , it is elementary to check that for large enough @xmath166,@xmath361 where their detailed proofs are given in appendix [ sec : appenda ] . due to lemma [ lemma : stopping_time ] , we can assume that @xmath362 and @xmath363 the sufficient conditions to prove lemma [ lemma : bernoulli_main ] are the following : 1 . for all @xmath332$],@xmath364 \leq \max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot { \boldsymbol{w}}(t).\ ] ] 2 . with probability @xmath365 , at least @xmath366 number of time instance @xmath367 $ ] satisfy @xmath368\leq { \boldsymbol{\sigma}}(t)\cdot{\boldsymbol{w}}(t).\label{eq : claimb}\ ] ] 3 . for all @xmath340 $ ] at which is satisfied , @xmath369 the proof of lemma [ lemma : bernoulli_main ] comes immediately from ( a ) , ( b ) and ( c ) as follows : @xmath370 & = & ( 1-\eta')^3\left[\max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot f({\boldsymbol{q}}(t))\right ] \\ & \leq & ( 1-\eta')^2\left[\max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot { \boldsymbol{w}}(t ) \right]\\ & \leq & ( 1-\eta ' ) \left({\boldsymbol{\sigma}}(t)\cdot{\boldsymbol{w}}(t)\right ) \\ & \leq & { \boldsymbol{\sigma}}(t)\cdot f({\boldsymbol{q}}(t)),\end{aligned}\ ] ] where with probability @xmath365 , at least @xmath366 number of time instance @xmath367 $ ] satisfy the second last and last inequalities . hence , we proceed toward proving ( a ) , ( b ) and ( c ) . * proof of ( a ) . * recall that our scheduling algorithm in section [ sec : algorithm_description ] maintains @xmath371 , where @xmath372 . thus , for @xmath15 and @xmath150 , we have @xmath373 and @xmath374 for large enough @xmath299 , combining above inequality with , we conclude that @xmath375}\\ & \leq & \left(1-\frac{2n}{f((1-c)q_{\max})}\right ) \left[\max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot f({\boldsymbol{q}}(t))\right]\\ & \leq & \max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot f({\boldsymbol{q}}(t))-2n\\ & \leq & \max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot { \boldsymbol{w}}(t),\end{aligned}\ ] ] where we use @xmath376 for @xmath332 $ ] from . * proof of ( b ) . * we first state the following key proposition for the proof of ( b ) . [ lem : assum1 ] suppose the assumption * a1 * holds . then , for any advice @xmath64 and @xmath377 , the following event occurs with probability @xmath378 : @xmath379 for @xmath75 , define a binary random variable @xmath380 such that @xmath381 if @xmath382 and @xmath383 otherwise . then , from the assumption * a1 * , @xmath384 < \delta$ ] and @xmath385 < \delta(l - h)$ ] . the conclusion of proposition [ lem : assum1 ] directly follows from the markov inequality applying to the random variable @xmath386 . from the above proposition , it follows that with probability @xmath378 , @xmath387 where from lemma [ lemma : stopping_time ] , we set @xmath388 due to @xmath389 . since @xmath58 changes at most @xmath0 times in @xmath302 $ ] from lemma [ lemma : stopping_time ] , one can use the union bound and conclude that with probability @xmath390 , @xmath391 for at least @xmath392 fraction of times in @xmath393 . furthermore , from , , and the definition of @xmath272 , we have @xmath394 thus , it follows that @xmath395 therefore , with probability @xmath365 , for at least @xmath396 fraction of times in the interval @xmath302 $ ] , holds . * proof of ( c ) . * from , we first have that @xmath397 for all @xmath340 $ ] at which is satisfied , @xmath398\\ & \leq & { \boldsymbol{\sigma}}(t)\cdot{\boldsymbol{w}}(t),\end{aligned}\ ] ] where we use , and @xmath399 . for large enough @xmath299 , combining the above inequality with leads to ( c ) : @xmath400 this completes the proof of lemma [ lemma : bernoulli_main ] . this section presents experimental results for the performance of our scheduling algorithm using various interactive oracle systems . we consider two network models : input - queued switch networks and wireless networks described in section [ sec : mcmc_wireless ] and section [ sec : bp ] , respectively . we compare the average queue - length in our scheduling algorithm using the mcmc , es and bp oracle systems with that of the mw algorithm @xcite . * input - queued switch network . * we first consider an input - queued switch network on @xmath401 complete bipartite graph topology in section [ sec : bp ] . we report the average queue lengths in the switch network for @xmath402 with load 90% , i.e. , arrival rates @xmath403 for all @xmath186 and any algorithm can not stabilize the queues if @xmath404 for all @xmath405 . we run the mw algorithm and our low - complexity scheduling algorithms using the mcmc , es , and bp oracle systems , where we consider the second bp oracle described in section [ sec : bp ] . here we use @xmath406 for es and bp oracles and @xmath407 for mcmc oracle . also , in bp oracle system , instead of using arbitrary schedule in @xmath21 when @xmath408 , we use a greedy algorithm with belief - weight to find a schedule , where belief at each @xmath202 is defined by @xmath409 : * find @xmath410 with maximum belief @xmath411 . * when @xmath412 are given , choose @xmath413 such that @xmath414 is a matching and @xmath415 is maximum among such @xmath416 . figure [ fig : switch_performance ] summarizes our experimental results and we observe that the performance of our scheduling algorithm using bp oracle system is as good as that of the mw algorithm , although it is much simpler to code and faster to run . grid topology.,title="fig:",width=288 ] grid topology.,title="fig:",width=288 ] * wireless networks in grid topology . * we also consider a wireless network with two dimensional grid interference topology . due to the high complexity of the mw algorithm , we chose the @xmath417 grid , i.e. , @xmath418 queues , where figure [ fig : wireless ] represents the @xmath419 grid . we again compare the evolution of the average queue lengths of the mw algorithm and our scheduling algorithms using es , mcmc and bp - es oracle systems . we note that we consider a minor variant of bp - es oracle so that it chooses a schedule greedily based on bp beliefs @xmath420 $ ] similarly as the second bp oracle in the input - queued switch network . we use the same weight functions as in the input - queued switch case and our experimental results are in figure [ fig : wireless_performance ] . we again observe that the performance of our scheduling algorithm using bp - es oracle system is as good as that of the mw algorithm , although it is much simpler to code and faster to run . the problem of dynamic resource allocation among network users contending resources has long been the subject of significant research for last four decades . in this paper , we develop a generic framework for designing resource allocation algorithms of low - complexity and high - performance via connecting iterative optimization and low - complexity scheduling . our work shows sufficient conditions on queue - length functions so that a queue - 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for large enough @xmath166 . due to conditions * c2 * and * c5 * , @xmath421 which proves and . now , follows from the condition * c1 * and * c2 * : @xmath422 where we use the following property for concave function @xmath98 : @xmath423 finally , for , let @xmath424 and we observe that @xmath425 as @xmath426 due to the condition * c6*. this completes the proof of .

since tassiulas and ephremides proposed the maximum weight scheduling algorithm of throughput - optimality for constrained queueing networks in 1992 , extensive research efforts have been made for resolving its high complexity issue under various directions . in this paper , we resolve the issue by developing a generic framework for designing throughput - optimal and low - complexity scheduling algorithms . under the framework , an algorithm updates current schedules via an interaction with a given oracle system that can generate a solution of a certain discrete optimization problem in a finite number of interactive queries . therefore , one can design a variety of scheduling under this framework by choosing different oracles , e.g. , the exhaustive search ( es ) , the markov chain monte carlo ( mcmc ) , the belief propagation ( bp ) and the cutting - plane ( cp ) algorithms . the complexity of the resulting algorithm is decided by the number of operations required for an oracle processing a single query , which is typically very small . somewhat surprisingly , we prove that an algorithm using any such oracle is throughput - optimal for general constrained queueing network models that arise in the context of emerging large - scale communication networks . in particular , the ` pick - and - compare ' algorithms developed by tassiulas in 1998 and recently developed queue - based csma algorithms can be also understood as special cases of such algorithms using es and mcmc oracles , respectively . to our best knowledge , our result is the first that establishes a rigorous connection between iterative optimization methods and low - complexity scheduling algorithms , which we believe provides various future directions and new insights in both areas .

<s>[INST]the problem of dynamic resource allocation in constrained queueing networks is fundamental to modern communication networks . this has long been the subject of significant research , where the @xcite of tassiulas and ephremides proposed the mw ( maximum weight ) scheduling algorithm of throughput - optimality . it has been also a powerful paradigm in cross - layer control and resource allocation @xcite . however , the algorithm can not be implemented in practice due to its high algorithmic complexity . been made since then for developing algorithms of lower complexity while maintaining the same performance guarantee . examples of such algorithms include greedy algorithms @xcite and random access algorithms @xcite . recently , there have been exciting progresses for the topic that even fully distributed random access algorithms based on csma ( carrier sense multiple access ) can achieve the desired high performance , i.e. , throughput - optimality , in wireless interference network models , e.g. , see @xcite . the main intuition underlying these results is that nodes in a network can adjust their csma parameters dynamically using local information such as queue - length so that they can simulate the mw algorithm asymptotically for throughput - optimality . however , it is known that the queue - based csma algorithms suffer from very poor delay performance . there have been also significant efforts formally addressing the limitation in the delay performance of the queue - based csma algorithms @xcite as well as designing better alternatives in delay under certain scenarios @xcite . in addition , another issue is that the throughput - optimality proof in @xcite is very sensitive to the underlying wireless network model . namely , it is not an easy task to design similar csma - like throughput - optimal algorithms in other network models since one has to reproduce painful , long and routine proof - arguments for throughput - optimality in each different model . the main goal of this paper is to resolve these issues of the recent queue - based csma algorithms by developing a general framework that can produce a variety of throughput - optimal and low - complexity scheduling algorithms , not to the underlying network models . design and analysis of resource allocation algorithms in constrained queueing networks have been of great interest for last four decades across various research communities , where the contention resolution protocols in multiple - access broadcast channels have been studied since the mid-1970s @xcite . the broadcast channels induce a special constraint in resources usages among queues ( i.e. , every queue contend with all other queues ) , and simple distributed contention resolution protocols gained much attention in the ages . it is the year 1992 that the seminal work by tassiulas and ephremides proposed a throughput - optimal algorithm , referred to as mw , for general resource constraints . its main appeal is that it does require only information on the current queue lengths ( and instantaneous service rates ) and does not rely on the knowledge of underlying system parameters . however , as we mentioned earlier , the mw algorithm suffers from the high implementation complexity , and a huge array of subsequent research has been made to develop algorithms with high performance guarantees and low - complexity . maximal scheduling or longest - queue - first algorithm are low - complexity alternatives to mw , but they achieve only some fraction of the maximal throughput region . parallel iterative matching @xcite and islip @xcite were shown to be 50% throughput - optimal @xcite . on the other hand , kumar et al . @xcite and dimakis and walrand @xcite identified sufficient conditions on the network topology for throughput - optimality . those conditions were further analyzed to obtain fractional throughput results about a class of wireless networks by joo et al . @xcite and leconte et al . these algorithms are generally not throughput - optimal and require multiple rounds of message exchanges between nodes . simpler or distributed implementations of mw has been also extensively studied in the literature . tassiulas @xcite provides linear - complexity versions of mw , called ` pick - and - compare ' , but it is known that they suffer from the bad delay performance . the works on this line also include a variant of mw by giaccone , prabhakar and shah @xcite and a gossip - based algorithm by modiano , shah and zussman @xcite . however , these algorithms are specific to certain network models and still require high information ( or message ) exchanges for each new scheduling decision . a few years ago , it was proven that even fully distributed queue - based random access algorithms based on csma with very little message passing can simulate the mw algorithm asymptotically and hence achieve throughput - optimality in wireless interference network models @xcite . however , the csma algorithms are known to suffer from the following two issues : the bad delay performance and the limited applicability to other network models . for the delay issue , bouman et al . @xcite formally established explicit lower bounds on the delay of queue - based random access algorithms . on the other hand , significant efforts have also been made to design csma algorithms with better delay performance , e.g. , see @xcite . the limited applicability issue is rather technical : it is a technically tedious task to design similar csma - like throughput - optimal algorithms in other network models since one has to reproduce painful , long and routine proof - arguments for analyzing ` time - varying ' markov chains in each different model , e.g. , see the buffered circuit switched network model @xcite . the main motivation of this paper is for resolving these issues and goes beyond csma - like algorithms for achieving high performance guarantees and low implementation complexity , not sensitive to the underlying network models . we develop a generic framework for designing throughput - optimal and low - complexity scheduling algorithms , where queue - based csma algorithms belong to it as special cases . under the framework , an algorithm updates current schedules via an interaction with a given oracle system that can generate a solution of a certain discrete optimization problem in a finite number of interactive queries . specifically , an algorithm maintains three parameters , ` schedule ' , ` weight ' and ` advice ' , at each time instance . the schedule and advice are kept being updated under interactions with the oracle system and the weight is decided by some function of current queue - size , which we call ` queue - length - function ' . therefore , the scheduling algorithm design is determined by ` which oracle is used ' and ` which queue - length - function is chosen ' . the oracle system can be designed through iterative optimization methods including the naive exhaustive search algorithm , the markov chain monte carlo ( e.g. , the glauber dynamics @xcite ) , the message - passing inference algorithms ( e.g. , the belief propagation @xcite ) and the linear / integer programming ( e.g. , the cutting - plane method @xcite ) . in this paper , we describe three oracle examples , the exhaustive search ( es ) , the markov chain monte carlo ( mcmc ) and the belief propagation ( bp ) in section [ sec : exam ] . in particular , the ` pick - and - compare ' algorithms @xcite and queue - based csma algorithms can be understood as such algorithms ( with minor modifications ) using es and mcmc oracles , respectively ( see section [ sec : exam ] ) . the scheduling complexity is decided by the number of operations required for an oracle processing a single query , which is typically very small , e.g. , es , mcmc and bp . we prove that given any oracle system , there exists a queue - length - function such that an algorithm using the oracle is throughput - optimal under general constrained queueing network models , which includes wireless network models , input - queued switch models , the buffered circuit switched network model , etc . in particular , we first show there exists a queue - length - function such that its value does not change too often ( i.e. , remains fixed for a long time ) and hence the mw optimization problem can be solved through ( enough ) interactions to the oracle , i.e. , the algorithm simulates mw and is throughput - optimal . this proof strategy is similar to those of @xcite in spirit . the main difference is that we force the queue - length - function value being ` rarely - varying ' in integers , while the authors in @xcite do it being ` slowly - varying ' in real numbers . due to such a difference , now we do not need to analyze ` time - varying ' algorithms ( e.g. , markov chains ) , i.e. , analysis when algorithm parameters are fixed is enough . this makes the proof much simpler and not sensitive to the given oracle and underlying network model . our strong theoretical statement provides a quite powerful paradigm for developing a variety of low - complexity scheduling algorithms of high performance . for example , our experimental results show that the delay performance of such an algorithm using the bp oracle is close to that of the mw algorithm , and it significantly outperforms csma algorithms ( see section [ sec : exp ] ) . moreover , one can also easily design other types of throughput - optimal algorithms , via designing various oracle systems , under a quite broad class of constrained queueing network models , without suffering from repeating tedious proofs sensitive to the underlying assumptions and setups . at a high level , we use the interactive oracle concept to provide a ` black - box ' tool for designing scheduling algorithms of high performance and low - complexity . this establishes a rigorous connection between iterative optimization methods and low - complexity scheduling algorithms , which we believe provides various future directions and new insights in both areas . in section [ sec : pre ] , we describe the constrained queueing network model of our interest and the performance metric ( i.e. , throughput - optimality ) for scheduling algorithms . section [ sec : main ] provides the main result of this paper , i.e. , our generic framework for designing a throughput - optimal and low - complexity scheduling algorithm which decides its current schedule via an interaction with an oracle system . in section [ sec : exam ] , we provide several examples of scheduling algorithms under the framework . section [ sec : pfmainthm ] provides the formal proof of the main result , and our experimental results are presented in section [ sec : exp ] . we consider a stochastic network of @xmath0 queues represented by @xmath1 with @xmath2 , and time is discrete indexed by @xmath3 . external packets ( or jobs ) arrive at each queue as per an exogenous stochastic process , where we let @xmath4 denote the number of packets arriving at queue @xmath5 during the time interval @xmath6 . we assume that @xmath7 are independent bernoulli random variables with @xmath8=\lambda_i\ ] ] for some @xmath9 $ ] , called the _ arrival rate _ for queue @xmath5 . packets in queues are served at unit rate subject to scheduling constraints . formally , a schedule is denoted by @xmath10\in \{0,1\}^n$ ] , where @xmath11 means queue @xmath5 is transmitting ( or active ) and @xmath12 otherwise . we let @xmath13 be a set of all available schedules and let @xmath14 be the schedule during @xmath6 for @xmath15 . to describe the dynamics in the network , we let @xmath16 denote the number of packets in @xmath5-th queue at time @xmath17 ( i.e. , _ length of queue _ ) and let @xmath18 $ ] be the vector of queue lengths . then the queueing dynamics for queue @xmath5 can be described as @xmath19 where @xmath15 and @xmath20 for given @xmath1 and @xmath21 , our goal is to develop low - complexity and high - performance scheduling algorithms which determine @xmath22 for each time instance @xmath15 . a scheduling algorithm is required to choose @xmath14 at each time instance @xmath15 . we say an algorithm is throughput - optimal if it keeps queues finite for as large a set of arrival rates @xmath23 $ ] as possible . to describe it formally , we define the capacity region as follows : @xmath24 where it is the convex hull of the feasible scheduling set @xmath21 . since @xmath14 , the effective ` service ' rate induced by any algorithm over time is essentially in @xmath25 . therefore , if arrival rates @xmath26 can be served by any algorithm , then there exists @xmath27 such that @xmath28 component - wise . we say @xmath26 is _ ( strictly ) admissible _ if @xmath29 is ( strictly ) less than @xmath30 for some @xmath31 . let @xmath32 and @xmath33 be the set of all admissible and strictly admissible rates , respectively : @xmath34 a throughput - optimal algorithm keeps queues finite for any @xmath35 , where there can be many different ways to argue the finiteness of queues . in this paper , we use the following popular definition of throughput - optimality . [ def : throughput - optimality ] a scheduling algorithm is called _ throughput - optimal _ if for any @xmath35 the ( appropriately defined ) network markov chain is positive recurrent . if the state of the network markov chain includes queue - sizes , then its positive recurrence implies that the queues remain finite with probability 1 , which motivates the above definition . we recall the definition of the positive recurrence of a markov chain @xmath36 on a countable state space @xmath37 . a state @xmath38 is said to be _ recurrent _ if @xmath39=1 $ ] , where @xmath40 . if @xmath41<\infty$ ] , a recurrent state @xmath42 is called _ positive recurrent_. if a markov chain is irreducible and it has a positive recurrent state , all states are positive recurrent . in this case , we call such a markov chain positive recurrent . one way to show the positive recurrence of a markov chain is using the following lyapunov - foster criteria . a function @xmath43 is called a ` lyapunov function ' if @xmath44 . the following theorem provides a criteria about the positive recurrence using a lyapunov function , e.g. , see @xcite . [ thm : lyapunov ] consider a lyapunov function @xmath45 such that @xmath46 is finite for any @xmath47 . suppose there exist functions @xmath48 such that @xmath49\leq -\kappa({\mathsf{x}}),~\forall x\in\omega,\ ] ] and they satisfy the following conditions : 1 . 2 . @xmath51 . @xmath52 for all @xmath47 . 4 . @xmath53 . then , @xmath54 is positive recurrent . this section presents our main result , throughput - optimal and low - complexity scheduling algorithms . we first describe the generic concept of our algorithms utilizing certain oracle systems . the oracle systems are motivated by ( randomized or deterministic ) iterative algorithms which find an approximate optimal solution to the following optimization problem : @xmath55 typically , in an iterative algorithm , the output at each iteration depends only on information from the previous iteration ( and weight @xmath56 ) . we call such information ` advice ' . one can understand an iteration of the algorithm as an interaction to an oracle system , where a query consisting of advice and weight is sent to an interactive oracle system , and the oracle returns a schedule together with an updated advice for the next iteration . this naturally suggests the following scheduling algorithm : at each time instance @xmath17 , ( a ) it sends a query consisting of the advice @xmath57 produced in the previous step and weight @xmath58 decided by current queue lengths to the oracle system , and then ( b ) the oracle returns a schedule to use at the next time instance @xmath59 . hence , the complexity of the scheduling algorithm is that of the oracle system processing a query ( equivalently , that of one iteration of an iterative algorithm ) , which is typically very small as we provide examples in section [ sec : exam ] . in the following sections , we provide the formal descriptions of oracle systems of interest and scheduling algorithms utilizing them . and weight @xmath58 is sent to the oracle . the oracle returns the schedule @xmath60 to use at the next time instance and updated advice @xmath61 . , width=288 ] we consider a network model introduced in section [ subsec : network_model ] with set of queues @xmath1 with @xmath2 and available schedules @xmath62 . then the oracle system we are interested in has an advice space @xmath63 with the following input and output : * it takes inputs @xmath64 and @xmath65 $ ] , * it outputs ( or returns ) @xmath66 and @xmath67 , where @xmath56 , @xmath68 , and @xmath69 are called ` weights ' on queues , ` advice ' , and ` updated advice ' , respectively . formally , let the outputs @xmath70 and @xmath71 , where the oracle can generate random outputs in general . we assume that the oracle system satisfies the following properties : 1 . for any @xmath72 , if @xmath73 is large enough , then there exists @xmath74 such that for any @xmath75 and advice @xmath64 , @xmath76 where @xmath77 is the function composing @xmath78 ` @xmath17 times ' , i.e. , @xmath79 . 2 . for any @xmath56 , @xmath80 the first assumption * a1 * implies that the schedule @xmath30 generated by the oracle system after @xmath81 interactions is an approximate solution to the optimization problem . the second assumption * a2 * is merely for a technical purpose : it provides the countability of the underlying space of the network markov chain which we define in the following section . in this section , we describe our scheduling algorithm given an oracle system . to this end , we let @xmath82 be positive - real - valued functions and @xmath83 where @xmath84 . the algorithm maintains parameters @xmath85 . it updates the schedule @xmath22 and parameters @xmath86 under an interaction with the oracle system as follows : ' '' '' * @xmath87 , * @xmath88 , * @xmath89 is the closest integer to @xmath90 if @xmath91 and @xmath92 otherwise . ' '' '' figure [ fig : oracle ] illustrates the above scheduling algorithm using an interactive oracle system . for each time @xmath93 , we let @xmath94 then , @xmath95 becomes a markov chain on the following state space @xmath37 : @xmath96 then , @xmath37 is countable due to the assumption * a2 * of the oracle system . now we are ready to state the main result in this paper , where its proof is presented in section [ sec : pfmainthm ] . [ thm : mainresult ] the above scheduling algorithm is throughput - optimal , i.e. , @xmath54 is positive recurrent for any @xmath35 , if functions @xmath97 satisfy the assumptions * a1-a2 * and the following conditions : 1 . @xmath98 and @xmath99 are increasing , differentiable and concave . 2 . @xmath100 and @xmath101 . 3 . @xmath102 . 5 . for any fixed @xmath104 , @xmath105 6 . there exists @xmath106 such that , for any fixed @xmath104 , @xmath107 in the following section , we provide several specific examples of throughput - optimal and low - complexity scheduling algorithms under theorem [ thm : mainresult ] . in this section , we show the wide - applicability of our framework by designing several throughput - optimal and low - complexity scheduling algorithms under it . in particular , we provide examples of low - complexity oracle systems with corresponding explicit functions @xmath97 so that they satisfy the assumptions * a1-a2 * and the conditions * c1-c6 * of theorem [ thm : mainresult ] . the first oracle system we introduce utilizes an exhaustive search ( es ) algorithm to find a maximum weight schedule @xmath66 , i.e. , it maximizes @xmath108 over @xmath66 for given @xmath1 with @xmath2 , @xmath62 , and @xmath109 . an es algorithm keeps a search - index @xmath110 which may not be in @xmath21 , and current maximum schedule @xmath66 . at each iteration , if @xmath111 is in @xmath21 and its weight is greater than the weight of @xmath30 , replace @xmath30 by @xmath111 . in addition , it updates the search index @xmath111 by @xmath112 where @xmath113 can be considered as a non - negative integer less than @xmath114 and @xmath112 is naturally defined under the interpretation . * es oracle system . * formally , the es oracle system has an advice space @xmath115 . for an advice @xmath116 and weights @xmath117 , the oracle outputs @xmath118 and @xmath119 are decided as follows : ' '' '' * set @xmath120 * set @xmath121 . ' '' '' since it compares all schedules in @xmath21 exhaustively , after @xmath114 interactions with the oracle system , it returns a schedule @xmath66 whose weight is maximum . thus we have , for all @xmath64 and @xmath122 , @xmath123 which implies that we can take @xmath124 for the the assumption * a1 * , i.e. , @xmath81 is a constant function with respect to @xmath125 . in addition , the assumption * a2 * holds obviously . using these facts and theorem [ thm : mainresult ] , the following corollary can be derived . [ cor : es ] the scheduling algorithm described in section [ sec : algorithm_description ] using the es oracle system is throughput - optimal if @xmath126 it is elementary to check the conditions * c1 * -*c5 * of theorem [ thm : mainresult ] , where @xmath124 . the condition * c6 * of theorem [ thm : mainresult ] can be derived as follows : for @xmath127 , @xmath128 this completes the proof of corollary [ cor : es ] . the second oracle system we introduce is the markov chain monte carlo ( mcmc ) algorithm . for a detailed description of the oracle , we consider a special setup of available schedules @xmath21 . [ fig : wireless ] queues in grid interference topology . available schedules are @xmath129 , @xmath130 , @xmath131 , @xmath132 , @xmath133 , @xmath134 , etc.,title="fig:",width=240 ] * wireless network model . * we consider an undirected graph @xmath135 and the set of available schedules @xmath21 is defined as : @xmath136 the above scheduling constraint has been popularly used for modeling interference in wireless networks @xcite , i.e. , two queues @xmath5 and @xmath137 can not transmit simultaneously if they share an edge in the ` interference ' graph @xmath138 . we let @xmath139 denote the set of interfering neighbors of queue @xmath5 . * mcmc oracle system . * in the mcmc oracle system , the advice space is @xmath140 and for an advice @xmath141 , the oracle outputs @xmath118 and @xmath142 are decided randomly as follows : ' '' '' 1 . choose a queue @xmath5 uniformly at random , and set @xmath143 2 . if @xmath144 for some @xmath145 , then set @xmath146 . otherwise , set @xmath147 @xmath148 where @xmath149 . 4 . for each @xmath150 , * if @xmath11 , then set @xmath151 * else if @xmath152 for all @xmath145 , then set @xmath153 * otherwise , set @xmath154 . ' '' '' then , using known results on the mixing time of mcmc , one can prove that the assumption * a1 * holds with @xmath155 where @xmath156 are some ( ` @xmath0-dependent ' ) constants independent of @xmath157 . the proof of is a direct consequence of lemma 3 and lemma 7 in @xcite , and we omit the details due to space constraints . the assumption * a2 * also holds obviously again . using these facts and theorem [ thm : mainresult ] , the following corollary can be derived . [ cor : mcmc ] the scheduling algorithm described in section [ sec : algorithm_description ] using the mcmc oracle system is throughput - optimal if @xmath158 it is elementary to check the conditions * c1 * -*c4 * of theorem [ thm : mainresult ] . the condition * c5 * is from and @xmath159 : @xmath160 furthermore , the condition * c6 * can be derived as follows : this completes the proof of corollary [ cor : mcmc ] . [ cor : mcmc ] the scheduling algorithm described in section [ sec : algorithm_description ] using the mcmc oracle system is throughput - optimal if @xmath161 where @xmath162 . it is elementary to check the conditions * c1 * -*c4 * of theorem [ thm : mainresult ] . for the condition * c5 * , @xmath163 which comes from and @xmath164 . then @xmath165 and it implies the condition * c5*. the condition * c6 * can be derived as follows : for large enough @xmath166 , @xmath167 . combining this with , we have that @xmath168 it completes the proof of corollary [ cor : mcmc ] . we note that the scheduling algorithm described in section [ sec : algorithm_description ] using the mcmc oracle system is the discrete - time version of the csma algorithm in @xcite . the third oracle system we introduce is the belief propagation ( bp ) algorithm , where bp is a popular heuristic iterative algorithm for solving inference problems arising in graphical models @xcite . for the provable throughput - optimality of the scheduling algorithm using the bp oracle system , we consider a special setup of available schedules @xmath21 which is described in what follows . * input - queued switch model . * we consider the undirected complete bipartite graph of left - vertices @xmath169 , right - vertices @xmath170 , and edges @xmath171 , where @xmath172 then , the set of queues is @xmath173 of @xmath174 queues and @xmath175 where this is a popular model for input - queued switches @xcite , and also a special case of the wireless network model described in the previous section . input ports and @xmath176 output ports , there are @xmath177 queues . available schedules are @xmath178 , @xmath179 , @xmath132 , @xmath133 , @xmath180 , and @xmath181.,width=240 ] * bp oracle system . * in the bp oracle system , the advice space is @xmath182 and for an advice @xmath183 , where @xmath184 $ ] , the oracle outputs @xmath118 and @xmath185 are decided as follows : ' '' '' * for each @xmath186 , set @xmath187 where @xmath188 * if @xmath189 , reset @xmath190 . ' '' '' in the above , one can set @xmath191\in [ 0,1]^{|\mathcal e|}$ ] such that @xmath192 is unique , and @xmath193 for some constant @xmath194 , e.g. , let @xmath195 be a random number in the interval @xmath196 $ ] . then , from the works by bayati et al . @xcite or sanghavi et al . @xcite , it follows that the assumption * a1 * holds with @xmath197 for the assumption * a2 * , one can observe that @xmath198 which is obviously a finite set given @xmath56 . using these facts and theorem [ thm : mainresult ] , the following corollary can be derived . in the bp oracle system , the advice space is @xmath199 and for an advice @xmath200\in \mathbb a$ ] , the oracle outputs @xmath118 and @xmath201 are decided as follows : * for each @xmath202 , set @xmath203 where @xmath204 * if @xmath189 , reset @xmath205 by an arbitrary schedule in @xmath21 . in the above , we carefully design @xmath206 so that ( a ) @xmath192 is unique , ( b ) @xmath207 and ( c ) @xmath208 . then , from the work by bayati et al . @xcite , it follows that the assumption * a1 * holds with @xmath209 for the assumption * a2 * , one can observe that @xmath210 which is obviously a finite set given @xmath56 . using these facts and theorem [ thm : mainresult ] , the following corollary follows . the ( max - product ) bp is an iterative , message - passing algorithm for finding @xmath66 which maximizes @xmath108 . the algorithm maintains messages @xmath211 at the @xmath17-th iteration , and they are updated as : @xmath212 where @xmath213 is @xmath166 if @xmath214 and @xmath215 otherwise . after enough iterations , the algorithm outputs @xmath216 if @xmath217 , and @xmath218 otherwise . bayati et al . @xcite establish the following result . * if the desired maximizer @xmath219 is unique , the bp algorithm outputs it for all @xmath220 , where @xmath221 is the difference between the weights of the maximum weight schedule and the second maximum weight schedule , i.e. , @xmath222 . the unique condition in the above theorem can be removed by adding small noises to weights . for example , for integer weight @xmath56 , by adding @xmath223 for the @xmath5-th weight , we guarantee unique maximizer . in our model , for @xmath224 and @xmath225 , we add @xmath226 to @xmath227 weight and we get the following conclusion : * for integer weight @xmath56 , the bp algorithm outputs @xmath219 for all @xmath228 . now we explain how the bp algorithm can be understood as an oracle system . an advice is represented by @xmath229 and , with input @xmath68 , the oracle system outputs following @xmath230 and @xmath231 : @xmath232 namely , the iterative bp mechanism can be thought as an interactive oracle system , where messages corresponds to advices . due to * bp2 * , we have @xmath233 and by theorem [ thm : mainresult ] , the following corollary follows . [ cor : bp ] the scheduling algorithm described in section [ sec : algorithm_description ] using the bp oracle system is throughput - optimal if @xmath234 it is elementary to check the conditions * c1 * -*c5 * of theorem [ thm : mainresult ] , where @xmath235 . the condition * c6 * of theorem [ thm : mainresult ] can be derived as follows : for @xmath236 , @xmath237 where @xmath238 is some constant depending on @xmath239 and the last equality is from @xmath240 and @xmath241 . this completes the proof of corollary [ cor : bp ] . we note that there are many different ways to design the bp oracle , for example , one can consider the following variant . ' '' '' * for each @xmath186 , set @xmath242 * choose @xmath186 so that @xmath243 is the largest one among those which @xmath244 after resetting @xmath245 . * reset @xmath245 and keep this procedure until no more edge is found in the step 2 . ' '' '' the scheduling algorithm described in section [ sec : algorithm_description ] using the above second bp oracle system is also throughput - optimal for the same set of functions @xmath246 in theorem [ cor : bp ] , where its proof is identical to that of the first bp oracle system . the main difference in the second bp oracle is that it decides the schedule @xmath247 greedily based on the ` belief ' @xmath248 $ ] , while the first one simply checks whether @xmath243 is positive or not . a similar version of the scheduling algorithm using the second oracle system was actually studied in @xcite heuristically , where by carefully choosing queue - length functions , theorem [ thm : mainresult ] provides its formal throughput - optimality proof which is missing in @xcite . in this section , we introduce the fourth oracle system combining two mechanisms , bp and es , in the wireless interference network model described in section [ sec : mcmc_wireless ] . we call it the bp - es oracle system . * bp - es oracle system . * in the oracle system , the advice space is @xmath249 , and for an advice @xmath250 where @xmath251 $ ] , the oracle outputs @xmath118 and @xmath252 are decided as follows : ' '' '' * for each edge @xmath186 , set @xmath253 * choose a queue @xmath5 uniformly at random , and set @xmath254 * set @xmath255 where @xmath256 $ ] is defined as @xmath257 ' '' '' as in section [ sec : mcmc_wireless ] , we consider an undirecteted graph @xmath258 and let @xmath259 the first algorithm we utilize for this model is exhaustive search ( es ) which is introduced in section [ sec : es ] and for fixed weight @xmath56 , it find a maximum weight scheduling in @xmath114 iterations . another algorithm is belief propagation ( bp ) for maximum weight independent set . in this algorithm , at every iteration @xmath17 , each node @xmath5 sends a message @xmath260 to each neighbor @xmath145 . each node also maintains a belief @xmath261 . the message and belief updates are as follows : * initially , set @xmath262 for all @xmath263 . * update messages : @xmath264 * for each @xmath150 , @xmath265 * output @xmath22 as @xmath266 bp algorithm for wireless networks sometimes finds a maximum weight schedule but it does not always converge . so , we combine two algorithms and call it es+bp . in the above , the second and third steps can be implementable in distributed fashions using poisson clocks @xcite and gossip algorithms for distributed averaging @xcite . the bp - es oracle system outputs schedule @xmath205 as the maximum weight one among three schedules @xmath30 , @xmath111 and @xmath267 , where @xmath30 is the current maximum schedule , @xmath111 is the es search index and @xmath267 is decided by the bp mechanism . since the search index @xmath111 is decided randomly , the bp - es oracle finds an maximum weight schedule with probability @xmath268 after @xmath269 interactions for the the assumption * a1*. the assumption * a2 * holds with similar reasons as before . using these facts and theorem [ thm : mainresult ] , the following corollary can be derived . [ cor : esbp ] the scheduling algorithm described in section [ sec : algorithm_description ] with the bp - es oracle system is throughput - optimal if @xmath270 the proof of corollary [ cor : esbp ] is almost identical to that of corollary [ cor : es ] . this section provides the proof of theorem [ thm : mainresult ] , i.e. , we show that @xmath36 described in section [ sec : algorithm_description ] is positive recurrent , as long as @xmath271 and @xmath97 satisfy the assumptions * a1-a2 * and the conditions * c1 * -*c6 * stated in theorem [ thm : mainresult ] . towards this , we shall construct a lyapunov function @xmath169 and auxiliary functions @xmath272 , @xmath273 so that they satisfy the conditions of theorem [ thm : lyapunov ] . first , note that the state space @xmath37 is countably infinite from the assumption * a2 * of the oracle system . for @xmath274 , we consider the following function : @xmath275 where @xmath276 . since @xmath277 from the condition * c2 * , we have @xmath278 as @xmath279 . thus , @xmath280 and @xmath43 is a lyapunov function . with an abuse of notation , we use @xmath281 to denote @xmath282 . now , given @xmath271 , there exists @xmath283 and @xmath284\in [ 0,1]^{|s|}$ ] so that @xmath285 for a state @xmath274 , we consider the following functions @xmath272 and @xmath273 : @xmath286 where @xmath287 is a constant in the condition * c6 * , @xmath288 is the largest integer not greater than @xmath166 , and @xmath289 are some constants satisfying @xmath290 for example , one can choose @xmath291 . using the above functions , we shall establish the following lemma . [ lemma : negative_drift ] for every initial state @xmath38 with large enough @xmath292 and every arrival rate @xmath35 , it follows that @xmath293\,|\,{\boldsymbol{x}}(0)={\mathsf{x}}]\leq -\kappa({\mathsf{x}}).\label{eq : negative_drift}\ ] ] the proof of the above lemma is presented in section [ sec : pf : lemma : negative_drift ] . in the remainder of this section , we check that @xmath272 and @xmath273 satisfy the desired conditions * l1-l4 * of theorem [ thm : lyapunov ] , which leads to the positive recurrence of the markov chain @xmath95 . first , it is easy to check that @xmath294 is finite . without loss of generality , we can also assume that holds for every @xmath38 by letting @xmath295 if @xmath292 is not large enough . from the conditions * c2 * and * c4 * , we have @xmath296 as @xmath297 . since @xmath98 is an unbounded increasing function due to * c1 * and * c2 * , we have @xmath298 as @xmath297 . thus , the first two conditions * l1 * and * l2 * are satisfied . by the definition of function @xmath272 , it is not hard to check that @xmath272 increases as @xmath299 does . therefore , it follows that @xmath300 which implies the condition * l3*. finally , as @xmath278 ( i.e. , @xmath297 ) , @xmath301^{-1}\to 0,\end{aligned}\ ] ] which implies the condition * l4*. this completes the proof of theorem [ thm : mainresult ] . to begin with , we describe the main steps to prove lemma [ lemma : negative_drift ] at a high level : 1 . for given initial state @xmath42 with large enough @xmath299 , @xmath58 does not change many times in @xmath302 $ ] , which is formally stated in lemma [ lemma : stopping_time ] . the schedule @xmath22 is close to a max - weight one with respect to @xmath303 ` mostly ' in the time interval @xmath304 $ ] , which is formally stated in lemma [ lemma : bernoulli_main ] . the first step plays a key role for establishing the second step : since @xmath58 does not change often , the interactive oracle system can find a max - weight schedule with respect to @xmath305 . the max - weight property in the second step will lead to the negative drift property in lemma [ lemma : negative_drift ] . now we proceed toward proving lemma [ lemma : negative_drift ] formally . let @xmath306 is the time at which the @xmath307-th change of @xmath58 occurs , i.e. , @xmath58 remains fixed during the time interval @xmath308 . formally , let @xmath309 and for @xmath310 , iteratively define @xmath311 in the following lemma , for initial state @xmath42 with large enough @xmath299 , we show that @xmath58 can be changed at most @xmath0 times in time interval @xmath302 $ ] , i.e. , @xmath312 . [ lemma : stopping_time ] for any initial state @xmath313 with large enough @xmath299 , the following event occurs with probability @xmath314 : @xmath312 and @xmath315,\label{eq : bound_of_q_max}\end{aligned}\ ] ] where @xmath287 is the constant in the condition * c6 * of theorem [ thm : mainresult ] . since @xmath58 remains fixed for @xmath316 , the assumption * a1 * implies that that with high probability , @xmath22 is close to the max - weight schedule with respect to @xmath58 for @xmath317 using this observation with lemma [ lemma : stopping_time ] , we obtain the following lemma that with high probability , the schedule @xmath22 is closed to a max - weight one with respect to @xmath303 ` mostly ' in the time interval @xmath304 $ ] . [ lemma : bernoulli_main ] for any @xmath318 and initial state @xmath274 with large enough @xmath299 , it follows that @xmath319~\geq~1-\beta,\ ] ] where @xmath320\,:\\ & { \boldsymbol{\sigma}}(t)\cdot f({\boldsymbol{q}}(t))\geq ( 1-\eta)\max_{{\boldsymbol{\rho}}\in s}{\boldsymbol{\rho}}\cdot f({\boldsymbol{q}}(t))\bigg\}. \end{aligned}\ ] ] in the remainder of this section , we shall establish the proof of lemma [ lemma : negative_drift ] using lemma [ lemma : stopping_time ] and lemma [ lemma : bernoulli_main ] . to this end , we first recall that @xmath321 from the conditions * c1 * and * c4 * , we have @xmath322 where @xmath323 $ ] . in addition , from , we have an upper bound on the expectation of the first term in : @xmath324 } \nonumber \\ & = & { \mathbb e}[{\boldsymbol{a}}(t)]\cdot { \mathbb e}[f({\boldsymbol{q}}(t))\;|\ ; { \boldsymbol{x}}(0)={\mathsf{x } } ] \nonumber \\ & \leq & \sum_{{\boldsymbol{\rho}}\in s } \alpha_{{\boldsymbol{\rho}}}{\boldsymbol{\rho}}\cdot { \mathbb e}[f({\boldsymbol{q}}(t))\;|\ ; { \boldsymbol{x}}(0)={\mathsf{x } } ] \nonumber \\ & \leq & ( 1-\varepsilon ) { \mathbb e}[\max_{{\boldsymbol{\rho}}\in s}{\boldsymbol{\rho}}\cdot f({\boldsymbol{q}}(t))\;|\ ; { \boldsymbol{x}}(0)={\mathsf{x } } ] . \label{eq : arrival_bound}\end{aligned}\ ] ] by combining and , it follows that @xmath325\,|\,{\boldsymbol{x}}(0)={\mathsf{x}}]}\\ & = & { \mathbb e}\left[\sum_{t=0}^{\tau({\mathsf{x}})-1}l(t+1)-l(t)\,\bigg|\,{\boldsymbol{x}}(0)={\mathsf{x}}\right]\\ & \leq & \sum_{t=0}^{\tau({\mathsf{x}})-1}{\mathbb e}\left [ { \boldsymbol{a}}(t)\cdot f({\boldsymbol{q}}(t))\,|\,{\boldsymbol{x}}(0)={\mathsf{x}}\right]\\ & & \mbox { } -\sum_{t=0}^{\tau({\mathsf{x}})-1}{\mathbb e}\left[{\boldsymbol{\sigma}}(t)\cdot f({\boldsymbol{q}}(t))\,|\,{\boldsymbol{x}}(0)={\mathsf{x}}\right ] + n f'(0)\tau({\mathsf{x}})\\ & = & { \mathbb e}\left[\sum_{t=0}^{\tau({\mathsf{x}})-1}\delta(t)\;\bigg|\ ; { \boldsymbol{x}}(0)={\mathsf{x}}\right],\end{aligned}\ ] ] where @xmath326 now we will bound @xmath327 . from lemma [ lemma : bernoulli_main ] with @xmath328 , where @xmath329 is defined in , it follows that for @xmath330 , @xmath331 where the last inequality is from lemma [ lemma : stopping_time ] . on the other hand , for any @xmath332 $ ] , we know that @xmath333 using these facts with lemma [ lemma : bernoulli_main ] , we further have that @xmath325\,|\,{\boldsymbol{x}}(0)={\mathsf{x}}]}\\ & \leq & { \mathbb e}\left[\sum_{t=0}^{\tau({\mathsf{x}})-1}\delta(t)\;\bigg|\ ; { \boldsymbol{x}}(0)={\mathsf{x}}\right]\\ & = & \pr [ \mathcal a^c]\cdot { \mathbb e}\left[\sum_{t=0}^{\tau({\mathsf{x}})-1}\delta(t)\;\bigg|\ ; { \boldsymbol{x}}(0)={\mathsf{x}},\mathcal a^c\right]\\ & & \qquad + ~\pr[\mathcal a]\cdot { \mathbb e}\left[\sum_{t=0}^{\tau({\mathsf{x}})-1}\delta(t)\;\bigg|\ ; { \boldsymbol{x}}(0)={\mathsf{x}},\mathcal a\right]\\ & \leq & \beta\,n\,f((1+c)q_{\max})\tau({\mathsf{x } } ) + n\,f'(0)\tau({\mathsf{x}})\\ & & \qquad + ( 1-\beta)\,n\,f((1+c)q_{\max})\alpha\,\tau({\mathsf{x}})\\ & & \qquad + \left(1-\beta\right)\left(-\frac{\varepsilon}{2 } f((1-c)q_{\max})\right)(1-\alpha)\tau({\mathsf{x}})\\ & \leq & \left ( -\frac{\varepsilon}{2}(1-\beta)(1-\alpha)+\frac{2n(\beta+(1-\beta)\alpha)}{1-c}\right)\times\\ & & \qquad f((1-c)q_{\max})\tau({\mathsf{x } } ) + n\,f'(0)\tau({\mathsf{x}})\\ & = & -\kappa({\mathsf{x}}),\end{aligned}\ ] ] where @xmath334 denotes the event that @xmath335 and in the last inequality , we use the following property for concave function @xmath98 : @xmath336 this completes the proof of lemma [ lemma : negative_drift ] . we first proceed toward proving in lemma [ lemma : stopping_time ] . it follows from the following observations : @xmath337 where the first inequality is from our modeling assumption that @xmath338 and @xmath339 , and the second inequality is from the definition of @xmath272 . hence , for @xmath340 $ ] , @xmath341 does not change more than @xmath342 from its initial value @xmath343 , which completes the proof of . now , we aim for proving @xmath312 . it suffices to show that , for given initial state @xmath42 with large enough @xmath299 , @xmath344,\ ] ] i.e. , @xmath345 does not change more than @xmath314 , and hence @xmath346 can be updated at most once for each @xmath150 . to prove , it is enough to show the following inequality : @xmath347 since using the definition of @xmath272 , @xmath348 to this end , for @xmath340 $ ] , consider following cases : 1 . if @xmath349 , then from the definition @xmath350 the amount of change @xmath351 is bounded by @xmath352 where we use and the condition * c1 * , i.e. , @xmath353 is decreasing . 2 . otherwise , it is bounded by @xmath354 where we use and the conditions * c1-c2 * , i.e. , @xmath353 is decreasing , @xmath355 and @xmath356 for large enough @xmath166 . this completes the proof of and hence that of lemma [ lemma : stopping_time ] . without loss of generality , assume that @xmath357 and let @xmath358 to simplify notation , we will use @xmath359 instead of @xmath360 . from conditions * c1 * -*c6 * , it is elementary to check that for large enough @xmath166,@xmath361 where their detailed proofs are given in appendix [ sec : appenda ] . due to lemma [ lemma : stopping_time ] , we can assume that @xmath362 and @xmath363 the sufficient conditions to prove lemma [ lemma : bernoulli_main ] are the following : 1 . for all @xmath332$],@xmath364 \leq \max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot { \boldsymbol{w}}(t).\ ] ] 2 . with probability @xmath365 , at least @xmath366 number of time instance @xmath367 $ ] satisfy @xmath368\leq { \boldsymbol{\sigma}}(t)\cdot{\boldsymbol{w}}(t).\label{eq : claimb}\ ] ] 3 . for all @xmath340 $ ] at which is satisfied , @xmath369 the proof of lemma [ lemma : bernoulli_main ] comes immediately from ( a ) , ( b ) and ( c ) as follows : @xmath370 & = & ( 1-\eta')^3\left[\max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot f({\boldsymbol{q}}(t))\right ] \\ & \leq & ( 1-\eta')^2\left[\max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot { \boldsymbol{w}}(t ) \right]\\ & \leq & ( 1-\eta ' ) \left({\boldsymbol{\sigma}}(t)\cdot{\boldsymbol{w}}(t)\right ) \\ & \leq & { \boldsymbol{\sigma}}(t)\cdot f({\boldsymbol{q}}(t)),\end{aligned}\ ] ] where with probability @xmath365 , at least @xmath366 number of time instance @xmath367 $ ] satisfy the second last and last inequalities . hence , we proceed toward proving ( a ) , ( b ) and ( c ) . * proof of ( a ) . * recall that our scheduling algorithm in section [ sec : algorithm_description ] maintains @xmath371 , where @xmath372 . thus , for @xmath15 and @xmath150 , we have @xmath373 and @xmath374 for large enough @xmath299 , combining above inequality with , we conclude that @xmath375}\\ & \leq & \left(1-\frac{2n}{f((1-c)q_{\max})}\right ) \left[\max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot f({\boldsymbol{q}}(t))\right]\\ & \leq & \max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot f({\boldsymbol{q}}(t))-2n\\ & \leq & \max_{{\boldsymbol{\rho}}\in s } { \boldsymbol{\rho}}\cdot { \boldsymbol{w}}(t),\end{aligned}\ ] ] where we use @xmath376 for @xmath332 $ ] from . * proof of ( b ) . * we first state the following key proposition for the proof of ( b ) . [ lem : assum1 ] suppose the assumption * a1 * holds . then , for any advice @xmath64 and @xmath377 , the following event occurs with probability @xmath378 : @xmath379 for @xmath75 , define a binary random variable @xmath380 such that @xmath381 if @xmath382 and @xmath383 otherwise . then , from the assumption * a1 * , @xmath384 < \delta$ ] and @xmath385 < \delta(l - h)$ ] . the conclusion of proposition [ lem : assum1 ] directly follows from the markov inequality applying to the random variable @xmath386 . from the above proposition , it follows that with probability @xmath378 , @xmath387 where from lemma [ lemma : stopping_time ] , we set @xmath388 due to @xmath389 . since @xmath58 changes at most @xmath0 times in @xmath302 $ ] from lemma [ lemma : stopping_time ] , one can use the union bound and conclude that with probability @xmath390 , @xmath391 for at least @xmath392 fraction of times in @xmath393 . furthermore , from , , and the definition of @xmath272 , we have @xmath394 thus , it follows that @xmath395 therefore , with probability @xmath365 , for at least @xmath396 fraction of times in the interval @xmath302 $ ] , holds . * proof of ( c ) . * from , we first have that @xmath397 for all @xmath340 $ ] at which is satisfied , @xmath398\\ & \leq & { \boldsymbol{\sigma}}(t)\cdot{\boldsymbol{w}}(t),\end{aligned}\ ] ] where we use , and @xmath399 . for large enough @xmath299 , combining the above inequality with leads to ( c ) : @xmath400 this completes the proof of lemma [ lemma : bernoulli_main ] . this section presents experimental results for the performance of our scheduling algorithm using various interactive oracle systems . we consider two network models : input - queued switch networks and wireless networks described in section [ sec : mcmc_wireless ] and section [ sec : bp ] , respectively . we compare the average queue - length in our scheduling algorithm using the mcmc , es and bp oracle systems with that of the mw algorithm @xcite . * input - queued switch network . * we first consider an input - queued switch network on @xmath401 complete bipartite graph topology in section [ sec : bp ] . we report the average queue lengths in the switch network for @xmath402 with load 90% , i.e. , arrival rates @xmath403 for all @xmath186 and any algorithm can not stabilize the queues if @xmath404 for all @xmath405 . we run the mw algorithm and our low - complexity scheduling algorithms using the mcmc , es , and bp oracle systems , where we consider the second bp oracle described in section [ sec : bp ] . here we use @xmath406 for es and bp oracles and @xmath407 for mcmc oracle . also , in bp oracle system , instead of using arbitrary schedule in @xmath21 when @xmath408 , we use a greedy algorithm with belief - weight to find a schedule , where belief at each @xmath202 is defined by @xmath409 : * find @xmath410 with maximum belief @xmath411 . * when @xmath412 are given , choose @xmath413 such that @xmath414 is a matching and @xmath415 is maximum among such @xmath416 . figure [ fig : switch_performance ] summarizes our experimental results and we observe that the performance of our scheduling algorithm using bp oracle system is as good as that of the mw algorithm , although it is much simpler to code and faster to run . grid topology.,title="fig:",width=288 ] grid topology.,title="fig:",width=288 ] * wireless networks in grid topology . * we also consider a wireless network with two dimensional grid interference topology . due to the high complexity of the mw algorithm , we chose the @xmath417 grid , i.e. , @xmath418 queues , where figure [ fig : wireless ] represents the @xmath419 grid . we again compare the evolution of the average queue lengths of the mw algorithm and our scheduling algorithms using es , mcmc and bp - es oracle systems . we note that we consider a minor variant of bp - es oracle so that it chooses a schedule greedily based on bp beliefs @xmath420 $ ] similarly as the second bp oracle in the input - queued switch network . we use the same weight functions as in the input - queued switch case and our experimental results are in figure [ fig : wireless_performance ] . we again observe that the performance of our scheduling algorithm using bp - es oracle system is as good as that of the mw algorithm , although it is much simpler to code and faster to run . the problem of dynamic resource allocation among network users contending resources has long been the subject of significant research for last four decades . in this paper , we develop a generic framework for designing resource allocation algorithms of low - complexity and high - performance via connecting iterative optimization and low - complexity scheduling . our work shows sufficient conditions on queue - length functions so that a queue - 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2312 , 2004 . g. cornuejols . valid inequalities for mixed integer linear programs . mathematical programming series b , 112:3 - 44 , 2008 . s. foss and t. konstantopoulos . an overview of some stochastic stability methods . _ journal of operations research , society of japan _ , 47(4 ) , 2004 . m. i. jordan . graphical models . _ statistical science _ , 19:140 - 155 , 2004 . m. bayati , d. shah , and m. sharma . max - product for maximum weight matching : convergence , correctness , and lp duality . _ ieee transactions on information theory _ , 54(3 ) : 1241 - 1251 , 2008 . s. sanghavi , d. malioutov , and a. s. willsky . linear programming analysis of loopy belief propagation for weighted matching . , 2007 . s. atalla , d. cuda , p. giaccone , m. pretti . belief - propagation assisted scheduling in input - queued switches . _ ieee 18th annual symposium on high performance interconnects ( hoti ) _ , 2010 d. shah . gossip algorithms . _ now publishers inc _ , 2009 . here , we provide the proofs of - for large enough @xmath166 . due to conditions * c2 * and * c5 * , @xmath421 which proves and . now , follows from the condition * c1 * and * c2 * : @xmath422 where we use the following property for concave function @xmath98 : @xmath423 finally , for , let @xmath424 and we observe that @xmath425 as @xmath426 due to the condition * c6*. this completes the proof of .[/INST] since tassiulas and ephremides proposed the maximum weight scheduling algorithm of throughput - optimality for constrained queueing networks in 1992 , extensive research efforts have been made for resolving its high complexity issue under various directions . in this paper , we resolve the issue by developing a generic framework for designing throughput - optimal and low - complexity scheduling algorithms . under the framework , an algorithm updates current schedules via an interaction with a given oracle system that can generate a solution of a certain discrete optimization problem in a finite number of interactive queries . therefore , one can design a variety of scheduling under this framework by choosing different oracles , e.g. , the exhaustive search ( es ) , the markov chain monte carlo ( mcmc ) , the belief propagation ( bp ) and the cutting - plane ( cp ) algorithms . the complexity of the resulting algorithm is decided by the number of operations required for an oracle processing a single query , which is typically very small . somewhat surprisingly , we prove that an algorithm using any such oracle is throughput - optimal for general constrained queueing network models that arise in the context of emerging large - scale communication networks . in particular , the ` pick - and - compare ' algorithms developed by tassiulas in 1998 and recently developed queue - based csma algorithms can be also understood as special cases of such algorithms using es and mcmc oracles , respectively . to our best knowledge , our result is the first that establishes a rigorous connection between iterative optimization methods and low - complexity scheduling algorithms , which we believe provides various future directions and new insights in both areas . </s>

the computational physics group@xcite at the zhongshan university is in a period of rapid development . the group s interests@xcite cover such topics as lattice study of hadron spectroscopy@xcite , glueball decay and mixing , qcd at finite density@xcite , quantum instontons@xcite and quantum chaos@xcite using the quantum action@xcite . most of these topics can be studied through monte carlo simulation , but can be quite costly in terms of computing power . in order to do large scale numerical investigations of these topics , we built a high performance parallel computer@xcite using pc components . qcd has been accepted to be the most successful gauge theory of strongly interacting particles . calculation of hadron spectroscopy remains to be an important task of non - perturbative studies of qcd using lattice methods . this paper is one of our first steps@xcite in the direction of studying hadron properties . our reasons for performing simulations with wilson valence quarks are twofold : first , we are interested in the analysis of hadronic spectroscopy for quenched wilson fermions ; second , we are interested in exploring the performance of our cluster in actual lattice qcd simulations . we decided to do a spectrum calculation on the @xmath4 lattice at @xmath8 and 5.85 , and on the @xmath9 and @xmath7 lattices at @xmath10 . the results at smaller @xmath5 values are used to compare with those in the literature , while those at a larger @xmath5 value , corresponding to smaller lattice spacing @xmath11 , are useful for extrapolating the lattice results to the continuum limit . the smearing technique is employed to improve the spectrum data . we hope our data will be an important addition to the lattice study of qcd spectrum . the remainder of this paper is organized as follows . in sect . [ sec2 ] , the basic ideas of lattice qcd with wilson quarks are given . in sect . [ sec3 ] , we describe the simulation parameters as well as some basic features of our cluster . in sect . [ sec4 ] , we present new calculation of some light hadron masses . finally , conclusions and outlook are given in sect . our starting point is the wilson action @xcite @xmath12 where @xmath3 , and @xmath13 is the ordered product of gauge link variables @xmath14 around an elementary plaquette . @xmath11 is the lattice spacing , @xmath15 is the unit vector and @xmath16 is the fermionic matrix : @xmath17.\end{aligned}\ ] ] the fermion field @xmath18 on the lattice is related to the continuum one @xmath19 by @xmath20 with @xmath21 . then all the physical quantities are calculable through monte carlo ( mc ) simulations with importance sampling . fermion fields must be integrated out before the simulations , leading to the vacuum expectation value for an operator @xmath22 @xmath23 \bar{f}([u ] ) e^{-s_{g}([u ] ) } \left ( \det m \right)^{n_f } \over \int [ du ] e^{-s_g([u])}\left ( \det m \right)^{n_f } } \approx { 1 \over n_{\rm config } } \sum_{\mathcal c } \bar{f}[{\mathcal c } ] . \end{aligned}\ ] ] here @xmath24 is the number of flavors , and @xmath25 is the corresponding operator after wick contraction of the fermion fields and the summation is over the gluonic configurations , @xmath26 , drawn from the boltzmann distribution . in quenched approximation , @xmath27 . the correlation functions of a hadron is : @xmath28 where @xmath29 is a hadron operator . for sufficiently large values of @xmath30 and the lattice time period @xmath31 , the correlation function is expected to approach the asymptotic form : @xmath32 . % \label{fit}\end{aligned}\ ] ] fitting the large @xmath30 behavior of the correlation function according to eq . ( [ fit ] ) , the hadron mass @xmath33 is obtained . the quenched gauge field configurations and quark propagators were obtained using the recently built zsu cluster@xcite . the full machine has 10 nodes , and each node consists of dual pentium cpus . the total internal memory is 1.28 gb and the sustained speed is around 2 gflops . an upgrade is planned . the cluster runs on the linux operating system . to operate the cluster as a parallel computer , the programmer must design the algorithm so that it appropriately divides the task among the individual processors . we use mpi ( message passing interface ) , one of the most popular message passing standards . we updated the pure su(3 ) gauge fields with cabibbo - marinari quasi - heat bath algorithm@xcite , each iteration followed by 4 over - relaxation sweeps . the simulation parameters are listed in tab . [ parameters ] . the distance between two nearest stored configurations is 100 . the auto - correlation time was computed to make sure that these configurations are independent . the @xmath34 quark and @xmath35 quark are assumed to be degenerate . the quark propagators are calculated in the coulomb gauge using the independent configurations mentioned above , and conjugate gradient for inversion of the dirac matrix with preconditioning via ilu decomposition by checkerboards@xcite . at @xmath10 , we computed the @xmath0 , @xmath1 and proton and @xmath2 masses on the @xmath6 and @xmath36 lattices at four values of hopping parameter : @xmath37 , 0.1486 , 0.1492 , and 0.1498 with point and smeared@xcite sources . in order to compare our results with those by milc and gf11 , the quenched simulations were also performed at @xmath38 and @xmath39 on the @xmath4 lattice . we repeated the quenched simulations of the milc and gf11 collaborations , using the same set of @xmath40 values @xcite but on a @xmath41 lattice . detailed data will be presented elsewhere @xcite . to extract masses from the hadron propagators , we must average the correlation function of the hadron over the ensemble of gauge configurations , and use a fitting routine to evaluate the hadron masses @xmath33 . we determined hadron masses by fitting our data under the assumption that there is a single particle in each channel @xcite . point source means a delta function , and smeared source means a spread - out distribution ( an approximation to the actual wave - function of the quantum state ) . for example , the simplest operator for a meson is just @xmath42 , i.e. the product of quark and anti - quark fields at a single point . a disadvantage of this point source , is that this operator creates not only the lightest meson , but all possible excited states too . to write down an operator which creates more of the single state , one must smear " the operator out , e.g. @xmath43 where @xmath44 is some smooth function . here we choose @xmath45 with @xmath46 a normalization factor . the size of the smeared operator should generally be comparable to the size of the hadron created . there is no automatic procedure @xcite for tuning the smearing parameter @xmath47 . one simply has to experiment with a couple of choices . the effective meson mass for @xmath0 and @xmath1 as a function of time @xmath30 at @xmath10 and on the @xmath7 lattice is depicted in figs . [ pion_6.25_36_48 ] and [ rho_6.25_36_48 ] respectively . as one sees , the plateau from which one can estimate the mass , is very narrow for point source , due to the reason mentioned above . when the smearing source is used , the width of the plateau changes with the smearing parameter @xmath47 . we tried many values of @xmath47 and found that when @xmath48 , the effective mass is almost independent on @xmath47 and the optimal value for @xmath47 is 26 , where we observe the widest plateau . the @xmath0 , @xmath1 , proton and @xmath2 masses @xcite at @xmath8 and on @xmath4 are consistent with the previous gf11 data @xcite and those for the mesons at @xmath49 and on @xmath4 are comparable with those in @xcite on the @xmath7 lattice . this means the finite size effects are very small . at @xmath49 , we also see that our results for the proton and @xmath2 masses@xcite are bigger than the milc data and consistent with the finite size behavior analysis in @xcite . more detailed results will be given in @xcite . in fig . [ edinburgh_5.7_5.85_6.25 ] , we show the edinburgh plot , ( @xmath50 ) vs. ( @xmath51 ) mass ratios . in figs . [ pion_kappa_6.25 ] , and [ rho_kappa_6.25 ] , we show respectively @xmath52 , @xmath53 , @xmath54 and @xmath55 as a function of @xmath56 at @xmath10 and on the @xmath36 lattice . assuming that @xmath52 is linear in @xmath57 , we can compute the critical coupling @xmath58 at which the pion becomes massless . we extrapolate the data using : @xmath59 the results for @xmath60 , and @xmath53 , @xmath61 and @xmath62 at @xmath60 on the @xmath9 and @xmath36 are given in tab.[tab2 ] , where the experimental value for the @xmath1 mass has been used as an input . the finite size effects are consistent with @xcite . also , the mass ratios @xmath63 and @xmath64 seem to be closer the experimental values , 1.222 and 1.604 on the larger lattice . to compare @xmath65 and @xmath66 with experiment , we need to do simulation on a larger lattice volume and carefully study the lattice spacing errors . in this aspect , it might be more efficient to use the improved action and some progress@xcite has been reported by some lattice groups in china . in this paper , we have presented new data on hadron masses in qcd with wilson valence quarks at @xmath10 on the @xmath67 and @xmath36 lattices . our results at @xmath8 are consistent and those at @xmath49 are comparable with the results in the literature . we have also made a more careful and systematic study of the smearing method . such large scale simulations had usually required supercomputing resources @xcite , but now they were all done on our recently built cluster for parallel computer . in the task of lattice qcd simulations , we are confident that zsu s pentium cluster can provide a very flexible and extremely economical computing solution , which fits the demands and budget of a developing lattice field theory group . we are going to use the machine to produce more useful results of non - perturbative physics . luo and e.b . gregory , hep - lat/0011028 . x.q . luo and q. chen , mod . lett . a*11 * ( 1996 ) 2435 . luo , q. chen , s. guo , x. fang , and j. liu , nucl . b(proc . suppl.)*53 * ( 1997 ) 243 . gregory , s. guo , h. kroger and x.q . luo , phys . rev . d*62 * ( 2000 ) 054508 . h. jirari , h. kroger , x.q . luo , k. moriarty , and s. rubin , phys . lett . a*281 * ( 2001 ) 1 . l. caron , h. jirari , h. kroger , x.q . luo , g. melkonyan , and k. moriarty , phys . lett . a*288 * ( 2001 ) 145 . h. jirari , h. kroger , x.q . luo , k. moriarty , and s. rubin , phys . * 86 * ( 2001 ) 187 . luo , e. gregory , h. xi , z. mei , j. yang , y. wang , and y. lin , hep - lat/0107017 . x.q . luo , e. gregory , h. xi , j. yang , y. wang , y. lin , and h. ying , nucl . suppl.)*106 * ( 2002 ) 1046 . wilson , phys . rev . * d10 * ( 1974 ) 2445 ; k.g.wilson , in new phenomena in sub - nuclear physics , erice lectures 1975 , a. zichichi , ed . ( plenum , new york , 1977 ) . n. cabibbo and e. marinari , phys . * b119 * ( 1982 ) 387 . t. degrand , comput . commum . * 52 * ( 1988 ) 161 . sesam - collaboration , nucl . b(proc . suppl.)*49 * ( 1996 ) 386 . bitar , et al , phys . d*46 * ( 1992 ) 2169 . c. bernard , et al . , ( milc collaboration ) , nucl . phys . b(proc . suppl.)*60a * ( 1998 ) 3 . f. bulter , h. chen , j. sexton , a. vacarrino , and d. weingarten , nucl . phys . b*430 * ( 1994 ) 179 . milc collaboration , http://physics.indiana.edu/@xmath68sg/milc.html

we present results for @xmath0 , @xmath1 and proton and @xmath2 masses from our recently built pentium cluster . the previous results for quenched wilson fermions by milc and gf11 collaborations are compared at @xmath3=5.7 and 5.85 with the same parameters on the @xmath4 lattice . new data are shown at @xmath5=6.25 on the @xmath6 and @xmath7 lattices . such a larger @xmath5 value is useful for extrapolating the lattice results to the continuum limit . the smearing technique is systematically investigated and shown to greatly improve the spectrum data . * keywords * : hadron spectrum , lattice qcd , monte carlo simulation on parallel computers * pacs : 11.15 ha , 12.38.gc , 02.70.lq *

<s>[INST]the computational physics group@xcite at the zhongshan university is in a period of rapid development . the group s interests@xcite cover such topics as lattice study of hadron spectroscopy@xcite , glueball decay and mixing , qcd at finite density@xcite , quantum instontons@xcite and quantum chaos@xcite using the quantum action@xcite . most of these topics can be studied through monte carlo simulation , but can be quite costly in terms of computing power . in order to do large scale numerical investigations of these topics , we built a high performance parallel computer@xcite using pc components . qcd has been accepted to be the most successful gauge theory of strongly interacting particles . calculation of hadron spectroscopy remains to be an important task of non - perturbative studies of qcd using lattice methods . this paper is one of our first steps@xcite in the direction of studying hadron properties . our reasons for performing simulations with wilson valence quarks are twofold : first , we are interested in the analysis of hadronic spectroscopy for quenched wilson fermions ; second , we are interested in exploring the performance of our cluster in actual lattice qcd simulations . we decided to do a spectrum calculation on the @xmath4 lattice at @xmath8 and 5.85 , and on the @xmath9 and @xmath7 lattices at @xmath10 . the results at smaller @xmath5 values are used to compare with those in the literature , while those at a larger @xmath5 value , corresponding to smaller lattice spacing @xmath11 , are useful for extrapolating the lattice results to the continuum limit . the smearing technique is employed to improve the spectrum data . we hope our data will be an important addition to the lattice study of qcd spectrum . the remainder of this paper is organized as follows . in sect . [ sec2 ] , the basic ideas of lattice qcd with wilson quarks are given . in sect . [ sec3 ] , we describe the simulation parameters as well as some basic features of our cluster . in sect . [ sec4 ] , we present new calculation of some light hadron masses . finally , conclusions and outlook are given in sect . our starting point is the wilson action @xcite @xmath12 where @xmath3 , and @xmath13 is the ordered product of gauge link variables @xmath14 around an elementary plaquette . @xmath11 is the lattice spacing , @xmath15 is the unit vector and @xmath16 is the fermionic matrix : @xmath17.\end{aligned}\ ] ] the fermion field @xmath18 on the lattice is related to the continuum one @xmath19 by @xmath20 with @xmath21 . then all the physical quantities are calculable through monte carlo ( mc ) simulations with importance sampling . fermion fields must be integrated out before the simulations , leading to the vacuum expectation value for an operator @xmath22 @xmath23 \bar{f}([u ] ) e^{-s_{g}([u ] ) } \left ( \det m \right)^{n_f } \over \int [ du ] e^{-s_g([u])}\left ( \det m \right)^{n_f } } \approx { 1 \over n_{\rm config } } \sum_{\mathcal c } \bar{f}[{\mathcal c } ] . \end{aligned}\ ] ] here @xmath24 is the number of flavors , and @xmath25 is the corresponding operator after wick contraction of the fermion fields and the summation is over the gluonic configurations , @xmath26 , drawn from the boltzmann distribution . in quenched approximation , @xmath27 . the correlation functions of a hadron is : @xmath28 where @xmath29 is a hadron operator . for sufficiently large values of @xmath30 and the lattice time period @xmath31 , the correlation function is expected to approach the asymptotic form : @xmath32 . % \label{fit}\end{aligned}\ ] ] fitting the large @xmath30 behavior of the correlation function according to eq . ( [ fit ] ) , the hadron mass @xmath33 is obtained . the quenched gauge field configurations and quark propagators were obtained using the recently built zsu cluster@xcite . the full machine has 10 nodes , and each node consists of dual pentium cpus . the total internal memory is 1.28 gb and the sustained speed is around 2 gflops . an upgrade is planned . the cluster runs on the linux operating system . to operate the cluster as a parallel computer , the programmer must design the algorithm so that it appropriately divides the task among the individual processors . we use mpi ( message passing interface ) , one of the most popular message passing standards . we updated the pure su(3 ) gauge fields with cabibbo - marinari quasi - heat bath algorithm@xcite , each iteration followed by 4 over - relaxation sweeps . the simulation parameters are listed in tab . [ parameters ] . the distance between two nearest stored configurations is 100 . the auto - correlation time was computed to make sure that these configurations are independent . the @xmath34 quark and @xmath35 quark are assumed to be degenerate . the quark propagators are calculated in the coulomb gauge using the independent configurations mentioned above , and conjugate gradient for inversion of the dirac matrix with preconditioning via ilu decomposition by checkerboards@xcite . at @xmath10 , we computed the @xmath0 , @xmath1 and proton and @xmath2 masses on the @xmath6 and @xmath36 lattices at four values of hopping parameter : @xmath37 , 0.1486 , 0.1492 , and 0.1498 with point and smeared@xcite sources . in order to compare our results with those by milc and gf11 , the quenched simulations were also performed at @xmath38 and @xmath39 on the @xmath4 lattice . we repeated the quenched simulations of the milc and gf11 collaborations , using the same set of @xmath40 values @xcite but on a @xmath41 lattice . detailed data will be presented elsewhere @xcite . to extract masses from the hadron propagators , we must average the correlation function of the hadron over the ensemble of gauge configurations , and use a fitting routine to evaluate the hadron masses @xmath33 . we determined hadron masses by fitting our data under the assumption that there is a single particle in each channel @xcite . point source means a delta function , and smeared source means a spread - out distribution ( an approximation to the actual wave - function of the quantum state ) . for example , the simplest operator for a meson is just @xmath42 , i.e. the product of quark and anti - quark fields at a single point . a disadvantage of this point source , is that this operator creates not only the lightest meson , but all possible excited states too . to write down an operator which creates more of the single state , one must smear " the operator out , e.g. @xmath43 where @xmath44 is some smooth function . here we choose @xmath45 with @xmath46 a normalization factor . the size of the smeared operator should generally be comparable to the size of the hadron created . there is no automatic procedure @xcite for tuning the smearing parameter @xmath47 . one simply has to experiment with a couple of choices . the effective meson mass for @xmath0 and @xmath1 as a function of time @xmath30 at @xmath10 and on the @xmath7 lattice is depicted in figs . [ pion_6.25_36_48 ] and [ rho_6.25_36_48 ] respectively . as one sees , the plateau from which one can estimate the mass , is very narrow for point source , due to the reason mentioned above . when the smearing source is used , the width of the plateau changes with the smearing parameter @xmath47 . we tried many values of @xmath47 and found that when @xmath48 , the effective mass is almost independent on @xmath47 and the optimal value for @xmath47 is 26 , where we observe the widest plateau . the @xmath0 , @xmath1 , proton and @xmath2 masses @xcite at @xmath8 and on @xmath4 are consistent with the previous gf11 data @xcite and those for the mesons at @xmath49 and on @xmath4 are comparable with those in @xcite on the @xmath7 lattice . this means the finite size effects are very small . at @xmath49 , we also see that our results for the proton and @xmath2 masses@xcite are bigger than the milc data and consistent with the finite size behavior analysis in @xcite . more detailed results will be given in @xcite . in fig . [ edinburgh_5.7_5.85_6.25 ] , we show the edinburgh plot , ( @xmath50 ) vs. ( @xmath51 ) mass ratios . in figs . [ pion_kappa_6.25 ] , and [ rho_kappa_6.25 ] , we show respectively @xmath52 , @xmath53 , @xmath54 and @xmath55 as a function of @xmath56 at @xmath10 and on the @xmath36 lattice . assuming that @xmath52 is linear in @xmath57 , we can compute the critical coupling @xmath58 at which the pion becomes massless . we extrapolate the data using : @xmath59 the results for @xmath60 , and @xmath53 , @xmath61 and @xmath62 at @xmath60 on the @xmath9 and @xmath36 are given in tab.[tab2 ] , where the experimental value for the @xmath1 mass has been used as an input . the finite size effects are consistent with @xcite . also , the mass ratios @xmath63 and @xmath64 seem to be closer the experimental values , 1.222 and 1.604 on the larger lattice . to compare @xmath65 and @xmath66 with experiment , we need to do simulation on a larger lattice volume and carefully study the lattice spacing errors . in this aspect , it might be more efficient to use the improved action and some progress@xcite has been reported by some lattice groups in china . in this paper , we have presented new data on hadron masses in qcd with wilson valence quarks at @xmath10 on the @xmath67 and @xmath36 lattices . our results at @xmath8 are consistent and those at @xmath49 are comparable with the results in the literature . we have also made a more careful and systematic study of the smearing method . such large scale simulations had usually required supercomputing resources @xcite , but now they were all done on our recently built cluster for parallel computer . in the task of lattice qcd simulations , we are confident that zsu s pentium cluster can provide a very flexible and extremely economical computing solution , which fits the demands and budget of a developing lattice field theory group . we are going to use the machine to produce more useful results of non - perturbative physics . luo and e.b . gregory , hep - lat/0011028 . x.q . luo and q. chen , mod . lett . a*11 * ( 1996 ) 2435 . luo , q. chen , s. guo , x. fang , and j. liu , nucl . b(proc . suppl.)*53 * ( 1997 ) 243 . gregory , s. guo , h. kroger and x.q . luo , phys . rev . d*62 * ( 2000 ) 054508 . h. jirari , h. kroger , x.q . luo , k. moriarty , and s. rubin , phys . lett . a*281 * ( 2001 ) 1 . l. caron , h. jirari , h. kroger , x.q . luo , g. melkonyan , and k. moriarty , phys . lett . a*288 * ( 2001 ) 145 . h. jirari , h. kroger , x.q . luo , k. moriarty , and s. rubin , phys . * 86 * ( 2001 ) 187 . luo , e. gregory , h. xi , z. mei , j. yang , y. wang , and y. lin , hep - lat/0107017 . x.q . luo , e. gregory , h. xi , j. yang , y. wang , y. lin , and h. ying , nucl . suppl.)*106 * ( 2002 ) 1046 . wilson , phys . rev . * d10 * ( 1974 ) 2445 ; k.g.wilson , in new phenomena in sub - nuclear physics , erice lectures 1975 , a. zichichi , ed . ( plenum , new york , 1977 ) . n. cabibbo and e. marinari , phys . * b119 * ( 1982 ) 387 . t. degrand , comput . commum . * 52 * ( 1988 ) 161 . sesam - collaboration , nucl . b(proc . suppl.)*49 * ( 1996 ) 386 . bitar , et al , phys . d*46 * ( 1992 ) 2169 . c. bernard , et al . , ( milc collaboration ) , nucl . phys . b(proc . suppl.)*60a * ( 1998 ) 3 . f. bulter , h. chen , j. sexton , a. vacarrino , and d. weingarten , nucl . phys . b*430 * ( 1994 ) 179 . milc collaboration , http://physics.indiana.edu/@xmath68sg/milc.html[/INST] we present results for @xmath0 , @xmath1 and proton and @xmath2 masses from our recently built pentium cluster . the previous results for quenched wilson fermions by milc and gf11 collaborations are compared at @xmath3=5.7 and 5.85 with the same parameters on the @xmath4 lattice . new data are shown at @xmath5=6.25 on the @xmath6 and @xmath7 lattices . such a larger @xmath5 value is useful for extrapolating the lattice results to the continuum limit . the smearing technique is systematically investigated and shown to greatly improve the spectrum data . * keywords * : hadron spectrum , lattice qcd , monte carlo simulation on parallel computers * pacs : 11.15 ha , 12.38.gc , 02.70.lq * </s>

SECTION 1. SHORT TITLE; TABLE OF CONTENTS. (a) Short Title.--This Act may be cited as the ``Alternative Energy Extender Act''. (b) Table of Contents.--The table of contents of this Act is as follows: Sec. 1. Short title; table of contents. TITLE I--ENERGY INFRASTRUCTURE TAX INCENTIVES Sec. 101. Extension of credit for electricity produced from certain renewable resources. Sec. 102. Extension and expansion of credit to holders of clean renewable energy bonds. Sec. 103. Extension and expansion of qualifying advanced coal project credit. Sec. 104. Extension and expansion of qualifying gasification project credit. TITLE II--DOMESTIC FOSSIL FUEL SECURITY Sec. 201. Extension of election to expense certain refineries. TITLE III--CONSERVATION AND ENERGY EFFICIENCY PROVISIONS Sec. 301. Extension of energy efficient commercial buildings deduction. Sec. 302. Extension of new energy efficient home credit. Sec. 303. Extension of residential energy efficient property credit. Sec. 304. Extension of credit for business installation of qualified fuel cells and stationary microturbine power plants. Sec. 305. Extension of business solar investment tax credit. TITLE IV--ALTERNATIVE FUELS AND VEHICLES INCENTIVES Sec. 401. Extension of excise tax provisions, income tax credits, and tariff duties. TITLE I--ENERGY INFRASTRUCTURE TAX INCENTIVES SEC. 101. EXTENSION OF CREDIT FOR ELECTRICITY PRODUCED FROM CERTAIN RENEWABLE RESOURCES. Section 45(d) of the Internal Revenue Code of 1986 (relating to qualified facilities) is amended by striking ``2008'' each place it appears and inserting ``2011''. SEC. 102. EXTENSION AND EXPANSION OF CREDIT TO HOLDERS OF CLEAN RENEWABLE ENERGY BONDS. (a) In General.--Section 54(m) of the Internal Revenue Code of 1986 (relating to termination) is amended by striking ``2007'' and inserting ``2010''. (b) Annual Volume Cap for Bonds Issued During Extension Period.-- Paragraph (1) of section 54(f) of the Internal Revenue Code of 1986 (relating to limitation on amount of bonds designated) is amended to read as follows: ``(1) National limitation.-- ``(A) Initial national limitation.--With respect to bonds issued after December 31, 2005, and before January 1, 2008, there is a national clean renewable energy bond limitation of $800,000,000. ``(B) Annual national limitation.--With respect to bonds issued after December 31, 2007, and before January 1, 2011, there is a national clean renewable energy bond limitation for each calendar year of $800,000,000.''. (c) Effective Date.--The amendments made by this section shall apply to bonds issued after the date of the enactment of this Act. SEC. 103. EXTENSION AND EXPANSION OF QUALIFYING ADVANCED COAL PROJECT CREDIT. (a) In General.--Section 48A(d)(3)(A) of the Internal Revenue Code of 1986 (relating to aggregate credits) is amended by striking ``$1,300,000,000'' and inserting ``$1,800,000,000''. (b) Authorization of Additional Integrated Gasification Combined Cycle Projects.--Subparagraph (B) of section 48A(d)(3) of te Internal Revenue Code of 1986 (relating to aggregate credits) is amended to read as follows: ``(B) Particular projects.--Of the dollar amount in subparagraph (A), the Secretary is authorized to certify-- ``(i) $800,000,000 for integrated gasification combined cycle projects the application for which is submitted during the period described in paragraph (2)(A)(i), ``(ii) $500,000,000 for projects which use other advanced coal-based generation technologies the application for which is submitted during the period described in paragraph (2)(A)(i), and ``(iii) $500,000,000 for integrated gasification combined cycle projects the application for which is submitted during the period described in paragraph (2)(A)(ii).''. (c) Application Period for Additional Projects.--Subparagraph (A) of section 48A(d)(2) of the Internal Revenue Code of 1986 (relating to certification) is amended to read as follows: ``(A) Application period.--Each applicant for certification under this paragraph shall submit an application meeting the requirements of subparagraph (B). An applicant may only submit an application-- ``(i) for an allocation from the dollar amount specified in clause (i) or (ii) of paragraph (3)(A) during the 3-year period beginning on the date the Secretary establishes the program under paragraph (1), and ``(ii) for an allocation from the dollar amount specified in paragraph (3)(A)(iii) during the 3-year period beginning at the termination of the period described in clause (i).''. (d) Effective Date.--The amendments made by this section shall take effect as if included in the amendments made by section 1307 of the Energy Policy Act of 2005. SEC. 104. EXTENSION AND EXPANSION OF QUALIFYING GASIFICATION PROJECT CREDIT. (a) In General.--Section 48B(d)(1) of the Internal Revenue Code of 1986 (relating to qualifying gasification project program) is amended by striking ``$350,000,000'' and inserting ``$850,000,000''. (b) Effective Date.--The amendment made by this section shall take effect as if included in the amendments made by section 1307 of the Energy Policy Act of 2005. TITLE II--DOMESTIC FOSSIL FUEL SECURITY SEC. 201. EXTENSION OF ELECTION TO EXPENSE CERTAIN REFINERIES. (a) In General.--Section 179C(c)(1) of the Internal Revenue Code of 1986 (defining qualified refinery property) is amended-- (1) by striking ``and before January 1, 2012'' in subparagraph (B) and inserting ``and, in the case of any qualified refinery described in subsection (d)(1), before January 1, 2012'', and (2) by inserting ``if described in subsection (d)(1)'' after ``of which'' in subparagraph (F)(i). (b) Conforming Amendment.--Subsection (d) of section 179C of the Internal Revenue Code of 1986 is amended to read as follows: ``(d) Qualified Refinery.--For purposes of this section, the term `qualified refinery' means any refinery located in the United States which is designed to serve the primary purpose of processing liquid fuel from-- ``(1) crude oil, or ``(2) qualified fuels (as defined in section 45K(c)).''. (c) Effective Date.--The amendments made by this section shall take effect as if included in the amendment made by section 1323(a) of the Energy Policy Act of 2005. TITLE III--CONSERVATION AND ENERGY EFFICIENCY PROVISIONS SEC. 301. EXTENSION OF ENERGY EFFICIENT COMMERCIAL BUILDINGS DEDUCTION. Section 179D(h) of the Internal Revenue Code of 1986 (relating to termination) is amended by striking ``2007'' and inserting ``2010''. SEC. 302. EXTENSION OF NEW ENERGY EFFICIENT HOME CREDIT. (a) In General.--Subsection (g) of section 45L of the Internal Revenue Code of 1986 (relating to new energy efficient home credit) is amended to read as follows: ``(g) Termination.--This section shall not apply to-- ``(1) any qualified new energy efficient home meeting the energy saving requirements of subsection (c)(1) acquired after December 31, 2010, and ``(2) any qualified new energy efficient home meeting the energy saving requirements of paragraph (2) or (3) of subsection (c) acquired after December 31, 2007.''. (b) Effective Date.--The amendment made by this section shall take effect as if included in the amendments made by section 1332 of the Energy Policy Act of 2005. SEC. 303. EXTENSION OF RESIDENTIAL ENERGY EFFICIENT PROPERTY CREDIT. Section 25D(g) of the Internal Revenue Code of 1986 (relating to termination) is amended by striking ``2007'' and inserting ``2010''. SEC. 304. EXTENSION OF CREDIT FOR BUSINESS INSTALLATION OF QUALIFIED FUEL CELLS AND STATIONARY MICROTURBINE POWER PLANTS. Sections 48(c)(1)(E) and 48(c)(2)(E) of the Internal Revenue Code of 1986 (relating to termination) are each amended by striking ``2007'' and inserting ``2010''. SEC. 305. EXTENSION OF BUSINESS SOLAR INVESTMENT TAX CREDIT. Sections 48(a)(2)(A)(i)(II) and 48(a)(3)(A)(ii) of the Internal Revenue Code of 1986 (relating to termination) are each amended by striking ``2008'' and inserting ``2011''. TITLE IV--ALTERNATIVE FUELS AND VEHICLES INCENTIVES SEC. 401. EXTENSION OF EXCISE TAX PROVISIONS, INCOME TAX CREDITS, AND TARIFF DUTIES. (a) Biodiesel.--Sections 40A(g), 6426(c)(6), and 6427(e)(5)(B) of the Internal Revenue Code of 1986 are each amended by striking ``2008'' and inserting ``2010''. (b) Alternative Fuel.-- (1) Fuels.--Sections 6426(d)(4) and 6427(e)(5)(C) of the Internal Revenue Code of 1986 are each amended by striking ``September 30, 2009'' and inserting ``December 31, 2010''. (2) Refueling property.--Section 30C(g) of such Code is amended by striking ``2009'' and inserting ``2010''. (c) Ethanol Tariff Schedule.--Headings 9901.00.50 and 9901.00.52 of the Harmonized Tariff Schedule of the United States (19 U.S.C. 3007) are each amended in the effective period column by striking ``10/1/ 2007'' each place it appears and inserting ``1/1/2011''. (d) Effective Date.--The amendments made by this section shall take effect on January 1, 2007.

Alternative Energy Extender Act - Amends the Internal Revenue Code to extend through 2010: (1) the tax credit for electricity produced from certain renewable resources; (2) the tax credit for holders of clean renewable energy bonds and the national volume cap for such bonds; (3) the tax deduction for energy efficient commercial buildings; (4) the tax credit for new energy efficient homes; (5) the tax credit for residential energy efficient property; (6) the tax credits for investment in qualified fuel cells, microturbine power plants, and solar energy property; and (7) the income and excise tax credits for biodiesel and alternative fuels and for alternative fuel vehicle refueling property. Increases the maximum tax credit amounts for the advanced coal and gasification project programs. Extends through 2012 the taxpayer election to expense certain crude oil refinery property. Amends the Harmonized Tariff Schedule of the United States to extend through 2010 the suspension of duties on mixtures of ethyl alcohol and ethyl tertiary-butyl ether.

<s>[INST]SECTION 1. SHORT TITLE; TABLE OF CONTENTS. (a) Short Title.--This Act may be cited as the ``Alternative Energy Extender Act''. (b) Table of Contents.--The table of contents of this Act is as follows: Sec. 1. Short title; table of contents. TITLE I--ENERGY INFRASTRUCTURE TAX INCENTIVES Sec. 101. Extension of credit for electricity produced from certain renewable resources. Sec. 102. Extension and expansion of credit to holders of clean renewable energy bonds. Sec. 103. Extension and expansion of qualifying advanced coal project credit. Sec. 104. Extension and expansion of qualifying gasification project credit. TITLE II--DOMESTIC FOSSIL FUEL SECURITY Sec. 201. Extension of election to expense certain refineries. TITLE III--CONSERVATION AND ENERGY EFFICIENCY PROVISIONS Sec. 301. Extension of energy efficient commercial buildings deduction. Sec. 302. Extension of new energy efficient home credit. Sec. 303. Extension of residential energy efficient property credit. Sec. 304. Extension of credit for business installation of qualified fuel cells and stationary microturbine power plants. Sec. 305. Extension of business solar investment tax credit. TITLE IV--ALTERNATIVE FUELS AND VEHICLES INCENTIVES Sec. 401. Extension of excise tax provisions, income tax credits, and tariff duties. TITLE I--ENERGY INFRASTRUCTURE TAX INCENTIVES SEC. 101. EXTENSION OF CREDIT FOR ELECTRICITY PRODUCED FROM CERTAIN RENEWABLE RESOURCES. Section 45(d) of the Internal Revenue Code of 1986 (relating to qualified facilities) is amended by striking ``2008'' each place it appears and inserting ``2011''. SEC. 102. EXTENSION AND EXPANSION OF CREDIT TO HOLDERS OF CLEAN RENEWABLE ENERGY BONDS. (a) In General.--Section 54(m) of the Internal Revenue Code of 1986 (relating to termination) is amended by striking ``2007'' and inserting ``2010''. (b) Annual Volume Cap for Bonds Issued During Extension Period.-- Paragraph (1) of section 54(f) of the Internal Revenue Code of 1986 (relating to limitation on amount of bonds designated) is amended to read as follows: ``(1) National limitation.-- ``(A) Initial national limitation.--With respect to bonds issued after December 31, 2005, and before January 1, 2008, there is a national clean renewable energy bond limitation of $800,000,000. ``(B) Annual national limitation.--With respect to bonds issued after December 31, 2007, and before January 1, 2011, there is a national clean renewable energy bond limitation for each calendar year of $800,000,000.''. (c) Effective Date.--The amendments made by this section shall apply to bonds issued after the date of the enactment of this Act. SEC. 103. EXTENSION AND EXPANSION OF QUALIFYING ADVANCED COAL PROJECT CREDIT. (a) In General.--Section 48A(d)(3)(A) of the Internal Revenue Code of 1986 (relating to aggregate credits) is amended by striking ``$1,300,000,000'' and inserting ``$1,800,000,000''. (b) Authorization of Additional Integrated Gasification Combined Cycle Projects.--Subparagraph (B) of section 48A(d)(3) of te Internal Revenue Code of 1986 (relating to aggregate credits) is amended to read as follows: ``(B) Particular projects.--Of the dollar amount in subparagraph (A), the Secretary is authorized to certify-- ``(i) $800,000,000 for integrated gasification combined cycle projects the application for which is submitted during the period described in paragraph (2)(A)(i), ``(ii) $500,000,000 for projects which use other advanced coal-based generation technologies the application for which is submitted during the period described in paragraph (2)(A)(i), and ``(iii) $500,000,000 for integrated gasification combined cycle projects the application for which is submitted during the period described in paragraph (2)(A)(ii).''. (c) Application Period for Additional Projects.--Subparagraph (A) of section 48A(d)(2) of the Internal Revenue Code of 1986 (relating to certification) is amended to read as follows: ``(A) Application period.--Each applicant for certification under this paragraph shall submit an application meeting the requirements of subparagraph (B). An applicant may only submit an application-- ``(i) for an allocation from the dollar amount specified in clause (i) or (ii) of paragraph (3)(A) during the 3-year period beginning on the date the Secretary establishes the program under paragraph (1), and ``(ii) for an allocation from the dollar amount specified in paragraph (3)(A)(iii) during the 3-year period beginning at the termination of the period described in clause (i).''. (d) Effective Date.--The amendments made by this section shall take effect as if included in the amendments made by section 1307 of the Energy Policy Act of 2005. SEC. 104. EXTENSION AND EXPANSION OF QUALIFYING GASIFICATION PROJECT CREDIT. (a) In General.--Section 48B(d)(1) of the Internal Revenue Code of 1986 (relating to qualifying gasification project program) is amended by striking ``$350,000,000'' and inserting ``$850,000,000''. (b) Effective Date.--The amendment made by this section shall take effect as if included in the amendments made by section 1307 of the Energy Policy Act of 2005. TITLE II--DOMESTIC FOSSIL FUEL SECURITY SEC. 201. EXTENSION OF ELECTION TO EXPENSE CERTAIN REFINERIES. (a) In General.--Section 179C(c)(1) of the Internal Revenue Code of 1986 (defining qualified refinery property) is amended-- (1) by striking ``and before January 1, 2012'' in subparagraph (B) and inserting ``and, in the case of any qualified refinery described in subsection (d)(1), before January 1, 2012'', and (2) by inserting ``if described in subsection (d)(1)'' after ``of which'' in subparagraph (F)(i). (b) Conforming Amendment.--Subsection (d) of section 179C of the Internal Revenue Code of 1986 is amended to read as follows: ``(d) Qualified Refinery.--For purposes of this section, the term `qualified refinery' means any refinery located in the United States which is designed to serve the primary purpose of processing liquid fuel from-- ``(1) crude oil, or ``(2) qualified fuels (as defined in section 45K(c)).''. (c) Effective Date.--The amendments made by this section shall take effect as if included in the amendment made by section 1323(a) of the Energy Policy Act of 2005. TITLE III--CONSERVATION AND ENERGY EFFICIENCY PROVISIONS SEC. 301. EXTENSION OF ENERGY EFFICIENT COMMERCIAL BUILDINGS DEDUCTION. Section 179D(h) of the Internal Revenue Code of 1986 (relating to termination) is amended by striking ``2007'' and inserting ``2010''. SEC. 302. EXTENSION OF NEW ENERGY EFFICIENT HOME CREDIT. (a) In General.--Subsection (g) of section 45L of the Internal Revenue Code of 1986 (relating to new energy efficient home credit) is amended to read as follows: ``(g) Termination.--This section shall not apply to-- ``(1) any qualified new energy efficient home meeting the energy saving requirements of subsection (c)(1) acquired after December 31, 2010, and ``(2) any qualified new energy efficient home meeting the energy saving requirements of paragraph (2) or (3) of subsection (c) acquired after December 31, 2007.''. (b) Effective Date.--The amendment made by this section shall take effect as if included in the amendments made by section 1332 of the Energy Policy Act of 2005. SEC. 303. EXTENSION OF RESIDENTIAL ENERGY EFFICIENT PROPERTY CREDIT. Section 25D(g) of the Internal Revenue Code of 1986 (relating to termination) is amended by striking ``2007'' and inserting ``2010''. SEC. 304. EXTENSION OF CREDIT FOR BUSINESS INSTALLATION OF QUALIFIED FUEL CELLS AND STATIONARY MICROTURBINE POWER PLANTS. Sections 48(c)(1)(E) and 48(c)(2)(E) of the Internal Revenue Code of 1986 (relating to termination) are each amended by striking ``2007'' and inserting ``2010''. SEC. 305. EXTENSION OF BUSINESS SOLAR INVESTMENT TAX CREDIT. Sections 48(a)(2)(A)(i)(II) and 48(a)(3)(A)(ii) of the Internal Revenue Code of 1986 (relating to termination) are each amended by striking ``2008'' and inserting ``2011''. TITLE IV--ALTERNATIVE FUELS AND VEHICLES INCENTIVES SEC. 401. EXTENSION OF EXCISE TAX PROVISIONS, INCOME TAX CREDITS, AND TARIFF DUTIES. (a) Biodiesel.--Sections 40A(g), 6426(c)(6), and 6427(e)(5)(B) of the Internal Revenue Code of 1986 are each amended by striking ``2008'' and inserting ``2010''. (b) Alternative Fuel.-- (1) Fuels.--Sections 6426(d)(4) and 6427(e)(5)(C) of the Internal Revenue Code of 1986 are each amended by striking ``September 30, 2009'' and inserting ``December 31, 2010''. (2) Refueling property.--Section 30C(g) of such Code is amended by striking ``2009'' and inserting ``2010''. (c) Ethanol Tariff Schedule.--Headings 9901.00.50 and 9901.00.52 of the Harmonized Tariff Schedule of the United States (19 U.S.C. 3007) are each amended in the effective period column by striking ``10/1/ 2007'' each place it appears and inserting ``1/1/2011''. (d) Effective Date.--The amendments made by this section shall take effect on January 1, 2007.[/INST]Alternative Energy Extender Act - Amends the Internal Revenue Code to extend through 2010: (1) the tax credit for electricity produced from certain renewable resources; (2) the tax credit for holders of clean renewable energy bonds and the national volume cap for such bonds; (3) the tax deduction for energy efficient commercial buildings; (4) the tax credit for new energy efficient homes; (5) the tax credit for residential energy efficient property; (6) the tax credits for investment in qualified fuel cells, microturbine power plants, and solar energy property; and (7) the income and excise tax credits for biodiesel and alternative fuels and for alternative fuel vehicle refueling property. Increases the maximum tax credit amounts for the advanced coal and gasification project programs. Extends through 2012 the taxpayer election to expense certain crude oil refinery property. Amends the Harmonized Tariff Schedule of the United States to extend through 2010 the suspension of duties on mixtures of ethyl alcohol and ethyl tertiary-butyl ether.</s>

the relation between the x - ray spectral / timing states of low - mass x - ray binaries ( lmxbs ) and their x - ray luminosity is puzzling . while on short time scales ( typically , hours ) x - ray spectral and timing parameters vary ( stochastically ) in a well - correlated fashion , on longer time scales ( typically , days ) the x - ray luminosity , particularly in the low - energy band ( @xmath0kev ) appears to vary largely independently from the other parameters . this is seen in the near - eddington neutron - star z sources ( e.g. , hasinger et al . 1990 , kuulkers et al . 1996 , wijnands et al . 1998 , jonker et al . 2000 ) as well as in the less luminous neutron - star atoll sources ( e.g. , van der klis et al . 1990 , ford et al . observations that could be interpreted in terms of a similar phenomenon in black - hole candidates ( e.g. , mndez and van der klis 1997 , rutledge et al . 1999 ) have recently been provided with solid empirical underpinnings by a study of the black - hole candidate xte j1550@xmath1564 ( homan et al . 2001 ) . in all these sources , timing properties , in particular the characteristic frequencies of qpo and noise components correlate much better to each other ( e.g. , ford and van der klis 1998 ) , and to measures of x - ray spectral shape such as position in the tracks lmxbs tend to trace out in an x - ray color - color diagram ( e.g. mndez and van der klis 1999 ) , x - ray colors ( mndez et al . 1999 ; particularly at higher energy ) , and sometimes parameters obtained from x - ray spectral fits ( kaaret et al . 1998 ) , than to luminosity ( see van der klis 2000 ) , although weak dependencies of timing and spectral properties on long - term luminosity variations are observed ( kuulkers et al . 1996 , wijnands et al . ( for example , spectral shape in the @xmath26kev band is usually somewhat affected by the longer time scale variations , spectral hardness in this band being positively correlated with flux ) . the time scale on which the correlated short - term variability takes place is hours to days in the z sources and in atoll sources in luminous states , but it is sometimes longer in black - hole candidates and in atoll sources in low - luminosity states . so , while on short time scales all properties including luminosity vary in a well - correlated fashion , on longer time scales x - ray luminosity is the odd one out in an otherwise still rather well - correlated set of spectral and timing parameters . when for a given source a plot is made of any spectral or timing parameter vs. x - ray flux , then , due to this phenomenon , the result tends to be a series of parallel tracks , each individual track reflecting the short - term correlated variations at a given epoch , and the offsets between the tracks resulting from the longer - term luminosity variations , combined with observational windowing . perhaps the most direct measurements of this parallel - track phenomenon have been made using the frequencies of the kilohertz quasi - periodic oscillations ( khz qpos ) in the z and atoll sources . for this reason , most of the remainder of this paper focuses on the parallel track phenomenon as seen in khz qpo sources ( fig.1 ) ; i return to the general case in [ sect : disc ] . kilohertz qpos are observed in the x - ray flux of some twenty z and atoll sources and are generally interpreted as being due to the motion of matter within a few stellar radii of the low - magnetic - field neutron star in these systems ( van der klis 2000 for a review ) . most models involve tight orbital motion of matter around the star at a preferred radius @xmath3 in the inner accretion disk , where @xmath4 km . because of this proximity of their site of origin to the compact object , khz qpos can potentially be used to constrain theories of strong gravity and dense matter . a discussion of the physics which might determine @xmath3 was given by miller et al . ( 1998 ) ( see also miller and lamb 1993 , 1996 ) . in their description , @xmath3 is the inner radius of the keplerian disk , which as long as it is larger than the innermost stable orbit from general relativity , is set by radiation drag on the orbiting matter . for a constant mass inflow , the radius @xmath3 increases when the x - ray flux impinging upon the inner edge of the disk increases ; for a constant radiation field , @xmath3 decreases when the amount of matter accreting in the disk increases . when both mass flow and radiation increase , it is not obvious what will be the effect on @xmath3 , but according to miller et al . ( 1998 ) if all radiation is due to accretion through the disk at a rate @xmath5 , then @xmath3 will decrease when the accretion rate increases . under certain simplifying assumptions , @xmath6 . other proposed khz qpo models involving the frequency of orbital motion ( e.g. , stella and vietri 1999 , titarchuk et al . 1999 , cui et al . 1998 , cui 2000 , campana 2000 , psaltis and norman 2000 ) either adopt the miller et al . ( 1998 ) mechanism , or rely on a magnetosphere to set the inner disk radius . the dependence of khz qpo frequency @xmath7 on x - ray flux @xmath8 shows the above - described parallel track pattern . whereas in a given source on short time scales ( less than several hrs ) a good correlation is observed between @xmath7 and @xmath8 , on longer time scales ( more than a day or so ) the correlation breaks down . on those longer time scales , different flux levels can correspond to approximately similar frequency ranges . observational windowing has so far prevented a careful study of what happens on intermediate time scales . in a frequency vs. flux plot of a series of observations of a given khz qpo source , each lasting several hours and separated by intervals of days or longer , a series of parallel tracks is observed , each track corresponding to the @xmath7 , @xmath8 relation of a single observation . these parallel tracks are perhaps most clearly seen in the transient atoll source 4u1608@xmath152 . in fig.1_a _ ; mndez et al . 1999 ) the parallel tracks are obvious ; they are steeply inclined , approximately straight lines . note how there seems to be a systematic trend in the steepness of these lines : at lower count rate they tend to be steeper . the range in flux over which in a given source identical frequencies are observed can be as large as a factor of 3 . note that there appears to be a tendency for the lines at the highest flux to cover a somewhat higher frequency range , and vv . a similar and perhaps related , but more extreme picture is presented by observations of different sources : the same range of qpo frequencies is observed in sources that differ in x - ray luminosity @xmath9 ( defined here as @xmath10 where @xmath11 is the distance ) by up to more than two orders of magnitude ( van der klis 1997 , ford et al . 2000 ) . in a plot of frequency vs. luminosity covering the ensemble of khz qpo sources this once again leads to a series of parallel tracks , each `` track '' now corresponding to a different source ( fig.1_b _ ; ford et al . 2000 ) . note , that these tracks are approximately parallel in a plot of frequency vs. the _ logarithm _ of @xmath9 , so the same trend of steeper lines at lower luminosity as observed in 4u1608@xmath152 clearly also applies across the ensemble of sources . ( in a semi - logarithmic version of the plot in fig.1_a _ , the lines are also more parallel ) . in both figures it is as if frequency depends not on @xmath9 , but on the percentage by which @xmath9 deviates from its average ( cf . van der klis 1999 ) . the question in both cases illustrated in fig.1 of course is : if at some epoch in some source frequency depends on luminosity according to some particular relation , then why at some other epoch or in some other source is there a very different frequency - luminosity relation , where very similar frequencies are attained at very different luminosities ? any explanation that succeeds in obtaining the _ same _ frequency at quite _ different _ luminosity would at first sight seem to defy itself , as it would at the same time remove the observed strong dependence of frequency on luminosity at any given epoch . as explained below , up to now the answer typically has been that at least two independently varying free parameters must characterize the problem . the phenomenology clearly suggests that a single quantity , variable on time scales of less than a few hours , dominates khz qpo frequency and most other spectral and timing parameters , but not the observed x - ray luminosity . usually , this parameter has been inferred to be the mass accretion rate @xmath5 , sometimes parametrized by the curve length @xmath12 measured along the track the source traces out on these time scales in the x - ray color - color diagram ( 1 ; hasinger and van der klis 1989 , van der klis 1995 for a review ) . a problem with this interpretation is that the x - ray luminosity , whose energy ultimately derives from this mass accretion , is on longer time scales not then well - correlated to inferred @xmath5 . another parameter , varying on time scales of more than a day or so , is therefore required to explain the slow luminosity variations that do not affect the khz qpo frequency , i.e. , the horizontal offset between the parallel lines in a given khz qpo source ( fig.1_a _ ) . slow variations in the accretion geometry leading to changes in x - ray beaming ( e.g. , van der klis 1995 ) or in the ratio between matter accreting in the disk and through some other channel such as a more radial inflow ( e.g. , wijnands et al . 1996 , kaaret et al . 1998 ) energy loss modes in unobservable spectral bands ( e.g. , van der klis et al . 1995 ) and mechanical energy in jets ( e.g. , mndez et al . 1999 ) , have all been suggested to provide this additional parameter , but in the absence of a specific mechanism to make these parameters vary independently from inferred @xmath5 , the true origin of the slow luminosity variations has been difficult to pin down ( see ford et al . 2000 for a discussion of these various possibilities ) . yet another parameter , different from source to source , is required in this picture to explain the parallel lines spanning two orders of magnitude in @xmath9 accross the ensemble of khz qpo sources ( fig.1_b _ ) . it has been proposed that this parameter is the neutron - star magnetic - field - strength , which should then be correlated to average source luminosity rather tightly ( white and zhang 1997 ) . systematic differences between sources with respect to one of the slowly varying parameters mentioned above could perhaps explain fig.1_b _ , but it has remained unclear which parameter could fulfill all requirements ( e.g. , ford et al . all proposals to date effectively require the existence of at least two independent time - variable parameters , and no compelling description was given of a mechanism that could make such a second time - variable parameter vary on its own accord independently of @xmath5 . it is the purpose of this paper to point out that the ensemble of observations described above can in fact be explained in terms of just a single time - variable independent parameter , varying on time scales of hours . this can be accomplished by exploiting the observed difference in time scale between correlated and uncorrelated behavior . the crucial requirement is that there exists both a prompt and a time - averaged component in the systemic response to the variations in the governing parameter . the basic class of scenarios that could accomplish this is outlined in 2 , and a specific proposal is made there , namely that the governing parameter is the mass accretion rate through the disk . in 3 it is quantitatively investigated to what extent such a model could explain the observational facts presented above . numerical simulations of the predicted luminosity , khz qpo frequency relation in a representative example of such a scenario are described there . in 4 i discuss the results , and the extent to which the scenario might be applicable to the parallel - track phenomena observed in neutron - star and black - hole low - mass x - ray binaries in general , as well as some of the the wider implications of the proposed explanation for the interpretation of states and tracks in lmxbs . if the khz qpo frequency @xmath7 depends on some parameter @xmath13 which varies on time scales of less than several hours , and the x - ray luminosity @xmath9 depends partly on @xmath13 and for another part on some running average of @xmath14 such as @xmath15 , where @xmath16 is a weight function with integral 1 that is non - zero on interval @xmath17 $ ] spanning between several hours and days , then this could explain the parallel tracks in a given khz qpo source . the correlation between @xmath7 and @xmath9 on time scales of hours would arise because both quantities depend on @xmath13 , the decorrelation on longer time scales because the slowly varying @xmath18 affects @xmath9 , but not @xmath7 . however , such a description would for plausible prescriptions for @xmath19 have trouble to explain that a similar range of frequencies is seen in 4u1608@xmath152 for fluxes different by a factor of 3 , and could certainly not explain that the same frequencies are observed over several orders of magnitude in luminosity across sources . for @xmath9 to be very different , @xmath14 , and hence @xmath7 would have to be very different , contrary to what is observed . also , in general the lines would not be parallel in @xmath7 vs. @xmath20 space . with an additional twist , such a scheme _ can _ explain both parallel - track phenomena . suppose , for example , that @xmath7 is proportional to @xmath21 , but @xmath9 is proportional to @xmath14 only . then , when @xmath14 increases , @xmath7 and @xmath9 immediately increase in correlation with it , but if @xmath14 remains the same for a while , then on a time scale of more than several hours @xmath7 would gradually drift to the value it has when @xmath22 . in such a picture a 100 times more luminous source can still show the same qpo frequency as its weaker kin because not only @xmath14 but also @xmath19 is approximately 100 times higher , so that @xmath23 is still approximately the same . note also that in such a scheme the same fractional variation in @xmath14 tends to cause a similar absolute change in @xmath7 , so that the lines are parallel in @xmath7 , @xmath20 space , as observed . several similar prescriptions for the dependence of @xmath7 and @xmath9 on @xmath14 and @xmath19 are possible that preserve the desirable qualities of this description . an attractive interpretation retaining the flavor of this basic idea that would work well within the framework of a model where the inner radius @xmath3 of the disk , and hence @xmath7 , is determined by some balance between accretion rate through the disk and radiative stresses ( 1.1 ) , would be one where @xmath7 depends on the ratio between instantaneous accretion rate through the disk @xmath24 varying on short time scales , and @xmath9 : @xmath25 and the luminosity has both an immediate response to @xmath26 and a filtered one : @xmath27 so , in this model @xmath13 is identified with the accretion rate @xmath28 through the disk , @xmath7 depends on @xmath29 , and @xmath9 on @xmath30 . note that @xmath31 where @xmath32 , so @xmath7 still only depends on the ratio @xmath33 as in the simpler prescription above . for this reason , the model retains the basic qualities of this simpler prescription . at epochs where @xmath34 , i.e. , @xmath35 too much radiation is produced for the amount of matter in the disk ( set by @xmath26 ) so @xmath3 is large and hence @xmath7 low , and vv . if @xmath26 remains the same for a while , then @xmath36 approaches @xmath26 , i.e. , @xmath37 , and @xmath3 and hence @xmath7 drift to their `` equilibrium '' value , no matter what the actual value of @xmath26 is . the lines tend to be parallel in @xmath7 , @xmath20 space as , depending only on the extent to which @xmath36 has converged to @xmath26 , the same fractional change in @xmath26 and hence @xmath9 tends to produce the same linear change in @xmath7 . note that no other independently time - varying parameter than @xmath26 is required now to explain the parallel - tracks phenomenon . the physical question is : what is the nature of the slowly varying component in the response of luminosity to accretion rate , the term @xmath38 ? physical implementations could be imagined using for example a mechanism for the storage and slow release of energy in the neutron star , such as through deposition and burning of nuclear fuel , energy storage in the crust or in the disk / star boundary ( inogamov and sunyaev 1999 , popham and sunyaev 2001 ) . another possibility would be energy storage in the neutron - star spin , with energy feeding back into the disk by magnetic or gravitational interaction ( cf . priedhorsky 1986 ) . alternatively , one could think of a mechanism where matter flowing in radially provides a second channel of accretion whose @xmath5 is derived from some running average over @xmath26 , for example because more matter in the disk leads to more matter blowing off it to feed the radial flow , or because disk and radial flow are both fed by the same external flow . note from these examples that the filtered response can technically be either causal ( e.g. , burning rate depends on amount of fuel accreted in the past ) , or acausal ( e.g. , matter blown from disk reaches neutron star before disk flow ) ; the response may even be symmetric . the basic feature of the model scenario discussed here is that more accretion through the disk produces more flux not only promptly , but also through some time - averaged response , and ( only ) when this filtered response is at the level it would have when the accretion were constant , do the effects on the qpo frequency cancel . for definiteness , assume the following description for the dependence of frequency on accretion rate and x - ray luminosity : @xmath39 where the luminosity is simply @xmath40 with @xmath41 the accretion mass - to - energy conversion efficiency , and where the radial accretion rate is related to the disk accretion rate via @xmath42 . so , in this description @xmath43 . frequency @xmath7 only depends on @xmath44 and @xmath9 on @xmath45 . the filtered response @xmath36 is given by an integral over the future disk accretion rate : @xmath46 results of numerical simulation of this description with a radial - to - disk accretion ratio @xmath47 of 1/3 , filter time scale @xmath48 and @xmath49 are shown in fig.[fig : simulation1608 ] , where a second - order red - noise signal ( random walk ) was used for @xmath24 , and 12 days of data were plotted in intervals of 8hrs separated by gaps of 16hrs to simulate typical observational windowing . note that these choices for @xmath50 and windowing time scales are illustrative ; the scenario will work for a variety of time scales . comparing fig.2 to fig.1_a _ , clearly the result of this simulation is rather similar to observation . not only do the parallel lines show up , also the steepening of the tracks towards lower luminosity is reproduced , as well as the tendency for lines at higher count rates to cover higher frequency ranges . as explained in 2 , the steepening effect is a consequence of the fact that frequency depends only on @xmath33 , so that same fractional change in @xmath26 tends to produce the same linear change in @xmath7 . the other effect arises because the highest count rates tend to be attained at the highest disk accretion rates @xmath26 . necessarily , these tend to be followed by intervals of lower @xmath26 , so that @xmath36 tends to be lower than @xmath26 at those epochs , i.e. , @xmath51 , which explains why relatively higher frequencies often occur there . at low count rates the opposite applies . fig.[fig : simulationallsources ] shows the result of the simulation of four sources differing in average @xmath26 but showing a similar fractional amplitude of @xmath26 variations . each source was simulated for 5 days , during which it varied randomly in luminosity by a factor of 2 . comparing fig.3 to fig.1_b _ , again the result of the simulation is similar to what is observed . in particular , the simulated tracks distributed over a factor @xmath52100 in @xmath9 , are approximately parallel in @xmath7 , @xmath20 space . very similar results were obtained from a simulation where the filtered response was representative of one due to nuclear burning of accreted material rather than of radial accretion . in that case , @xmath53 with @xmath54 and @xmath55 , respectively , the accretion and the nuclear burning mass - to - energy conversion efficiencies , typically 0.1 and 0.003 , and @xmath56 now given by a _ past _ integral over @xmath24 . however , in order for the observed steep dependencies of @xmath7 on @xmath9 to be reproduced in those simulations , a large value of @xmath57 between 10 and 15 had to be used . this is because of the small value of @xmath58 appropriate to that physical example . the work of miller and lamb ( 1993 , 1996 ) suggests that lower values of @xmath57 such as the value of 2 used in the first example are more appropriate . the velocity of a radial flow is expected to be much higher than the radial component of the motion of the matter accreting in the disk . this is expressed in eq.2b by making @xmath59 reflect the _ future _ evolution of @xmath26 . therefore , it might seem surprising that the variations in @xmath59 would be a low - pass filtered version of , i.e. , slower than , those in @xmath26 . however , note that the disk is expected to feed the radial flow over an annulus covering a range of radii . the density fluctuations in the disk would contribute to the radial flow for the full time they take to cross this feeding annulus , i.e. , for much longer than they take to cross the inner disk edge and accrete in the end . alternatively , the short - term fluctuations in @xmath26 could form at small radii in the disk , within the feeding annulus . in both cases @xmath59 would be a smoothed version of @xmath26 , which is all that is required to make the scenario work . the parallel tracks observed in khz qpo sources in plots of qpo frequency vs. logarithmic x - ray luminosity within a given source as well as across sources ( fig.[fig : parlines1608 ] ) can be explained in terms of just one time - variable independent parameter @xmath13 , provided that there is both a prompt ( @xmath2 hrs ) and a filtered ( @xmath60 a day ) systemic response to the time variations in this parameter . numerical simulations of a version of this scenario where qpo frequency depends on the balance between x - ray luminosity and accretion rate via the accretion disk , and luminosity depends on this accretion rate , both promptly and filtered by some averaging mechanism , show a remarkable similarity to what is actually observed . the basic prediction of this entire class of models is that it should be possible to reconstruct qpo frequency from the time variations of the governing parameter @xmath14 using a model involving some running average of @xmath14 . in the example simulated , @xmath14 is identified with the accretion rate through the disk @xmath26 and @xmath9 is @xmath61 , where @xmath36 is @xmath26 convolved with a response function with characteristic time scale @xmath50 , so that we are faced with a deconvolution problem which might in principle be solved using time series of simultaneous measurements of instantaneous @xmath9 and qpo frequency long enough to cover a sufficient number of correlation time scales @xmath50 , and dense enough to sample the short time scale variations well . perhaps this can be accomplished by combining rxte pca and asm observations , although pca observations extending over several weeks would be much preferable . for models of the general type expressed in eqs.1 , both the long - term and short - term variations in @xmath9 are caused by variations in @xmath26 ; the changes in khz qpo frequency and presumably in the other frequencies associated with the short - term @xmath9 variations arise from changes in the inner disk radius @xmath3 , which in turn are related to changes in the ratio @xmath32 between instantaneous and long - term average @xmath26 . note , that while the changes in x - ray spectral parameters and qpo amplitudes are also affected by changes in this ratio , this occurs not necessarily exclusively through the effect @xmath33 has on @xmath3 . for the example simulated , if both disk and radial accretion contribute to @xmath9 with a different spectral shape , then the spectrum would be more similar if the ratio of their rates is similar . if there are radiative - transfer effects of the radial flow on spectrum or qpo amplitudes , these would be stronger when the radial flow is denser ; i.e. , these effects depend on @xmath36 instead of on @xmath33 . so , in this scenario , the elusive time - variable parameter ( often dubbed `` inferred @xmath5 '' in the literature ) that to first order determines all qpo frequencies and a number of other timing and spectral parameters ( but not @xmath9 ) turns out to be @xmath33 , the disk accretion rate normalized by its own long - term average , rather than any straight accretion rate . curve length @xmath12 along the track of a source in the color - color diagram is in this picture a measure of @xmath33 . depending on the precise nature of the filtered response @xmath36 ( e.g. , nuclear burning or radial accretion ) , @xmath9 may or may not be a pure measure of the total accretion rate @xmath5 , but even if it is , as in the model expressed in eqs.2 , neither @xmath9 nor total @xmath5 are directly correlated with @xmath33 and hence with all the associated observable parameters . although the short - term variations in @xmath33 , @xmath3 and associated observable parameters such as @xmath12 and @xmath7 , as well as those in @xmath9 do indeed result directly from short - term variations in the disk accretion rate @xmath26 , the value of @xmath33 does not follow from the actual value of @xmath26 or @xmath9 , nor from that of any other instantaneous accretion rate such as total @xmath5 . this leads to several further predictions . two observations characterized by different @xmath9 but the same @xmath7 in this description find the source with a disk that has the same @xmath3 and hence @xmath33 , but different @xmath26 and @xmath36 . no strong decrease of qpo fractional amplitude with luminosity is predicted as would be the case if the luminosity variations would be dominated by an extra source of x - rays unrelated to the qpos this seems to be borne out by observations ( mndez et al . 2000 ) . which spectral variations are seen for luminosity variations along or across parallel lines depends on how variations in respectively @xmath33 and @xmath5 affect the spectrum . motion from one parallel track to the other in the @xmath9 , @xmath7 diagram could happen along any trajectory depending on the @xmath26 record and the precise nature of the filtered response , but no sudden jumps in the frequency - luminosity plane connecting branches far apart would be expected . note that _ each _ correlated quantity is predicted to depend to first order on @xmath33 ; two qpo frequencies , one depending on @xmath33 and another on @xmath26 would not in the long run remain well correlated to each other . the scenario discussed in this paper does not aim to explain the _ differences _ with respect to spectral / timing properties observed as a function of luminosity , which of course exist . clearly , even if the basic idea is correct that disk accretion rate normalized by its own long - term average , @xmath62 , to first order determines most of the phenomenology either because it sets inner disk radius @xmath3 or directly , it is not difficult to think of mechanisms that could explain subtle differences in phenomenology at similar @xmath3 as a function of modest changes in @xmath9 such as described by , e.g. , kuulkers et al . ( 1996 ) , and more obvious differences such as those between z and atoll sources for large @xmath9 differences ( hasinger and van der klis 1989 ) . it is beyond the scope of this paper to speculate on the precise nature of such mechanisms . finally , it is of interest to consider to what extent this type of scenario could be of relevance to black - hole candidates . in those sources , a similar type of correlation on short and decorrelation on longer time scales is sometimes observed between @xmath9 on the one hand and spectral hardness and timing parameters on the other ( 1 ) . in the black - hole candidate xte j1550@xmath1564 , parallel tracks are in fact observed in an @xmath9 vs. spectral hardness diagram , with similar hardness and qpo variations occurring along tracks in a hardness vs. count rate diagram at very different luminosity ( homan et al . 2001 , who also discuss the possibility that @xmath3 varies more or less independently from @xmath9 ) . perhaps a similar mechanism such as that explaining the similar phenomenology in the neutron star systems underlies this behavior , although matters are complicated by the absence of a solid surface allowing ( but not requiring ) matter to accrete without producing much radiation ( e.g. , esin , mcclintock and narayan 1997 ) , so that the radiative stresses determining @xmath3 are harder to predict from the accretion flows . reports of `` hysteresis '' in the flux from black - hole candidates ( miyamoto et al . 1995 , smith , heindl and swank 2001 ; these latter authors discuss their results in terms of two independent accretion flows ) , with a tendency towards hard spectra when the count rate rises and soft spectra when it falls , suggest that a disk plus radial flow pattern related by a filtered response as described here could play a role in these systems : if the count rate is dominated by the disk accretion rate , and spectral hardness is representative of inner disk radius then this is exactly what would be expected from the model described in 3 : for a long - term dropping count rate @xmath51 so @xmath3 is small and the spectrum soft , and vv . this means that parallel tracks could be produced in the way explained in this paper . different from the neutron stars , where there are usually no cross - tracks connecting the parallel tracks , the parallel tracks in xte j1550@xmath1564 are connected together in what was interpreted to be a comb - like pattern ( homan et al . 2001 ) . the very quiet , soft ( `` high '' ) state the source is in when it is on the connecting track ( the back of the comb ) may hence be unique to black holes , perhaps because it is associated to a flow mode where the matter that accretes radially flows into the hole without producing much radiation , so that the radiative stress on the inner edge of the disk flow is low and hence @xmath3 small and insensitive to small variations in the accretion flows . the parallel tracks ( the teeth of the comb ) on which the other black - hole states are observed ( `` very high '' , `` intermediate '' and `` low '' states ) , may correspond to a mode where , perhaps due to interaction with a jet , the radial flow does produce considerable radiation so that @xmath3 is larger and sensitively dependent on the accretion flows , as in neutron stars . this scenario would require the radial flow to produce considerable radiation with low angular momentum at radii smaller than @xmath3 ; it is unclear if there is a mechanism by which this could be accomplished . the scenario described in this paper can , for the first time , explain how it is possible that khz qpo frequency and several other timing and spectral parameters are the same in sources differing by more than two orders of magnitude in @xmath9 , and in a given source for @xmath9 levels different by a factor of several , even when those properties in any given source at any given instant do themselves strongly depend on @xmath9 . the proposed solution is that such properties to first order depend on @xmath33 , disk accretion rate normalized by its own long - term average . this at the same time removes the need for additional independent , slowly varying or fixed source - dependent parameters affecting the phenomenology , and provides a way in which most of the observed short - term variations can arise as a consequence of short - term accretion rate variations while preserving the expected strong dependence of luminosity on total accretion rate . the physical mechanism providing the long - term averaged response to the disk accretion rate variations required in this scenario can be the accretion of matter flowing off the disk vertically and accreting radially , in combination with a mechanism to make the inner disk radius dependent on the ratio of luminosity to disk accretion rate . the radiation produced by this radial accretion flow in the inner disk region is crucial in that case in determining much of the phenomenology . if in black holes , contrary to neutron stars , there is a mode for this radial flow to accrete while producing little radiation ( and another where it produces considerable radiation ) , then this additional option available to black holes might explain the more complicated phenomenology of those sources as compared to neutron stars . this work was supported in part by the netherlands organization for scientific research ( nwo ) . it is a pleasure to acknowledge stimulating discussion and useful comments by lars bildsten , mariano mndez and demetris psaltis . campana , s. , 2000 , apj 534 , l79 cui , w. , 2000 , apj 534 , l71 cui , w. , barret , d. , zhang , s.n . , chen , w. , boirin , l. , swank , j. , 1998 , apj 502 , l49 esin , a.a . , mcclintock , j.e . , narayan , r. , 1997 , apj 489 , 865 ford , e. , kaaret , p. , tavani , m. , barret , d. , bloser , p. , grindlay , j. , harmon , b.a . , paciesas , w.s . , zhang , s.n . , 1997 , apj 475 , l123 inogamov , n.a . , sunyaev , r.a . , 1999 , 25 , 269 ford , e.c . , van der klis , m. , 1998 , apj 506 , l39 hasinger , g. , van der klis , m. , 1989 , a&a 225 , 79 hasinger , g. , van der klis , m. , ebisawa , k. , dotani , t. , mitsuda , k. , 1990 , a&a 235 , 131 homan , j. , wijnands , r. , van der klis , m. , belloni , t. , van paradijs , j. , klein - wolt , m. , fender , r. , mndez , m. , 2001 , apjs 132 , 377 jonker , p.g . , van der klis , m. , wijnands , r. , homan , j. , van paradijs , j. , mndez , m. , ford , e.c . , kuulkers , e. , lamb , f.k . , 2000 , apj 537 , 374 kaaret , p. , yu , w. , ford , e.c . , zhang , s.n . , 1998 , apj 497 , l93 kuulkers , e. , van der klis , m. , vaughan , b.a . , 1996 , a&a 311 , 197 mndez , m. , van der klis , m. , ford , e.c . , wijnands , r. , van paradijs , j. , 1999 , apj 511 , l49 mndez , m. , van der klis , m. , 1999 , apj 517 , l51 mndez , m. , van der klis , m. , ford , e.c . , 2000 , apj submitted , astro - ph/0006245 miller , m.c . , lamb , f.k . , psaltis , d. , 1998 , apj 508 , 791 miller , m.c . , lamb , f.k . , 1993 , apj 413 , l43 miller , m.c . , lamb , f.k . , 1996 , apj 470 , 1033 miyamoto , s. , kitamoto , s. , hayashida , k. , egoshi , w. , 1995 , apj 442 , l13 popham , r. , sunyaev , r. , 2001 , apj 547 , 355 priedhorsky , w. , 1986 , apj 306 , l97 psaltis , d. , norman , c. , 2000 , apj , submitted ; 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an explanation is proposed for the observation that in low - mass x - ray binaries the correlation between most observable x - ray spectral and timing parameters on the one hand , and x - ray luminosity on the other , while generally good in a given source on a time scale of hours , is absent both on longer time scales and between sources . this phenomenon , particularly evident in khz qpo sources , leads to parallel tracks in plots of such parameters vs. luminosity . it is pointed out that where previously proposed explanations require at least two time - variable independent parameters , such as accretion rate through the disk and through a more radial inflow , just one independent variable is in fact sufficient , provided that the systemic response to time variations in this variable has both a prompt and a time - averaged component . a specific scenario is explored in which most observable spectral and timing parameters to first order depend on disk accretion rate normalized by its own long - term average rather than on any individual accretion rate ( luminosity , on the contrary , just depends on the total accretion rate ) . this provides a way in which parameters can be uncorrelated to accretion rate , yet vary in response to variations in accretion rate . numerical simulations are presented of such a model describing the relation between khz qpo frequency and x - ray luminosity , which observationally is characterized by a striking pattern of parallel tracks in the frequency vs. luminosity plane both in individual sources and across sources . the model turns out to reproduce the observations remarkably well . physical interpretations are suggested that would produce such a scenario ; particularly promising seems an interpretation involving a radial inflow with a rate that derives through a time - averaging process from the disk accretion rate , and an inner disk radius that depends on the balance between the accretion through the disk and the total luminosity . the consequences of this idea for our understanding of states and tracks in lmxbs are discussed , and the applicability of the idea to black - hole candidates , where the observational situation is more complex , is briefly addressed .

<s>[INST]the relation between the x - ray spectral / timing states of low - mass x - ray binaries ( lmxbs ) and their x - ray luminosity is puzzling . while on short time scales ( typically , hours ) x - ray spectral and timing parameters vary ( stochastically ) in a well - correlated fashion , on longer time scales ( typically , days ) the x - ray luminosity , particularly in the low - energy band ( @xmath0kev ) appears to vary largely independently from the other parameters . this is seen in the near - eddington neutron - star z sources ( e.g. , hasinger et al . 1990 , kuulkers et al . 1996 , wijnands et al . 1998 , jonker et al . 2000 ) as well as in the less luminous neutron - star atoll sources ( e.g. , van der klis et al . 1990 , ford et al . observations that could be interpreted in terms of a similar phenomenon in black - hole candidates ( e.g. , mndez and van der klis 1997 , rutledge et al . 1999 ) have recently been provided with solid empirical underpinnings by a study of the black - hole candidate xte j1550@xmath1564 ( homan et al . 2001 ) . in all these sources , timing properties , in particular the characteristic frequencies of qpo and noise components correlate much better to each other ( e.g. , ford and van der klis 1998 ) , and to measures of x - ray spectral shape such as position in the tracks lmxbs tend to trace out in an x - ray color - color diagram ( e.g. mndez and van der klis 1999 ) , x - ray colors ( mndez et al . 1999 ; particularly at higher energy ) , and sometimes parameters obtained from x - ray spectral fits ( kaaret et al . 1998 ) , than to luminosity ( see van der klis 2000 ) , although weak dependencies of timing and spectral properties on long - term luminosity variations are observed ( kuulkers et al . 1996 , wijnands et al . ( for example , spectral shape in the @xmath26kev band is usually somewhat affected by the longer time scale variations , spectral hardness in this band being positively correlated with flux ) . the time scale on which the correlated short - term variability takes place is hours to days in the z sources and in atoll sources in luminous states , but it is sometimes longer in black - hole candidates and in atoll sources in low - luminosity states . so , while on short time scales all properties including luminosity vary in a well - correlated fashion , on longer time scales x - ray luminosity is the odd one out in an otherwise still rather well - correlated set of spectral and timing parameters . when for a given source a plot is made of any spectral or timing parameter vs. x - ray flux , then , due to this phenomenon , the result tends to be a series of parallel tracks , each individual track reflecting the short - term correlated variations at a given epoch , and the offsets between the tracks resulting from the longer - term luminosity variations , combined with observational windowing . perhaps the most direct measurements of this parallel - track phenomenon have been made using the frequencies of the kilohertz quasi - periodic oscillations ( khz qpos ) in the z and atoll sources . for this reason , most of the remainder of this paper focuses on the parallel track phenomenon as seen in khz qpo sources ( fig.1 ) ; i return to the general case in [ sect : disc ] . kilohertz qpos are observed in the x - ray flux of some twenty z and atoll sources and are generally interpreted as being due to the motion of matter within a few stellar radii of the low - magnetic - field neutron star in these systems ( van der klis 2000 for a review ) . most models involve tight orbital motion of matter around the star at a preferred radius @xmath3 in the inner accretion disk , where @xmath4 km . because of this proximity of their site of origin to the compact object , khz qpos can potentially be used to constrain theories of strong gravity and dense matter . a discussion of the physics which might determine @xmath3 was given by miller et al . ( 1998 ) ( see also miller and lamb 1993 , 1996 ) . in their description , @xmath3 is the inner radius of the keplerian disk , which as long as it is larger than the innermost stable orbit from general relativity , is set by radiation drag on the orbiting matter . for a constant mass inflow , the radius @xmath3 increases when the x - ray flux impinging upon the inner edge of the disk increases ; for a constant radiation field , @xmath3 decreases when the amount of matter accreting in the disk increases . when both mass flow and radiation increase , it is not obvious what will be the effect on @xmath3 , but according to miller et al . ( 1998 ) if all radiation is due to accretion through the disk at a rate @xmath5 , then @xmath3 will decrease when the accretion rate increases . under certain simplifying assumptions , @xmath6 . other proposed khz qpo models involving the frequency of orbital motion ( e.g. , stella and vietri 1999 , titarchuk et al . 1999 , cui et al . 1998 , cui 2000 , campana 2000 , psaltis and norman 2000 ) either adopt the miller et al . ( 1998 ) mechanism , or rely on a magnetosphere to set the inner disk radius . the dependence of khz qpo frequency @xmath7 on x - ray flux @xmath8 shows the above - described parallel track pattern . whereas in a given source on short time scales ( less than several hrs ) a good correlation is observed between @xmath7 and @xmath8 , on longer time scales ( more than a day or so ) the correlation breaks down . on those longer time scales , different flux levels can correspond to approximately similar frequency ranges . observational windowing has so far prevented a careful study of what happens on intermediate time scales . in a frequency vs. flux plot of a series of observations of a given khz qpo source , each lasting several hours and separated by intervals of days or longer , a series of parallel tracks is observed , each track corresponding to the @xmath7 , @xmath8 relation of a single observation . these parallel tracks are perhaps most clearly seen in the transient atoll source 4u1608@xmath152 . in fig.1_a _ ; mndez et al . 1999 ) the parallel tracks are obvious ; they are steeply inclined , approximately straight lines . note how there seems to be a systematic trend in the steepness of these lines : at lower count rate they tend to be steeper . the range in flux over which in a given source identical frequencies are observed can be as large as a factor of 3 . note that there appears to be a tendency for the lines at the highest flux to cover a somewhat higher frequency range , and vv . a similar and perhaps related , but more extreme picture is presented by observations of different sources : the same range of qpo frequencies is observed in sources that differ in x - ray luminosity @xmath9 ( defined here as @xmath10 where @xmath11 is the distance ) by up to more than two orders of magnitude ( van der klis 1997 , ford et al . 2000 ) . in a plot of frequency vs. luminosity covering the ensemble of khz qpo sources this once again leads to a series of parallel tracks , each `` track '' now corresponding to a different source ( fig.1_b _ ; ford et al . 2000 ) . note , that these tracks are approximately parallel in a plot of frequency vs. the _ logarithm _ of @xmath9 , so the same trend of steeper lines at lower luminosity as observed in 4u1608@xmath152 clearly also applies across the ensemble of sources . ( in a semi - logarithmic version of the plot in fig.1_a _ , the lines are also more parallel ) . in both figures it is as if frequency depends not on @xmath9 , but on the percentage by which @xmath9 deviates from its average ( cf . van der klis 1999 ) . the question in both cases illustrated in fig.1 of course is : if at some epoch in some source frequency depends on luminosity according to some particular relation , then why at some other epoch or in some other source is there a very different frequency - luminosity relation , where very similar frequencies are attained at very different luminosities ? any explanation that succeeds in obtaining the _ same _ frequency at quite _ different _ luminosity would at first sight seem to defy itself , as it would at the same time remove the observed strong dependence of frequency on luminosity at any given epoch . as explained below , up to now the answer typically has been that at least two independently varying free parameters must characterize the problem . the phenomenology clearly suggests that a single quantity , variable on time scales of less than a few hours , dominates khz qpo frequency and most other spectral and timing parameters , but not the observed x - ray luminosity . usually , this parameter has been inferred to be the mass accretion rate @xmath5 , sometimes parametrized by the curve length @xmath12 measured along the track the source traces out on these time scales in the x - ray color - color diagram ( 1 ; hasinger and van der klis 1989 , van der klis 1995 for a review ) . a problem with this interpretation is that the x - ray luminosity , whose energy ultimately derives from this mass accretion , is on longer time scales not then well - correlated to inferred @xmath5 . another parameter , varying on time scales of more than a day or so , is therefore required to explain the slow luminosity variations that do not affect the khz qpo frequency , i.e. , the horizontal offset between the parallel lines in a given khz qpo source ( fig.1_a _ ) . slow variations in the accretion geometry leading to changes in x - ray beaming ( e.g. , van der klis 1995 ) or in the ratio between matter accreting in the disk and through some other channel such as a more radial inflow ( e.g. , wijnands et al . 1996 , kaaret et al . 1998 ) energy loss modes in unobservable spectral bands ( e.g. , van der klis et al . 1995 ) and mechanical energy in jets ( e.g. , mndez et al . 1999 ) , have all been suggested to provide this additional parameter , but in the absence of a specific mechanism to make these parameters vary independently from inferred @xmath5 , the true origin of the slow luminosity variations has been difficult to pin down ( see ford et al . 2000 for a discussion of these various possibilities ) . yet another parameter , different from source to source , is required in this picture to explain the parallel lines spanning two orders of magnitude in @xmath9 accross the ensemble of khz qpo sources ( fig.1_b _ ) . it has been proposed that this parameter is the neutron - star magnetic - field - strength , which should then be correlated to average source luminosity rather tightly ( white and zhang 1997 ) . systematic differences between sources with respect to one of the slowly varying parameters mentioned above could perhaps explain fig.1_b _ , but it has remained unclear which parameter could fulfill all requirements ( e.g. , ford et al . all proposals to date effectively require the existence of at least two independent time - variable parameters , and no compelling description was given of a mechanism that could make such a second time - variable parameter vary on its own accord independently of @xmath5 . it is the purpose of this paper to point out that the ensemble of observations described above can in fact be explained in terms of just a single time - variable independent parameter , varying on time scales of hours . this can be accomplished by exploiting the observed difference in time scale between correlated and uncorrelated behavior . the crucial requirement is that there exists both a prompt and a time - averaged component in the systemic response to the variations in the governing parameter . the basic class of scenarios that could accomplish this is outlined in 2 , and a specific proposal is made there , namely that the governing parameter is the mass accretion rate through the disk . in 3 it is quantitatively investigated to what extent such a model could explain the observational facts presented above . numerical simulations of the predicted luminosity , khz qpo frequency relation in a representative example of such a scenario are described there . in 4 i discuss the results , and the extent to which the scenario might be applicable to the parallel - track phenomena observed in neutron - star and black - hole low - mass x - ray binaries in general , as well as some of the the wider implications of the proposed explanation for the interpretation of states and tracks in lmxbs . if the khz qpo frequency @xmath7 depends on some parameter @xmath13 which varies on time scales of less than several hours , and the x - ray luminosity @xmath9 depends partly on @xmath13 and for another part on some running average of @xmath14 such as @xmath15 , where @xmath16 is a weight function with integral 1 that is non - zero on interval @xmath17 $ ] spanning between several hours and days , then this could explain the parallel tracks in a given khz qpo source . the correlation between @xmath7 and @xmath9 on time scales of hours would arise because both quantities depend on @xmath13 , the decorrelation on longer time scales because the slowly varying @xmath18 affects @xmath9 , but not @xmath7 . however , such a description would for plausible prescriptions for @xmath19 have trouble to explain that a similar range of frequencies is seen in 4u1608@xmath152 for fluxes different by a factor of 3 , and could certainly not explain that the same frequencies are observed over several orders of magnitude in luminosity across sources . for @xmath9 to be very different , @xmath14 , and hence @xmath7 would have to be very different , contrary to what is observed . also , in general the lines would not be parallel in @xmath7 vs. @xmath20 space . with an additional twist , such a scheme _ can _ explain both parallel - track phenomena . suppose , for example , that @xmath7 is proportional to @xmath21 , but @xmath9 is proportional to @xmath14 only . then , when @xmath14 increases , @xmath7 and @xmath9 immediately increase in correlation with it , but if @xmath14 remains the same for a while , then on a time scale of more than several hours @xmath7 would gradually drift to the value it has when @xmath22 . in such a picture a 100 times more luminous source can still show the same qpo frequency as its weaker kin because not only @xmath14 but also @xmath19 is approximately 100 times higher , so that @xmath23 is still approximately the same . note also that in such a scheme the same fractional variation in @xmath14 tends to cause a similar absolute change in @xmath7 , so that the lines are parallel in @xmath7 , @xmath20 space , as observed . several similar prescriptions for the dependence of @xmath7 and @xmath9 on @xmath14 and @xmath19 are possible that preserve the desirable qualities of this description . an attractive interpretation retaining the flavor of this basic idea that would work well within the framework of a model where the inner radius @xmath3 of the disk , and hence @xmath7 , is determined by some balance between accretion rate through the disk and radiative stresses ( 1.1 ) , would be one where @xmath7 depends on the ratio between instantaneous accretion rate through the disk @xmath24 varying on short time scales , and @xmath9 : @xmath25 and the luminosity has both an immediate response to @xmath26 and a filtered one : @xmath27 so , in this model @xmath13 is identified with the accretion rate @xmath28 through the disk , @xmath7 depends on @xmath29 , and @xmath9 on @xmath30 . note that @xmath31 where @xmath32 , so @xmath7 still only depends on the ratio @xmath33 as in the simpler prescription above . for this reason , the model retains the basic qualities of this simpler prescription . at epochs where @xmath34 , i.e. , @xmath35 too much radiation is produced for the amount of matter in the disk ( set by @xmath26 ) so @xmath3 is large and hence @xmath7 low , and vv . if @xmath26 remains the same for a while , then @xmath36 approaches @xmath26 , i.e. , @xmath37 , and @xmath3 and hence @xmath7 drift to their `` equilibrium '' value , no matter what the actual value of @xmath26 is . the lines tend to be parallel in @xmath7 , @xmath20 space as , depending only on the extent to which @xmath36 has converged to @xmath26 , the same fractional change in @xmath26 and hence @xmath9 tends to produce the same linear change in @xmath7 . note that no other independently time - varying parameter than @xmath26 is required now to explain the parallel - tracks phenomenon . the physical question is : what is the nature of the slowly varying component in the response of luminosity to accretion rate , the term @xmath38 ? physical implementations could be imagined using for example a mechanism for the storage and slow release of energy in the neutron star , such as through deposition and burning of nuclear fuel , energy storage in the crust or in the disk / star boundary ( inogamov and sunyaev 1999 , popham and sunyaev 2001 ) . another possibility would be energy storage in the neutron - star spin , with energy feeding back into the disk by magnetic or gravitational interaction ( cf . priedhorsky 1986 ) . alternatively , one could think of a mechanism where matter flowing in radially provides a second channel of accretion whose @xmath5 is derived from some running average over @xmath26 , for example because more matter in the disk leads to more matter blowing off it to feed the radial flow , or because disk and radial flow are both fed by the same external flow . note from these examples that the filtered response can technically be either causal ( e.g. , burning rate depends on amount of fuel accreted in the past ) , or acausal ( e.g. , matter blown from disk reaches neutron star before disk flow ) ; the response may even be symmetric . the basic feature of the model scenario discussed here is that more accretion through the disk produces more flux not only promptly , but also through some time - averaged response , and ( only ) when this filtered response is at the level it would have when the accretion were constant , do the effects on the qpo frequency cancel . for definiteness , assume the following description for the dependence of frequency on accretion rate and x - ray luminosity : @xmath39 where the luminosity is simply @xmath40 with @xmath41 the accretion mass - to - energy conversion efficiency , and where the radial accretion rate is related to the disk accretion rate via @xmath42 . so , in this description @xmath43 . frequency @xmath7 only depends on @xmath44 and @xmath9 on @xmath45 . the filtered response @xmath36 is given by an integral over the future disk accretion rate : @xmath46 results of numerical simulation of this description with a radial - to - disk accretion ratio @xmath47 of 1/3 , filter time scale @xmath48 and @xmath49 are shown in fig.[fig : simulation1608 ] , where a second - order red - noise signal ( random walk ) was used for @xmath24 , and 12 days of data were plotted in intervals of 8hrs separated by gaps of 16hrs to simulate typical observational windowing . note that these choices for @xmath50 and windowing time scales are illustrative ; the scenario will work for a variety of time scales . comparing fig.2 to fig.1_a _ , clearly the result of this simulation is rather similar to observation . not only do the parallel lines show up , also the steepening of the tracks towards lower luminosity is reproduced , as well as the tendency for lines at higher count rates to cover higher frequency ranges . as explained in 2 , the steepening effect is a consequence of the fact that frequency depends only on @xmath33 , so that same fractional change in @xmath26 tends to produce the same linear change in @xmath7 . the other effect arises because the highest count rates tend to be attained at the highest disk accretion rates @xmath26 . necessarily , these tend to be followed by intervals of lower @xmath26 , so that @xmath36 tends to be lower than @xmath26 at those epochs , i.e. , @xmath51 , which explains why relatively higher frequencies often occur there . at low count rates the opposite applies . fig.[fig : simulationallsources ] shows the result of the simulation of four sources differing in average @xmath26 but showing a similar fractional amplitude of @xmath26 variations . each source was simulated for 5 days , during which it varied randomly in luminosity by a factor of 2 . comparing fig.3 to fig.1_b _ , again the result of the simulation is similar to what is observed . in particular , the simulated tracks distributed over a factor @xmath52100 in @xmath9 , are approximately parallel in @xmath7 , @xmath20 space . very similar results were obtained from a simulation where the filtered response was representative of one due to nuclear burning of accreted material rather than of radial accretion . in that case , @xmath53 with @xmath54 and @xmath55 , respectively , the accretion and the nuclear burning mass - to - energy conversion efficiencies , typically 0.1 and 0.003 , and @xmath56 now given by a _ past _ integral over @xmath24 . however , in order for the observed steep dependencies of @xmath7 on @xmath9 to be reproduced in those simulations , a large value of @xmath57 between 10 and 15 had to be used . this is because of the small value of @xmath58 appropriate to that physical example . the work of miller and lamb ( 1993 , 1996 ) suggests that lower values of @xmath57 such as the value of 2 used in the first example are more appropriate . the velocity of a radial flow is expected to be much higher than the radial component of the motion of the matter accreting in the disk . this is expressed in eq.2b by making @xmath59 reflect the _ future _ evolution of @xmath26 . therefore , it might seem surprising that the variations in @xmath59 would be a low - pass filtered version of , i.e. , slower than , those in @xmath26 . however , note that the disk is expected to feed the radial flow over an annulus covering a range of radii . the density fluctuations in the disk would contribute to the radial flow for the full time they take to cross this feeding annulus , i.e. , for much longer than they take to cross the inner disk edge and accrete in the end . alternatively , the short - term fluctuations in @xmath26 could form at small radii in the disk , within the feeding annulus . in both cases @xmath59 would be a smoothed version of @xmath26 , which is all that is required to make the scenario work . the parallel tracks observed in khz qpo sources in plots of qpo frequency vs. logarithmic x - ray luminosity within a given source as well as across sources ( fig.[fig : parlines1608 ] ) can be explained in terms of just one time - variable independent parameter @xmath13 , provided that there is both a prompt ( @xmath2 hrs ) and a filtered ( @xmath60 a day ) systemic response to the time variations in this parameter . numerical simulations of a version of this scenario where qpo frequency depends on the balance between x - ray luminosity and accretion rate via the accretion disk , and luminosity depends on this accretion rate , both promptly and filtered by some averaging mechanism , show a remarkable similarity to what is actually observed . the basic prediction of this entire class of models is that it should be possible to reconstruct qpo frequency from the time variations of the governing parameter @xmath14 using a model involving some running average of @xmath14 . in the example simulated , @xmath14 is identified with the accretion rate through the disk @xmath26 and @xmath9 is @xmath61 , where @xmath36 is @xmath26 convolved with a response function with characteristic time scale @xmath50 , so that we are faced with a deconvolution problem which might in principle be solved using time series of simultaneous measurements of instantaneous @xmath9 and qpo frequency long enough to cover a sufficient number of correlation time scales @xmath50 , and dense enough to sample the short time scale variations well . perhaps this can be accomplished by combining rxte pca and asm observations , although pca observations extending over several weeks would be much preferable . for models of the general type expressed in eqs.1 , both the long - term and short - term variations in @xmath9 are caused by variations in @xmath26 ; the changes in khz qpo frequency and presumably in the other frequencies associated with the short - term @xmath9 variations arise from changes in the inner disk radius @xmath3 , which in turn are related to changes in the ratio @xmath32 between instantaneous and long - term average @xmath26 . note , that while the changes in x - ray spectral parameters and qpo amplitudes are also affected by changes in this ratio , this occurs not necessarily exclusively through the effect @xmath33 has on @xmath3 . for the example simulated , if both disk and radial accretion contribute to @xmath9 with a different spectral shape , then the spectrum would be more similar if the ratio of their rates is similar . if there are radiative - transfer effects of the radial flow on spectrum or qpo amplitudes , these would be stronger when the radial flow is denser ; i.e. , these effects depend on @xmath36 instead of on @xmath33 . so , in this scenario , the elusive time - variable parameter ( often dubbed `` inferred @xmath5 '' in the literature ) that to first order determines all qpo frequencies and a number of other timing and spectral parameters ( but not @xmath9 ) turns out to be @xmath33 , the disk accretion rate normalized by its own long - term average , rather than any straight accretion rate . curve length @xmath12 along the track of a source in the color - color diagram is in this picture a measure of @xmath33 . depending on the precise nature of the filtered response @xmath36 ( e.g. , nuclear burning or radial accretion ) , @xmath9 may or may not be a pure measure of the total accretion rate @xmath5 , but even if it is , as in the model expressed in eqs.2 , neither @xmath9 nor total @xmath5 are directly correlated with @xmath33 and hence with all the associated observable parameters . although the short - term variations in @xmath33 , @xmath3 and associated observable parameters such as @xmath12 and @xmath7 , as well as those in @xmath9 do indeed result directly from short - term variations in the disk accretion rate @xmath26 , the value of @xmath33 does not follow from the actual value of @xmath26 or @xmath9 , nor from that of any other instantaneous accretion rate such as total @xmath5 . this leads to several further predictions . two observations characterized by different @xmath9 but the same @xmath7 in this description find the source with a disk that has the same @xmath3 and hence @xmath33 , but different @xmath26 and @xmath36 . no strong decrease of qpo fractional amplitude with luminosity is predicted as would be the case if the luminosity variations would be dominated by an extra source of x - rays unrelated to the qpos this seems to be borne out by observations ( mndez et al . 2000 ) . which spectral variations are seen for luminosity variations along or across parallel lines depends on how variations in respectively @xmath33 and @xmath5 affect the spectrum . motion from one parallel track to the other in the @xmath9 , @xmath7 diagram could happen along any trajectory depending on the @xmath26 record and the precise nature of the filtered response , but no sudden jumps in the frequency - luminosity plane connecting branches far apart would be expected . note that _ each _ correlated quantity is predicted to depend to first order on @xmath33 ; two qpo frequencies , one depending on @xmath33 and another on @xmath26 would not in the long run remain well correlated to each other . the scenario discussed in this paper does not aim to explain the _ differences _ with respect to spectral / timing properties observed as a function of luminosity , which of course exist . clearly , even if the basic idea is correct that disk accretion rate normalized by its own long - term average , @xmath62 , to first order determines most of the phenomenology either because it sets inner disk radius @xmath3 or directly , it is not difficult to think of mechanisms that could explain subtle differences in phenomenology at similar @xmath3 as a function of modest changes in @xmath9 such as described by , e.g. , kuulkers et al . ( 1996 ) , and more obvious differences such as those between z and atoll sources for large @xmath9 differences ( hasinger and van der klis 1989 ) . it is beyond the scope of this paper to speculate on the precise nature of such mechanisms . finally , it is of interest to consider to what extent this type of scenario could be of relevance to black - hole candidates . in those sources , a similar type of correlation on short and decorrelation on longer time scales is sometimes observed between @xmath9 on the one hand and spectral hardness and timing parameters on the other ( 1 ) . in the black - hole candidate xte j1550@xmath1564 , parallel tracks are in fact observed in an @xmath9 vs. spectral hardness diagram , with similar hardness and qpo variations occurring along tracks in a hardness vs. count rate diagram at very different luminosity ( homan et al . 2001 , who also discuss the possibility that @xmath3 varies more or less independently from @xmath9 ) . perhaps a similar mechanism such as that explaining the similar phenomenology in the neutron star systems underlies this behavior , although matters are complicated by the absence of a solid surface allowing ( but not requiring ) matter to accrete without producing much radiation ( e.g. , esin , mcclintock and narayan 1997 ) , so that the radiative stresses determining @xmath3 are harder to predict from the accretion flows . reports of `` hysteresis '' in the flux from black - hole candidates ( miyamoto et al . 1995 , smith , heindl and swank 2001 ; these latter authors discuss their results in terms of two independent accretion flows ) , with a tendency towards hard spectra when the count rate rises and soft spectra when it falls , suggest that a disk plus radial flow pattern related by a filtered response as described here could play a role in these systems : if the count rate is dominated by the disk accretion rate , and spectral hardness is representative of inner disk radius then this is exactly what would be expected from the model described in 3 : for a long - term dropping count rate @xmath51 so @xmath3 is small and the spectrum soft , and vv . this means that parallel tracks could be produced in the way explained in this paper . different from the neutron stars , where there are usually no cross - tracks connecting the parallel tracks , the parallel tracks in xte j1550@xmath1564 are connected together in what was interpreted to be a comb - like pattern ( homan et al . 2001 ) . the very quiet , soft ( `` high '' ) state the source is in when it is on the connecting track ( the back of the comb ) may hence be unique to black holes , perhaps because it is associated to a flow mode where the matter that accretes radially flows into the hole without producing much radiation , so that the radiative stress on the inner edge of the disk flow is low and hence @xmath3 small and insensitive to small variations in the accretion flows . the parallel tracks ( the teeth of the comb ) on which the other black - hole states are observed ( `` very high '' , `` intermediate '' and `` low '' states ) , may correspond to a mode where , perhaps due to interaction with a jet , the radial flow does produce considerable radiation so that @xmath3 is larger and sensitively dependent on the accretion flows , as in neutron stars . this scenario would require the radial flow to produce considerable radiation with low angular momentum at radii smaller than @xmath3 ; it is unclear if there is a mechanism by which this could be accomplished . the scenario described in this paper can , for the first time , explain how it is possible that khz qpo frequency and several other timing and spectral parameters are the same in sources differing by more than two orders of magnitude in @xmath9 , and in a given source for @xmath9 levels different by a factor of several , even when those properties in any given source at any given instant do themselves strongly depend on @xmath9 . the proposed solution is that such properties to first order depend on @xmath33 , disk accretion rate normalized by its own long - term average . this at the same time removes the need for additional independent , slowly varying or fixed source - dependent parameters affecting the phenomenology , and provides a way in which most of the observed short - term variations can arise as a consequence of short - term accretion rate variations while preserving the expected strong dependence of luminosity on total accretion rate . the physical mechanism providing the long - term averaged response to the disk accretion rate variations required in this scenario can be the accretion of matter flowing off the disk vertically and accreting radially , in combination with a mechanism to make the inner disk radius dependent on the ratio of luminosity to disk accretion rate . the radiation produced by this radial accretion flow in the inner disk region is crucial in that case in determining much of the phenomenology . if in black holes , contrary to neutron stars , there is a mode for this radial flow to accrete while producing little radiation ( and another where it produces considerable radiation ) , then this additional option available to black holes might explain the more complicated phenomenology of those sources as compared to neutron stars . this work was supported in part by the netherlands organization for scientific research ( nwo ) . it is a pleasure to acknowledge stimulating discussion and useful comments by lars bildsten , mariano mndez and demetris psaltis . campana , s. , 2000 , apj 534 , l79 cui , w. , 2000 , apj 534 , l71 cui , w. , barret , d. , zhang , s.n . , chen , w. , boirin , l. , swank , j. , 1998 , apj 502 , l49 esin , a.a . , mcclintock , j.e . , narayan , r. , 1997 , apj 489 , 865 ford , e. , kaaret , p. , tavani , m. , barret , d. , bloser , p. , grindlay , j. , harmon , b.a . , paciesas , w.s . , zhang , s.n . , 1997 , apj 475 , l123 inogamov , n.a . , sunyaev , r.a . , 1999 , 25 , 269 ford , e.c . , van der klis , m. , 1998 , apj 506 , l39 hasinger , g. , van der klis , m. , 1989 , a&a 225 , 79 hasinger , g. , van der klis , m. , ebisawa , k. , dotani , t. , mitsuda , k. , 1990 , a&a 235 , 131 homan , j. , wijnands , r. , van der klis , m. , belloni , t. , van paradijs , j. , klein - wolt , m. , fender , r. , mndez , m. , 2001 , apjs 132 , 377 jonker , p.g . , van der klis , m. , wijnands , r. , homan , j. , van paradijs , j. , mndez , m. , ford , e.c . , kuulkers , e. , lamb , f.k . , 2000 , apj 537 , 374 kaaret , p. , yu , w. , ford , e.c . , zhang , s.n . , 1998 , apj 497 , l93 kuulkers , e. , van der klis , m. , vaughan , b.a . , 1996 , a&a 311 , 197 mndez , m. , van der klis , m. , ford , e.c . , wijnands , r. , van paradijs , j. , 1999 , apj 511 , l49 mndez , m. , van der klis , m. , 1999 , apj 517 , l51 mndez , m. , van der klis , m. , ford , e.c . , 2000 , apj submitted , astro - ph/0006245 miller , m.c . , lamb , f.k . , psaltis , d. , 1998 , apj 508 , 791 miller , m.c . , lamb , f.k . , 1993 , apj 413 , l43 miller , m.c . , lamb , f.k . , 1996 , apj 470 , 1033 miyamoto , s. , kitamoto , s. , hayashida , k. , egoshi , w. , 1995 , apj 442 , l13 popham , r. , sunyaev , r. , 2001 , apj 547 , 355 priedhorsky , w. , 1986 , apj 306 , l97 psaltis , d. , norman , c. , 2000 , apj , submitted ; 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( ed . ) , ( cambridge : cambridge univ . press ) 26 , 252 van der klis , m. , hasinger , g. , damen , e. , penninx , w. , van paradijs , j. , lewin , w.h.g . , 1990 , apj 360 , l19 van der klis , m. , 1997 , in astronomical time series , ed . d. maoz et al . ( dordrecht : kluwer ) 218 , 121 white , n.e . , zhang , w. , 1997 , 490 , l87 wijnands , r.a.d . , van der klis , m. , psaltis , d. , lamb , f.k . , kuulkers , e. , et al . , apj 469 wijnands , r. , van der klis , m. , kuulkers , e. , asai , k. , hasinger , g. , 1997 , a&a 323 , 399 wijnands , r. , mndez , m. , van der klis , m. , psaltis , d. , kuulkers , e. , lamb , f.k . , 1998 , apj 504 , l35[/INST] an explanation is proposed for the observation that in low - mass x - ray binaries the correlation between most observable x - ray spectral and timing parameters on the one hand , and x - ray luminosity on the other , while generally good in a given source on a time scale of hours , is absent both on longer time scales and between sources . this phenomenon , particularly evident in khz qpo sources , leads to parallel tracks in plots of such parameters vs. luminosity . it is pointed out that where previously proposed explanations require at least two time - variable independent parameters , such as accretion rate through the disk and through a more radial inflow , just one independent variable is in fact sufficient , provided that the systemic response to time variations in this variable has both a prompt and a time - averaged component . a specific scenario is explored in which most observable spectral and timing parameters to first order depend on disk accretion rate normalized by its own long - term average rather than on any individual accretion rate ( luminosity , on the contrary , just depends on the total accretion rate ) . this provides a way in which parameters can be uncorrelated to accretion rate , yet vary in response to variations in accretion rate . numerical simulations are presented of such a model describing the relation between khz qpo frequency and x - ray luminosity , which observationally is characterized by a striking pattern of parallel tracks in the frequency vs. luminosity plane both in individual sources and across sources . the model turns out to reproduce the observations remarkably well . physical interpretations are suggested that would produce such a scenario ; particularly promising seems an interpretation involving a radial inflow with a rate that derives through a time - averaging process from the disk accretion rate , and an inner disk radius that depends on the balance between the accretion through the disk and the total luminosity . the consequences of this idea for our understanding of states and tracks in lmxbs are discussed , and the applicability of the idea to black - hole candidates , where the observational situation is more complex , is briefly addressed . </s>

Brace yourself for a new Central Asian conflict involving powerful American forces, and count on this one to last a while. The combatants: 60 Minutes and Jon Krakauer, who have squared off against Greg Mortenson, the best-selling author of Three Cups of Tea and Stones Into Schools and the charismatic leader of the Central Asia Institute (CAI), the Bozeman, Montana-based nonprofit that raises millions to build schools in remote parts of Afghanistan and Pakistan. In a report that aired Sunday night April 17, 2011, on 60 Minutes, and in a separate investigative piece forthcoming from Krakauer, Mortenson is under heavy attack over everything from the veracity of his nonfiction memoirs—particularly a famous story in Three Cups of Tea recounting his first visit to Korphe, a mountain village in Pakistan—to the financial management of CAI. Assessing the possible damage, Time’s Nick Carbone wrote, “Looks like Mortenson’s writing has the potential to be shattered into a million little pieces.” Mortenson himself kept a low profile over the weekend, on the mend from a heart condition that has left him with chest pains and breathing difficulties. He spoke only to his local newspaper, The Bozeman Daily Chronicle, and to Outside. In an exclusive series of interviews with editorial director Alex Heard, Mortenson admitted to making mistakes both as a writer and nonprofit manager, but he made it clear that he intends to fight against the most serious allegations and can count on extensive support. Watch Outside’s Facebook page and Twitter feed (@outsidemagazine) for further updates. To see previous coverage of Greg Mortenson and CAI, check out Kevin Fedarko’s December 2008 profile, “No Bachcheh Left Behind,” and Mark Jenkins’s December 2001 column, “Seismic Shift.” Greg, the 60 Minutes segment claimed that there are major fabrications in Three Cups of Tea. Are there factual errors in the book, and if so, how did they get there? To answer that, it’s important to have some background. I started writing Three Cups of Tea in 2002, doing six chapters myself. I went to New York to four publishers and they all said the same thing: The story’s great but the writing sucks. [Laughs.] That fall, Kevin Fedarko came over to Pakistan to do a story for Outside about the Siachen Glacier war—we arranged all the logistics to get him to the front lines of the India-Pakistan war zone—and on the way out he came to Korphe with me, where he witnessed a scene in which a woman named Jahan came up, walked into a circle of elders I was sitting with, and said, “I’m ready to go to medical training. You promised me you’d help, so here’s my proposal.” After that trip, Kevin wrote a Parade magazine article about me in 2003, and the Siachen story and Parade put us on the map. Then Lee Kravitz, who was the editor of Parade, called me and said, I’ve got a book writer for you. This was David Oliver Relin, who co-authored Three Cups of Tea with me and has joint copyright. That’s where some of the issues are. It’s really complicated, but I’m not a journalist. I don’t take a lot of notes. David and I collaborated. He did nearly all the writing, and along with hundreds of interviews of those involved in the story, I helped him piece together the whole timeline, and from that we started creating the narrative arc and everything. David insisted on writing the book in third person, which is really awkward. The publisher said, Greg, you’re too understated, so this needs to be in the third person. My wife, Tara, also told me that if I wrote a book, it would be a pamphlet. What happens then is, when you re-create the scenes, you have my recollections, the different memories of those involved, you have his writing, and sometimes things come out different. In order to be convenient, there were some omissions. If we included everything I did from 1993 to 2003 it would take three books to write it. So there were some omissions and compressions, and ... I don’t know, what that’s called? Literary license? Yeah. So, rather than me going two or three times to one place, he would synthesize it into one trip. I would squawk about it and be told that it would all work out. This was my first book. I’m an introverted guy, running ragged for months on end, and in those days I was overseas all the time, and also trying to raise money. My regret—what I wish I would have done—is that I should have taken off several months and really focused on the book. But I was trying to raise a family, be gone most of the year, and work 16- to 20-hour days without stopping. ||||| You're Almost There... Your custom domain mapping may take as little as 15-30 minutes to resolve, but in some cases mapping a new custom domain can take up to 24 hours. If you need additional information about domain mapping, please visit our help center.

– Viking is launching a review of its bestseller Three Cups of Tea following reports that facts were fudged in the memoir and a multi-million-dollar charity that grew out of the book may largely be a fraud. Several facts in writer Greg Mortenson's book and the sequel, Stones Into Schools—including his account that he was kidnapped by the Taliban—have been challenged by a 60 Minutes investigation and journalist Jon Krakauer. The former treasurer for Mortenson's charity, Central Asia Institute, has also charged that more money was spent on promoting Mortenson and the charity than on its stated aim of building schools for girls in Pakistan and Afghanistan. Mortenson’s work "has provided tens of thousands of children with an education,” said a Viking spokeswoman. But "in the wake of" of the 60 Minutes report, Viking "plans to carefully review the materials with the author.” The statement is a clear sign that the publisher has serious concerns about the book's accuracy, reports the New York Times. Mortenson has said the 60 Minutes report was based on "inaccurate information" without going into specifics. In a new interview with Outside magazine, he admits the books compress various experiences into one, and blames some issues with his accounts on his co-author.

<s>[INST]Brace yourself for a new Central Asian conflict involving powerful American forces, and count on this one to last a while. The combatants: 60 Minutes and Jon Krakauer, who have squared off against Greg Mortenson, the best-selling author of Three Cups of Tea and Stones Into Schools and the charismatic leader of the Central Asia Institute (CAI), the Bozeman, Montana-based nonprofit that raises millions to build schools in remote parts of Afghanistan and Pakistan. In a report that aired Sunday night April 17, 2011, on 60 Minutes, and in a separate investigative piece forthcoming from Krakauer, Mortenson is under heavy attack over everything from the veracity of his nonfiction memoirs—particularly a famous story in Three Cups of Tea recounting his first visit to Korphe, a mountain village in Pakistan—to the financial management of CAI. Assessing the possible damage, Time’s Nick Carbone wrote, “Looks like Mortenson’s writing has the potential to be shattered into a million little pieces.” Mortenson himself kept a low profile over the weekend, on the mend from a heart condition that has left him with chest pains and breathing difficulties. He spoke only to his local newspaper, The Bozeman Daily Chronicle, and to Outside. In an exclusive series of interviews with editorial director Alex Heard, Mortenson admitted to making mistakes both as a writer and nonprofit manager, but he made it clear that he intends to fight against the most serious allegations and can count on extensive support. Watch Outside’s Facebook page and Twitter feed (@outsidemagazine) for further updates. To see previous coverage of Greg Mortenson and CAI, check out Kevin Fedarko’s December 2008 profile, “No Bachcheh Left Behind,” and Mark Jenkins’s December 2001 column, “Seismic Shift.” Greg, the 60 Minutes segment claimed that there are major fabrications in Three Cups of Tea. Are there factual errors in the book, and if so, how did they get there? To answer that, it’s important to have some background. I started writing Three Cups of Tea in 2002, doing six chapters myself. I went to New York to four publishers and they all said the same thing: The story’s great but the writing sucks. [Laughs.] That fall, Kevin Fedarko came over to Pakistan to do a story for Outside about the Siachen Glacier war—we arranged all the logistics to get him to the front lines of the India-Pakistan war zone—and on the way out he came to Korphe with me, where he witnessed a scene in which a woman named Jahan came up, walked into a circle of elders I was sitting with, and said, “I’m ready to go to medical training. You promised me you’d help, so here’s my proposal.” After that trip, Kevin wrote a Parade magazine article about me in 2003, and the Siachen story and Parade put us on the map. Then Lee Kravitz, who was the editor of Parade, called me and said, I’ve got a book writer for you. This was David Oliver Relin, who co-authored Three Cups of Tea with me and has joint copyright. That’s where some of the issues are. It’s really complicated, but I’m not a journalist. I don’t take a lot of notes. David and I collaborated. He did nearly all the writing, and along with hundreds of interviews of those involved in the story, I helped him piece together the whole timeline, and from that we started creating the narrative arc and everything. David insisted on writing the book in third person, which is really awkward. The publisher said, Greg, you’re too understated, so this needs to be in the third person. My wife, Tara, also told me that if I wrote a book, it would be a pamphlet. What happens then is, when you re-create the scenes, you have my recollections, the different memories of those involved, you have his writing, and sometimes things come out different. In order to be convenient, there were some omissions. If we included everything I did from 1993 to 2003 it would take three books to write it. So there were some omissions and compressions, and ... I don’t know, what that’s called? Literary license? Yeah. So, rather than me going two or three times to one place, he would synthesize it into one trip. I would squawk about it and be told that it would all work out. This was my first book. I’m an introverted guy, running ragged for months on end, and in those days I was overseas all the time, and also trying to raise money. My regret—what I wish I would have done—is that I should have taken off several months and really focused on the book. But I was trying to raise a family, be gone most of the year, and work 16- to 20-hour days without stopping. ||||| You're Almost There... Your custom domain mapping may take as little as 15-30 minutes to resolve, but in some cases mapping a new custom domain can take up to 24 hours. If you need additional information about domain mapping, please visit our help center.[/INST]– Viking is launching a review of its bestseller Three Cups of Tea following reports that facts were fudged in the memoir and a multi-million-dollar charity that grew out of the book may largely be a fraud. Several facts in writer Greg Mortenson's book and the sequel, Stones Into Schools—including his account that he was kidnapped by the Taliban—have been challenged by a 60 Minutes investigation and journalist Jon Krakauer. The former treasurer for Mortenson's charity, Central Asia Institute, has also charged that more money was spent on promoting Mortenson and the charity than on its stated aim of building schools for girls in Pakistan and Afghanistan. Mortenson’s work "has provided tens of thousands of children with an education,” said a Viking spokeswoman. But "in the wake of" of the 60 Minutes report, Viking "plans to carefully review the materials with the author.” The statement is a clear sign that the publisher has serious concerns about the book's accuracy, reports the New York Times. Mortenson has said the 60 Minutes report was based on "inaccurate information" without going into specifics. In a new interview with Outside magazine, he admits the books compress various experiences into one, and blames some issues with his accounts on his co-author.</s>

applying an electric gate voltage to graphene provides exotic tuning of the electronic , vibrational , and optical properties of graphene samples @xcite . since the beginning of graphene s discovery , electronic gating has played an important role in elucidating the room temperature quantum hall effect @xcite , the klein tunneling @xcite , and many body coupling effects @xcite . similar gating techniques are extensively applied not only to monolayer , but also to multilayer graphene to obtain tunable transport @xcite , a tunable band gap @xcite , p - n junctions @xcite , and photodetectors @xcite . all of these exciting phenomena could be observed due to the ability of tuning graphene s fermi energy @xmath0 through the applied gate voltage . a combination of electronic gating and inelastic scattering of light , known as the gate modulated raman spectroscopy @xcite , opens up a new possibility to understand more thouroughly the interplay of the electron , photon and phonon exitations in graphene . several phenomena have been probed by gate modulated raman spectroscopy in graphene , such as the kohn anomaly ( ka ) effect or the phonon frequency renormalization @xcite , the quantum interference effect @xcite , electron - electron interaction @xcite , and the fano resonance in the raman spectra of graphene @xcite . studying gate modulated raman spectroscopy in graphene has also enriched our knowledge of phonon spectra characterization @xcite , experimental evaluation of electron - phonon coupling @xcite , and various edge characterization effects @xcite . some theoretical works have been previously performed to understand the kohn anomaly ( ka ) effect for the first - order raman ( g band ) spectra with a raman shift of @xmath1@xmath2 in graphene , such as those by ando and the mauri s groups @xcite . in the ka process , phonon renormalization occurs through the excitation of an electron - hole pair by the electron - phonon interaction . as a result , the phonon energy is modified and the phonon lifetime becomes shorter . the previous theories mention that the phonon frequency shows a logarithmic singularity at @xmath3 k when the absolute value of the fermi energy @xmath0 matches half of the phonon energy @xmath4 . for @xmath5 , the frequency shift is linearly proportional to @xmath6 . these predictions were already confirmed by raman measurements @xcite . recently , additional experimental results allow us to study the ka effect in the second - order raman spectra , also . in contrast to the first - order raman spectra that consist of only a single @xmath7 value of the phonon momentum , the second - order raman spectra deals with the whole range of phonon momenta in the brillouin zone satisfying the double resonance raman condition @xcite . raman spectral features such as the @xmath8 or 2d band ( @xmath9 ) and the @xmath10 or @xmath11 band ( @xmath12 ) are observed as the second - order raman spectra for @xmath13 . the nonzero momentum phonon leads to a different ka effect compared with that for the @xmath7 phonon . araujo _ et al . _ and mafra _ et al . _ have shown that the frequency shift of the @xmath8 band as a function of @xmath0 is monotonically decreasing as a function of @xmath6 which is opposite to that of the g band @xcite . the other band at @xmath14 is , however , dispersionless as a function of @xmath0 . yan _ et al . _ show opposite results , that the @xmath8 band frequency as a function of @xmath0 has the same trends as that of the g band @xcite . further , das _ et al . _ show an asymmetric @xmath8 band dispersion , i.e. , a positive ( negative ) slope of frequency shift at negative ( positive ) @xmath0 , which is inconsistent with a symmetric dispersion shown experimentally by araujo _ et al . _ @xcite . based on the controversies in experimental results , we present calculated results of the second - order raman spectra as a function of @xmath0 from which we understand the origin of the controvertial results . sasaki et al , attempted to understand why the frequency shift of the @xmath8 band ka has an opposite slope when compared with that of the @xmath15 band from the viewpoint of the competition of interband and intraband electron - hole excitation in phonon perturbation @xcite . however , since the theory is done within the effective mass approximation , it is not sufficient to explain the asymmetry of the @xmath8 band frequency shift at positive and negative @xmath0 . moreover , since the raman intensity as a function of @xmath0 is not calculated , different dispersion of raman peaks as a function of @xmath0 can not be explained from that theory . observing the change of raman intensity as a function of @xmath0 reveals the quantum interference effect . when @xmath16 , some raman scattering paths are suppressed due to the pauli exclusion principle . even with the reduced number of scattering paths , the raman intensity surprisingly increases at a particular value of @xmath0 when constructive raman phases among various scattering paths are enhanced . chen _ et al . _ show that the g band raman intensity gives a maximum value when @xmath17 , where @xmath18 is the laser energy @xcite . however , the theoretical analysis in their work assumes a constant matrix element therefore neglecting the change of the raman phase due to the electron - phonon matrix elements . previous theoretical calculations show that the electron - phonon matrix elements change sign along electronic equi - energy lines in graphene and therefore can change the raman phase @xcite . a comprehensive calculation is , therefore , necessary to understand how the quantum interference effect affects the first- and the second - order raman intensity . in this work we calculate the @xmath0 dependece of the first - order and the second - order raman spectra . the calculated spectral quantities are the raman peak shift , spectral linewidth , and the raman intensity as a function of @xmath0 . the ka correction including both the phonon frequency shift and the linewidth is modeled based on second - order perturbation theory . the ka of the first - order raman spectra or of the @xmath7 phonon is calculated so as to reproduce the existing theoretical and experimental results and to compare with the ka of the @xmath19 phonon.we now focus on the intervalley scatterings which give three prominent peaks in the experimental spectra , namely , the @xmath8 , the @xmath10 , and the @xmath20 bands , and are relevant to @xmath13 . the @xmath18 dependence of those raman peak positions is compared with experimental results in order to justify the present calculation methods . finally the @xmath0 dependence of those three raman spectra are analized and compared to the experimental results . ( color online ) schematics of ( a ) the first- and ( b ) the second - order raman process . in ( b ) , ee means two consecutive electron - phonon interactions while eh means electron - phonon interaction followed by hole - phonon interaction.,width=302 ] the organization of this paper is as follows . section [ subsec : ramanintens ] shows the method for calculating the raman intensities for the first- and second - order raman spectra . section [ subsec : ka ] explains the method for numerically calculating the ka effect . section [ subsec : first ] presents the calculated results of the ka effect for the @xmath7 phonon and the @xmath0 dependence of the g band intensity . section [ subsec : second ] presents the calculation results of the ka effect for @xmath19 , and the @xmath18 and @xmath0 dependences of the second - order raman spectra . finally , the conclusion is given in sect . [ sec : conclusion ] . the first - order raman process as shown in fig.[fig1](a ) consists of ( 1 ) excitation of an electron - hole pair by the electron - photon interaction , ( 2 ) phonon emission by means of the electron - phonon interaction , and ( 3 ) electron - hole recombination and photoemission by the electron - photon interaction . based on the three subprocesses , the raman intensity formula for the first - order raman process is given by @xmath21 } { ( \elaser - e_\kvec^{\cond\val}-i\gamma ) ( \elaser - e_\kvec^{\cond\val}-\omega^\nu_0-i\gamma)}\right|^2 \nonumber\\ & \times\delta(\elaser-\omega^\nu_0-e_{\rm s } ) , \end{aligned}\ ] ] where @xmath18 is the laser excitation energy , @xmath22 is the scattered photon energy , @xmath23 is the electron energy difference between the conduction ( @xmath24 ) and the valence ( @xmath25 ) bands at a wave vector @xmath26 , @xmath27 is the carrier scattering rate due to the electron - phonon interaction @xcite , and @xmath28 is the fermi distribution function which depends on temperature . @xmath29 is the electron - photon matrix element acounting for the optical transition of an electron in a state @xmath26 from a valence band to a conduction band , @xmath30 is the carrier - phonon interaction considering an electron ( @xmath31 ) in a conduction band or a hole ( @xmath32 ) in a valence band making a transition from a state @xmath33 to a state @xmath34 by emitting a phonon with momentum @xmath35 , mode @xmath36 , and frequency @xmath37 . hereafter , @xmath38 is used , so that @xmath37 has units of energy . for the case of a one phonon process , only zero momentum or the @xmath39 point phonon is relevant . the summation over @xmath26 in eq . is taken to occur in a uniform square mesh , with a mesh spacing @xmath40 , and @xmath41 is the slope of the electron energy dispersion of graphene and @xmath42 is the weight of the integration . we set a cutoff energy @xmath43 for @xmath44 so as to reduce the number of mesh points in the brillouin zone integration . it is important to note that both the numerator and denominator of eq . are complex numbers , thus the summation of @xmath26 before taking the square plays an important role in the quantum interference effect @xcite . the electronic structure of graphene is calculated within an extended tight binding method considering up to 20 nearest neighbors and the four atomic orbitals ( @xmath45 , @xmath46 , @xmath47 , @xmath48 ) @xcite . calculation of the phonon dispersion relations is performed within a force constant model with the interatomic potential including up to 20 nearest neighbors which is fitted from a first - principles calculation @xcite . figure [ fig - phdisp](a ) shows the calculated results of the phonon dispersion relations ( solid lines ) and the corresponding experimental phonon dispersion relations ( red dots ) for comparison from refs . . because of the ka effect , the dispersion of the in - plane tangential optic ( ito ) branch near the @xmath49 point is discontinuous along the @xmath50 path which can not be reproduced by the force constant model @xcite . we fit the ito frequency from the experiment @xcite and use the following fitting formula for the raman spectra calculation [ fig . [ fig - phdisp](b ) ] : @xmath51 where @xmath52 is defined using polar coordinates @xmath53 whose center is at the k point and @xmath54 is measured from the km direction . eq . is valid only for @xmath55 , and when @xmath56 , we use the results from the force constant model for @xmath57 . ( color online ) ( a ) calculated ( solid lines , this work ) and experimental ( red dots , from refs . ) phonon dispersion relations . ( b ) fitting of eq . ( blue line ) to the ito branch from ref . ( dots ) near the k point.,width=302 ] in the electron - photon interaction , we adopt a dipole approximation , i.e. , assuming a slowly varying electric field in space because the laser wavelength is much greater than the inter - atomic distance @xcite . the electron - phonon interaction is calculated using the tight binding method with the deformation potential fitted from the gw method for the k and @xmath39 points @xcite . in the second - order raman processes , phonons with modes @xmath36 and @xmath58 and momenta @xmath52 and @xmath59 , respectively , are emitted [ fig . [ fig1](b ) ] . depending on the carriers taking part in the scattering event , the raman intensity formula is given by : @xmath60 where @xmath61 is a raman amplitude for each process : ( 1 ) an electron ( e ) , first , emits a @xmath36 phonon with momentum @xmath52 and , ( 2 ) a hole ( h ) emits the @xmath58 phonon with momentum @xmath59 . here , @xmath61 and @xmath62 are not equivalent to each other due to the different time order of the two phonon emission . next , we show examples of the raman amplitude formula for @xmath63 and @xmath61 : @xmath64 } { ( \elaser - e_\kvec^{\cond\val}-i\gamma ) ( \elaser - e_{\kvec+\qvec}^{\cond}+e_{\kvec}^{\val}-\omega^\nu_{-\qvec}-i\gamma ) ( \elaser - e_{\kvec}^{\cond\val}-\omega^\nu_{-\qvec}-\omega^\mu_{\qvec}-i\gamma)},\ ] ] @xmath65 } { ( \elaser - e_\kvec^{\cond\val}-i\gamma ) ( \elaser - e_{\kvec+\qvec}^{\cond}+e_{\kvec}^{\val}-\omega^\nu_{-\qvec}-i\gamma ) ( \elaser - e_{\kvec+\qvec}^{\cond\val}-\omega^\nu_{-\qvec}-\omega^\mu_{\qvec}-i\gamma)}.\ ] ] the minus sign in eq . corresponds to the opposite charge of the hole from the electron in the hole - phonon matrix elements @xcite . ( color online ) ( a ) a schematic of the @xmath66 kohn anomaly process . a phonon with zero wave vector ( @xmath66 ) and frequency @xmath67 vertically excites an electron - hole pair via the electron - phonon interaction . the electron - hole pair then recombines by emitting a phonon with frequency @xmath68 . ( b ) a schematic of the @xmath69 kohn anomaly process . an electron exists at the @xmath70 point leaving a hole behind at the @xmath49 point with a distance in reciprocal space of @xmath71 . if the @xmath70 point is then translated by a vector @xmath72 , we can then imagine a virtual vertical transition of electron and hole . when @xmath73 , both interband ( c ) and intraband ( d ) transitions are expected.,width=302 ] kohn mentions that conduction electrons are able to screen phonons in a metal @xcite . this screening leads to a phonon frequency change , given by : @xmath74 where @xmath75 is the unperturbed phonon energy from the phonon dispersion relation . here , @xmath76 is the correction term taken from the second - order perturbation of the electron - phonon interaction by the excitation and recombination of an electron - hole pair ( fig . [ fig2a ] ) : @xmath77 } { \omega^{(0),\nu}_{\qvec}-e_{\kvec+\qvec}^{s'}+e_\kvec^{s}+i\eta},\ ] ] where the prefactor @xmath78 in eq . accounts for the spin degeneracy , while the valley degeneracy is considered in the summation over @xmath26 . the value of @xmath76 is a complex number , in which @xmath79 [ @xmath80 gives the phonon frequency shift [ phonon linewidth ] . in eq . , the contribution of the interband ( intraband ) electron - hole pair appears at @xmath81 ( @xmath82 ) . in a conventional 2d electron gas , the ka effect occurs at @xmath83 , where @xmath84 is the fermi wave vector . in graphene , due to its unique linear energy bands , the ka occurs at @xmath85 and @xmath86 . the schematics of the ka process for @xmath87 and @xmath69 are shown in figs . [ fig2a](a ) and ( b ) , respectively . in the @xmath88 ka , a phonon with frequency @xmath67 vertically excites an electron - hole pair via the electron - phonon interaction [ fig . [ fig2a](a ) ] . the electron - hole pair then recombines by emitting a phonon with frequency @xmath68 . in the @xmath86 ka , an electron exists at the @xmath70 point , leaving a hole behind at the @xmath49 point with a distance in reciprocal space @xmath89 [ fig . [ fig2a](b ) ] . if the @xmath70 point is translated by a vector @xmath72 , we can imagine a virtually vertical excitation of an electron - hole pair . when @xmath73 , both the interband [ fig . [ fig2a](c ) ] and intraband [ fig . [ fig2a](d ) ] transitions are expected . ( color online ) the calculated ( dotted line ) and experimental ( open circles ) results for the g band peak shift ( a ) and the g band linewidth ( b ) as a function of the fermi energy , respectively , for @xmath90 k.,width=302 ] employing eq . at @xmath7 , we can obtain the frequency shift [ fig . [ fig2](a ) ] and phonon linewidth [ fig . [ fig2](b ) ] for the g band as a function of the fermi energy at @xmath91 @xmath49 . in fig . [ fig2 ] we show the calculated ( dotted line ) and experimental ( open circles ) results @xcite of the g band peak shift and linewidth as a function of the fermi energy , respectively . the calculated results are in good agreement with the experimental results . in fig . [ fig2](a ) , we see dips when @xmath92 for the calculation , while the experimental results do not show such dips . these dips are originated from the logarithmic singularities at @xmath3 @xmath49 and are related to interband resonances @xcite . for @xmath93 , the g band frequency increases linearly as a function of the fermi energy . at @xmath94 k , the phonon linewidth shows a step function @xmath95 . the step function indicates that when @xmath93 , the phonon linewidth from the ka effect becomes zero since no excited electron - hole pair meets the resonance condition of eq . . at finite @xmath96 , on the other hand , the fermi distribution function becomes a smooth function and that is why we get a smooth function of the linewidth as a function of @xmath0 . it is noted that we add an extrinsic broadening of @xmath97 in our calculations in order to fit with experimental results @xcite in fig . [ fig2](b ) . ( color online ) calculated results of the real and imaginary parts of the first - order ( a ) lo and ( b ) ito raman amplitudes in a two dimensional brillouin zone near the @xmath49 and @xmath70 points with @xmath98 ev.,width=302 ] next , we calculate the raman spectra of the g band using eq . . the g band consists of both the @xmath87 longitudinal optic ( lo ) and in - plane - tangential optic ( ito ) modes . in order to understand their contributions to the raman amplitudes at each @xmath26 point , we plot the real and imaginary parts of the raman amplitude in eq . for lo and ito phonons in fig . [ fig3](a ) and ( b ) , respectively . here we use @xmath98 ev and take @xmath99 so as to reduce the total points of integration for saving computational time . it will be clear that neglecting the contributions from energies above @xmath100 in the integration is reasonable since the raman intensity is quickly decreasing when @xmath101 . in fig . [ fig3 ] , deformed triangles near the @xmath49 and the @xmath70 points indicate equi - energy lines that match the resonant conditions . the lower ( higher ) resonant condition corresponds to the scattered ( incident ) resonance when @xmath102 ( @xmath103 ) which is shown by a large amplitude at the inner ( outer ) line . we see changes in the sign for both the real and imaginary parts of the lo and ito raman amplitudes in both the radial and azimuthal directions . the change of sign at the radial direction is related to an opposite phase between the scattered resonance and the incident resonance . meanwhile , the change of sign in the azimuthal direction is related to the sign of the electron - phonon matrix element as reported by jiang et al @xcite . the lo ( ito ) phonon has a zero matrix element at the 0 ( @xmath104 ) phase . ( color online ) ( a ) calculated results ( black dots ) and experimental results ( blue squares from ref . and red squares from ref . ) of the g band raman intensity as a function of the reduced fermi energy . ( b ) schematic diagram showing an opposite phase between the incident ( i ) and scattered ( s ) resonances . when @xmath105 , the scattered resonance is suppressed , and therefore , the raman intensity gives a maximum value.,width=302 ] the opposite phase of the scattered resonance to the incident resonance is essential insofar as both terms give destructive interference . therefore , only taking the resonant term for calculating the g band intensity is not sufficient . we need to at least consider up to @xmath106 to get a realistic intensity . moreover if we plot the raman intensity as a function of the fermi energy as shown in fig . [ fig4](a ) , it becomes clear that destructive interference between the scattered resonance and the incident resonance can be suppressed when we set the fermi energy close to the laser excitation energy . when @xmath105 , the scattered resonance can not occur due to the pauli blocking effect [ fig . [ fig4](b ) ] . therefore , in fig . [ fig4](a ) we see the largest g band intensity at @xmath105 as pointed out by chen _ et al _ @xcite . the difference of the intensity at positive and negative @xmath0 which comes from the electron - hole asymmetry has been confirmed by liu _ et al _ @xcite . anisotropy in the azimuthal direction should give destructive interference , but the effect is negligible . in fig . [ fig5 ] , we show the calculated results of the @xmath19 ka effect from eq . . first , let us consider the case of @xmath107 in figs . [ fig5](b ) and ( e ) . if we compare respectively figs . [ fig5](b ) and ( e ) with figs . [ fig2](a ) and ( b ) , both the frequency shift and phonon linewidth show the same trends as that of @xmath7 ka because both @xmath7 and @xmath107 are dominated by the interband electron - hole excitation . the reason why the interband excitation is dominant at @xmath108 , is that the @xmath49 and @xmath70 points coincide upon translation of the @xmath70 point by a vector @xmath109 [ @xmath110 in fig . [ fig2a](c ) ] . therefore , at the @xmath111 ka , only virtually vertical interband excitation , the same as at @xmath87 ka , is possible @xcite . the previous work did not consider the interband contribution , therefore assigning the @xmath107 phonon frequency shift to be dispersionless as a function of @xmath0 @xcite . next , if we shift by @xmath112 from @xmath108 , competition between the intraband and interband excitations take place as shown in figs . [ fig5](a ) , ( c ) , ( d ) , and ( f ) . according to the analytical formula @xcite , the intraband contribution to the frequency shift is proportional to @xmath113 by assuming @xmath114 , where @xmath115 is the slope of the linear energy dispersion of graphene which is @xmath116 . the phonon linewidth is increasing linearly with @xmath6 in the case of the intraband excitation [ figs . [ fig5](d ) and ( f ) ] because the electron - phonon scattering rate is proportional to the carrier concentration . the asymmetry at positive and negative @xmath0 is related to electron - hole band asymmetry considered in the tight binding calculation . after considering the ka effect on the @xmath117 phonon , in fig [ fig7 ] we show the calculated raman spectra from eq . . figure [ fig7](a ) shows three bands , respectively , assigned as the @xmath8 @xmath118 , @xmath10 @xmath119 , and @xmath20 @xmath120 for @xmath121 . we confirm the origin of the @xmath8 bands from the overtone of the ito ( 2ito ) modes while the @xmath10 bands come from a combination of ito and la modes . the major contributions to the @xmath8 intensity come from the @xmath122 and @xmath123 terms as shown by @xmath124 in fig . [ fig7](b ) . this confirms the previous calculation that the @xmath125 and @xmath126 terms are negligible [ @xmath127 in fig . [ fig7](b ) ] because of the quantum interference effect during the @xmath26 integration @xcite . figure [ fig7](c ) shows the second - order raman intensities for @xmath128 . the intensities of all these raman bands are inversely proportional to @xmath18 because of the increase of the electron - phonon scattering rate @xmath129 as a function of @xmath18 @xcite . assuming that each band can be represented by a single peak , the @xmath8 , @xmath10 , and @xmath20 peak dispersions as a function of @xmath18 are shown in fig . [ fig7](d ) . the @xmath8 band shows a positive slope as a function of @xmath0 , i.e. , @xmath130 in this work , @xmath131 in ref . , and @xmath132 in ref . . meanwhile the @xmath10 band shows a negative slope , i.e. , @xmath133 in this work and @xmath133 in ref . and the @xmath20 band slope is @xmath134 in this work , @xmath135 in ref . , and @xmath136 in ref . [ not shown in fig . [ fig7](d ) ] . good agreement between theory and experiment in the slope of the @xmath18 dispersion indicates the reliability of our phonon dispersion used in the calculation . however , discrepancies with the experiments of about @xmath137 in the @xmath8 and the @xmath20 bands for a given @xmath18 show that the calculated electronic energy dispersion underestimates the experimenal results . this can be seen insofar as the @xmath8 and @xmath20 peaks at @xmath138 in theory give relatively the same value for @xmath139 in the experiment , thus the present electronic energy dispersion near @xmath18 underestimate the real value by @xmath140 . this might be because we neglect the many body effects in the band calculations . nevertheless , the overal agreement is sufficient for us to proceed and consider the @xmath0 dependence of the raman intensity for a particular @xmath18 . figure [ fig8 ] shows the evolution of the second order raman spectra for several values of @xmath0 : @xmath141 ( black solid lines ) , @xmath142 ( red dashed lines ) , @xmath143 @xmath144 ( green dashed lines ) , @xmath145 @xmath146 ( blue dashed lines ) , @xmath147 @xmath148 ( violet dashed lines ) . we use the same @xmath149 as araujo _ et al _ . figures [ fig8](a ) and ( d ) show that the @xmath8 raman spectrum is redshifted , decreases its peak intensity [ indicated by a blue arrow in fig . [ fig8](d ) ] and broadens as @xmath0 increases . these results are consistent with the experiment @xcite . however , the raman intensity of the @xmath10 and @xmath20 bands dramatically increases especially when @xmath150 [ indicated by the blue arrows in figs . [ fig8](b ) and ( c ) ] . we find that the increase of the intensity comes from the quantum interference effect and not from the ka effect . although the ka effect broadens the second - order raman spectra at a finite @xmath0 , however the broadening order should not be @xmath151 . figures [ fig8](a ) , ( b ) , and ( c ) show that the spectra where combination of the phonon modes are located ( @xmath152 ) dramatically broadens like a continous spectrum . the broadening should come from the increased intensity of many different @xmath52 phonon modes that are suppressed at @xmath153 during integration on @xmath26 but now appears at @xmath154 thanks to the suppression of the destructive interference . these results give clues about how the raman phase governed by the electron - phonon matrix elements distinguishes between the @xmath0 dependence of the raman intensity of the combination modes from that of the overtone modes as is also observed in experiments @xcite . although @xmath155 is too high for experiments on graphene , one can reduce the @xmath18 to become @xmath156 to satisfy the condition of @xmath157 to get proper conditions for observing the quantum interference effect . the calculated raman spectra at @xmath158 and @xmath149 in fig . [ fig8](c ) and ( d ) clearly show that the @xmath10 and @xmath8 bands can not be fit by a single lorentian for each band . figure [ fig9](a ) shows the lorentzian fitting results on the second order raman spectra for @xmath153 . the dotted line is the calculated raman intensity fitted by six lorentzians . we fit the @xmath8 bands with two lorentzians labelled by @xmath159 ( blue ) and @xmath160 ( red ) which reffer to @xmath8 bands from outer ( @xmath52 in km direction ) and inner ( @xmath52 in @xmath161 direction ) scattering processes , respectively @xcite . three lorentzians are needed to fit the @xmath10 band , labelled by @xmath162 ( green ) , @xmath163 ( blue ) , and @xmath164 ( red ) . finally one lorentzian is used to fit the @xmath20 band . after lorentzian fitting , we compare both the peak shift and the spectral linewidth as a function of @xmath0 as shown in figs . [ fig9](b)-(e ) . we do not show the @xmath159 and @xmath162 for simplicity because there is no experimental data available for comparison . the calculated results in fig . [ fig9](b)-(e ) can not fit the experimental value of both the peak position and the linewidth due to the underestimation of the electronic energy dispersion as previously discussed in the @xmath18 dependence of the second - order raman spectra [ see fig . [ fig7](d ) ] . but we can discuss the change of both quantities as a function of @xmath0 , where the ka effect takes place . in figs . [ fig9](b)-(e ) , both the spectral peak position and the linewidth as a function of @xmath0 are plotted in the same range , comparing the theory and experiments . reasonable agreements between experiments and theory are achieved . the three major peaks , i.e. , the @xmath160 , @xmath164 , and @xmath20 bands show `` @xmath165 '' ( `` v '' ) shapes of the raman peak shift ( spectral linewidth ) as a function of @xmath0 . these behaviors exist because of the intraband electron - hole excitation renormalization of phonons as shown in fig . [ fig5 ] . the @xmath163 band in fig . [ fig9](d ) is relatively dispersionless in @xmath0 because it is located in the shoulder of the @xmath8 band where 2ito @xmath166 exists . therefore , for these bands , the competition between interband and intraband electron - hole excitations are expected . the calculated results overestimate the experimental spectral linewidths of all bands , which is related to the choice of @xmath167 in the @xmath26 integration . we can tackle this issue by reducing the value of @xmath168 by @xmath169 ; however , the computational burden becomes @xmath170 times larger . in conclusion , we calculated the first- and second - order raman spectra as a function of @xmath0 . the opposite effect of the kohn anomaly that is found experimentally between the first- and the second - order raman spectra occurs because the ka effect on the first - order raman spectra is dominated by the renormalization of phonons by the interband electron - hole excitation , while in the second - order raman spectra , the intraband electron - hole excitation dominates over the ka effect . we also discussed the quantum interference effect observed in the change of the raman intensity as a function of @xmath0 . both the first- and the second - order raman spectra exhibit an impact of the quantum interference effect , especially when @xmath171 . present calculated results found that not only is the resonance condition important , but also the explicit consideration of the electron - phonon matrix elements are essential to determine the @xmath0 dependence of the raman spectral lineshape . e.h . is supported by a mext scholarship . acknowledges the interdepartmental doctoral degree program for material science leaders at tohoku university for providing a financial support . r.s . acknowledges mext grants no . 25286005 and no . m.s.d . acknowledges nsf - dmr grant no . 15 - 07806 .

intensity of the first- and the second - order raman spectra are calculated as a function of the fermi energy . we show that the kohn anomaly effect , i.e. , phonon frequency renormalization , in the first - order raman spectra originates from the phonon renormalization by the interband electron - hole excitation , whereas in the second - order raman spectra , a competition between the interband and intraband electron - hole excitations takes place . by this calculation , we confirm the presence of different dispersive behaviors of the raman peak frequency as a function of the fermi energy for the first- and the second - order raman spectra , as observed in experiments . moreover , the calculated results of the raman intensity sensitively depend on the fermi energy for both the first- and the second - order raman spectra . these results thus also show the importance of quantum interference effect phenomena .

<s>[INST]applying an electric gate voltage to graphene provides exotic tuning of the electronic , vibrational , and optical properties of graphene samples @xcite . since the beginning of graphene s discovery , electronic gating has played an important role in elucidating the room temperature quantum hall effect @xcite , the klein tunneling @xcite , and many body coupling effects @xcite . similar gating techniques are extensively applied not only to monolayer , but also to multilayer graphene to obtain tunable transport @xcite , a tunable band gap @xcite , p - n junctions @xcite , and photodetectors @xcite . all of these exciting phenomena could be observed due to the ability of tuning graphene s fermi energy @xmath0 through the applied gate voltage . a combination of electronic gating and inelastic scattering of light , known as the gate modulated raman spectroscopy @xcite , opens up a new possibility to understand more thouroughly the interplay of the electron , photon and phonon exitations in graphene . several phenomena have been probed by gate modulated raman spectroscopy in graphene , such as the kohn anomaly ( ka ) effect or the phonon frequency renormalization @xcite , the quantum interference effect @xcite , electron - electron interaction @xcite , and the fano resonance in the raman spectra of graphene @xcite . studying gate modulated raman spectroscopy in graphene has also enriched our knowledge of phonon spectra characterization @xcite , experimental evaluation of electron - phonon coupling @xcite , and various edge characterization effects @xcite . some theoretical works have been previously performed to understand the kohn anomaly ( ka ) effect for the first - order raman ( g band ) spectra with a raman shift of @xmath1@xmath2 in graphene , such as those by ando and the mauri s groups @xcite . in the ka process , phonon renormalization occurs through the excitation of an electron - hole pair by the electron - phonon interaction . as a result , the phonon energy is modified and the phonon lifetime becomes shorter . the previous theories mention that the phonon frequency shows a logarithmic singularity at @xmath3 k when the absolute value of the fermi energy @xmath0 matches half of the phonon energy @xmath4 . for @xmath5 , the frequency shift is linearly proportional to @xmath6 . these predictions were already confirmed by raman measurements @xcite . recently , additional experimental results allow us to study the ka effect in the second - order raman spectra , also . in contrast to the first - order raman spectra that consist of only a single @xmath7 value of the phonon momentum , the second - order raman spectra deals with the whole range of phonon momenta in the brillouin zone satisfying the double resonance raman condition @xcite . raman spectral features such as the @xmath8 or 2d band ( @xmath9 ) and the @xmath10 or @xmath11 band ( @xmath12 ) are observed as the second - order raman spectra for @xmath13 . the nonzero momentum phonon leads to a different ka effect compared with that for the @xmath7 phonon . araujo _ et al . _ and mafra _ et al . _ have shown that the frequency shift of the @xmath8 band as a function of @xmath0 is monotonically decreasing as a function of @xmath6 which is opposite to that of the g band @xcite . the other band at @xmath14 is , however , dispersionless as a function of @xmath0 . yan _ et al . _ show opposite results , that the @xmath8 band frequency as a function of @xmath0 has the same trends as that of the g band @xcite . further , das _ et al . _ show an asymmetric @xmath8 band dispersion , i.e. , a positive ( negative ) slope of frequency shift at negative ( positive ) @xmath0 , which is inconsistent with a symmetric dispersion shown experimentally by araujo _ et al . _ @xcite . based on the controversies in experimental results , we present calculated results of the second - order raman spectra as a function of @xmath0 from which we understand the origin of the controvertial results . sasaki et al , attempted to understand why the frequency shift of the @xmath8 band ka has an opposite slope when compared with that of the @xmath15 band from the viewpoint of the competition of interband and intraband electron - hole excitation in phonon perturbation @xcite . however , since the theory is done within the effective mass approximation , it is not sufficient to explain the asymmetry of the @xmath8 band frequency shift at positive and negative @xmath0 . moreover , since the raman intensity as a function of @xmath0 is not calculated , different dispersion of raman peaks as a function of @xmath0 can not be explained from that theory . observing the change of raman intensity as a function of @xmath0 reveals the quantum interference effect . when @xmath16 , some raman scattering paths are suppressed due to the pauli exclusion principle . even with the reduced number of scattering paths , the raman intensity surprisingly increases at a particular value of @xmath0 when constructive raman phases among various scattering paths are enhanced . chen _ et al . _ show that the g band raman intensity gives a maximum value when @xmath17 , where @xmath18 is the laser energy @xcite . however , the theoretical analysis in their work assumes a constant matrix element therefore neglecting the change of the raman phase due to the electron - phonon matrix elements . previous theoretical calculations show that the electron - phonon matrix elements change sign along electronic equi - energy lines in graphene and therefore can change the raman phase @xcite . a comprehensive calculation is , therefore , necessary to understand how the quantum interference effect affects the first- and the second - order raman intensity . in this work we calculate the @xmath0 dependece of the first - order and the second - order raman spectra . the calculated spectral quantities are the raman peak shift , spectral linewidth , and the raman intensity as a function of @xmath0 . the ka correction including both the phonon frequency shift and the linewidth is modeled based on second - order perturbation theory . the ka of the first - order raman spectra or of the @xmath7 phonon is calculated so as to reproduce the existing theoretical and experimental results and to compare with the ka of the @xmath19 phonon.we now focus on the intervalley scatterings which give three prominent peaks in the experimental spectra , namely , the @xmath8 , the @xmath10 , and the @xmath20 bands , and are relevant to @xmath13 . the @xmath18 dependence of those raman peak positions is compared with experimental results in order to justify the present calculation methods . finally the @xmath0 dependence of those three raman spectra are analized and compared to the experimental results . ( color online ) schematics of ( a ) the first- and ( b ) the second - order raman process . in ( b ) , ee means two consecutive electron - phonon interactions while eh means electron - phonon interaction followed by hole - phonon interaction.,width=302 ] the organization of this paper is as follows . section [ subsec : ramanintens ] shows the method for calculating the raman intensities for the first- and second - order raman spectra . section [ subsec : ka ] explains the method for numerically calculating the ka effect . section [ subsec : first ] presents the calculated results of the ka effect for the @xmath7 phonon and the @xmath0 dependence of the g band intensity . section [ subsec : second ] presents the calculation results of the ka effect for @xmath19 , and the @xmath18 and @xmath0 dependences of the second - order raman spectra . finally , the conclusion is given in sect . [ sec : conclusion ] . the first - order raman process as shown in fig.[fig1](a ) consists of ( 1 ) excitation of an electron - hole pair by the electron - photon interaction , ( 2 ) phonon emission by means of the electron - phonon interaction , and ( 3 ) electron - hole recombination and photoemission by the electron - photon interaction . based on the three subprocesses , the raman intensity formula for the first - order raman process is given by @xmath21 } { ( \elaser - e_\kvec^{\cond\val}-i\gamma ) ( \elaser - e_\kvec^{\cond\val}-\omega^\nu_0-i\gamma)}\right|^2 \nonumber\\ & \times\delta(\elaser-\omega^\nu_0-e_{\rm s } ) , \end{aligned}\ ] ] where @xmath18 is the laser excitation energy , @xmath22 is the scattered photon energy , @xmath23 is the electron energy difference between the conduction ( @xmath24 ) and the valence ( @xmath25 ) bands at a wave vector @xmath26 , @xmath27 is the carrier scattering rate due to the electron - phonon interaction @xcite , and @xmath28 is the fermi distribution function which depends on temperature . @xmath29 is the electron - photon matrix element acounting for the optical transition of an electron in a state @xmath26 from a valence band to a conduction band , @xmath30 is the carrier - phonon interaction considering an electron ( @xmath31 ) in a conduction band or a hole ( @xmath32 ) in a valence band making a transition from a state @xmath33 to a state @xmath34 by emitting a phonon with momentum @xmath35 , mode @xmath36 , and frequency @xmath37 . hereafter , @xmath38 is used , so that @xmath37 has units of energy . for the case of a one phonon process , only zero momentum or the @xmath39 point phonon is relevant . the summation over @xmath26 in eq . is taken to occur in a uniform square mesh , with a mesh spacing @xmath40 , and @xmath41 is the slope of the electron energy dispersion of graphene and @xmath42 is the weight of the integration . we set a cutoff energy @xmath43 for @xmath44 so as to reduce the number of mesh points in the brillouin zone integration . it is important to note that both the numerator and denominator of eq . are complex numbers , thus the summation of @xmath26 before taking the square plays an important role in the quantum interference effect @xcite . the electronic structure of graphene is calculated within an extended tight binding method considering up to 20 nearest neighbors and the four atomic orbitals ( @xmath45 , @xmath46 , @xmath47 , @xmath48 ) @xcite . calculation of the phonon dispersion relations is performed within a force constant model with the interatomic potential including up to 20 nearest neighbors which is fitted from a first - principles calculation @xcite . figure [ fig - phdisp](a ) shows the calculated results of the phonon dispersion relations ( solid lines ) and the corresponding experimental phonon dispersion relations ( red dots ) for comparison from refs . . because of the ka effect , the dispersion of the in - plane tangential optic ( ito ) branch near the @xmath49 point is discontinuous along the @xmath50 path which can not be reproduced by the force constant model @xcite . we fit the ito frequency from the experiment @xcite and use the following fitting formula for the raman spectra calculation [ fig . [ fig - phdisp](b ) ] : @xmath51 where @xmath52 is defined using polar coordinates @xmath53 whose center is at the k point and @xmath54 is measured from the km direction . eq . is valid only for @xmath55 , and when @xmath56 , we use the results from the force constant model for @xmath57 . ( color online ) ( a ) calculated ( solid lines , this work ) and experimental ( red dots , from refs . ) phonon dispersion relations . ( b ) fitting of eq . ( blue line ) to the ito branch from ref . ( dots ) near the k point.,width=302 ] in the electron - photon interaction , we adopt a dipole approximation , i.e. , assuming a slowly varying electric field in space because the laser wavelength is much greater than the inter - atomic distance @xcite . the electron - phonon interaction is calculated using the tight binding method with the deformation potential fitted from the gw method for the k and @xmath39 points @xcite . in the second - order raman processes , phonons with modes @xmath36 and @xmath58 and momenta @xmath52 and @xmath59 , respectively , are emitted [ fig . [ fig1](b ) ] . depending on the carriers taking part in the scattering event , the raman intensity formula is given by : @xmath60 where @xmath61 is a raman amplitude for each process : ( 1 ) an electron ( e ) , first , emits a @xmath36 phonon with momentum @xmath52 and , ( 2 ) a hole ( h ) emits the @xmath58 phonon with momentum @xmath59 . here , @xmath61 and @xmath62 are not equivalent to each other due to the different time order of the two phonon emission . next , we show examples of the raman amplitude formula for @xmath63 and @xmath61 : @xmath64 } { ( \elaser - e_\kvec^{\cond\val}-i\gamma ) ( \elaser - e_{\kvec+\qvec}^{\cond}+e_{\kvec}^{\val}-\omega^\nu_{-\qvec}-i\gamma ) ( \elaser - e_{\kvec}^{\cond\val}-\omega^\nu_{-\qvec}-\omega^\mu_{\qvec}-i\gamma)},\ ] ] @xmath65 } { ( \elaser - e_\kvec^{\cond\val}-i\gamma ) ( \elaser - e_{\kvec+\qvec}^{\cond}+e_{\kvec}^{\val}-\omega^\nu_{-\qvec}-i\gamma ) ( \elaser - e_{\kvec+\qvec}^{\cond\val}-\omega^\nu_{-\qvec}-\omega^\mu_{\qvec}-i\gamma)}.\ ] ] the minus sign in eq . corresponds to the opposite charge of the hole from the electron in the hole - phonon matrix elements @xcite . ( color online ) ( a ) a schematic of the @xmath66 kohn anomaly process . a phonon with zero wave vector ( @xmath66 ) and frequency @xmath67 vertically excites an electron - hole pair via the electron - phonon interaction . the electron - hole pair then recombines by emitting a phonon with frequency @xmath68 . ( b ) a schematic of the @xmath69 kohn anomaly process . an electron exists at the @xmath70 point leaving a hole behind at the @xmath49 point with a distance in reciprocal space of @xmath71 . if the @xmath70 point is then translated by a vector @xmath72 , we can then imagine a virtual vertical transition of electron and hole . when @xmath73 , both interband ( c ) and intraband ( d ) transitions are expected.,width=302 ] kohn mentions that conduction electrons are able to screen phonons in a metal @xcite . this screening leads to a phonon frequency change , given by : @xmath74 where @xmath75 is the unperturbed phonon energy from the phonon dispersion relation . here , @xmath76 is the correction term taken from the second - order perturbation of the electron - phonon interaction by the excitation and recombination of an electron - hole pair ( fig . [ fig2a ] ) : @xmath77 } { \omega^{(0),\nu}_{\qvec}-e_{\kvec+\qvec}^{s'}+e_\kvec^{s}+i\eta},\ ] ] where the prefactor @xmath78 in eq . accounts for the spin degeneracy , while the valley degeneracy is considered in the summation over @xmath26 . the value of @xmath76 is a complex number , in which @xmath79 [ @xmath80 gives the phonon frequency shift [ phonon linewidth ] . in eq . , the contribution of the interband ( intraband ) electron - hole pair appears at @xmath81 ( @xmath82 ) . in a conventional 2d electron gas , the ka effect occurs at @xmath83 , where @xmath84 is the fermi wave vector . in graphene , due to its unique linear energy bands , the ka occurs at @xmath85 and @xmath86 . the schematics of the ka process for @xmath87 and @xmath69 are shown in figs . [ fig2a](a ) and ( b ) , respectively . in the @xmath88 ka , a phonon with frequency @xmath67 vertically excites an electron - hole pair via the electron - phonon interaction [ fig . [ fig2a](a ) ] . the electron - hole pair then recombines by emitting a phonon with frequency @xmath68 . in the @xmath86 ka , an electron exists at the @xmath70 point , leaving a hole behind at the @xmath49 point with a distance in reciprocal space @xmath89 [ fig . [ fig2a](b ) ] . if the @xmath70 point is translated by a vector @xmath72 , we can imagine a virtually vertical excitation of an electron - hole pair . when @xmath73 , both the interband [ fig . [ fig2a](c ) ] and intraband [ fig . [ fig2a](d ) ] transitions are expected . ( color online ) the calculated ( dotted line ) and experimental ( open circles ) results for the g band peak shift ( a ) and the g band linewidth ( b ) as a function of the fermi energy , respectively , for @xmath90 k.,width=302 ] employing eq . at @xmath7 , we can obtain the frequency shift [ fig . [ fig2](a ) ] and phonon linewidth [ fig . [ fig2](b ) ] for the g band as a function of the fermi energy at @xmath91 @xmath49 . in fig . [ fig2 ] we show the calculated ( dotted line ) and experimental ( open circles ) results @xcite of the g band peak shift and linewidth as a function of the fermi energy , respectively . the calculated results are in good agreement with the experimental results . in fig . [ fig2](a ) , we see dips when @xmath92 for the calculation , while the experimental results do not show such dips . these dips are originated from the logarithmic singularities at @xmath3 @xmath49 and are related to interband resonances @xcite . for @xmath93 , the g band frequency increases linearly as a function of the fermi energy . at @xmath94 k , the phonon linewidth shows a step function @xmath95 . the step function indicates that when @xmath93 , the phonon linewidth from the ka effect becomes zero since no excited electron - hole pair meets the resonance condition of eq . . at finite @xmath96 , on the other hand , the fermi distribution function becomes a smooth function and that is why we get a smooth function of the linewidth as a function of @xmath0 . it is noted that we add an extrinsic broadening of @xmath97 in our calculations in order to fit with experimental results @xcite in fig . [ fig2](b ) . ( color online ) calculated results of the real and imaginary parts of the first - order ( a ) lo and ( b ) ito raman amplitudes in a two dimensional brillouin zone near the @xmath49 and @xmath70 points with @xmath98 ev.,width=302 ] next , we calculate the raman spectra of the g band using eq . . the g band consists of both the @xmath87 longitudinal optic ( lo ) and in - plane - tangential optic ( ito ) modes . in order to understand their contributions to the raman amplitudes at each @xmath26 point , we plot the real and imaginary parts of the raman amplitude in eq . for lo and ito phonons in fig . [ fig3](a ) and ( b ) , respectively . here we use @xmath98 ev and take @xmath99 so as to reduce the total points of integration for saving computational time . it will be clear that neglecting the contributions from energies above @xmath100 in the integration is reasonable since the raman intensity is quickly decreasing when @xmath101 . in fig . [ fig3 ] , deformed triangles near the @xmath49 and the @xmath70 points indicate equi - energy lines that match the resonant conditions . the lower ( higher ) resonant condition corresponds to the scattered ( incident ) resonance when @xmath102 ( @xmath103 ) which is shown by a large amplitude at the inner ( outer ) line . we see changes in the sign for both the real and imaginary parts of the lo and ito raman amplitudes in both the radial and azimuthal directions . the change of sign at the radial direction is related to an opposite phase between the scattered resonance and the incident resonance . meanwhile , the change of sign in the azimuthal direction is related to the sign of the electron - phonon matrix element as reported by jiang et al @xcite . the lo ( ito ) phonon has a zero matrix element at the 0 ( @xmath104 ) phase . ( color online ) ( a ) calculated results ( black dots ) and experimental results ( blue squares from ref . and red squares from ref . ) of the g band raman intensity as a function of the reduced fermi energy . ( b ) schematic diagram showing an opposite phase between the incident ( i ) and scattered ( s ) resonances . when @xmath105 , the scattered resonance is suppressed , and therefore , the raman intensity gives a maximum value.,width=302 ] the opposite phase of the scattered resonance to the incident resonance is essential insofar as both terms give destructive interference . therefore , only taking the resonant term for calculating the g band intensity is not sufficient . we need to at least consider up to @xmath106 to get a realistic intensity . moreover if we plot the raman intensity as a function of the fermi energy as shown in fig . [ fig4](a ) , it becomes clear that destructive interference between the scattered resonance and the incident resonance can be suppressed when we set the fermi energy close to the laser excitation energy . when @xmath105 , the scattered resonance can not occur due to the pauli blocking effect [ fig . [ fig4](b ) ] . therefore , in fig . [ fig4](a ) we see the largest g band intensity at @xmath105 as pointed out by chen _ et al _ @xcite . the difference of the intensity at positive and negative @xmath0 which comes from the electron - hole asymmetry has been confirmed by liu _ et al _ @xcite . anisotropy in the azimuthal direction should give destructive interference , but the effect is negligible . in fig . [ fig5 ] , we show the calculated results of the @xmath19 ka effect from eq . . first , let us consider the case of @xmath107 in figs . [ fig5](b ) and ( e ) . if we compare respectively figs . [ fig5](b ) and ( e ) with figs . [ fig2](a ) and ( b ) , both the frequency shift and phonon linewidth show the same trends as that of @xmath7 ka because both @xmath7 and @xmath107 are dominated by the interband electron - hole excitation . the reason why the interband excitation is dominant at @xmath108 , is that the @xmath49 and @xmath70 points coincide upon translation of the @xmath70 point by a vector @xmath109 [ @xmath110 in fig . [ fig2a](c ) ] . therefore , at the @xmath111 ka , only virtually vertical interband excitation , the same as at @xmath87 ka , is possible @xcite . the previous work did not consider the interband contribution , therefore assigning the @xmath107 phonon frequency shift to be dispersionless as a function of @xmath0 @xcite . next , if we shift by @xmath112 from @xmath108 , competition between the intraband and interband excitations take place as shown in figs . [ fig5](a ) , ( c ) , ( d ) , and ( f ) . according to the analytical formula @xcite , the intraband contribution to the frequency shift is proportional to @xmath113 by assuming @xmath114 , where @xmath115 is the slope of the linear energy dispersion of graphene which is @xmath116 . the phonon linewidth is increasing linearly with @xmath6 in the case of the intraband excitation [ figs . [ fig5](d ) and ( f ) ] because the electron - phonon scattering rate is proportional to the carrier concentration . the asymmetry at positive and negative @xmath0 is related to electron - hole band asymmetry considered in the tight binding calculation . after considering the ka effect on the @xmath117 phonon , in fig [ fig7 ] we show the calculated raman spectra from eq . . figure [ fig7](a ) shows three bands , respectively , assigned as the @xmath8 @xmath118 , @xmath10 @xmath119 , and @xmath20 @xmath120 for @xmath121 . we confirm the origin of the @xmath8 bands from the overtone of the ito ( 2ito ) modes while the @xmath10 bands come from a combination of ito and la modes . the major contributions to the @xmath8 intensity come from the @xmath122 and @xmath123 terms as shown by @xmath124 in fig . [ fig7](b ) . this confirms the previous calculation that the @xmath125 and @xmath126 terms are negligible [ @xmath127 in fig . [ fig7](b ) ] because of the quantum interference effect during the @xmath26 integration @xcite . figure [ fig7](c ) shows the second - order raman intensities for @xmath128 . the intensities of all these raman bands are inversely proportional to @xmath18 because of the increase of the electron - phonon scattering rate @xmath129 as a function of @xmath18 @xcite . assuming that each band can be represented by a single peak , the @xmath8 , @xmath10 , and @xmath20 peak dispersions as a function of @xmath18 are shown in fig . [ fig7](d ) . the @xmath8 band shows a positive slope as a function of @xmath0 , i.e. , @xmath130 in this work , @xmath131 in ref . , and @xmath132 in ref . . meanwhile the @xmath10 band shows a negative slope , i.e. , @xmath133 in this work and @xmath133 in ref . and the @xmath20 band slope is @xmath134 in this work , @xmath135 in ref . , and @xmath136 in ref . [ not shown in fig . [ fig7](d ) ] . good agreement between theory and experiment in the slope of the @xmath18 dispersion indicates the reliability of our phonon dispersion used in the calculation . however , discrepancies with the experiments of about @xmath137 in the @xmath8 and the @xmath20 bands for a given @xmath18 show that the calculated electronic energy dispersion underestimates the experimenal results . this can be seen insofar as the @xmath8 and @xmath20 peaks at @xmath138 in theory give relatively the same value for @xmath139 in the experiment , thus the present electronic energy dispersion near @xmath18 underestimate the real value by @xmath140 . this might be because we neglect the many body effects in the band calculations . nevertheless , the overal agreement is sufficient for us to proceed and consider the @xmath0 dependence of the raman intensity for a particular @xmath18 . figure [ fig8 ] shows the evolution of the second order raman spectra for several values of @xmath0 : @xmath141 ( black solid lines ) , @xmath142 ( red dashed lines ) , @xmath143 @xmath144 ( green dashed lines ) , @xmath145 @xmath146 ( blue dashed lines ) , @xmath147 @xmath148 ( violet dashed lines ) . we use the same @xmath149 as araujo _ et al _ . figures [ fig8](a ) and ( d ) show that the @xmath8 raman spectrum is redshifted , decreases its peak intensity [ indicated by a blue arrow in fig . [ fig8](d ) ] and broadens as @xmath0 increases . these results are consistent with the experiment @xcite . however , the raman intensity of the @xmath10 and @xmath20 bands dramatically increases especially when @xmath150 [ indicated by the blue arrows in figs . [ fig8](b ) and ( c ) ] . we find that the increase of the intensity comes from the quantum interference effect and not from the ka effect . although the ka effect broadens the second - order raman spectra at a finite @xmath0 , however the broadening order should not be @xmath151 . figures [ fig8](a ) , ( b ) , and ( c ) show that the spectra where combination of the phonon modes are located ( @xmath152 ) dramatically broadens like a continous spectrum . the broadening should come from the increased intensity of many different @xmath52 phonon modes that are suppressed at @xmath153 during integration on @xmath26 but now appears at @xmath154 thanks to the suppression of the destructive interference . these results give clues about how the raman phase governed by the electron - phonon matrix elements distinguishes between the @xmath0 dependence of the raman intensity of the combination modes from that of the overtone modes as is also observed in experiments @xcite . although @xmath155 is too high for experiments on graphene , one can reduce the @xmath18 to become @xmath156 to satisfy the condition of @xmath157 to get proper conditions for observing the quantum interference effect . the calculated raman spectra at @xmath158 and @xmath149 in fig . [ fig8](c ) and ( d ) clearly show that the @xmath10 and @xmath8 bands can not be fit by a single lorentian for each band . figure [ fig9](a ) shows the lorentzian fitting results on the second order raman spectra for @xmath153 . the dotted line is the calculated raman intensity fitted by six lorentzians . we fit the @xmath8 bands with two lorentzians labelled by @xmath159 ( blue ) and @xmath160 ( red ) which reffer to @xmath8 bands from outer ( @xmath52 in km direction ) and inner ( @xmath52 in @xmath161 direction ) scattering processes , respectively @xcite . three lorentzians are needed to fit the @xmath10 band , labelled by @xmath162 ( green ) , @xmath163 ( blue ) , and @xmath164 ( red ) . finally one lorentzian is used to fit the @xmath20 band . after lorentzian fitting , we compare both the peak shift and the spectral linewidth as a function of @xmath0 as shown in figs . [ fig9](b)-(e ) . we do not show the @xmath159 and @xmath162 for simplicity because there is no experimental data available for comparison . the calculated results in fig . [ fig9](b)-(e ) can not fit the experimental value of both the peak position and the linewidth due to the underestimation of the electronic energy dispersion as previously discussed in the @xmath18 dependence of the second - order raman spectra [ see fig . [ fig7](d ) ] . but we can discuss the change of both quantities as a function of @xmath0 , where the ka effect takes place . in figs . [ fig9](b)-(e ) , both the spectral peak position and the linewidth as a function of @xmath0 are plotted in the same range , comparing the theory and experiments . reasonable agreements between experiments and theory are achieved . the three major peaks , i.e. , the @xmath160 , @xmath164 , and @xmath20 bands show `` @xmath165 '' ( `` v '' ) shapes of the raman peak shift ( spectral linewidth ) as a function of @xmath0 . these behaviors exist because of the intraband electron - hole excitation renormalization of phonons as shown in fig . [ fig5 ] . the @xmath163 band in fig . [ fig9](d ) is relatively dispersionless in @xmath0 because it is located in the shoulder of the @xmath8 band where 2ito @xmath166 exists . therefore , for these bands , the competition between interband and intraband electron - hole excitations are expected . the calculated results overestimate the experimental spectral linewidths of all bands , which is related to the choice of @xmath167 in the @xmath26 integration . we can tackle this issue by reducing the value of @xmath168 by @xmath169 ; however , the computational burden becomes @xmath170 times larger . in conclusion , we calculated the first- and second - order raman spectra as a function of @xmath0 . the opposite effect of the kohn anomaly that is found experimentally between the first- and the second - order raman spectra occurs because the ka effect on the first - order raman spectra is dominated by the renormalization of phonons by the interband electron - hole excitation , while in the second - order raman spectra , the intraband electron - hole excitation dominates over the ka effect . we also discussed the quantum interference effect observed in the change of the raman intensity as a function of @xmath0 . both the first- and the second - order raman spectra exhibit an impact of the quantum interference effect , especially when @xmath171 . present calculated results found that not only is the resonance condition important , but also the explicit consideration of the electron - phonon matrix elements are essential to determine the @xmath0 dependence of the raman spectral lineshape . e.h . is supported by a mext scholarship . acknowledges the interdepartmental doctoral degree program for material science leaders at tohoku university for providing a financial support . r.s . acknowledges mext grants no . 25286005 and no . m.s.d . acknowledges nsf - dmr grant no . 15 - 07806 .[/INST] intensity of the first- and the second - order raman spectra are calculated as a function of the fermi energy . we show that the kohn anomaly effect , i.e. , phonon frequency renormalization , in the first - order raman spectra originates from the phonon renormalization by the interband electron - hole excitation , whereas in the second - order raman spectra , a competition between the interband and intraband electron - hole excitations takes place . by this calculation , we confirm the presence of different dispersive behaviors of the raman peak frequency as a function of the fermi energy for the first- and the second - order raman spectra , as observed in experiments . moreover , the calculated results of the raman intensity sensitively depend on the fermi energy for both the first- and the second - order raman spectra . these results thus also show the importance of quantum interference effect phenomena . </s>

with the exotic beam facilities all over the world - and more are to come - direct reaction theories are experiencing a renaissance . we give a minireview of indirect methods for nuclear astrophysics reporting on recent work on coulomb dissociation of halo nuclei @xcite and on transfer reactions to bound and scattering states . the chemical evolution of the universe and the role of radioactive beams has recently been reviewed in @xcite . in @xcite it is remarked that high energy ( radioactive ) beams are a valuable tool to obtain information on low energy nuclear reactions of astrophysical importance . we discuss coulomb dissociation @xcite and the trojan horse method @xcite as examples . coulomb dissociation of a neutron halo nucleus in the limit of a zero - range neutron - core interaction in the coulomb field of a target nucleus can be studied in various limits of the parameter space and rather simple analytical solutions can be found . we propose to solve the scattering problem for this model hamiltonian by means of the various advanced numerical methods that are available nowadays . in this way their range of applicability can be studied by comparison to the analytical benchmark solutions , for work in this direction see @xcite . the trojan - horse method @xcite is a particular case of transfer reactions to the continuum under quasi - free scattering conditions . special attention is paid to the transition from reactions to bound and unbound states and the role of subthreshold resonances . since the binding energies of nuclei close to the drip line tend to be small , this is expected to be an important general feature in exotic nuclei . at low energies the effect of the nuclear potential is conveniently described by the effective - range expansion @xcite . an effective - range approach for the electromagnetic strength distribution in neutron halo nuclei was introduced in @xcite and applied to the single neutron halo nucleus @xmath0be . recently , the same method was applied to the description of electromagnetic dipole strength in @xmath1o @xcite . a systematic study sheds light on the sensitivity of the electromagnetic strength distribution to the interaction in the continuum . we expose the dependence on the binding energy of the nucleon and on the angular momentum quantum numbers . our approach extends the familiar textbook case of the deuteron , that can be considered as the prime example of a halo nucleus , to arbitrary nucleon+core systems , for related work see @xcite . we also investigate in detail the square - well potential model . it has great merits : it can be solved analytically , it shows the main characteristic features and it leads to rather simple and transparent formulae . as far as we know , some of these formulae have not been published before . these explicit results can be compared to our general theory for low energies ( effective - range approach ) and also to more realistic woods - saxon models . due to shape independence , the results of these various approaches will not differ for low energies . it will be interesting to delineate the range of validity of the simple models . our effective - range approach is closely related to effective field theories that are nowadays used for the description of the nucleon - nucleon system and halo nuclei @xcite . the characteristic low - energy parameters are linked to qcd in systematic expansions . similar methods are also used in the study of exotic atoms ( @xmath2 , @xmath3 , @xmath4 , ) in terms of effective - range parameters . the close relation of effective field theory to the effective - range approach for hadronic atoms was discussed in ref . @xcite . in fig . [ fig:1 ] we show the application of the method to the electromagnetic dipole strength in @xmath5be . the reduced transition probability was deduced from high - energy @xmath0be coulomb dissociation at gsi @xcite . using a cutoff radius of @xmath6 fm and an inverse bound - state decay length of @xmath7 @xmath8 as input parameters we extract an anc of @xmath9 @xmath10 from the fit to the experimental data . the anc can be converted to a spectroscopic factor of @xmath11 that is consistent with results from other methods . in the lowest order of the effective - range expansion the phase shift @xmath12 in the partial wave with orbital angular momentum @xmath13 and total angular momentum @xmath14 is written as @xmath15 , where @xmath16 is the halo expansion parameter and @xmath17 with the neutron separation energy @xmath18 . the effective range term @xmath19 term can be neglected , since it leads to a contribution with an extra @xmath20 factor which is small in the halo nucleus limit @xmath21 ( at least in the case where the scattering length is of natural order ) . the parameter @xmath22 corresponds to the scattering length @xmath23 . we obtain @xmath24 and @xmath25 . the latter is unnaturally large because of the existence of a bound @xmath26 state close to the neutron breakup threshold in @xmath0be . the connection of the scattering length @xmath27 and the bound state parameter q for @xmath28 is given by @xmath29 . this is a generalization of the well - known relation @xmath30 for @xmath31 in a square well model , where r denotes the range of the potential . the @xmath32 channel in @xmath5be is an example for the influence of a halo state on the continuum . the binding energy of this state is given by 184 kev , which corresponds to @xmath33 fm . with @xmath6 fm one has @xmath34 . for @xmath35 one has @xmath36 @xmath37 which translates into @xmath38 . this compares favourably with the fit value given in table 1 of @xcite : @xmath39 . for a further discussion we refer to @xcite . reduced probability for dipole transitions as a function of the excitation energy @xmath40 in comparison to experimental data extracted from coulomb dissociation of @xmath0be @xcite . ] we consider a three - body system consisting of a neutron n , a core c and an ( infinitely heavy ) target nucleus with charge ze . the hamiltonian is given by @xmath41 where @xmath42 is the kinetic energy of the system the coulomb interaction between the core and the target is given by @xmath43 and @xmath44 is a zero - range interaction between @xmath45 and @xmath46 . the s - wave bound state of the @xmath47 system is given by the wave function @xmath48 , where @xmath49 is related to the binding energy @xmath50 by @xmath51 and the reduced mass of the @xmath52 system is denoted by @xmath53 . this system can be studied analytically in various approximations . it can serve as a benchmark for the comparison of various analytical as well as numerical approaches . we refer to @xcite ( see especially ch . 4 there ) for details . the kinematics of the breakup process is given by @xmath54 where @xmath55 and @xmath56 are directly related to @xmath57 and @xmath58 , respectively . analytic results are known for the plane - wave limit , the coulomb - wave born approximation ( cwba , `` bremsstrahlung integral '' ) and the adiabatic approximation @xcite ) . a first derivation of the `` bremsstrahlung formula '' was given by landau and lifshitz @xcite , it was improved by breit in @xcite ; an early review is given in @xcite . it was first applied to heavy ions ( @xmath5be ) in @xcite . in the plane - wave limit the result does not depend on @xmath59 itself but only on the `` coulomb push '' @xmath60 . in the semiclassical high energy straight - line and electric dipole limit , first and second order analytical results are available , as well as for the sudden limit . e.g. , in the straight - line dipole approximation a shape parameter @xmath61 and a strength parameter @xmath62 $ ] determine the breakup probability ( in the sudden limit ) . the impact parameter is denoted by @xmath63 and the coulomb parameter is @xmath64 . in @xcite it was found that the breakup probability is given in leading order by @xmath65 and in next - to - leading order by @xmath66 depending on the parameter @xmath67 , the latter contribution leads to an enhancement or a reduction of the breakup probability as compared to the leading - order result . another important scaling parameter , in addition to @xmath67 and @xmath68 , is @xmath69 , where @xmath70 is the excitation energy of the @xmath71 system . in the sudden approximation we have @xmath72 and there is an analytical solution @xcite . the dependence of the post - acceleration effect on the beam energy was studied in post - form cwba in @xcite . postacceleration is very important for low beam energies and tends to diminish with high energies , see especially sect . 4.2 of @xcite . this may pose a problem for the cdcc approach at low beam energies . the choice of the jacobi coordinates to represent the cdcc basis is discussed in @xcite . the status of coulomb dissociation has been reviewed until about 2003 in @xcite . in addition to the general theoretical framework , this review also contains a discussion of the experimental results along with their astrophysical significance . the last years saw progress for various cases . this is a very brief summary of the experimental results . the @xmath73be(@xmath74)@xmath75b reaction plays a key role in the determination of the solar neutrino flux . @xmath75b coulomb dissociation experiments have been carried out over decades at riken , msu and gsi , with increasing beam energies . a careful analysis of the gsi @xmath75b experiment gsi-2 is now avialable @xcite , see also @xcite . particular emphasis was placed on the angular correlations of the breakup particles.these correlations demonstrate clearly that @xmath76 multipolarity dominates . the deduced astrophysical @xmath77 factor shows good agreement with most recent direct @xmath73be(@xmath74)@xmath75b measurements . high beam energies help to reduce higher order effects . the equivalent photon spectrum weights the @xmath78 contribution more than the @xmath76 contribution . this effect diminishes with increasing beam energy . thus the high beam energy of 254 a mev used at gsi helps to reduce the importance of the @xmath78 contribution . the origin of @xmath79li in the early universe is an interesting topic at present @xcite . @xmath79li is produced via the @xmath80li@xmath81 radiative capture reaction in big bang nucleosynthesis . the s factor of this radiative capture reaction can be determined in a @xmath79li coulomb breakup experiment . ( the fragility of @xmath79li is due to the large cross section of the @xmath79li(@xmath82)@xmath83he reaction , see ch . 5.3 below ) . the results of the @xmath79li @xmath84 coulomb dissociation experiment at @xmath85150 a mev at the kaos spectrometer at gsi have recently been presented @xcite . compared to the pilot experiment with @xmath86 a mev @xcite , lower @xmath87 relative energies down to 50 kev could be reached with rather small error bars . again , the high beam energy is very useful . experimental results for the coulomb breakup of psd - shell neutron rich nuclei from gsi were presented in @xcite . there is valuable spectroscopic information on various isotopes . the observed electromagnetic @xmath76 strength above the one - neutron threshold of neutron - rich c , be , b and o isotopes is explained by a non - resonant transition of a neutron into the continuum . the effective - range theory of halo nuclei given in ch . 2 is well suited to describe these effects . the neutron capture cross section for the @xmath88c(@xmath89)@xmath90c reaction , which is of astrophysical relevance , is also deduced . the discrepancy between the coulomb dissociation eperiments at gsi @xcite and msu as well as with the @xmath91- capture results from karlsruhe still persists . recently the e1-strength above neutron treshold in the neutron - rich @xmath92sn and @xmath93sn isotopes was investigated in a coulomb dissociation experiment at gsi @xcite . low lying strength was found ( pygmy resonance ) . the authors conclude that this e1 strength arises from oscilllations of the excess neutrons but it is under debate to what extent a collective mode is formed. the explosive hydrogen burning process synthesizes nuclei in hot , dense and hydrogen - rich stellar environments . proton capture processes are important to understand this rp - process . progress has been achieved in the coulomb dissociation of p - rich nuclei which is an indirect way to study these capture processes . there are examples of coulomb dissociation of proton rich nuclei which allow to deduce s factors for @xmath94 reactions . t.gomi et al . @xcite performed a coulomb dissociation experiment on @xmath95al in order to study the stellar @xmath96mg(@xmath74)@xmath95al reaction . they determine the radiative width @xmath97 of the first excited state in @xmath95al by measuring the @xmath95al@xmath98 mg @xmath99 coulomb dissociation . the coulomb breakup of @xmath100p was studied in @xcite in order to determine the s factor for the @xmath101si(@xmath74)@xmath100p reaction . the @xmath78 @xmath102-decay width of the first excited state in @xmath100p was extracted . assuming the same @xmath103 mixing ratio as the one for the mirror nucleus @xmath100 mg the astrophysically interesting @xmath102-width can be estimated . coulomb dissociation experiments with @xmath1al and @xmath104p are also planned at gsi with higher beam energies in the near future . for heavier nuclei with increasing charge the continuum contributions will diminish , due to the increase of the coulomb barrier . the s factor will be dominated by resonance contributions that can be calculated in the hauser - feshbach approach , if the statistical assumptions are fulfilled . exotic nuclei have low thresholds for particle emission . it is expected that in transfer reactions one will often meet a situation where the transferred particle is in a state close to the particle threshold . in `` normal '' nuclei , the neutron threshold is around an excitation energy of about 8 mev , and the pure single particle picture is not directly applicable . much is known from stripping reactions like @xmath105 and thermal neutron scattering , see , e.g. , @xcite . the single - particle strength is fragmented over many more complicated compound states . the interesting quantity is the strength function . it is proportional to @xmath106 where @xmath107 is the width and d the level spacing . one has @xmath108 , as can be estimated from a square well model ( see , e.g. , @xcite ) . for neutron rich ( halo ) nuclei the neutron threshold is much lower , of the order of one mev . in this case the single - particle properties are dominant and the ideas developed in the following can become relevant , see also @xcite . the level density is also much lower . in normal nuclei the level density at particle threshold is generally so high that the single - particle structure is very much dissolved . this can be quite different in exotic nuclei which can show a very pronounced single - particle structure . a similarity between cross sections for two - body and closely related three - body reactions under certain kinematical conditions @xcite led to the introduction of the trojan - horse method @xcite . in this indirect approach a two - body reaction @xmath109 that is relevant to nuclear astrophysics is replaced by a reaction @xmath110 with three particles in the final state . one assumes that the trojan horse @xmath111 is composed predominantly of clusters @xmath67 and @xmath63 , i.e. @xmath112 . this reaction can be considered as a special case of a transfer reaction to the continuum . it is studied experimentally under quasi - free scattering conditions , i.e. when the momentum transfer to the spectator @xmath63 is small . the method was primarily applied to the extraction of the low - energy cross section of reaction ( [ apreac ] ) that is relevant for astrophysics . however , the method can also be applied to the study of single - particle states in exotic nuclei around the particle threshold . the basic assumptions of the trojan horse method are discussed in detail in @xcite , see especially section 2 there . in view of a recent preprint @xcite we give here a very short outline of the reasoning ( see also @xcite ) . the method is based on the assumption that the transfer of particle @xmath67 is a direct reaction process , for which the well known dwba description @xcite is appropriate . in contrast to @xcite no such assumption is needed for the subprocess @xmath113 , which is of interest in this context . although the post- and prior forms are equivalent , it is simpler to use the post form dwba . the equivalence of post and prior sum rules for inclusive breakup reactions are elucidated in @xcite(iav ) , see also @xcite , where details also to the more formal aspects and further references can be found . the basic approximation of @xcite is the surface approximation , which allows one to relate the t - matrix of the process ( [ threac ] ) to the ( on - shell ) s - matrix elements of the astrophysical reaction ( [ apreac ] ) . the surface approximation was checked numerically in the inclusive breakup formalism of iav in @xcite . it proved to be very well fulfilled in this example . this exercise can be performed for every individual case in a similar manner . motivated by this we look again at the relation between transfer to bound and unbound states . our notation is as follows : we have the reaction @xmath114 where @xmath115 and b denotes the final @xmath116 system . it can be a bound state @xmath117 with binding energy @xmath118 , the open channel @xmath119 , or another channel @xmath120 of the system @xmath116 . in particular , the reaction @xmath121 can have a positive @xmath122 value and the energy @xmath123 can be negative as well as positive . as an example we quote the recently studied trojan horse reaction @xmath124+@xmath125li @xcite applied to the @xmath125li@xmath126he two - body reaction ( the neutron being the spectator ) . in this case there are two charged particles in the initial state ( @xmath125li+@xmath127 ) . another example with a neutral particle @xmath67 would be @xmath128be@xmath129be@xmath130 . the general question which we want to answer here is how the two regions @xmath131 and @xmath132 are related to each other . e.g. , in fig . 7 of @xcite the coincidence yield is plotted as a function of the @xmath125li-@xmath127 relative energy . it is nonzero at zero relative energy . how does the theory @xcite ( and the experiment ) continue to negative relative energies ? with this method , subtreshold resonances can be investigated rather directly . we treat two cases separately , one where system @xmath117 is always in the @xmath133 channel , with a real potential @xmath134 between @xmath135 and @xmath67 . in the other case , there are also other channels @xmath120 , at positive and negative energies @xmath123 . the cross section is a quantity which only exists for @xmath131 . however , a quantity like the s factor ( or related to it ) can be continued to energies below the threshold . an instructive example is the modified shape function @xmath136 in ch . 6 of @xcite . in analogy to the astrophysical s factor , where the coulomb barrier is taken out , the angular momentum barrier is taken out in the quantity @xmath136 . as can be seen from table 3 or 4 of @xcite the quantity @xmath136 is well defined for @xmath137 , with the characteristic pole at @xmath138 , corresponding to the binding energy of the @xmath139-system . we refer to @xcite for further discussion . it is mainly the catania group led by claudio spitaleri that has shown in many examples how the trojan - horse method can be developed into a useful tool for nuclear astrophysics . many interesting results have been obtained which we summarize very briefly below . an especially interesting aspect is the following : at sufficiently low energies , electronic screening affects the cross section of astrophysical reactions . for a recent experimental study see @xcite , a theoretical analysis is provided in @xcite . these effects depend on the laboratory environments and can also be different from the astrophysical conditions . due to the high beam energy in the trojan horse method , there is no screening of the coulomb potential by the electron cloud and one determines the bare nucleus astrophysical s factor . the knowledge of this bare s factor - derived with the help of an indirect method - is useful in judging the screening effects in the direct reaction under specific laboratory conditions . one can also determine the s factor at higher energies where screening is negligible . for the application of the trojan - horse method it is mainly necessary that the theoretical description yields the correct energy dependence , and not necessarily the absolute value of the cross section . eventually one has to determine - by means of model calculations - the astrophysical s factor under the astrophysical conditions , this is the quantity one is most interested in . for a list of experiments see sect . . 1 of @xcite and also the introduction of @xcite . the two stable isotopes of li with @xmath140 , are valuable probes for conditions in the early universe . while it is safe to say that the issue is far from settled at the present times , input from nuclear astrophysics is certainly important . the formation of @xmath79li in the early universe proceeds mainly by the @xmath141 radiative capture process mentioned in sect . 4 , the reactions which destroy @xmath125li have been studied using the trojan - horse method . the destruction of @xmath79li can proceed by the reaction @xmath142li,@xmath143 . this reaction was studied by the trojan horse reaction @xmath79li(@xmath79li,@xmath144he , where one of the @xmath145 particles has to be considered as a spectator ( trojan horse ) @xcite . the spectator condition , i.e. small momentum transfer in the three - body reaction , is ensured by the quasi - free kinematics . another reaction which depletes @xmath146 is @xmath147li,@xmath148he . it was studied in @xcite by means of the trojan horse reaction @xmath149h(@xmath79li,@xmath150he)@xmath46 . coincidence spectra were measured in a kinematically complete experiment at @xmath151 mev . they show the presence of the quasifree @xmath79li-@xmath127 process . cross sections for the @xmath79li(@xmath152he from @xmath153 mev down to astrophysical energies were extracted . ( actually , the experimental results extend also to negative @xmath79li-@xmath127-energies ) . the @xmath5b(@xmath154be reaction was studied from 1 mev down to astrophysical energies by means of the trojan - horse method applied to the three - body reaction @xmath155b,@xmath156be)@xmath46 @xcite . this reaction is responsible for the boron destruction in stellar environments . the reaction @xmath83he(@xmath157he was studied in @xcite by means of the @xmath79li(@xmath83he,@xmath158he three - body reaction . the bare astrophysical @xmath159 factor was deduced . this allowed an independent estimate of the screening potential , confirming the discrepancy with the adiabatic limit . the reaction @xmath83he(@xmath157he is important for primordial nucleosynthesis @xcite . one may also envisage applications of the trojan - horse method with exotic beams . an unstable ( exotic ) projectile hits a trojan - horse target allowing to study specific reactions on exotic nuclei that are unaccessible in direct experiments . we mention the @xmath160ni,@xmath161ni reaction studied in inverse kinematics in 1998 @xcite . in this paper , stripping to bound states was studied . in the meantime , more ( d , p ) transfer reactions were studied in inverse kinematics @xcite . an extension to stripping into the continuum would be of interest for this and other kinds of reactions . while the foundations of direct reaction theory have been laid several decades ago , the new possibilites which have opened up with the rare isotope beams are an invitation to revisit this field . the general frame is set by nonrelativistic many - body quantum scattering theory , however , the increasing level of precision demands a good understanding of relativistic effects notably in intermediate - energy coulomb excitation . the properties of halo nuclei depend very sensitively on the binding energy and despite the ever increasing precision of microscopic approaches using realistic nn forces it will not be possible , say , to predict the binding energies of nuclei to a level of about 100 kev . thus halo nuclei ask for new approaches in terms of some effective low - energy constants . such a treatment was provided in ch . 2 and an example with the one - neutron halo nucleus @xmath5be was given . with the radioactive beam facilities at riken , gsi and ria one will be able to study also neutron halo nuclei for intermediate masses in the years to come . this is expected to be relevant also for the astrophysical r - process . it is a great challenge to extend the present approach for one - nucleon halo nuclei to more complicated cases , like two - 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indirect methods in nuclear astrophysics are discussed . recent work on coulomb dissociation and an effective - range theory of low - lying electromagnetic strength of halo nuclei is presented . coulomb dissociation of a halo nucleus bound by a zero - range potential is proposed as a homework problem ( for further references see g. baur and s. typel , nucl - th/0504068 ) . it is pointed out that the trojan - horse method ( g. baur , f. rsel , d. trautmann and r. shyam , phys . rep . 111 ( 1984 ) 333 ) is a suitable tool to investigate subthreshold resonances . address = institut fr kernphysik , forschungszentrum jlich , d-52425 jlich , germany address = gesellschaft fr schwerionenforschung mbh ( gsi ) , planckstrae 1 , d-64291 darmstadt , germany

<s>[INST]with the exotic beam facilities all over the world - and more are to come - direct reaction theories are experiencing a renaissance . we give a minireview of indirect methods for nuclear astrophysics reporting on recent work on coulomb dissociation of halo nuclei @xcite and on transfer reactions to bound and scattering states . the chemical evolution of the universe and the role of radioactive beams has recently been reviewed in @xcite . in @xcite it is remarked that high energy ( radioactive ) beams are a valuable tool to obtain information on low energy nuclear reactions of astrophysical importance . we discuss coulomb dissociation @xcite and the trojan horse method @xcite as examples . coulomb dissociation of a neutron halo nucleus in the limit of a zero - range neutron - core interaction in the coulomb field of a target nucleus can be studied in various limits of the parameter space and rather simple analytical solutions can be found . we propose to solve the scattering problem for this model hamiltonian by means of the various advanced numerical methods that are available nowadays . in this way their range of applicability can be studied by comparison to the analytical benchmark solutions , for work in this direction see @xcite . the trojan - horse method @xcite is a particular case of transfer reactions to the continuum under quasi - free scattering conditions . special attention is paid to the transition from reactions to bound and unbound states and the role of subthreshold resonances . since the binding energies of nuclei close to the drip line tend to be small , this is expected to be an important general feature in exotic nuclei . at low energies the effect of the nuclear potential is conveniently described by the effective - range expansion @xcite . an effective - range approach for the electromagnetic strength distribution in neutron halo nuclei was introduced in @xcite and applied to the single neutron halo nucleus @xmath0be . recently , the same method was applied to the description of electromagnetic dipole strength in @xmath1o @xcite . a systematic study sheds light on the sensitivity of the electromagnetic strength distribution to the interaction in the continuum . we expose the dependence on the binding energy of the nucleon and on the angular momentum quantum numbers . our approach extends the familiar textbook case of the deuteron , that can be considered as the prime example of a halo nucleus , to arbitrary nucleon+core systems , for related work see @xcite . we also investigate in detail the square - well potential model . it has great merits : it can be solved analytically , it shows the main characteristic features and it leads to rather simple and transparent formulae . as far as we know , some of these formulae have not been published before . these explicit results can be compared to our general theory for low energies ( effective - range approach ) and also to more realistic woods - saxon models . due to shape independence , the results of these various approaches will not differ for low energies . it will be interesting to delineate the range of validity of the simple models . our effective - range approach is closely related to effective field theories that are nowadays used for the description of the nucleon - nucleon system and halo nuclei @xcite . the characteristic low - energy parameters are linked to qcd in systematic expansions . similar methods are also used in the study of exotic atoms ( @xmath2 , @xmath3 , @xmath4 , ) in terms of effective - range parameters . the close relation of effective field theory to the effective - range approach for hadronic atoms was discussed in ref . @xcite . in fig . [ fig:1 ] we show the application of the method to the electromagnetic dipole strength in @xmath5be . the reduced transition probability was deduced from high - energy @xmath0be coulomb dissociation at gsi @xcite . using a cutoff radius of @xmath6 fm and an inverse bound - state decay length of @xmath7 @xmath8 as input parameters we extract an anc of @xmath9 @xmath10 from the fit to the experimental data . the anc can be converted to a spectroscopic factor of @xmath11 that is consistent with results from other methods . in the lowest order of the effective - range expansion the phase shift @xmath12 in the partial wave with orbital angular momentum @xmath13 and total angular momentum @xmath14 is written as @xmath15 , where @xmath16 is the halo expansion parameter and @xmath17 with the neutron separation energy @xmath18 . the effective range term @xmath19 term can be neglected , since it leads to a contribution with an extra @xmath20 factor which is small in the halo nucleus limit @xmath21 ( at least in the case where the scattering length is of natural order ) . the parameter @xmath22 corresponds to the scattering length @xmath23 . we obtain @xmath24 and @xmath25 . the latter is unnaturally large because of the existence of a bound @xmath26 state close to the neutron breakup threshold in @xmath0be . the connection of the scattering length @xmath27 and the bound state parameter q for @xmath28 is given by @xmath29 . this is a generalization of the well - known relation @xmath30 for @xmath31 in a square well model , where r denotes the range of the potential . the @xmath32 channel in @xmath5be is an example for the influence of a halo state on the continuum . the binding energy of this state is given by 184 kev , which corresponds to @xmath33 fm . with @xmath6 fm one has @xmath34 . for @xmath35 one has @xmath36 @xmath37 which translates into @xmath38 . this compares favourably with the fit value given in table 1 of @xcite : @xmath39 . for a further discussion we refer to @xcite . reduced probability for dipole transitions as a function of the excitation energy @xmath40 in comparison to experimental data extracted from coulomb dissociation of @xmath0be @xcite . ] we consider a three - body system consisting of a neutron n , a core c and an ( infinitely heavy ) target nucleus with charge ze . the hamiltonian is given by @xmath41 where @xmath42 is the kinetic energy of the system the coulomb interaction between the core and the target is given by @xmath43 and @xmath44 is a zero - range interaction between @xmath45 and @xmath46 . the s - wave bound state of the @xmath47 system is given by the wave function @xmath48 , where @xmath49 is related to the binding energy @xmath50 by @xmath51 and the reduced mass of the @xmath52 system is denoted by @xmath53 . this system can be studied analytically in various approximations . it can serve as a benchmark for the comparison of various analytical as well as numerical approaches . we refer to @xcite ( see especially ch . 4 there ) for details . the kinematics of the breakup process is given by @xmath54 where @xmath55 and @xmath56 are directly related to @xmath57 and @xmath58 , respectively . analytic results are known for the plane - wave limit , the coulomb - wave born approximation ( cwba , `` bremsstrahlung integral '' ) and the adiabatic approximation @xcite ) . a first derivation of the `` bremsstrahlung formula '' was given by landau and lifshitz @xcite , it was improved by breit in @xcite ; an early review is given in @xcite . it was first applied to heavy ions ( @xmath5be ) in @xcite . in the plane - wave limit the result does not depend on @xmath59 itself but only on the `` coulomb push '' @xmath60 . in the semiclassical high energy straight - line and electric dipole limit , first and second order analytical results are available , as well as for the sudden limit . e.g. , in the straight - line dipole approximation a shape parameter @xmath61 and a strength parameter @xmath62 $ ] determine the breakup probability ( in the sudden limit ) . the impact parameter is denoted by @xmath63 and the coulomb parameter is @xmath64 . in @xcite it was found that the breakup probability is given in leading order by @xmath65 and in next - to - leading order by @xmath66 depending on the parameter @xmath67 , the latter contribution leads to an enhancement or a reduction of the breakup probability as compared to the leading - order result . another important scaling parameter , in addition to @xmath67 and @xmath68 , is @xmath69 , where @xmath70 is the excitation energy of the @xmath71 system . in the sudden approximation we have @xmath72 and there is an analytical solution @xcite . the dependence of the post - acceleration effect on the beam energy was studied in post - form cwba in @xcite . postacceleration is very important for low beam energies and tends to diminish with high energies , see especially sect . 4.2 of @xcite . this may pose a problem for the cdcc approach at low beam energies . the choice of the jacobi coordinates to represent the cdcc basis is discussed in @xcite . the status of coulomb dissociation has been reviewed until about 2003 in @xcite . in addition to the general theoretical framework , this review also contains a discussion of the experimental results along with their astrophysical significance . the last years saw progress for various cases . this is a very brief summary of the experimental results . the @xmath73be(@xmath74)@xmath75b reaction plays a key role in the determination of the solar neutrino flux . @xmath75b coulomb dissociation experiments have been carried out over decades at riken , msu and gsi , with increasing beam energies . a careful analysis of the gsi @xmath75b experiment gsi-2 is now avialable @xcite , see also @xcite . particular emphasis was placed on the angular correlations of the breakup particles.these correlations demonstrate clearly that @xmath76 multipolarity dominates . the deduced astrophysical @xmath77 factor shows good agreement with most recent direct @xmath73be(@xmath74)@xmath75b measurements . high beam energies help to reduce higher order effects . the equivalent photon spectrum weights the @xmath78 contribution more than the @xmath76 contribution . this effect diminishes with increasing beam energy . thus the high beam energy of 254 a mev used at gsi helps to reduce the importance of the @xmath78 contribution . the origin of @xmath79li in the early universe is an interesting topic at present @xcite . @xmath79li is produced via the @xmath80li@xmath81 radiative capture reaction in big bang nucleosynthesis . the s factor of this radiative capture reaction can be determined in a @xmath79li coulomb breakup experiment . ( the fragility of @xmath79li is due to the large cross section of the @xmath79li(@xmath82)@xmath83he reaction , see ch . 5.3 below ) . the results of the @xmath79li @xmath84 coulomb dissociation experiment at @xmath85150 a mev at the kaos spectrometer at gsi have recently been presented @xcite . compared to the pilot experiment with @xmath86 a mev @xcite , lower @xmath87 relative energies down to 50 kev could be reached with rather small error bars . again , the high beam energy is very useful . experimental results for the coulomb breakup of psd - shell neutron rich nuclei from gsi were presented in @xcite . there is valuable spectroscopic information on various isotopes . the observed electromagnetic @xmath76 strength above the one - neutron threshold of neutron - rich c , be , b and o isotopes is explained by a non - resonant transition of a neutron into the continuum . the effective - range theory of halo nuclei given in ch . 2 is well suited to describe these effects . the neutron capture cross section for the @xmath88c(@xmath89)@xmath90c reaction , which is of astrophysical relevance , is also deduced . the discrepancy between the coulomb dissociation eperiments at gsi @xcite and msu as well as with the @xmath91- capture results from karlsruhe still persists . recently the e1-strength above neutron treshold in the neutron - rich @xmath92sn and @xmath93sn isotopes was investigated in a coulomb dissociation experiment at gsi @xcite . low lying strength was found ( pygmy resonance ) . the authors conclude that this e1 strength arises from oscilllations of the excess neutrons but it is under debate to what extent a collective mode is formed. the explosive hydrogen burning process synthesizes nuclei in hot , dense and hydrogen - rich stellar environments . proton capture processes are important to understand this rp - process . progress has been achieved in the coulomb dissociation of p - rich nuclei which is an indirect way to study these capture processes . there are examples of coulomb dissociation of proton rich nuclei which allow to deduce s factors for @xmath94 reactions . t.gomi et al . @xcite performed a coulomb dissociation experiment on @xmath95al in order to study the stellar @xmath96mg(@xmath74)@xmath95al reaction . they determine the radiative width @xmath97 of the first excited state in @xmath95al by measuring the @xmath95al@xmath98 mg @xmath99 coulomb dissociation . the coulomb breakup of @xmath100p was studied in @xcite in order to determine the s factor for the @xmath101si(@xmath74)@xmath100p reaction . the @xmath78 @xmath102-decay width of the first excited state in @xmath100p was extracted . assuming the same @xmath103 mixing ratio as the one for the mirror nucleus @xmath100 mg the astrophysically interesting @xmath102-width can be estimated . coulomb dissociation experiments with @xmath1al and @xmath104p are also planned at gsi with higher beam energies in the near future . for heavier nuclei with increasing charge the continuum contributions will diminish , due to the increase of the coulomb barrier . the s factor will be dominated by resonance contributions that can be calculated in the hauser - feshbach approach , if the statistical assumptions are fulfilled . exotic nuclei have low thresholds for particle emission . it is expected that in transfer reactions one will often meet a situation where the transferred particle is in a state close to the particle threshold . in `` normal '' nuclei , the neutron threshold is around an excitation energy of about 8 mev , and the pure single particle picture is not directly applicable . much is known from stripping reactions like @xmath105 and thermal neutron scattering , see , e.g. , @xcite . the single - particle strength is fragmented over many more complicated compound states . the interesting quantity is the strength function . it is proportional to @xmath106 where @xmath107 is the width and d the level spacing . one has @xmath108 , as can be estimated from a square well model ( see , e.g. , @xcite ) . for neutron rich ( halo ) nuclei the neutron threshold is much lower , of the order of one mev . in this case the single - particle properties are dominant and the ideas developed in the following can become relevant , see also @xcite . the level density is also much lower . in normal nuclei the level density at particle threshold is generally so high that the single - particle structure is very much dissolved . this can be quite different in exotic nuclei which can show a very pronounced single - particle structure . a similarity between cross sections for two - body and closely related three - body reactions under certain kinematical conditions @xcite led to the introduction of the trojan - horse method @xcite . in this indirect approach a two - body reaction @xmath109 that is relevant to nuclear astrophysics is replaced by a reaction @xmath110 with three particles in the final state . one assumes that the trojan horse @xmath111 is composed predominantly of clusters @xmath67 and @xmath63 , i.e. @xmath112 . this reaction can be considered as a special case of a transfer reaction to the continuum . it is studied experimentally under quasi - free scattering conditions , i.e. when the momentum transfer to the spectator @xmath63 is small . the method was primarily applied to the extraction of the low - energy cross section of reaction ( [ apreac ] ) that is relevant for astrophysics . however , the method can also be applied to the study of single - particle states in exotic nuclei around the particle threshold . the basic assumptions of the trojan horse method are discussed in detail in @xcite , see especially section 2 there . in view of a recent preprint @xcite we give here a very short outline of the reasoning ( see also @xcite ) . the method is based on the assumption that the transfer of particle @xmath67 is a direct reaction process , for which the well known dwba description @xcite is appropriate . in contrast to @xcite no such assumption is needed for the subprocess @xmath113 , which is of interest in this context . although the post- and prior forms are equivalent , it is simpler to use the post form dwba . the equivalence of post and prior sum rules for inclusive breakup reactions are elucidated in @xcite(iav ) , see also @xcite , where details also to the more formal aspects and further references can be found . the basic approximation of @xcite is the surface approximation , which allows one to relate the t - matrix of the process ( [ threac ] ) to the ( on - shell ) s - matrix elements of the astrophysical reaction ( [ apreac ] ) . the surface approximation was checked numerically in the inclusive breakup formalism of iav in @xcite . it proved to be very well fulfilled in this example . this exercise can be performed for every individual case in a similar manner . motivated by this we look again at the relation between transfer to bound and unbound states . our notation is as follows : we have the reaction @xmath114 where @xmath115 and b denotes the final @xmath116 system . it can be a bound state @xmath117 with binding energy @xmath118 , the open channel @xmath119 , or another channel @xmath120 of the system @xmath116 . in particular , the reaction @xmath121 can have a positive @xmath122 value and the energy @xmath123 can be negative as well as positive . as an example we quote the recently studied trojan horse reaction @xmath124+@xmath125li @xcite applied to the @xmath125li@xmath126he two - body reaction ( the neutron being the spectator ) . in this case there are two charged particles in the initial state ( @xmath125li+@xmath127 ) . another example with a neutral particle @xmath67 would be @xmath128be@xmath129be@xmath130 . the general question which we want to answer here is how the two regions @xmath131 and @xmath132 are related to each other . e.g. , in fig . 7 of @xcite the coincidence yield is plotted as a function of the @xmath125li-@xmath127 relative energy . it is nonzero at zero relative energy . how does the theory @xcite ( and the experiment ) continue to negative relative energies ? with this method , subtreshold resonances can be investigated rather directly . we treat two cases separately , one where system @xmath117 is always in the @xmath133 channel , with a real potential @xmath134 between @xmath135 and @xmath67 . in the other case , there are also other channels @xmath120 , at positive and negative energies @xmath123 . the cross section is a quantity which only exists for @xmath131 . however , a quantity like the s factor ( or related to it ) can be continued to energies below the threshold . an instructive example is the modified shape function @xmath136 in ch . 6 of @xcite . in analogy to the astrophysical s factor , where the coulomb barrier is taken out , the angular momentum barrier is taken out in the quantity @xmath136 . as can be seen from table 3 or 4 of @xcite the quantity @xmath136 is well defined for @xmath137 , with the characteristic pole at @xmath138 , corresponding to the binding energy of the @xmath139-system . we refer to @xcite for further discussion . it is mainly the catania group led by claudio spitaleri that has shown in many examples how the trojan - horse method can be developed into a useful tool for nuclear astrophysics . many interesting results have been obtained which we summarize very briefly below . an especially interesting aspect is the following : at sufficiently low energies , electronic screening affects the cross section of astrophysical reactions . for a recent experimental study see @xcite , a theoretical analysis is provided in @xcite . these effects depend on the laboratory environments and can also be different from the astrophysical conditions . due to the high beam energy in the trojan horse method , there is no screening of the coulomb potential by the electron cloud and one determines the bare nucleus astrophysical s factor . the knowledge of this bare s factor - derived with the help of an indirect method - is useful in judging the screening effects in the direct reaction under specific laboratory conditions . one can also determine the s factor at higher energies where screening is negligible . for the application of the trojan - horse method it is mainly necessary that the theoretical description yields the correct energy dependence , and not necessarily the absolute value of the cross section . eventually one has to determine - by means of model calculations - the astrophysical s factor under the astrophysical conditions , this is the quantity one is most interested in . for a list of experiments see sect . . 1 of @xcite and also the introduction of @xcite . the two stable isotopes of li with @xmath140 , are valuable probes for conditions in the early universe . while it is safe to say that the issue is far from settled at the present times , input from nuclear astrophysics is certainly important . the formation of @xmath79li in the early universe proceeds mainly by the @xmath141 radiative capture process mentioned in sect . 4 , the reactions which destroy @xmath125li have been studied using the trojan - horse method . the destruction of @xmath79li can proceed by the reaction @xmath142li,@xmath143 . this reaction was studied by the trojan horse reaction @xmath79li(@xmath79li,@xmath144he , where one of the @xmath145 particles has to be considered as a spectator ( trojan horse ) @xcite . the spectator condition , i.e. small momentum transfer in the three - body reaction , is ensured by the quasi - free kinematics . another reaction which depletes @xmath146 is @xmath147li,@xmath148he . it was studied in @xcite by means of the trojan horse reaction @xmath149h(@xmath79li,@xmath150he)@xmath46 . coincidence spectra were measured in a kinematically complete experiment at @xmath151 mev . they show the presence of the quasifree @xmath79li-@xmath127 process . cross sections for the @xmath79li(@xmath152he from @xmath153 mev down to astrophysical energies were extracted . ( actually , the experimental results extend also to negative @xmath79li-@xmath127-energies ) . the @xmath5b(@xmath154be reaction was studied from 1 mev down to astrophysical energies by means of the trojan - horse method applied to the three - body reaction @xmath155b,@xmath156be)@xmath46 @xcite . this reaction is responsible for the boron destruction in stellar environments . the reaction @xmath83he(@xmath157he was studied in @xcite by means of the @xmath79li(@xmath83he,@xmath158he three - body reaction . the bare astrophysical @xmath159 factor was deduced . this allowed an independent estimate of the screening potential , confirming the discrepancy with the adiabatic limit . the reaction @xmath83he(@xmath157he is important for primordial nucleosynthesis @xcite . one may also envisage applications of the trojan - horse method with exotic beams . an unstable ( exotic ) projectile hits a trojan - horse target allowing to study specific reactions on exotic nuclei that are unaccessible in direct experiments . we mention the @xmath160ni,@xmath161ni reaction studied in inverse kinematics in 1998 @xcite . in this paper , stripping to bound states was studied . in the meantime , more ( d , p ) transfer reactions were studied in inverse kinematics @xcite . an extension to stripping into the continuum would be of interest for this and other kinds of reactions . while the foundations of direct reaction theory have been laid several decades ago , the new possibilites which have opened up with the rare isotope beams are an invitation to revisit this field . the general frame is set by nonrelativistic many - body quantum scattering theory , however , the increasing level of precision demands a good understanding of relativistic effects notably in intermediate - energy coulomb excitation . the properties of halo nuclei depend very sensitively on the binding energy and despite the ever increasing precision of microscopic approaches using realistic nn forces it will not be possible , say , to predict the binding energies of nuclei to a level of about 100 kev . thus halo nuclei ask for new approaches in terms of some effective low - energy constants . such a treatment was provided in ch . 2 and an example with the one - neutron halo nucleus @xmath5be was given . with the radioactive beam facilities at riken , gsi and ria one will be able to study also neutron halo nuclei for intermediate masses in the years to come . this is expected to be relevant also for the astrophysical r - process . it is a great challenge to extend the present approach for one - nucleon halo nuclei to more complicated cases , like two - neutron halo nuclei . the treatment of the continuum is a general problem , which becomes more and more urgent when the dripline is approached . in the present proceedings we studied the transition from bound to unbound states as a typical example . beautiful experiments have to be matched with good theoretical developments and painstaking analysis . while the coulomb dissociation method relies essentially only on qed , precise experiments can give , in combination with a thorough theoretical analysis , precise answers for the astrophysical s factors . in the trojan - horse method more phenomenological aspects enter , like optical model parameters and effective nuclear interactions . this makes the interpretation of the experimental results in terms of astrophysical s factors less precise . however , this is not a new aspect in nuclear physics . in the interpretation of screening effects one relies on the accuracy of the energy dependence . this is certainly better fulfilled than the accuracy of the absolute values . 99 s. typel and g. baur , _ phys . _ , * 93 * , 142502 ( 2004 ) . s. typel and g. baur , _ nucl . a759 _ , 247 ( 2005 ) , nucl - 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quantum phase transitions @xmath7 are sudden changes in the structure of a physical system . nuclear physics has important contributions to make to their study because nuclei display a variety of phases in systems ranging from few to many particles @xcite.the signs of @xmath8 in nuclear physics are changes in mass and radius of nuclei and quantities such as level crossing and electromagnetic transition rates when the number of protons or neutrons is modified . phase transition happens in both even - even and @xmath9 nuclei . phase transitions investigations have been mostly performed on even - even systems @xcite within the framework of the interacting boson model @xmath10 @xcite , which describe nuclei in terms of correlated pairs of nucleons with @xmath11,@xmath12 treated as bosons @xmath13 . the ibm hamiltonian has exact solutions in three dynamical symmetry limits ( @xmath14,@xmath15 , and @xmath16 ) . these situations correspond to the spherical , axially deformed , and gamma - unstable ground state shapes , respectively . the transition between the @xmath14-@xmath17 limits is a first - order shape - phase transition while a second - order shape - phase transition occurs between the @xmath18 and @xmath19 limits @xcite . during a transition from one limit to another , meet the points in which potential has flat behavior . these points are called critical point.recently iachello introduced the so - called critical point symmetries in the framework of the collective model for even - even nuclei . the critical point from spherical to @xmath20 shapes , called @xmath21 @xcite , the critical point from spherical to axially deformed shapes , called @xmath22 @xcite , and the critical point from axially deformed shapes to triaxial shapes , called y(5 ) @xcite . phase transitions is also investigate in odd - a nuclei within the framework of interacting boson - fermion model @xmath23@xcite , which describe nuclei in terms of correlated pairs , with @xmath24 ( @xmath25 , @xmath26 bosons ) , and unpaired particles of angular momentum @xmath27 @xmath28.studies of @xmath8 in odd - even nuclei were implicitly initiated years ago by scholten and blasi @xcite . several explicit studies have recently been made by alonso et al . @xcite and by boyukata et al . @xcite , who also have suggested a simple form of the ibfm hamiltonian , particularly well - suited to study @xmath29 in odd - even nuclei because of their supersymmetric properties . similar to even - even nuclei , also exists critical point for odd - even and even - odd nuclei but in this case , critical points show with @xmath30 and @xmath31 that @xmath27 is the angular momentum of single nucleon . iachello @xcite has been the case of a @xmath32 fermion coupled to a boson core that undergoes a transition from spherical to @xmath33 shapes . at the critical point , an elegant analytic solution , called @xmath34 , has been obtained starting from the bohr hamiltonian @xcite . in this study , we investigate the transition @xmath35 in @xmath36 nuclei . the new algebraic solution for a - odd nuclei is introduced . for this transition only the boson core experience the transition and fermion with @xmath37 and @xmath2 coupled to boson core . we evaluate exact solutions for eigenstate and energy eigenvalues for transitional region in the ibfm by using the dual algebraic structure for the two level pairing model that based on richardson - gaudin method and changing the control parameter that based on affine @xmath0 lie algebra . in order to the investigation of phase transition , we calculate observables such as level crossing , expectation values of the d - boson number operator , ground - state energy and its first derivative . the low - lying states of @xmath38 and @xmath39 isotopes have been studied within suggested model . the results of calculations for these nuclei will present for energy levels and transitions probabilities , two neutron separation energies and will compare with the corresponding the experimental data . + this paper is organized as follows : section 2 briefly summarizes theoretical aspects of transitional hamiltonian and affine @xmath0 algebraic technique . sections 3 and 4 include the results and experimental evidence and sect . 5 is devoted to the summary and some conclusions . the @xmath40 algebra has been explained in detail in refs @xcite.the @xmath40 algebra is produced by @xmath41 , @xmath42 and @xmath43 , which satisfies the following commutation relations @xmath44={\pm}s^{\pm } \quad , \,\,\ , [ s^{+},s^{- } ] = -2s^{0}\ ] ] the quadratic casimir operator of @xmath40 can be written as @xmath45 the basis states of an irreducible representation @xmath46 @xmath47 , @xmath48 , are determined by a single number @xmath49 , @xmath49 where can be any positive number and @xmath50 therefore@xcite , @xmath51 in ibm , the generators of @xmath52 generated by the d - boson pairing algebra @xmath53 similarly , s- boson pairing algebra forms another @xmath54 algebra generated by @xmath55 @xmath56is the s and d boson pairing algebras generated by @xmath57 because of duality relationships @xcite , it is known that the base of @xmath58 and @xmath59 are simultaneously the basis of @xmath60 and @xmath61 , respectively . by use of duality relations @xcite , the casimir operators of @xmath62 and @xmath63 can also be expressed in terms of the casimir operators of @xmath52 and @xmath56 , respectively @xmath64 @xmath65 the infinite dimensional @xmath40 algebra that is generated by use of @xcite @xmath66 where @xmath67 and @xmath68 are real parameters and @xmath69 can be @xmath70 . these generators satisfy the commutation relations @xmath71=\pm s_{m+n}^{\pm } \quad\quad , \quad\quad [ s_{m}^{+},s_{n}^{- } ] = -2s_{m+n+1}^{0}\ ] ] then,@xmath72generate an affine lie algebra@xmath0without central extension . in odd a nuclei the bose @xmath73 fermi symmetries are associated with each of the dynamic symmetries of ibm-1@xcite . so , the boson algebraic structure will be always taken to be @xmath74 , while the fermion algebraic structure will depend on the values of the angular momenta , j , taken into consideration @xcite . first we considered the case that a system of n bosons ( with l=0 , 2 ) coupled to a fermion with angular momentum j=1/2 . the lattice of algebras in this case is shown in fig.1.in figs 1 , 2 , the chain 1 show the state that bosons have @xmath75 dynamical symmetric while bosons in chain 2 have @xmath76 dynamical symmetric.by employing the generators of algebra @xmath0 and casimir operators of subalgebras , the following hamiltonian for transitional region between @xmath77 limits is prepared ) coupled to a fermion with angular momentum @xmath78.[fig:12],height=302 ] ) coupled to a fermion with angular momentum @xmath79.[fig:13],height=302 ] @xmath80 following this , we considered the state that the odd nucleon being in a j=3/2 shell . the lattice of algebras in this case is also shown in fig.2 .the following hamiltonian for state that odd nucleon being in a j=3/2 shell for transitional region between @xmath77 limits is prepared @xmath81 eqs.(11 ) and ( 12 ) are the suggested hamiltonians for boson - fermion systems with @xmath82 , respectively and @xmath83 , @xmath84 , @xmath85 , @xmath86 are real parameters . by considering eqs.(2),(7),(8 ) , it can be shown that hamiltonians ( 11 ) and ( 12 ) are equivalent with @xmath87 hamiltonian when @xmath88 and with @xmath89 hamiltonian if @xmath90 and @xmath91 . thus , as mentioned because that only the boson core experience the transition and fermion coupled to boson core , the @xmath92 situation just corresponds to @xmath93 transitional region . in our calculation , we take @xmath94 constant value and @xmath67 change between 0 and @xmath68 . for evaluating the eigenvalues of hamiltonians ( 11 ) and ( 12 ) the eigenstates are considered as @xcite @xmath95 eigenstates of hamiltonians ( 11 ) and ( 12 ) can obtain with using the fourier - laurent expansion of eigenstates and @xmath96 generators in terms of c - unknown number parameters @xmath97 with @xmath98 . it means , one can consider the eigenstates as @xcite @xmath99 where @xmath100 is the normalization factor and @xmath101 the c - numbers @xmath102 are determined through the following set of equations : @xmath103 with @xmath104 coefficient , we can calculate lowest weight state , @xmath105 , in terms of boson and fermion part.for the j=1/2 case we have : @xmath106 @xmath107 the lowest weight state for the j=3/2 case is calculated as : @xmath108 @xmath109 the @xmath110symbols represent clebsch - gordan coefficients . where @xmath111 @xmath112 the eigenvalues of hamiltonians ( 11 ) , ( 12 ) can then be expressed ; @xmath113 @xmath114 @xmath115 the quantum number @xmath116 is related to the total boson number @xmath117 by @xmath118 in order to obtain the numerical results for energy spectra @xmath119 of considered nuclei , a set of non - linear @xmath120 equations ( bae ) with k- unknowns for k - pair excitations must be solved @xcite also constants of hamiltonian with least square fitting processes to experimental data is obtained . to this aim , we have changed variables as @xmath121 so , the new form of eq.(16 ) would be @xmath122 to calculate the roots of @xmath123 equations ( bae ) with specified values of @xmath124 and @xmath125 , we have solved eq . ( 24 ) with definite values of c and @xmath126 @xcite.then , we carry out this procedure with different values of c and @xmath126 to give energy spectra with minimum variation in compare to experimental values @xcite ; @xmath127 ( @xmath128 the number of energy levels where included in the fitting processes ) . the method for optimizing the set of parameters in the hamiltonian @xmath129 includes carrying out a least - square fit ( lsf ) of the excitation energies of selected states @xcite this section presented the calculated phase transition observables such as level crossing , ground - state energy and the derivative of the energy , expectation values of the d - boson number operator and energy differences . to display how the energy levels change as a function of the control parameter c and the total number of bosons n , the lowest energy levels as a function of c for @xmath130 bosons are shown in fig.3 and fig.4 , where in fig.3 other fixed parameters are @xmath131 , @xmath132 , @xmath133 , @xmath134 and fig.4 obtained with @xmath135 , @xmath136 , @xmath137 . figs show how the energy levels as a function of the control parameter c evolve from one dynamical symmetry limit to the other . it can be seen from figs that numerous level crossings occur ; especially in the region around @xmath138 . the crossings are due to the fact that @xmath139 , @xmath140 quantum number called seniority , is preserved along the whole path between @xmath16 and @xmath14 @xcite . with increasing n , level crossing increase that in fig.4 clearly shows . in the hamiltonian ( 11 ) for @xmath130 bosons with@xmath141.[fig:1],title="fig:",height=226 ] in the hamiltonian ( 11 ) for @xmath130 bosons with@xmath141.[fig:1],title="fig:",height=226 ] .[fig:2],title="fig:",height=226 ] .[fig:2],title="fig:",height=226 ] for a system with @xmath142 bosons.[fig:3],title="fig:",height=226 ] for a system with @xmath142 bosons.[fig:3],title="fig:",height=226 ] the ground state energy is an important observable of phase transition . so , we calculated the ground - state energy , @xmath143 and its first derivative , @xmath144 . fig.5 shows changing of the ground - state energy and its first derivative versus the control parameter c. both operators , @xmath143 and @xmath144 , are approximately zero in one phase and different from zero in the other phase . since low n bosons is chosen , it is not possible to distinguish whether the transition is first or second order such as done in the even - even case @xcite . an appropriate quantal order parameter is : @xmath145 in order to obtain @xmath146 , we act @xmath147 on the eigenstate , @xmath148 @xmath149 -boson number operator for the lowest states as a function of @xmath150 control parameter for a @xmath78 particle coupled to a system of @xmath151 bosons undergoing a @xmath152 transition ( left panel ) and single fermion with @xmath79 coupled to a system of @xmath151 bosons ( right panel).[fig:4],title="fig:",height=226 ] -boson number operator for the lowest states as a function of @xmath150 control parameter for a @xmath78 particle coupled to a system of @xmath151 bosons undergoing a @xmath152 transition ( left panel ) and single fermion with @xmath79 coupled to a system of @xmath151 bosons ( right panel).[fig:4],title="fig:",height=226 ] fig.6 shows the expectation values of the d - boson number operator for the lowest states as a function of c control parameter for n=10 bosons . fig.6 displays that the expectation values of the number of d bosons for each j , @xmath153 , remain approximately constant for @xmath154 and only begin to change rapidly for @xmath155 . the near constancy of @xmath153 for @xmath156 , is a obvious indication that @xmath18 dynamical symmetry preserves in this region to a high degree and also the @xmath153 values change rapidly with c over the range @xmath157 . it can be seen from fig.6 that in due to the presence of the fermion , the transition is made sharper for states that a @xmath78 particle coupled to a system of @xmath151 bosons undergoing a @xmath152 transition ( left panel ) while is made smoother for a @xmath79 particle coupled to a system of @xmath151 bosons ( right panel ) . fig.7 displays continues energy differences in terms of control parameter , c , for states that a @xmath78 and @xmath79 particle coupled to a system of ( s , d ) bosons . fig.7 shows that during transition from one limit to another exist the points that energy is minimum or maximum near the critical point . , for states that a @xmath79 ( top ) and @xmath78(bottom ) particle coupled to a system of @xmath151 bosons.[fig:5],title="fig:",height=226 ] , for states that a @xmath79 ( top ) and @xmath78(bottom ) particle coupled to a system of @xmath151 bosons.[fig:5],title="fig:",height=226 ] , for states that a @xmath79 ( top ) and @xmath78(bottom ) particle coupled to a system of @xmath151 bosons.[fig:5],title="fig:",height=226 ] , for states that a @xmath79 ( top ) and @xmath78(bottom ) particle coupled to a system of @xmath151 bosons.[fig:5],title="fig:",height=226 ] this section presented the calculated results of low - lying states of the odd -a ba and rh isotopes . the results include energy levels and the b ( e2)values and two - neutron separation energies . nuclei in the mass regions around @xmath158 @xcite and @xmath159 @xcite have transitional characteristics intermediate between spherical and gamma - unstable shapes . the theoretical and experimental studies of energy spectra done in refs.@xcite show rh and ba isotopes have @xmath160 transitional characteristics . .the possible occurrence of this symmetry in @xmath161 has been recently suggested @xcite.the negative parity states in the odd - even nuclei rh are built mainly on the @xmath162 shell model orbit@xcite . the single - particle orbits @xmath163 establish the positive parity states in odd - mass ba isotopes@xcite . in this study , a simplifying assumption is made that single particle states are built on the @xmath164 and @xmath165 . we therefore analyze the negative parity states of the odd - proton nuclei , @xmath166 and positive parity states of the odd - neutron nuclei , @xmath167 . in order to obtain energy spectrum and realistic calculation for these nuclei , we need to specify hamiltonian parameters ( 11 ) , ( 12 ) . eigenvalues of these systems are obtained by solving bethe - ansatz equations with least square fitting processes to experimental data to obtain constants of hamiltonian . the best fits for hamiltonian s parameters , namely @xmath168 , @xmath169 , @xmath170 and @xmath171 , used in the present work are shown in table 1 , 2.tables 3(a , b ... e ) and 4(a , b ... f ) are shown calculated energy spectra along with the experimental values . figure.8 and figure.9 are also shown a comparison between the available experimental levels and the predictions of our results for the @xmath166 and @xmath167 isotopes in the low - lying region of spectra . an acceptable degree of agreement is obvious between them . we have tried to extract the best set of parameters which reproduce these complete spectra with minimum variations . it means that our suggestion to use this transitional hamiltonian for the description of the rh and ba isotopic chain would not have any contradiction with other theoretical studies done with special hypotheses about mixing of intruder and normal configurations . on the other hand , predictions of our model for the control parameter of considered nuclei , c , describe the vibrational , i.e.@xmath172 , or rotational , namely @xmath173 , confirm this mixing of both vibrating and rotating structures in these nuclei when @xmath174 . fig.10 and fig.11 display a comparison between the calculated continues energy differences and experimental data for ba and rh isotopes , respectively . it can be seen from figs that our results for ba isotopes are better than for rh isotopes . one of the most basic structural predictions of @xmath175 transition is a @xmath176 value . the ratio equal to @xmath177 indicates the spectrum of transitional nuclei @xcite . thus we calculated this quantity for rh and ba isotopes . fig.12 shows @xmath178 prediction values for rh and ba isotopes . for rh isotopes this value evolves from @xmath179 to @xmath180 while ba isotopes vary of @xmath181 to @xmath182 . fig.12 displays that @xmath178 values for @xmath183 and @xmath184 isotopes are approximately @xmath185 . [ cols= " < " , ] shape phase transitions in nuclei can be studied experimentally by considering the behavior of the ground state energies of a series of isotopes , or , more conveniently , the behavior of the two - neutron separation energies , @xmath186 @xcite.on the other hand , the ground - state two - neutron separation energies , @xmath187 , are observables very sensitive to the details of the nuclear structure . the occurrence of continuities in the behavior of two - neutron separation energies describe a second - order shape - phase transition between spherical and @xmath188 rotor limits @xcite.in due to , we have investigated the evolution of two - neutron separation energies along the ba and rh isotopic chains by both experimental and theoretical values , which have been presented in fig.13 . the binding energy as a function of proton and neutron number is given by @xcite @xmath189 where @xmath190 is the number of proton ( neutron ) bosons in the valence shell , @xmath191 the contribution from the core and @xmath192 is the contribution to the binding energy due to the deformation . using eq . ( 35 ) , one obtains the following relation for the two - neutron separation energy@xcite : @xmath193 using the @xmath194 empirical values for these isotopic chains @xcite we have extracted @xmath195 mev and @xmath196 mev for ba and rh , respectively . then , we obtained the two - neutron separation energies , which are shown in fig.13 , together with the experimental values . it can be seen from fig.13 that exist continuities ( linear variation ) in the behavior of two - neutron separation energies thus the phase transition for ba and rh isotopic chains is of second order .our result confirmed the predictions of done in refs . @xcite , where they suggest a linear variation of @xmath194 with respect to the neutron number for the @xmath197 transitional region . ( in kev ) for ba isotopes ( 1eft panel ) and rh isotopes ( right panel ) . experimental data from @xcite.[fig:11],title="fig:",height=226 ] ( in kev ) for ba isotopes ( 1eft panel ) and rh isotopes ( right panel ) . experimental data from @xcite.[fig:11],title="fig:",height=226 ] in this paper , we have analyzed transition from spherical to @xmath20 shapes in odd -a nuclei . key observables of phase transition such as level crossing , ground - state energy and derivative of the ground - state energy and expectation values of the d - boson number operator have calculated . we have presented experimental evidence for the @xmath198 transition for negative parity states of the @xmath166 isotopic chain and positive parity states of @xmath38 isotopic chain , and performed an analysis for these isotopes via a su(1,1)-based hamiltonian . the results indicate that the energy spectra of the rh and ba isotopes can be reproduced quite well . the calculated b(e2)values and two neutron separation energies are agreements with the available experimental data . our results show that rh isotopes have gamma - unstable rotor features but the vibrational character is dominant while a dominancy of dynamical symmetry o(6 ) exist for ba isotopic chain and also @xmath199 and @xmath200 isotopes are as the best candidates for @xmath201 transition . d. rowe , nuclear physics a 745 , 47 ( 2004 ) . f. iachello and a. arima , the interacting boson model ( cambridge university press , 1987 ) . f. iachello , physical review letters 85 , 3580 ( 2000 ) . f. iachello , physical review letters 87 , 052502 ( 2001 ) . r. gilmore , s. deans , et al . , physical review c 23 , 1254 ( 1981 ) . p. cejnar , j. jolie , and r. f. casten , reviews of modern physics 82 , 2155 ( 2010 ) . f. iachello , physical review letters 91 , 132502 ( 2003 ) . f. iachello and p. van isacker , the interacting boson - fermion model ( cambridge university press , 1991 ) . o. scholten and n. blasi , nuclear physics a 380 , 509 ( 1982 ) . c. alonso , j. arias , l. fortunato , and a. vitturi , physical review c 72 , 061302 ( 2005 ) . c. alonso , j. arias , and a. vitturi , physical review c 75 , 064316 ( 2007 ) . c. alonso , j. arias , l. fortunato , and a. vitturi , physical review c 79 , 014306 ( 2009 ) . m. bykata , c. alonso , j. arias , l. fortunato , and a. vitturi , physical review c 82 , 014317 ( 2010 ) . f. iachello , physical review letters 95 , 052503 ( 2005 ) . m. caprio and f. iachello , nuclear physics a 781 , 26 ( 2007 ) . m. jafarizadeh , n. fouladi , h. sabri , and b. r. maleki , nuclear physics a 890 , 29 ( 2012 ) . f. pan and j. draayer , nuclear physics a 636 , 156 ( 1998 ) . f. pan , x. zhang , and j. draayer , journal of physics a : mathematical and general 35 , 7173 ( 2002 ) . m. caprio , j. skrabacz , and f. iachello , journal of physics a : mathematical and theoretical 44 , 075303 ( 2011 ) . d. rowe , m. carvalho , and j. repka , reviews of modern physics 84 , 711 ( 2012 ) . national nuclear data center , http : www.nndc.bnl.gov/chart/recolor.jspnewcolor=dm . j. jolie , s. heinze , p. van isacker , and r. casten , physical review c 70 , 011305 ( 2004 ) . d. petrellis , a. leviatan , and f. iachello , annals of physics 326 , 926 ( 2011 ) . e. williams , r. casperson , and v. werner , physical review c 81 , 054306 ( 2010 ) . g. maino , a. ventura , a. bizzeti - sona , and p. blasi , zeitschrift fr physik a hadrons and nuclei 340 , 241 ( 1991 ) . j. arias , c. alonso , and m. lozano , nuclear physics a 466 , 295 ( 1987 ) . s. abu - musleh , h. abu - zeid , and o. scholten , nuclear physics a 927 , 91 ( 2014 ) . m. fetea , r. cakirli , r. casten , d. warner , e. mccutchan , d. meyer , a. heinz , h. ai , g. grdal , j. qian , et al . , physical review c 73 , 051301 ( 2006 ) . c. alonso , j. arias , and m. lozano , journal of physics g : nuclear physics 13 , 1269 ( 1987 ) . r. casten and e. mccutchan , journal of physics g : nuclear and particle physics 34 , r285 ( 2007 ) . b. singh , a. a. rodionov , and y. l. khazov , nuclear data sheets 109 , 517 ( 2008 ) . n. zamfir , s. anghel , and g. cata - danil , in aip conference proceedings , vol . 1072 ( 2008 ) .

the spherical to gamma - unstable nuclei shape- phase transition in odd - a nuclei is investigated by using the dual algebraic structures and the affine @xmath0 lie algebra within the framework of the interacting boson - fermion model . the new algebraic solution for a - odd nuclei is introduced . in this model , single @xmath1 and @xmath2 fermions are coupled with an even - even boson core . energy spectra , quadrupole electromagnetic transitions and an expectation value of the d - boson number operator are presented . experimental evidence for the @xmath3 transition in odd -a @xmath4 and @xmath5 isotopes is presented . the low - states energy spectra and @xmath6values for these nuclei have been also calculated and compared with the experimental data .

<s>[INST]quantum phase transitions @xmath7 are sudden changes in the structure of a physical system . nuclear physics has important contributions to make to their study because nuclei display a variety of phases in systems ranging from few to many particles @xcite.the signs of @xmath8 in nuclear physics are changes in mass and radius of nuclei and quantities such as level crossing and electromagnetic transition rates when the number of protons or neutrons is modified . phase transition happens in both even - even and @xmath9 nuclei . phase transitions investigations have been mostly performed on even - even systems @xcite within the framework of the interacting boson model @xmath10 @xcite , which describe nuclei in terms of correlated pairs of nucleons with @xmath11,@xmath12 treated as bosons @xmath13 . the ibm hamiltonian has exact solutions in three dynamical symmetry limits ( @xmath14,@xmath15 , and @xmath16 ) . these situations correspond to the spherical , axially deformed , and gamma - unstable ground state shapes , respectively . the transition between the @xmath14-@xmath17 limits is a first - order shape - phase transition while a second - order shape - phase transition occurs between the @xmath18 and @xmath19 limits @xcite . during a transition from one limit to another , meet the points in which potential has flat behavior . these points are called critical point.recently iachello introduced the so - called critical point symmetries in the framework of the collective model for even - even nuclei . the critical point from spherical to @xmath20 shapes , called @xmath21 @xcite , the critical point from spherical to axially deformed shapes , called @xmath22 @xcite , and the critical point from axially deformed shapes to triaxial shapes , called y(5 ) @xcite . phase transitions is also investigate in odd - a nuclei within the framework of interacting boson - fermion model @xmath23@xcite , which describe nuclei in terms of correlated pairs , with @xmath24 ( @xmath25 , @xmath26 bosons ) , and unpaired particles of angular momentum @xmath27 @xmath28.studies of @xmath8 in odd - even nuclei were implicitly initiated years ago by scholten and blasi @xcite . several explicit studies have recently been made by alonso et al . @xcite and by boyukata et al . @xcite , who also have suggested a simple form of the ibfm hamiltonian , particularly well - suited to study @xmath29 in odd - even nuclei because of their supersymmetric properties . similar to even - even nuclei , also exists critical point for odd - even and even - odd nuclei but in this case , critical points show with @xmath30 and @xmath31 that @xmath27 is the angular momentum of single nucleon . iachello @xcite has been the case of a @xmath32 fermion coupled to a boson core that undergoes a transition from spherical to @xmath33 shapes . at the critical point , an elegant analytic solution , called @xmath34 , has been obtained starting from the bohr hamiltonian @xcite . in this study , we investigate the transition @xmath35 in @xmath36 nuclei . the new algebraic solution for a - odd nuclei is introduced . for this transition only the boson core experience the transition and fermion with @xmath37 and @xmath2 coupled to boson core . we evaluate exact solutions for eigenstate and energy eigenvalues for transitional region in the ibfm by using the dual algebraic structure for the two level pairing model that based on richardson - gaudin method and changing the control parameter that based on affine @xmath0 lie algebra . in order to the investigation of phase transition , we calculate observables such as level crossing , expectation values of the d - boson number operator , ground - state energy and its first derivative . the low - lying states of @xmath38 and @xmath39 isotopes have been studied within suggested model . the results of calculations for these nuclei will present for energy levels and transitions probabilities , two neutron separation energies and will compare with the corresponding the experimental data . + this paper is organized as follows : section 2 briefly summarizes theoretical aspects of transitional hamiltonian and affine @xmath0 algebraic technique . sections 3 and 4 include the results and experimental evidence and sect . 5 is devoted to the summary and some conclusions . the @xmath40 algebra has been explained in detail in refs @xcite.the @xmath40 algebra is produced by @xmath41 , @xmath42 and @xmath43 , which satisfies the following commutation relations @xmath44={\pm}s^{\pm } \quad , \,\,\ , [ s^{+},s^{- } ] = -2s^{0}\ ] ] the quadratic casimir operator of @xmath40 can be written as @xmath45 the basis states of an irreducible representation @xmath46 @xmath47 , @xmath48 , are determined by a single number @xmath49 , @xmath49 where can be any positive number and @xmath50 therefore@xcite , @xmath51 in ibm , the generators of @xmath52 generated by the d - boson pairing algebra @xmath53 similarly , s- boson pairing algebra forms another @xmath54 algebra generated by @xmath55 @xmath56is the s and d boson pairing algebras generated by @xmath57 because of duality relationships @xcite , it is known that the base of @xmath58 and @xmath59 are simultaneously the basis of @xmath60 and @xmath61 , respectively . by use of duality relations @xcite , the casimir operators of @xmath62 and @xmath63 can also be expressed in terms of the casimir operators of @xmath52 and @xmath56 , respectively @xmath64 @xmath65 the infinite dimensional @xmath40 algebra that is generated by use of @xcite @xmath66 where @xmath67 and @xmath68 are real parameters and @xmath69 can be @xmath70 . these generators satisfy the commutation relations @xmath71=\pm s_{m+n}^{\pm } \quad\quad , \quad\quad [ s_{m}^{+},s_{n}^{- } ] = -2s_{m+n+1}^{0}\ ] ] then,@xmath72generate an affine lie algebra@xmath0without central extension . in odd a nuclei the bose @xmath73 fermi symmetries are associated with each of the dynamic symmetries of ibm-1@xcite . so , the boson algebraic structure will be always taken to be @xmath74 , while the fermion algebraic structure will depend on the values of the angular momenta , j , taken into consideration @xcite . first we considered the case that a system of n bosons ( with l=0 , 2 ) coupled to a fermion with angular momentum j=1/2 . the lattice of algebras in this case is shown in fig.1.in figs 1 , 2 , the chain 1 show the state that bosons have @xmath75 dynamical symmetric while bosons in chain 2 have @xmath76 dynamical symmetric.by employing the generators of algebra @xmath0 and casimir operators of subalgebras , the following hamiltonian for transitional region between @xmath77 limits is prepared ) coupled to a fermion with angular momentum @xmath78.[fig:12],height=302 ] ) coupled to a fermion with angular momentum @xmath79.[fig:13],height=302 ] @xmath80 following this , we considered the state that the odd nucleon being in a j=3/2 shell . the lattice of algebras in this case is also shown in fig.2 .the following hamiltonian for state that odd nucleon being in a j=3/2 shell for transitional region between @xmath77 limits is prepared @xmath81 eqs.(11 ) and ( 12 ) are the suggested hamiltonians for boson - fermion systems with @xmath82 , respectively and @xmath83 , @xmath84 , @xmath85 , @xmath86 are real parameters . by considering eqs.(2),(7),(8 ) , it can be shown that hamiltonians ( 11 ) and ( 12 ) are equivalent with @xmath87 hamiltonian when @xmath88 and with @xmath89 hamiltonian if @xmath90 and @xmath91 . thus , as mentioned because that only the boson core experience the transition and fermion coupled to boson core , the @xmath92 situation just corresponds to @xmath93 transitional region . in our calculation , we take @xmath94 constant value and @xmath67 change between 0 and @xmath68 . for evaluating the eigenvalues of hamiltonians ( 11 ) and ( 12 ) the eigenstates are considered as @xcite @xmath95 eigenstates of hamiltonians ( 11 ) and ( 12 ) can obtain with using the fourier - laurent expansion of eigenstates and @xmath96 generators in terms of c - unknown number parameters @xmath97 with @xmath98 . it means , one can consider the eigenstates as @xcite @xmath99 where @xmath100 is the normalization factor and @xmath101 the c - numbers @xmath102 are determined through the following set of equations : @xmath103 with @xmath104 coefficient , we can calculate lowest weight state , @xmath105 , in terms of boson and fermion part.for the j=1/2 case we have : @xmath106 @xmath107 the lowest weight state for the j=3/2 case is calculated as : @xmath108 @xmath109 the @xmath110symbols represent clebsch - gordan coefficients . where @xmath111 @xmath112 the eigenvalues of hamiltonians ( 11 ) , ( 12 ) can then be expressed ; @xmath113 @xmath114 @xmath115 the quantum number @xmath116 is related to the total boson number @xmath117 by @xmath118 in order to obtain the numerical results for energy spectra @xmath119 of considered nuclei , a set of non - linear @xmath120 equations ( bae ) with k- unknowns for k - pair excitations must be solved @xcite also constants of hamiltonian with least square fitting processes to experimental data is obtained . to this aim , we have changed variables as @xmath121 so , the new form of eq.(16 ) would be @xmath122 to calculate the roots of @xmath123 equations ( bae ) with specified values of @xmath124 and @xmath125 , we have solved eq . ( 24 ) with definite values of c and @xmath126 @xcite.then , we carry out this procedure with different values of c and @xmath126 to give energy spectra with minimum variation in compare to experimental values @xcite ; @xmath127 ( @xmath128 the number of energy levels where included in the fitting processes ) . the method for optimizing the set of parameters in the hamiltonian @xmath129 includes carrying out a least - square fit ( lsf ) of the excitation energies of selected states @xcite this section presented the calculated phase transition observables such as level crossing , ground - state energy and the derivative of the energy , expectation values of the d - boson number operator and energy differences . to display how the energy levels change as a function of the control parameter c and the total number of bosons n , the lowest energy levels as a function of c for @xmath130 bosons are shown in fig.3 and fig.4 , where in fig.3 other fixed parameters are @xmath131 , @xmath132 , @xmath133 , @xmath134 and fig.4 obtained with @xmath135 , @xmath136 , @xmath137 . figs show how the energy levels as a function of the control parameter c evolve from one dynamical symmetry limit to the other . it can be seen from figs that numerous level crossings occur ; especially in the region around @xmath138 . the crossings are due to the fact that @xmath139 , @xmath140 quantum number called seniority , is preserved along the whole path between @xmath16 and @xmath14 @xcite . with increasing n , level crossing increase that in fig.4 clearly shows . in the hamiltonian ( 11 ) for @xmath130 bosons with@xmath141.[fig:1],title="fig:",height=226 ] in the hamiltonian ( 11 ) for @xmath130 bosons with@xmath141.[fig:1],title="fig:",height=226 ] .[fig:2],title="fig:",height=226 ] .[fig:2],title="fig:",height=226 ] for a system with @xmath142 bosons.[fig:3],title="fig:",height=226 ] for a system with @xmath142 bosons.[fig:3],title="fig:",height=226 ] the ground state energy is an important observable of phase transition . so , we calculated the ground - state energy , @xmath143 and its first derivative , @xmath144 . fig.5 shows changing of the ground - state energy and its first derivative versus the control parameter c. both operators , @xmath143 and @xmath144 , are approximately zero in one phase and different from zero in the other phase . since low n bosons is chosen , it is not possible to distinguish whether the transition is first or second order such as done in the even - even case @xcite . an appropriate quantal order parameter is : @xmath145 in order to obtain @xmath146 , we act @xmath147 on the eigenstate , @xmath148 @xmath149 -boson number operator for the lowest states as a function of @xmath150 control parameter for a @xmath78 particle coupled to a system of @xmath151 bosons undergoing a @xmath152 transition ( left panel ) and single fermion with @xmath79 coupled to a system of @xmath151 bosons ( right panel).[fig:4],title="fig:",height=226 ] -boson number operator for the lowest states as a function of @xmath150 control parameter for a @xmath78 particle coupled to a system of @xmath151 bosons undergoing a @xmath152 transition ( left panel ) and single fermion with @xmath79 coupled to a system of @xmath151 bosons ( right panel).[fig:4],title="fig:",height=226 ] fig.6 shows the expectation values of the d - boson number operator for the lowest states as a function of c control parameter for n=10 bosons . fig.6 displays that the expectation values of the number of d bosons for each j , @xmath153 , remain approximately constant for @xmath154 and only begin to change rapidly for @xmath155 . the near constancy of @xmath153 for @xmath156 , is a obvious indication that @xmath18 dynamical symmetry preserves in this region to a high degree and also the @xmath153 values change rapidly with c over the range @xmath157 . it can be seen from fig.6 that in due to the presence of the fermion , the transition is made sharper for states that a @xmath78 particle coupled to a system of @xmath151 bosons undergoing a @xmath152 transition ( left panel ) while is made smoother for a @xmath79 particle coupled to a system of @xmath151 bosons ( right panel ) . fig.7 displays continues energy differences in terms of control parameter , c , for states that a @xmath78 and @xmath79 particle coupled to a system of ( s , d ) bosons . fig.7 shows that during transition from one limit to another exist the points that energy is minimum or maximum near the critical point . , for states that a @xmath79 ( top ) and @xmath78(bottom ) particle coupled to a system of @xmath151 bosons.[fig:5],title="fig:",height=226 ] , for states that a @xmath79 ( top ) and @xmath78(bottom ) particle coupled to a system of @xmath151 bosons.[fig:5],title="fig:",height=226 ] , for states that a @xmath79 ( top ) and @xmath78(bottom ) particle coupled to a system of @xmath151 bosons.[fig:5],title="fig:",height=226 ] , for states that a @xmath79 ( top ) and @xmath78(bottom ) particle coupled to a system of @xmath151 bosons.[fig:5],title="fig:",height=226 ] this section presented the calculated results of low - lying states of the odd -a ba and rh isotopes . the results include energy levels and the b ( e2)values and two - neutron separation energies . nuclei in the mass regions around @xmath158 @xcite and @xmath159 @xcite have transitional characteristics intermediate between spherical and gamma - unstable shapes . the theoretical and experimental studies of energy spectra done in refs.@xcite show rh and ba isotopes have @xmath160 transitional characteristics . .the possible occurrence of this symmetry in @xmath161 has been recently suggested @xcite.the negative parity states in the odd - even nuclei rh are built mainly on the @xmath162 shell model orbit@xcite . the single - particle orbits @xmath163 establish the positive parity states in odd - mass ba isotopes@xcite . in this study , a simplifying assumption is made that single particle states are built on the @xmath164 and @xmath165 . we therefore analyze the negative parity states of the odd - proton nuclei , @xmath166 and positive parity states of the odd - neutron nuclei , @xmath167 . in order to obtain energy spectrum and realistic calculation for these nuclei , we need to specify hamiltonian parameters ( 11 ) , ( 12 ) . eigenvalues of these systems are obtained by solving bethe - ansatz equations with least square fitting processes to experimental data to obtain constants of hamiltonian . the best fits for hamiltonian s parameters , namely @xmath168 , @xmath169 , @xmath170 and @xmath171 , used in the present work are shown in table 1 , 2.tables 3(a , b ... e ) and 4(a , b ... f ) are shown calculated energy spectra along with the experimental values . figure.8 and figure.9 are also shown a comparison between the available experimental levels and the predictions of our results for the @xmath166 and @xmath167 isotopes in the low - lying region of spectra . an acceptable degree of agreement is obvious between them . we have tried to extract the best set of parameters which reproduce these complete spectra with minimum variations . it means that our suggestion to use this transitional hamiltonian for the description of the rh and ba isotopic chain would not have any contradiction with other theoretical studies done with special hypotheses about mixing of intruder and normal configurations . on the other hand , predictions of our model for the control parameter of considered nuclei , c , describe the vibrational , i.e.@xmath172 , or rotational , namely @xmath173 , confirm this mixing of both vibrating and rotating structures in these nuclei when @xmath174 . fig.10 and fig.11 display a comparison between the calculated continues energy differences and experimental data for ba and rh isotopes , respectively . it can be seen from figs that our results for ba isotopes are better than for rh isotopes . one of the most basic structural predictions of @xmath175 transition is a @xmath176 value . the ratio equal to @xmath177 indicates the spectrum of transitional nuclei @xcite . thus we calculated this quantity for rh and ba isotopes . fig.12 shows @xmath178 prediction values for rh and ba isotopes . for rh isotopes this value evolves from @xmath179 to @xmath180 while ba isotopes vary of @xmath181 to @xmath182 . fig.12 displays that @xmath178 values for @xmath183 and @xmath184 isotopes are approximately @xmath185 . [ cols= " < " , ] shape phase transitions in nuclei can be studied experimentally by considering the behavior of the ground state energies of a series of isotopes , or , more conveniently , the behavior of the two - neutron separation energies , @xmath186 @xcite.on the other hand , the ground - state two - neutron separation energies , @xmath187 , are observables very sensitive to the details of the nuclear structure . the occurrence of continuities in the behavior of two - neutron separation energies describe a second - order shape - phase transition between spherical and @xmath188 rotor limits @xcite.in due to , we have investigated the evolution of two - neutron separation energies along the ba and rh isotopic chains by both experimental and theoretical values , which have been presented in fig.13 . the binding energy as a function of proton and neutron number is given by @xcite @xmath189 where @xmath190 is the number of proton ( neutron ) bosons in the valence shell , @xmath191 the contribution from the core and @xmath192 is the contribution to the binding energy due to the deformation . using eq . ( 35 ) , one obtains the following relation for the two - neutron separation energy@xcite : @xmath193 using the @xmath194 empirical values for these isotopic chains @xcite we have extracted @xmath195 mev and @xmath196 mev for ba and rh , respectively . then , we obtained the two - neutron separation energies , which are shown in fig.13 , together with the experimental values . it can be seen from fig.13 that exist continuities ( linear variation ) in the behavior of two - neutron separation energies thus the phase transition for ba and rh isotopic chains is of second order .our result confirmed the predictions of done in refs . @xcite , where they suggest a linear variation of @xmath194 with respect to the neutron number for the @xmath197 transitional region . ( in kev ) for ba isotopes ( 1eft panel ) and rh isotopes ( right panel ) . experimental data from @xcite.[fig:11],title="fig:",height=226 ] ( in kev ) for ba isotopes ( 1eft panel ) and rh isotopes ( right panel ) . experimental data from @xcite.[fig:11],title="fig:",height=226 ] in this paper , we have analyzed transition from spherical to @xmath20 shapes in odd -a nuclei . key observables of phase transition such as level crossing , ground - state energy and derivative of the ground - state energy and expectation values of the d - boson number operator have calculated . we have presented experimental evidence for the @xmath198 transition for negative parity states of the @xmath166 isotopic chain and positive parity states of @xmath38 isotopic chain , and performed an analysis for these isotopes via a su(1,1)-based hamiltonian . the results indicate that the energy spectra of the rh and ba isotopes can be reproduced quite well . the calculated b(e2)values and two neutron separation energies are agreements with the available experimental data . our results show that rh isotopes have gamma - unstable rotor features but the vibrational character is dominant while a dominancy of dynamical symmetry o(6 ) exist for ba isotopic chain and also @xmath199 and @xmath200 isotopes are as the best candidates for @xmath201 transition . d. rowe , nuclear physics a 745 , 47 ( 2004 ) . f. iachello and a. arima , the interacting boson model ( cambridge university press , 1987 ) . f. iachello , physical review letters 85 , 3580 ( 2000 ) . f. iachello , physical review letters 87 , 052502 ( 2001 ) . r. gilmore , s. deans , et al . , physical review c 23 , 1254 ( 1981 ) . p. cejnar , j. jolie , and r. f. casten , reviews of modern physics 82 , 2155 ( 2010 ) . f. iachello , physical review letters 91 , 132502 ( 2003 ) . f. iachello and p. van isacker , the interacting boson - fermion model ( cambridge university press , 1991 ) . o. scholten and n. blasi , nuclear physics a 380 , 509 ( 1982 ) . c. alonso , j. arias , l. fortunato , and a. vitturi , physical review c 72 , 061302 ( 2005 ) . c. alonso , j. arias , and a. vitturi , physical review c 75 , 064316 ( 2007 ) . c. alonso , j. arias , l. fortunato , and a. vitturi , physical review c 79 , 014306 ( 2009 ) . m. bykata , c. alonso , j. arias , l. fortunato , and a. vitturi , physical review c 82 , 014317 ( 2010 ) . f. iachello , physical review letters 95 , 052503 ( 2005 ) . m. caprio and f. iachello , nuclear physics a 781 , 26 ( 2007 ) . m. jafarizadeh , n. fouladi , h. sabri , and b. r. maleki , nuclear physics a 890 , 29 ( 2012 ) . f. pan and j. draayer , nuclear physics a 636 , 156 ( 1998 ) . f. pan , x. zhang , and j. draayer , journal of physics a : mathematical and general 35 , 7173 ( 2002 ) . m. caprio , j. skrabacz , and f. iachello , journal of physics a : mathematical and theoretical 44 , 075303 ( 2011 ) . d. rowe , m. carvalho , and j. repka , reviews of modern physics 84 , 711 ( 2012 ) . national nuclear data center , http : www.nndc.bnl.gov/chart/recolor.jspnewcolor=dm . j. jolie , s. heinze , p. van isacker , and r. casten , physical review c 70 , 011305 ( 2004 ) . d. petrellis , a. leviatan , and f. iachello , annals of physics 326 , 926 ( 2011 ) . e. williams , r. casperson , and v. werner , physical review c 81 , 054306 ( 2010 ) . g. maino , a. ventura , a. bizzeti - sona , and p. blasi , zeitschrift fr physik a hadrons and nuclei 340 , 241 ( 1991 ) . j. arias , c. alonso , and m. lozano , nuclear physics a 466 , 295 ( 1987 ) . s. abu - musleh , h. abu - zeid , and o. scholten , nuclear physics a 927 , 91 ( 2014 ) . m. fetea , r. cakirli , r. casten , d. warner , e. mccutchan , d. meyer , a. heinz , h. ai , g. grdal , j. qian , et al . , physical review c 73 , 051301 ( 2006 ) . c. alonso , j. arias , and m. lozano , journal of physics g : nuclear physics 13 , 1269 ( 1987 ) . r. casten and e. mccutchan , journal of physics g : nuclear and particle physics 34 , r285 ( 2007 ) . b. singh , a. a. rodionov , and y. l. khazov , nuclear data sheets 109 , 517 ( 2008 ) . n. zamfir , s. anghel , and g. cata - danil , in aip conference proceedings , vol . 1072 ( 2008 ) .[/INST] the spherical to gamma - unstable nuclei shape- phase transition in odd - a nuclei is investigated by using the dual algebraic structures and the affine @xmath0 lie algebra within the framework of the interacting boson - fermion model . the new algebraic solution for a - odd nuclei is introduced . in this model , single @xmath1 and @xmath2 fermions are coupled with an even - even boson core . energy spectra , quadrupole electromagnetic transitions and an expectation value of the d - boson number operator are presented . experimental evidence for the @xmath3 transition in odd -a @xmath4 and @xmath5 isotopes is presented . the low - states energy spectra and @xmath6values for these nuclei have been also calculated and compared with the experimental data . </s>

sensor networks consist of a large number of small , inexpensive sensor nodes . these nodes have small batteries with limited power and also have limited computational power and storage space . when the battery of a node is exhausted , it is not replaced and the node dies . when sufficient number of nodes die , the network may not be able to perform its designated task . thus the life time of a network is an important characteristic of a sensor network and it is tied up with the life time of a node . various studies have been conducted to increase the life time of the battery of a node by reducing the energy intensive tasks , e.g. , reducing the number of bits to transmit ( @xcite , @xcite ) , making a node to go into power saving modes : ( sleep / listen ) periodically ( @xcite ) , using energy efficient routing ( @xcite , @xcite ) and mac ( @xcite ) . studies that estimate the life time of a sensor network include @xcite . a general survey on sensor networks is @xcite which provides many more references on these issues . in this paper we focus on increasing the life time of the battery itself by energy harvesting techniques ( @xcite , @xcite ) . common energy harvesting devices are solar cells , wind turbines and piezo - electric cells , which extract energy from the environment . among these , solar harvesting energy through photo - voltaic effect seems to have emerged as a technology of choice for many sensor nodes ( @xcite , @xcite ) . unlike for a battery operated sensor node , now there is potentially an _ infinite _ amount of energy available to the node . hence energy conservation need not be the dominant theme . rather , the issues involved in a node with an energy harvesting source can be quite different . the source of energy and the energy harvesting device may be such that the energy can not be generated at all times ( e.g. , a solar cell ) . however one may want to use the sensor nodes at such times also . furthermore the rate of generation of energy can be limited . thus one may want to match the energy generation profile of the harvesting source with the energy consumption profile of the sensor node . it should be done in such a way that the node can perform satisfactorily for a long time , i.e. , at least energy starvation should not be the reason for the node to die . furthermore , in a sensor network , the mac protocol , routing and relaying of data through the network may need to be suitably modified to match the energy generation profiles of different nodes , which may vary with the nodes . in the following we survey the literature on sensor networks with energy harvesting nodes . early papers on energy harvesting in sensor networks are @xcite and @xcite . a practical solar energy harvesting sensor node prototype is described in @xcite . a good recent contribution is @xcite . it provides various deterministic theoretical models for energy generation and energy consumption profiles ( based on @xmath0 traffic models and provides conditions for _ energy neutral operation _ , , when the node can operate indefinitely . in @xcite a sensor node is considered which is sensing certain interesting events . the authors study optimal sleep - wake cycles such that the event detection probability is maximized . a recent survey is @xcite which also provides an optimal sleep - wake cycle for solar cells so as to obtain qos for a sensor node . mac protocols for sensor networks are studied in @xcite , @xcite and @xcite . a general survey is available in @xcite and @xcite . throughput optimal opportunistic mac protocols are discussed in @xcite . in this paper we summarize our recent results ( @xcite ) , on sensor networks with energy harvesting nodes and based on them propose new schemes for scheduling a mac for such networks . the motivating application is estimation of a random field which is one of the canonical applications of sensor networks . the above mentioned theoretical studies are motivated by other applications of sensor networks . in our application , the sensor nodes sense the random field periodically . after sensing , a node generates a packet ( possibly after efficient compression ) . this packet needs to be transmitted to a central node , possibly via other sensor nodes . in an energy harvesting node , sometimes there may not be sufficient energy to transmit the generated packets ( or even sense ) at regular intervals and then the node may need to store the packets till they are transmitted . the energy generated can be stored ( possibly in a finite storage ) for later use . initially we will assume that most of the energy is consumed in transmission only . we will relax this assumption later on . we find conditions for energy neutral operation of a node , i.e. , when the node can work forever and its data queue is stable . we will obtain policies which can support maximum possible data rate . we also obtain energy management ( power control ) policies for transmission which minimize the mean delay of the packets in the queue . we use the above energy mangement policies to develop channel sharing policies at a mac ( multiple access channel ) used by energy harvesting sensor nodes . we are currently investigating appropriate routing algorithms for a network of energy harvesting sensor nodes . the paper is organized as follows . section [ model ] describes the model for a single node and provides the assumptions made for data and energy generation . section [ stability ] provides conditions for energy neutral operation of a node . we obtain stable , power control policies which are throughput optimal . section [ opt ] obtains the power control policies which minimize the mean delay via markov decision theory . a greedy policy is shown to be throughput optimal and provides minimum mean delays for linear transmission . section [ general ] provides a throughput optimal policy when the energy consumed in sensing and processing is non - negligible . a sensor node with a fading channel is also considered . section [ simulation ] provides simulation results to confirm our theoretical findings and compares various energy management policies . section [ tree ] introduces a multiple access channel ( mac ) for energy harvesting nodes . section [ orthogonal ] provides efficient energy management schemes for orthogonal mac protocols . sections [ opportunistic ] and [ csma ] consider macs with fading channels ( orthogonal and csma respectively ) . section [ msimulation ] compares the different mac policies via simulations . section [ conclude ] concludes the paper . in this section we present our model for a single energy harvesting sensor node . we consider a sensor node ( fig . [ fig1 ] ) which is sensing a random field and generating packets to be transmitted to a central node via a network of sensor nodes . the system is slotted . during slot @xmath1 ( defined as time interval @xmath2 $ ] , i.e. , a slot is a unit of time ) @xmath3 bits are generated by the sensor node . although the sensor node may generate data as packets , we will allow arbitrary fragmentation of packets during transmission . thus , packet boundaries are not important and we consider bit strings ( or just fluid ) . the bits @xmath3 are eligible for transmission in @xmath4st slot . the queue length ( in bits ) at time @xmath1 is @xmath5 . the sensor node is able to transmit @xmath6 bits in slot @xmath1 if it uses energy @xmath7 . we assume that transmission consumes most of the energy in a sensor node and ignore other causes of energy consumption ( this is true for many low quality , low rate sensor nodes ( @xcite ) ) . this assumption will be removed in section [ general ] . we denote by @xmath8 the energy available in the node at time @xmath1 . the sensor node is able to replenish energy by @xmath9 in slot @xmath1 . we will initially assume that @xmath10 and @xmath11 are _ iid _ ( independent , identically distributed ) but will generalize this assumption later . it is important to generalize this assumption to capture realistic traffic streams and energy generation profiles . the processes @xmath12 and @xmath13 satisfy @xmath14 where @xmath15 . this assumes that the data buffer and the energy storage buffer are infinite . if in practice these buffers are large enough , this is a good approximation . if not , even then the results obtained provide important insights and the policies obtained often perform well for the finite buffer case . the function @xmath16 will be assumed to be monotonically non - decreasing . an important such function is given by shannon s capacity formula @xmath17 for gaussian channels where @xmath18 is a constant such that @xmath19 is the snr . this is a non - decreasing concave function . at low values of @xmath7 , @xmath20 , i.e. , @xmath16 becomes a linear function . since sensor nodes are energy constrained , this is a practically important case . thus in the following we limit our attention to linear and concave nondecreasing functions @xmath16 . we will also assume that @xmath21 which always holds in practice . many of our results ( especially the stability results ) will be valid when @xmath22 and @xmath23 are stationary , ergodic . these assumptions are general enough to cover most of the stochastic models developed for traffic ( e.g. , markov modulated ) and energy harvesting . of course , in practice , statistics of the traffic and energy harvesting models will be time varying ( e.g. , solar cell energy harvesting will depend on the time of day ) . but often they can be approximated by piecewise stationary processes . for example , energy harvesting by solar cells could be taken as being stationary over one hour periods . then our results could be used over these time periods . often these periods are long enough for the system to attain ( approximate ) stationarity and for our results to remain meaningful . in section [ stability ] we study the stability of this queue and identify easily implementable energy management policies which provide good performance . we will obtain a necessary condition for stability . then we present a transmission policy which achieves the necessary condition , i.e. , the policy is throughput optimal . the mean delay for this policy is not minimal . thus , we obtain other policies which provide lower mean delay . in the next section we will consider policies which minimize mean delay . the proofs of lemma 1 and theorems 1 - 4 are provided in @xcite . let us assume that we have obtained an ( asymptotically ) stationary and ergodic transmission policy @xmath24 which makes @xmath25 ( asymptotically ) stationary with the limiting distribution independent of @xmath26 . taking @xmath27 asymptotically stationary seems to be a natural requirement to obtain ( asymptotic ) stationarity of @xmath25 . in the following @xmath28 will denote generic r.v.s with the distributions of @xmath29 respectively . * lemma 1 * let @xmath16 be concave nondeceasing and @xmath30 be stationary , ergodic sequences . for @xmath24 to be an asymptotically stationary , ergodic energy management policy that makes @xmath31 asymptotically stationary with a proper stationary distribution @xmath32 , it is necessary that @xmath33 < e_{\pi } [ g(t ) ] \leq g(e[y]).$ ] @xmath34 let @xmath35-\epsilon ) \label{disp}\ ] ] where @xmath36 is an appropriately chosen small constant ( see statement of theorem 1 ) . we show that it is a throughput optimal policy , i.e. , using this @xmath7 with @xmath16 satisfying the assumptions in lemma 1 , @xmath25 is asymptotically stationary and ergodic . * theorem 1 * if @xmath37 are stationary , ergodic and @xmath16 is continuous , nondecreasing , concave then if @xmath38 < g(e[y])$ ] , ( [ disp ] ) makes the queue stable ( with @xmath39 such that @xmath40 < g(e[y ] - \epsilon)$ ] ) , i.e. , it has a unique , stationary , ergodic distribution and starting from any initial distribution , @xmath5 converges in total variation to the stationary distribution . henceforth we denote the policy ( [ disp ] ) by to . from results on gi / gi/1 queues ( @xcite ) , if @xmath22 are _ iid _ , @xmath38 < g(e[y ] ) , t_k = min(e_k , e[y ] - \epsilon)$ ] and @xmath41 < \infty $ ] for some @xmath42 then the stationary solution @xmath12 of ( [ eqn1 ] ) satisfies @xmath43 < \infty$ ] . taking @xmath44 for all @xmath1 will provide stability of the queue if @xmath38 < e[g(y)]$ ] . if @xmath16 is linear then this coincides with the necessary condition . if @xmath16 is strictly concave then @xmath45 < g(e[y ] ) $ ] unless @xmath46 $ ] . thus @xmath44 provides a strictly smaller stability region . we will be forced to use this policy if there is no buffer to store the energy harvested . this shows that storing energy allows us to have a larger stability region . we will see in section [ simulation ] that storing energy can also provide lower mean delays . although to is a throughput optimal policy , if @xmath5 is small , we may be wasting some energy . thus , it appears that this policy does not minimize mean delay . it is useful to look for policies which minimize mean delay . based on our experience in @xcite , the greedy policy @xmath47 where @xmath48 , looks promising . in theorem 2 , we will show that the stability condition for this policy is @xmath38 < e[g(y ) ] $ ] which is optimal for linear @xmath16 but strictly suboptimal for a strictly concave @xmath16 ( just as the policy @xmath44 discussed above ) . we will show in section [ opt ] that when @xmath16 is linear , ( [ eqn5 ] ) is not only throughput optimal , it also minimizes long term mean delay . for concave @xmath16 , we will show via simulations that ( [ eqn5 ] ) provides less mean delay than to at low load . however since its stability region is smaller than that of the to policy , at @xmath38 $ ] close to @xmath45 $ ] , the greedy performance rapidly deteriorates . thus it is worthwhile to look for some other good policy . notice that the to policy wastes energy if @xmath49 - \epsilon)$ ] . therfore , we can improve upon it by saving the energy @xmath50-\epsilon - g^{-1}(q_k))$ ] and using it when the @xmath5 is greater than @xmath51-\epsilon)$ ] . however for @xmath16 a log function , using a large amount of energy @xmath52 is also wasteful even when @xmath53 . taking into account these facts we improve over the to policy as @xmath54 + 0.001 ( e_k - cq_k)^+ ) ) \label{onestar}\ ] ] where @xmath55 is a positive constant . the improvement over the to also comes from the fact that if @xmath8 is large , we allow @xmath56 $ ] but only if @xmath5 is not very large . the constants 0.99 and 0.001 were chosen by trial and error from simulations after experimenting with different scenarios . we will see in section [ simulation ] via simulations that this policy , to be denoted by mto can indeed provide lower mean delays than to at loads above @xmath45 $ ] . one advantage of ( [ disp ] ) over ( [ eqn5 ] ) and ( [ onestar ] ) is that while using ( [ disp ] ) , after some time @xmath57-\epsilon$ ] . also , at any time , either one uses up all the energy or uses @xmath58-\epsilon$ ] . thus one can use this policy even if exact information about @xmath8 is not available ( measuring @xmath8 may be difficult in practice ) . in fact , ( [ disp ] ) does not need even @xmath5 while ( [ eqn5 ] ) either uses up all the energy or uses @xmath59 and hence needs only @xmath5 exactly . now we show that under the greedy policy ( [ eqn5 ] ) the queueing process is stable when @xmath38 < e[g(y)]$ ] . in next few results ( theorems 2 and 3 ) we assume that the energy buffer is finite , although large . for this case lemma 1 and theorem 1 also hold under the same assumptions with slight modifications in their proofs . * theorem 2 * if the energy buffer is finite , i.e. , @xmath60 ( but @xmath61 is large enough ) and @xmath38 < e[g(y ) ] $ ] then under the greedy policy ( [ eqn5 ] ) , @xmath62 has an ergodic set . @xmath34 the above result will ensure that the markov chain @xmath63 is ergodic and hence has a unique stationary distribution if @xmath64 is irreducible . a sufficient condition for this is @xmath65 < 1 $ ] and @xmath66 < 1 $ ] because then the state @xmath67 can be reached from any state with a positive probability . in general , @xmath63 can have multiple ergodic sets . then , depending on the initial state , @xmath63 will converge to one of the ergodic sets and the limiting distribution depends on the initial conditions . in this section we choose @xmath7 at time @xmath1 as a function of @xmath5 and @xmath8 such that @xmath68\ ] ] is minimized where @xmath69 is a suitable constant . the minimizing policy is called @xmath70-discount optimal . when @xmath71 , we minimize @xmath72.\ ] ] this optimizing policy is called average cost optimal . by little s law ( @xcite ) an average cost optimal policy also minimizes mean delay . if for a given @xmath73 , the optimal policy @xmath7 does not depend on the past values , and is time invariant , it is called a stationary markov policy . if @xmath22 and @xmath23 are markov chains then these optimization problems are markov decision problems ( mdp ) . for simplicity , in the following we consider these problems when @xmath22 and @xmath23 are _ iid_. we obtain the existence of optimal @xmath70-discount and average cost stationary markov policies . * theorem 3 * if @xmath16 is continuous and the energy buffer is finite , i.e. , @xmath74 then there exists an optimal @xmath70-discounted markov stationary policy . if in addition @xmath38 < g(e[y])$ ] and @xmath75 < \infty$ ] , then there exists an average cost optimal stationary markov policy . the optimal cost @xmath76 does not depend on the initial state . also , then the optimal @xmath70-discount policies tend to an optimal average cost policy as @xmath77 . furthermore , if @xmath78 is the optimal @xmath70-discount cost for the initial state @xmath79 then @xmath80 @xmath34 in section [ stability ] we identified a throughput optimal policy when @xmath16 is nondecreasing , concave . theorem 3 guarantees the existence of an optimal mean delay policy . it is of interest to identify one such policy also . in general one can compute an optimal policy numerically via value iteration or policy iteration but that can be computationally intensive ( especially for large data and energy buffer sizes ) . also it does not provide any insight and requires traffic and energy profile statistics . in section [ stability ] we also provided a greedy policy ( [ eqn5 ] ) which is very intuitive , and is throughput optimal for linear @xmath16 . however for concave @xmath16 ( including the cost function @xmath81 it is _ not _ throughput optimal and provides low mean delays only for low load . next we show that it provides minimum mean delay for linear @xmath16 . * theorem 4 * the greedy policy ( [ eqn5 ] ) is @xmath70-discount optimal for @xmath82 when @xmath83 for some @xmath84 . it is also average cost optimal . @xmath34 the fact that greedy is @xmath70-discount optimal as well as average cost optimal implies that it is good not only for long term average delay but also for transient mean delays . in this section we consider two generalizations . first we will extend the results to the case of fading channels and then to the case where the sensing and the processing energy at a sensor node are non - negligible with respect to the transmission energy . in case of fading channels , we assume flat fading during a slot . in slot @xmath1 the channel gain is @xmath85 . the sequence @xmath86 is assumed stationary , ergodic , independent of the traffic sequence @xmath22 and the energy generation sequence @xmath23 . then if @xmath7 energy is spent in transmission in slot @xmath1 , the @xmath25 process evolves as @xmath87 if the channel state information ( csi ) is not known to the sensor node , then @xmath7 will depend only on @xmath73 . one can then consider the policies used above . for example we could use @xmath88-\epsilon)$ ] . then the data queue is stable if @xmath38 < e[g(h(e[y]-\epsilon))]$ ] . we will call this policy unfaded to . if we use greedy ( [ eqn5 ] ) , then the data queue is stable if @xmath38 < e[g(hy)]$ ] . if csi @xmath85 is available to the node at time @xmath1 , then the following are the throughput optimal policies . if @xmath16 is linear , then @xmath89 for some @xmath90 . then , if @xmath91 and @xmath92 , the optimal policy is : @xmath93-\epsilon)/p(h=\bar{h})$ ] and @xmath94 otherwise . thus if @xmath95 can take an arbitrarily large value with positive probability , then @xmath96 = \infty$ ] at the optimal solution . if @xmath97 , then the water filling ( wf ) policy @xmath98 where @xmath99 is obtained from the average power constraint @xmath100 = e[y ] - \epsilon$ ] , is throughput optimal . this is because it maximizes @xmath101 $ ] with the given constraints . both of the above policies can be improved as before , by not wasting energy when there is not enough data . as in ( [ onestar ] ) in section [ stability ] , we can further improve wf by taking @xmath102 we will call it mwf . these policies will not minimize mean delay . for that , we can use the mdp framework used in section [ opt ] and numerically compute the optimal policies . till now we assumed that all the energy that a node consumes is for transmission . however , sensing , processing and receiving ( from other nodes ) also require significant energy , especially in more recent higher end sensor nodes ( @xcite ) . since we have been considering a single node so far , we will now include the energy consumed by sensing and processing only . for simplicity , we will assume that the node is always in one energy mode ( e.g. , lower energy modes ( @xcite ) available for sensor nodes will not be considered ) . if a sensor node with an energy harvesting system can be operated in energy neutral operation in normal mode itself ( i.e. , it satisfies the conditions in lemma 1 ) , then there is no need to have lower energy modes . otherwise one has to resort to energy saving modes . we will assume that @xmath103 is the energy consumed by the node for sensing and processing in slot @xmath1 . unlike @xmath7 ( which can vary according to @xmath5 ) , @xmath104 can be considered a stationary , ergodic sequence . the rest of the system is as in section [ model ] . now we briefly describe a energy management policy which is an extension of the to policy in section [ stability ] . this can provide an energy neutral operation in the present case . improved / optimal policies can be obtained for this system also but will not be discussed due to lack of space . let @xmath55 be the minimum positive constant such that @xmath38 < g(c)$ ] . then if @xmath105 < e[y]-\delta $ ] , ( where @xmath106 is a small positive constant ) the system can be operated in energy neutral operation : if we take @xmath107 ( which can be done with high probability for all @xmath1 large enough ) , the process @xmath12 will have a unique stationary , ergodic distribution and there will always be energy @xmath103 for sensing and processing for all @xmath1 large enough . the result holds if @xmath108 is an ergodic stationary sequence . the arguments to show this are similar to those in section [ stability ] and are omitted . when the channel has fading , we need @xmath38 < e[g(ch ) ] $ ] in the above paragraph . in this section , we compare the different policies we have studied via simulations . the @xmath16 function is taken as linear @xmath109 or as @xmath110 . the sequences @xmath22 and @xmath23 are _ iid_. ( we have also done limited simulations when @xmath22 and @xmath23 are autoregressive and found that conclusions drawn in this section continue to hold ) . we consider the cases when @xmath111 and @xmath112 have truncated poisson , exponential , erlang or hyperexponential distributions . the policies considered are : greedy , to , @xmath113 , mto ( with @xmath114 ) and the mean delay optimal . at the end , we will also consider channels with fading . for fading channels we compare unfaded to and mto against fading to and fading mto . for the linear @xmath16 , we already know that the greedy policy is throughput optimal as well as mean delay optimal . ; finite , quantized data and energy buffers ; @xmath115 : poisson truncated at 5 ; @xmath58=1,e[g(y)]=0.92,g(e[y])=1 $ ] ] ; @xmath115 : exponential ; @xmath58=1,e[g(y)]=10,g(e[y])=10 $ ] ] ; @xmath115 : exponential ; @xmath58=10,e[g(y)]=2.01,g(e[y])=2.4 $ ] ] ; @xmath115 : hyperexponential(5 ) ; @xmath58=1,e[g(y)]=10,g(e[y])=10 $ ] ] ; @xmath115 : erlang(5 ) ; @xmath58=1,e[g(hy)]=0.62,e[g(he[y])]=0.64 $ ] ; wf , mod . wf stable for @xmath38<0.70 $ ] ] the mean queue lengths for the different cases are plotted in figs . [ plot1]-[plot8 ] . in fig . [ plot1 ] , we compare greedy , to and mean - delay optimal ( op ) policies for nonlinear @xmath16 . the op was computed via policy iteration . for numerical computations , all quantities need to be finite . so we took data and energy buffer sizes to be @xmath116 and used quantized versions of @xmath5 and @xmath8 . the distribution of @xmath111 and @xmath112 is poisson truncated at @xmath117 . these changes were made only for this example . now @xmath51 ) = 1 $ ] and @xmath45 = 0.92 $ ] . we see that the mean queue length of the three policies are negligible till @xmath38=0.8 $ ] . after that , the mean queue length of the greedy policy rapidly increases while performances of the other two policies are comparable till @xmath118 ( although from @xmath38 = 0.6 $ ] till close to @xmath118 , mean queue length of to is approximately double of op ) . at low loads , greedy has less mean queue length than to . [ plot2 ] considers the case when @xmath111 and @xmath112 are exponential and @xmath16 is linear . now @xmath119 = 1 $ ] and @xmath51 ) = e[g(y ) ] = 10.$ ] now all the policies considered are throughput optimal but their delay performances _ differ_. we observe that the policy @xmath113 ( henceforth called unbuffered ) has the worst performance . next is the to . [ plot4 ] provides the above results for @xmath16 nonlinear , when @xmath111 and @xmath112 are exponential . now , as before , @xmath113 is the worst . the greedy performs better than the other policies for low values of @xmath38 $ ] . but greedy becomes unstable at @xmath45=2.01 $ ] while the throughput optimal policies become unstable at @xmath51 ) = 2.40 $ ] . now for higher values of @xmath38 $ ] , the modified to performs the best and is close to greedy at low @xmath38 $ ] . figs . [ plot7]-[plot8 ] provide results for fading channels . the fading process @xmath86 is _ iid _ taking values @xmath120 and @xmath121 with probabilities @xmath122 and @xmath123 respectively . [ plot7 ] is for linear @xmath16 and fig . [ plot8 ] is for nonlinear @xmath16 . the policies compared are unbuffered , greedy , unfaded to ( [ disp ] ) and fading to . in fig . [ plot8 ] , we have also considered modified unfaded to ( [ onestar ] ) and modified fading to ( mwf ) with @xmath114 ( [ twostar ] ) . in fig . [ plot7 ] , @xmath111 and @xmath112 have hyperexponential distributions . the distribution of r.v . @xmath111 is a mixture of 5 exponential distributions with means @xmath38/4.9 , 2e[x]/4.9 , 3e[x]/4.9 , 6e[x]/4.9 $ ] and @xmath124/4.9 $ ] and probabilities @xmath125 and @xmath123 respectively . the distribution of @xmath112 is obtained in the same way . now @xmath58 = 1 $ ] , @xmath126=10 $ ] and @xmath127)]=10 $ ] . the stability region of fading to is @xmath38<e[g(\bar{h}y ) ] = 22.0 $ ] while that of the other three policies is @xmath38<10 $ ] . however , mean queue length of fading to is larger from the beginning till almost 10 . this is because in fading to , we transmit only when @xmath128 which has a small probability ( @xmath129 ) . [ plot8 ] considers nonlinear @xmath16 with @xmath115 erlang distributed . also , @xmath58=1 , e[g(hy)]=0.62 , e[g(he[y ] ) ] = 0.64 $ ] . now we see that the stability region of unbuffered and greedy is the smallest , then of to and mto while wf and mwf provide the largest region and are stable for @xmath38<0.70 $ ] . mto and mwf provide improvements in mean queue lengths over to and wf . in a sensor network , all the nodes need to transmit their data to a fusion node . thus , for this a natural network to consider is a tree ( @xcite ) . in the present scenario of nodes with energy harvesting sources , selection of a tree can depend on the energy profiles of different nodes . this will be subject of another study . here we assume that an appropriate tree has been formed and will concentrate on the link layer . an important building block for this network is a multiple access channel . in sensor networks contention based ( e.g. , csma ) and contention - free ( tdma / cdma / fdma ) mac protocols are considered suitable ( @xcite , @xcite ) . in fact for estimation of a random field , contention - free protocols are more appropriate . we consider the case where @xmath130 nodes with data queues @xmath131 are sharing a wireless channel . each queue generates its traffic , stores in a queue and transmits as in section [ model ] . also , each node has its own energy harvesting mechanism . the traffic generated at different queues and their energy mechanisms are assumed independent of each other . let @xmath132 and @xmath133 be the sequences corresponding to node @xmath134 . for simplicity we will assume @xmath135 and @xmath136 to be _ iid _ although these assumptions can be weakened as for a single queue . as mentioned at the end of section [ general ] , the energy consumption @xmath133 can be taken care of if we simply replace @xmath137 $ ] by @xmath137 - e[z(i)]$ ] in our algorithms . in the following we do that and write it as @xmath137 $ ] only ( and hence ignore @xmath138 ) . the @xmath130 queues can share the channel in different ways . the stability region of @xmath139 and optimal ( good ) transmit policies depend upon the sharing mechanism used . we consider a few commonly used scenarios in the rest of the paper . the @xmath130 sensor nodes use tdma / orthogonal cdma / fdma / ofdma to transmit . then the @xmath130 queues become independent , decoupled queues and can be considered separately . thus , the transmission policies developed in previous sections for a single queue can be used here . in the following we explain them in the context of tdma . if the queues have to use the channel in a tdma fashion then necessary conditions for stability of the @xmath130 queues are : there exist @xmath140 and @xmath141 such that @xmath142 < \alpha_i \ g_i \ \left ( \frac{e[y(i)]}{\alpha_i } \right ) , \ \ i=1,2 , ... , n , \label{meqn6}\ ] ] where @xmath143 is the energy to bit mapping for @xmath144 . a stable policy for each queue will be as in section [ stability ] : @xmath144 is given @xmath145 fraction of slots ( on a long term basis ) and it uses energy @xmath146 - \epsilon)/ \alpha_i$ ] whenever it transmits . for better delay performance , the slots allocated to different queues should be uniformly spaced . we can improve on the mean delay by using ( [ onestar ] ) . it is possible that more than one set of @xmath147 satisfy the stability condition ( [ meqn6 ] ) . then one should select the values which minimize a cost function , ( say ) weighted sum of mean delays . now we discuss the mac with fading . let @xmath148 be the channel gain process for @xmath144 . it is assumed stationary , ergodic and independent of the fading process for @xmath149 . we discuss opportunistic scheduling for the contention free mac . we will study the csma based algorithms in the next section . if we assume that each of @xmath144 has infinite data backlog , then the policy that maximizes the sum of throughputs for @xmath150 and for symmetric statistics ( i.e. , each @xmath151 has same statistics and all @xmath137 $ ] are same ) is to choose @xmath152 @xmath153 in slot @xmath1 and use @xmath154 via the water - filling formula ( [ fto ] ) with the average power constraint @xmath155 = n e[y(i^*_k)-\epsilon].\ ] ] this is an extension of an algorithm in @xcite to the energy harvesting nodes . a modification of this policy is available in @xcite for asymmetric case . if @xmath16 is linear , then for the symmetric case , a channel is selected only if it has the highest possible gain ( for @xmath95 bounded ) . if more than one channel is in the best state , select one of them with equal probability . although ( [ meqn10 ] ) maximizes throughput , it may be unfair to different queues and may not provide the qos . furthermore , in our setup infinite backlog is not a realistic assumption . without this assumption a throughput optimal policy ( in the class of policies which use constant powers ) is to choose queue @xmath156-\epsilon}{\alpha(i ) } \right ) \right ) \right)\ ] ] and then use @xmath157 - \epsilon ) / \alpha(i^*_k)$ ] . here @xmath158 is the fraction of time slots assigned to @xmath159 . however now we do not know @xmath158 and this may be estimated ( see the end of this section ) . if @xmath158 is replaced with the true value , then stability of the queues in the mac follows from @xcite if the fading states take values in a finite set and the system satisfies the following condition . let there exist a function @xmath160 which picks one of the queues as a function of @xmath161 where @xmath162 - \epsilon}{\alpha_i } \right)$ ] , @xmath163 $ ] and @xmath164 is the stationary distribution of @xmath165 . then if @xmath166 < \sum r_i 1 \ { f(r_1 , ... , r_n)=i \ } \pi ( r_1 , ... , r_n)$ ] for each @xmath134 , the system is stable . this policy tries to satisfy the traffic requirements of different nodes but may not be delay optimal . based on experience in @xcite , a greedy policy @xmath167-\epsilon}{\alpha(i ) } \right),q_k(i ) \right ) \right ) \right)\ ] ] provides better mean delays . however , it is throughput optimal only for symmetric traffic statistics and when @xmath137 = e[y(j)],$ ] for all @xmath168 . but it can be made throughput optimal ( as ( [ meqn11 ] ) ) while still retaining ( partially ) its mean delay performance as follows . choose an appropriately large positive constant @xmath169 . if none of @xmath170 is greater than @xmath169 , use ( [ meqn12 ] ) ; otherwise , on the set @xmath171 , use ( [ meqn11 ] ) . we call this modified greedy policy . the mean delay of the above policies can be further improved , if instead of @xmath172 - \epsilon ) / \alpha(i)$ ] , we use ( [ onestar ] ) . but the stability region remains same . the policies ( [ meqn11 ] ) and ( [ meqn12 ] ) can be further improved if instead of using @xmath173 - \epsilon$ ] , we use waterfilling for @xmath16 in ( [ allert3 ] ) . of course we reduce transmit power as in ( [ onestar ] ) if there is not enough data to transmit . now not only the mean delays reduce but the stability region also enlarges . the policies ( [ meqn11 ] ) , ( [ meqn12 ] ) and modified greedy provide good performance , require minimal information ( only @xmath137 $ ] ) , are easy to implement and have low computational requirements . in addition they naturally adapt to changing traffic and channel conditions . in ( [ meqn11])-([meqn12 ] ) we need @xmath174 to obtain the energy @xmath7 . but unlike for tdma , @xmath175 is not available in these algorithms and depends on the algorithm used . thus , in these algorithms we use a simple variant of the lms ( least mean square ) algorithm ( @xcite ) to estimate @xmath174 : initially start with guess @xmath176 run the algorithm for ( say ) @xmath177 number of slots . each node @xmath134 computes the fraction @xmath178 of slots it gets and recomputes @xmath179 where @xmath180 is a small postive constant . at any time the current estimate of @xmath174 is used by the algorithms . since zigbee and 802.11 use csma , we discuss opportunistic scheduling for csma also . as against ( [ meqn11])-([meqn12 ] ) , this is a completely decentralized algorithm . this is used by zhao and tong @xcite . the basic idea in @xcite is to make the back - off mechanism in a node to be a function of the channel state of that node . the nodes that are to be given priority are given smaller back - off time . this mechanism has also been used in ieee 802.11e to provide priority to voice and video traffic . in this section we take this idea further by also including the effect of queue lengths and power control in deciding the back - off interval as against only the channel state in @xcite . let @xmath181 be a nonincreasing function with values in @xmath182 $ ] where @xmath183 is the maximum allowed back - off time in slots . if @xmath95 is the channel gain in a slot then in @xcite the back - off time is taken to be @xmath184 . in our setup , to use opportunistic scheduling in csma , we use the above mentioned monotonic function @xmath181 on each of the sensor nodes contending for the channel . the @xmath144 uses the back off time of @xmath185-\epsilon)}{\alpha(i ) } \right ) \right).\ ] ] when a node gets the channel , it will transmit a complete packet and use energy per slot as @xmath186 -\epsilon ] / \alpha(i^*_k).\ ] ] now we are making the usual assumption that the channel gains stay constant during the transmission of a packet . we can use ( [ onestar ] ) to improve performance . using the ideas in the last section we can develop better algorithms than ( [ meqn14])-([meqn15 ] ) . indeed , with ( [ meqn14 ] ) , instead of ( [ meqn15 ] ) , we can use waterfilling ( for @xmath16 in ( [ allert3 ] ) ) . we can also improve over ( [ meqn14 ] ) by using , for back - off time of @xmath134th node , @xmath187 - \epsilon}{\alpha(i ) } \right ) \right)\ ] ] which takes care of the traffic requirements of different nodes . we can also use the ( modified ) greedy in ( [ meqn12 ] ) . the @xmath174 in the above algorithms will be computed via lms in ( [ meqn13 ] ) . we will compare the performance of these algorithms via simulations in section [ msimulation ] . an advantage of above algorithms over the algorithms in section [ opportunistic ] are that these are completely decentralized : each node uses only its own queue length , channel state and @xmath137 $ ] to decide when to transmit . the algorithms in section [ opportunistic ] require a central controller ( may be a cluster head ) for implementation . centralized algorithms have also been considered in sensor networks and provide better performance . in this section for simplicity , we simulate the system under symmetric conditions , apply the different algorithms , and compare their performances . we use @xmath188 . the fading of each channel changes from slot to slot independently ; @xmath189 are _ iid _ with values 0.1 , 0.6 , 1.8 and 5 with probabilities 4/12 , 5/12 , 2/12 and 1/12 . the @xmath190 and @xmath191 are iid expontential . the lms ( [ meqn13 ] ) was taken with @xmath192 and the @xmath193s were updated after 30 - 50 slots . for orthogonal channels , under symmetric conditions with 3 queues , average queue lengths are shown in fig . [ orth ] for to ( [ meqn11 ] ) , greedy ( [ meqn12 ] ) , tdma , greedy with water - filling and tdma with water - filling policies . the @xmath189 are _ iid _ exponential with mean 1 . for symmetric conditions , greedy is throughput optimal and hence modified greedy is not implemented . we see that tdma becomes unstable much before the other policies , and that its average queue length is much worse even when it is stable . greedy performs better than to near the stability boundary which is @xmath38=0.39 $ ] . water - filling improves the stability region of tdma as well as greedy . for csma , figs . [ delay ] and [ pl ] show mean delays and packet loss probabilities under symmetric conditions with 10 queues and with normal exponential backoff , zhao - tong @xcite , our policy ( [ meqn16 ] ) and our policy with water - filling ( with @xmath194 and @xmath195 at @xmath196 assumes values 0.1,0.5,1.0,2.2 for time fractions 0.1,0.3,0.4,0.2 ) . we simulated the 10 queues in continuous time . also , @xmath58=1 $ ] and the data packets of unit size arrive at each queue as poisson streams . we see that opportunistic policies improve mean delays substantially . we have considered sensor nodes with energy harvesting sources , deployed for random field estimation . throughput optimal and mean delay optimal energy management policies for single nodes are identified which can make them work in energy neutral operation . next these results are extended to fading channels and when energy at the sensor node is also consumed in sensing and data processing . similarly we can include leakage / wastage of energy when it is stored in the energy buffer and when it is extracted . finally these policies are used to develop efficient mac protocols for such nodes . in particular versions of tdma , opportunistic macs for fading channels and csma are developed . their performance is compared via simulations . it is shown that opportunistic policies can substantially improve the performance . i. f. akyildiz , w. su , y. sankara subramaniam and e. cayirei , a survey on sensor networks " , _ ieee communications magazine _ , vol 40 , 2002 , pp . 102 - 114 . s. asmussen , applied probability and queues " , _ john wiley and sons_,n.y . , s. j. baek , g. veciana and x. su , minimizing energy consumption in large - scale sensor networks through distributed data compression and hierarchical aggregation " , _ ieee jsac _ , vol 22 , 2004 , pp . 1130 - 1140 . d. niyato , e. hossain , m. m. rashid and v. k. bhargava , wireless sensor networks with energy harvesting technologies : a game - theoretic approach to optimal energy management " , _ ieee wireless communications _ , aug . 2007 , pp . 90 - 96 . s. ratnaraj , s. jagannathan and v. rao , optimal energy - delay subnetwork routing protocol for wireless sensor networks " , _ proc . of ieee conf . on networking , sensing and control _ , april 2006 , pp . 787 - 792 . q. zhao and l. tong , opportunistic carrier sensing for energy - efficient information retrieval in sensor networks " , _ eurasip journal on wireless communications and networking _ , vol . 2 , 2005 , pp . 231 - 241 .

we study sensor networks with energy harvesting nodes . the generated energy at a node can be stored in a buffer . a sensor node periodically senses a random field and generates a packet . these packets are stored in a queue and transmitted using the energy available at that time at the node . for such networks we develop efficient energy management policies . first , for a single node , we obtain policies that are throughput optimal , i.e. , the data queue stays stable for the largest possible data rate . next we obtain energy management policies which minimize the mean delay in the queue . we also compare performance of several easily implementable sub - optimal policies . a greedy policy is identified which , in low snr regime , is throughput optimal and also minimizes mean delay . next using the results for a single node , we develop efficient mac policies . * keywords : * optimal energy management policies , energy harvesting , sensor networks , mac protocols .

<s>[INST]sensor networks consist of a large number of small , inexpensive sensor nodes . these nodes have small batteries with limited power and also have limited computational power and storage space . when the battery of a node is exhausted , it is not replaced and the node dies . when sufficient number of nodes die , the network may not be able to perform its designated task . thus the life time of a network is an important characteristic of a sensor network and it is tied up with the life time of a node . various studies have been conducted to increase the life time of the battery of a node by reducing the energy intensive tasks , e.g. , reducing the number of bits to transmit ( @xcite , @xcite ) , making a node to go into power saving modes : ( sleep / listen ) periodically ( @xcite ) , using energy efficient routing ( @xcite , @xcite ) and mac ( @xcite ) . studies that estimate the life time of a sensor network include @xcite . a general survey on sensor networks is @xcite which provides many more references on these issues . in this paper we focus on increasing the life time of the battery itself by energy harvesting techniques ( @xcite , @xcite ) . common energy harvesting devices are solar cells , wind turbines and piezo - electric cells , which extract energy from the environment . among these , solar harvesting energy through photo - voltaic effect seems to have emerged as a technology of choice for many sensor nodes ( @xcite , @xcite ) . unlike for a battery operated sensor node , now there is potentially an _ infinite _ amount of energy available to the node . hence energy conservation need not be the dominant theme . rather , the issues involved in a node with an energy harvesting source can be quite different . the source of energy and the energy harvesting device may be such that the energy can not be generated at all times ( e.g. , a solar cell ) . however one may want to use the sensor nodes at such times also . furthermore the rate of generation of energy can be limited . thus one may want to match the energy generation profile of the harvesting source with the energy consumption profile of the sensor node . it should be done in such a way that the node can perform satisfactorily for a long time , i.e. , at least energy starvation should not be the reason for the node to die . furthermore , in a sensor network , the mac protocol , routing and relaying of data through the network may need to be suitably modified to match the energy generation profiles of different nodes , which may vary with the nodes . in the following we survey the literature on sensor networks with energy harvesting nodes . early papers on energy harvesting in sensor networks are @xcite and @xcite . a practical solar energy harvesting sensor node prototype is described in @xcite . a good recent contribution is @xcite . it provides various deterministic theoretical models for energy generation and energy consumption profiles ( based on @xmath0 traffic models and provides conditions for _ energy neutral operation _ , , when the node can operate indefinitely . in @xcite a sensor node is considered which is sensing certain interesting events . the authors study optimal sleep - wake cycles such that the event detection probability is maximized . a recent survey is @xcite which also provides an optimal sleep - wake cycle for solar cells so as to obtain qos for a sensor node . mac protocols for sensor networks are studied in @xcite , @xcite and @xcite . a general survey is available in @xcite and @xcite . throughput optimal opportunistic mac protocols are discussed in @xcite . in this paper we summarize our recent results ( @xcite ) , on sensor networks with energy harvesting nodes and based on them propose new schemes for scheduling a mac for such networks . the motivating application is estimation of a random field which is one of the canonical applications of sensor networks . the above mentioned theoretical studies are motivated by other applications of sensor networks . in our application , the sensor nodes sense the random field periodically . after sensing , a node generates a packet ( possibly after efficient compression ) . this packet needs to be transmitted to a central node , possibly via other sensor nodes . in an energy harvesting node , sometimes there may not be sufficient energy to transmit the generated packets ( or even sense ) at regular intervals and then the node may need to store the packets till they are transmitted . the energy generated can be stored ( possibly in a finite storage ) for later use . initially we will assume that most of the energy is consumed in transmission only . we will relax this assumption later on . we find conditions for energy neutral operation of a node , i.e. , when the node can work forever and its data queue is stable . we will obtain policies which can support maximum possible data rate . we also obtain energy management ( power control ) policies for transmission which minimize the mean delay of the packets in the queue . we use the above energy mangement policies to develop channel sharing policies at a mac ( multiple access channel ) used by energy harvesting sensor nodes . we are currently investigating appropriate routing algorithms for a network of energy harvesting sensor nodes . the paper is organized as follows . section [ model ] describes the model for a single node and provides the assumptions made for data and energy generation . section [ stability ] provides conditions for energy neutral operation of a node . we obtain stable , power control policies which are throughput optimal . section [ opt ] obtains the power control policies which minimize the mean delay via markov decision theory . a greedy policy is shown to be throughput optimal and provides minimum mean delays for linear transmission . section [ general ] provides a throughput optimal policy when the energy consumed in sensing and processing is non - negligible . a sensor node with a fading channel is also considered . section [ simulation ] provides simulation results to confirm our theoretical findings and compares various energy management policies . section [ tree ] introduces a multiple access channel ( mac ) for energy harvesting nodes . section [ orthogonal ] provides efficient energy management schemes for orthogonal mac protocols . sections [ opportunistic ] and [ csma ] consider macs with fading channels ( orthogonal and csma respectively ) . section [ msimulation ] compares the different mac policies via simulations . section [ conclude ] concludes the paper . in this section we present our model for a single energy harvesting sensor node . we consider a sensor node ( fig . [ fig1 ] ) which is sensing a random field and generating packets to be transmitted to a central node via a network of sensor nodes . the system is slotted . during slot @xmath1 ( defined as time interval @xmath2 $ ] , i.e. , a slot is a unit of time ) @xmath3 bits are generated by the sensor node . although the sensor node may generate data as packets , we will allow arbitrary fragmentation of packets during transmission . thus , packet boundaries are not important and we consider bit strings ( or just fluid ) . the bits @xmath3 are eligible for transmission in @xmath4st slot . the queue length ( in bits ) at time @xmath1 is @xmath5 . the sensor node is able to transmit @xmath6 bits in slot @xmath1 if it uses energy @xmath7 . we assume that transmission consumes most of the energy in a sensor node and ignore other causes of energy consumption ( this is true for many low quality , low rate sensor nodes ( @xcite ) ) . this assumption will be removed in section [ general ] . we denote by @xmath8 the energy available in the node at time @xmath1 . the sensor node is able to replenish energy by @xmath9 in slot @xmath1 . we will initially assume that @xmath10 and @xmath11 are _ iid _ ( independent , identically distributed ) but will generalize this assumption later . it is important to generalize this assumption to capture realistic traffic streams and energy generation profiles . the processes @xmath12 and @xmath13 satisfy @xmath14 where @xmath15 . this assumes that the data buffer and the energy storage buffer are infinite . if in practice these buffers are large enough , this is a good approximation . if not , even then the results obtained provide important insights and the policies obtained often perform well for the finite buffer case . the function @xmath16 will be assumed to be monotonically non - decreasing . an important such function is given by shannon s capacity formula @xmath17 for gaussian channels where @xmath18 is a constant such that @xmath19 is the snr . this is a non - decreasing concave function . at low values of @xmath7 , @xmath20 , i.e. , @xmath16 becomes a linear function . since sensor nodes are energy constrained , this is a practically important case . thus in the following we limit our attention to linear and concave nondecreasing functions @xmath16 . we will also assume that @xmath21 which always holds in practice . many of our results ( especially the stability results ) will be valid when @xmath22 and @xmath23 are stationary , ergodic . these assumptions are general enough to cover most of the stochastic models developed for traffic ( e.g. , markov modulated ) and energy harvesting . of course , in practice , statistics of the traffic and energy harvesting models will be time varying ( e.g. , solar cell energy harvesting will depend on the time of day ) . but often they can be approximated by piecewise stationary processes . for example , energy harvesting by solar cells could be taken as being stationary over one hour periods . then our results could be used over these time periods . often these periods are long enough for the system to attain ( approximate ) stationarity and for our results to remain meaningful . in section [ stability ] we study the stability of this queue and identify easily implementable energy management policies which provide good performance . we will obtain a necessary condition for stability . then we present a transmission policy which achieves the necessary condition , i.e. , the policy is throughput optimal . the mean delay for this policy is not minimal . thus , we obtain other policies which provide lower mean delay . in the next section we will consider policies which minimize mean delay . the proofs of lemma 1 and theorems 1 - 4 are provided in @xcite . let us assume that we have obtained an ( asymptotically ) stationary and ergodic transmission policy @xmath24 which makes @xmath25 ( asymptotically ) stationary with the limiting distribution independent of @xmath26 . taking @xmath27 asymptotically stationary seems to be a natural requirement to obtain ( asymptotic ) stationarity of @xmath25 . in the following @xmath28 will denote generic r.v.s with the distributions of @xmath29 respectively . * lemma 1 * let @xmath16 be concave nondeceasing and @xmath30 be stationary , ergodic sequences . for @xmath24 to be an asymptotically stationary , ergodic energy management policy that makes @xmath31 asymptotically stationary with a proper stationary distribution @xmath32 , it is necessary that @xmath33 < e_{\pi } [ g(t ) ] \leq g(e[y]).$ ] @xmath34 let @xmath35-\epsilon ) \label{disp}\ ] ] where @xmath36 is an appropriately chosen small constant ( see statement of theorem 1 ) . we show that it is a throughput optimal policy , i.e. , using this @xmath7 with @xmath16 satisfying the assumptions in lemma 1 , @xmath25 is asymptotically stationary and ergodic . * theorem 1 * if @xmath37 are stationary , ergodic and @xmath16 is continuous , nondecreasing , concave then if @xmath38 < g(e[y])$ ] , ( [ disp ] ) makes the queue stable ( with @xmath39 such that @xmath40 < g(e[y ] - \epsilon)$ ] ) , i.e. , it has a unique , stationary , ergodic distribution and starting from any initial distribution , @xmath5 converges in total variation to the stationary distribution . henceforth we denote the policy ( [ disp ] ) by to . from results on gi / gi/1 queues ( @xcite ) , if @xmath22 are _ iid _ , @xmath38 < g(e[y ] ) , t_k = min(e_k , e[y ] - \epsilon)$ ] and @xmath41 < \infty $ ] for some @xmath42 then the stationary solution @xmath12 of ( [ eqn1 ] ) satisfies @xmath43 < \infty$ ] . taking @xmath44 for all @xmath1 will provide stability of the queue if @xmath38 < e[g(y)]$ ] . if @xmath16 is linear then this coincides with the necessary condition . if @xmath16 is strictly concave then @xmath45 < g(e[y ] ) $ ] unless @xmath46 $ ] . thus @xmath44 provides a strictly smaller stability region . we will be forced to use this policy if there is no buffer to store the energy harvested . this shows that storing energy allows us to have a larger stability region . we will see in section [ simulation ] that storing energy can also provide lower mean delays . although to is a throughput optimal policy , if @xmath5 is small , we may be wasting some energy . thus , it appears that this policy does not minimize mean delay . it is useful to look for policies which minimize mean delay . based on our experience in @xcite , the greedy policy @xmath47 where @xmath48 , looks promising . in theorem 2 , we will show that the stability condition for this policy is @xmath38 < e[g(y ) ] $ ] which is optimal for linear @xmath16 but strictly suboptimal for a strictly concave @xmath16 ( just as the policy @xmath44 discussed above ) . we will show in section [ opt ] that when @xmath16 is linear , ( [ eqn5 ] ) is not only throughput optimal , it also minimizes long term mean delay . for concave @xmath16 , we will show via simulations that ( [ eqn5 ] ) provides less mean delay than to at low load . however since its stability region is smaller than that of the to policy , at @xmath38 $ ] close to @xmath45 $ ] , the greedy performance rapidly deteriorates . thus it is worthwhile to look for some other good policy . notice that the to policy wastes energy if @xmath49 - \epsilon)$ ] . therfore , we can improve upon it by saving the energy @xmath50-\epsilon - g^{-1}(q_k))$ ] and using it when the @xmath5 is greater than @xmath51-\epsilon)$ ] . however for @xmath16 a log function , using a large amount of energy @xmath52 is also wasteful even when @xmath53 . taking into account these facts we improve over the to policy as @xmath54 + 0.001 ( e_k - cq_k)^+ ) ) \label{onestar}\ ] ] where @xmath55 is a positive constant . the improvement over the to also comes from the fact that if @xmath8 is large , we allow @xmath56 $ ] but only if @xmath5 is not very large . the constants 0.99 and 0.001 were chosen by trial and error from simulations after experimenting with different scenarios . we will see in section [ simulation ] via simulations that this policy , to be denoted by mto can indeed provide lower mean delays than to at loads above @xmath45 $ ] . one advantage of ( [ disp ] ) over ( [ eqn5 ] ) and ( [ onestar ] ) is that while using ( [ disp ] ) , after some time @xmath57-\epsilon$ ] . also , at any time , either one uses up all the energy or uses @xmath58-\epsilon$ ] . thus one can use this policy even if exact information about @xmath8 is not available ( measuring @xmath8 may be difficult in practice ) . in fact , ( [ disp ] ) does not need even @xmath5 while ( [ eqn5 ] ) either uses up all the energy or uses @xmath59 and hence needs only @xmath5 exactly . now we show that under the greedy policy ( [ eqn5 ] ) the queueing process is stable when @xmath38 < e[g(y)]$ ] . in next few results ( theorems 2 and 3 ) we assume that the energy buffer is finite , although large . for this case lemma 1 and theorem 1 also hold under the same assumptions with slight modifications in their proofs . * theorem 2 * if the energy buffer is finite , i.e. , @xmath60 ( but @xmath61 is large enough ) and @xmath38 < e[g(y ) ] $ ] then under the greedy policy ( [ eqn5 ] ) , @xmath62 has an ergodic set . @xmath34 the above result will ensure that the markov chain @xmath63 is ergodic and hence has a unique stationary distribution if @xmath64 is irreducible . a sufficient condition for this is @xmath65 < 1 $ ] and @xmath66 < 1 $ ] because then the state @xmath67 can be reached from any state with a positive probability . in general , @xmath63 can have multiple ergodic sets . then , depending on the initial state , @xmath63 will converge to one of the ergodic sets and the limiting distribution depends on the initial conditions . in this section we choose @xmath7 at time @xmath1 as a function of @xmath5 and @xmath8 such that @xmath68\ ] ] is minimized where @xmath69 is a suitable constant . the minimizing policy is called @xmath70-discount optimal . when @xmath71 , we minimize @xmath72.\ ] ] this optimizing policy is called average cost optimal . by little s law ( @xcite ) an average cost optimal policy also minimizes mean delay . if for a given @xmath73 , the optimal policy @xmath7 does not depend on the past values , and is time invariant , it is called a stationary markov policy . if @xmath22 and @xmath23 are markov chains then these optimization problems are markov decision problems ( mdp ) . for simplicity , in the following we consider these problems when @xmath22 and @xmath23 are _ iid_. we obtain the existence of optimal @xmath70-discount and average cost stationary markov policies . * theorem 3 * if @xmath16 is continuous and the energy buffer is finite , i.e. , @xmath74 then there exists an optimal @xmath70-discounted markov stationary policy . if in addition @xmath38 < g(e[y])$ ] and @xmath75 < \infty$ ] , then there exists an average cost optimal stationary markov policy . the optimal cost @xmath76 does not depend on the initial state . also , then the optimal @xmath70-discount policies tend to an optimal average cost policy as @xmath77 . furthermore , if @xmath78 is the optimal @xmath70-discount cost for the initial state @xmath79 then @xmath80 @xmath34 in section [ stability ] we identified a throughput optimal policy when @xmath16 is nondecreasing , concave . theorem 3 guarantees the existence of an optimal mean delay policy . it is of interest to identify one such policy also . in general one can compute an optimal policy numerically via value iteration or policy iteration but that can be computationally intensive ( especially for large data and energy buffer sizes ) . also it does not provide any insight and requires traffic and energy profile statistics . in section [ stability ] we also provided a greedy policy ( [ eqn5 ] ) which is very intuitive , and is throughput optimal for linear @xmath16 . however for concave @xmath16 ( including the cost function @xmath81 it is _ not _ throughput optimal and provides low mean delays only for low load . next we show that it provides minimum mean delay for linear @xmath16 . * theorem 4 * the greedy policy ( [ eqn5 ] ) is @xmath70-discount optimal for @xmath82 when @xmath83 for some @xmath84 . it is also average cost optimal . @xmath34 the fact that greedy is @xmath70-discount optimal as well as average cost optimal implies that it is good not only for long term average delay but also for transient mean delays . in this section we consider two generalizations . first we will extend the results to the case of fading channels and then to the case where the sensing and the processing energy at a sensor node are non - negligible with respect to the transmission energy . in case of fading channels , we assume flat fading during a slot . in slot @xmath1 the channel gain is @xmath85 . the sequence @xmath86 is assumed stationary , ergodic , independent of the traffic sequence @xmath22 and the energy generation sequence @xmath23 . then if @xmath7 energy is spent in transmission in slot @xmath1 , the @xmath25 process evolves as @xmath87 if the channel state information ( csi ) is not known to the sensor node , then @xmath7 will depend only on @xmath73 . one can then consider the policies used above . for example we could use @xmath88-\epsilon)$ ] . then the data queue is stable if @xmath38 < e[g(h(e[y]-\epsilon))]$ ] . we will call this policy unfaded to . if we use greedy ( [ eqn5 ] ) , then the data queue is stable if @xmath38 < e[g(hy)]$ ] . if csi @xmath85 is available to the node at time @xmath1 , then the following are the throughput optimal policies . if @xmath16 is linear , then @xmath89 for some @xmath90 . then , if @xmath91 and @xmath92 , the optimal policy is : @xmath93-\epsilon)/p(h=\bar{h})$ ] and @xmath94 otherwise . thus if @xmath95 can take an arbitrarily large value with positive probability , then @xmath96 = \infty$ ] at the optimal solution . if @xmath97 , then the water filling ( wf ) policy @xmath98 where @xmath99 is obtained from the average power constraint @xmath100 = e[y ] - \epsilon$ ] , is throughput optimal . this is because it maximizes @xmath101 $ ] with the given constraints . both of the above policies can be improved as before , by not wasting energy when there is not enough data . as in ( [ onestar ] ) in section [ stability ] , we can further improve wf by taking @xmath102 we will call it mwf . these policies will not minimize mean delay . for that , we can use the mdp framework used in section [ opt ] and numerically compute the optimal policies . till now we assumed that all the energy that a node consumes is for transmission . however , sensing , processing and receiving ( from other nodes ) also require significant energy , especially in more recent higher end sensor nodes ( @xcite ) . since we have been considering a single node so far , we will now include the energy consumed by sensing and processing only . for simplicity , we will assume that the node is always in one energy mode ( e.g. , lower energy modes ( @xcite ) available for sensor nodes will not be considered ) . if a sensor node with an energy harvesting system can be operated in energy neutral operation in normal mode itself ( i.e. , it satisfies the conditions in lemma 1 ) , then there is no need to have lower energy modes . otherwise one has to resort to energy saving modes . we will assume that @xmath103 is the energy consumed by the node for sensing and processing in slot @xmath1 . unlike @xmath7 ( which can vary according to @xmath5 ) , @xmath104 can be considered a stationary , ergodic sequence . the rest of the system is as in section [ model ] . now we briefly describe a energy management policy which is an extension of the to policy in section [ stability ] . this can provide an energy neutral operation in the present case . improved / optimal policies can be obtained for this system also but will not be discussed due to lack of space . let @xmath55 be the minimum positive constant such that @xmath38 < g(c)$ ] . then if @xmath105 < e[y]-\delta $ ] , ( where @xmath106 is a small positive constant ) the system can be operated in energy neutral operation : if we take @xmath107 ( which can be done with high probability for all @xmath1 large enough ) , the process @xmath12 will have a unique stationary , ergodic distribution and there will always be energy @xmath103 for sensing and processing for all @xmath1 large enough . the result holds if @xmath108 is an ergodic stationary sequence . the arguments to show this are similar to those in section [ stability ] and are omitted . when the channel has fading , we need @xmath38 < e[g(ch ) ] $ ] in the above paragraph . in this section , we compare the different policies we have studied via simulations . the @xmath16 function is taken as linear @xmath109 or as @xmath110 . the sequences @xmath22 and @xmath23 are _ iid_. ( we have also done limited simulations when @xmath22 and @xmath23 are autoregressive and found that conclusions drawn in this section continue to hold ) . we consider the cases when @xmath111 and @xmath112 have truncated poisson , exponential , erlang or hyperexponential distributions . the policies considered are : greedy , to , @xmath113 , mto ( with @xmath114 ) and the mean delay optimal . at the end , we will also consider channels with fading . for fading channels we compare unfaded to and mto against fading to and fading mto . for the linear @xmath16 , we already know that the greedy policy is throughput optimal as well as mean delay optimal . ; finite , quantized data and energy buffers ; @xmath115 : poisson truncated at 5 ; @xmath58=1,e[g(y)]=0.92,g(e[y])=1 $ ] ] ; @xmath115 : exponential ; @xmath58=1,e[g(y)]=10,g(e[y])=10 $ ] ] ; @xmath115 : exponential ; @xmath58=10,e[g(y)]=2.01,g(e[y])=2.4 $ ] ] ; @xmath115 : hyperexponential(5 ) ; @xmath58=1,e[g(y)]=10,g(e[y])=10 $ ] ] ; @xmath115 : erlang(5 ) ; @xmath58=1,e[g(hy)]=0.62,e[g(he[y])]=0.64 $ ] ; wf , mod . wf stable for @xmath38<0.70 $ ] ] the mean queue lengths for the different cases are plotted in figs . [ plot1]-[plot8 ] . in fig . [ plot1 ] , we compare greedy , to and mean - delay optimal ( op ) policies for nonlinear @xmath16 . the op was computed via policy iteration . for numerical computations , all quantities need to be finite . so we took data and energy buffer sizes to be @xmath116 and used quantized versions of @xmath5 and @xmath8 . the distribution of @xmath111 and @xmath112 is poisson truncated at @xmath117 . these changes were made only for this example . now @xmath51 ) = 1 $ ] and @xmath45 = 0.92 $ ] . we see that the mean queue length of the three policies are negligible till @xmath38=0.8 $ ] . after that , the mean queue length of the greedy policy rapidly increases while performances of the other two policies are comparable till @xmath118 ( although from @xmath38 = 0.6 $ ] till close to @xmath118 , mean queue length of to is approximately double of op ) . at low loads , greedy has less mean queue length than to . [ plot2 ] considers the case when @xmath111 and @xmath112 are exponential and @xmath16 is linear . now @xmath119 = 1 $ ] and @xmath51 ) = e[g(y ) ] = 10.$ ] now all the policies considered are throughput optimal but their delay performances _ differ_. we observe that the policy @xmath113 ( henceforth called unbuffered ) has the worst performance . next is the to . [ plot4 ] provides the above results for @xmath16 nonlinear , when @xmath111 and @xmath112 are exponential . now , as before , @xmath113 is the worst . the greedy performs better than the other policies for low values of @xmath38 $ ] . but greedy becomes unstable at @xmath45=2.01 $ ] while the throughput optimal policies become unstable at @xmath51 ) = 2.40 $ ] . now for higher values of @xmath38 $ ] , the modified to performs the best and is close to greedy at low @xmath38 $ ] . figs . [ plot7]-[plot8 ] provide results for fading channels . the fading process @xmath86 is _ iid _ taking values @xmath120 and @xmath121 with probabilities @xmath122 and @xmath123 respectively . [ plot7 ] is for linear @xmath16 and fig . [ plot8 ] is for nonlinear @xmath16 . the policies compared are unbuffered , greedy , unfaded to ( [ disp ] ) and fading to . in fig . [ plot8 ] , we have also considered modified unfaded to ( [ onestar ] ) and modified fading to ( mwf ) with @xmath114 ( [ twostar ] ) . in fig . [ plot7 ] , @xmath111 and @xmath112 have hyperexponential distributions . the distribution of r.v . @xmath111 is a mixture of 5 exponential distributions with means @xmath38/4.9 , 2e[x]/4.9 , 3e[x]/4.9 , 6e[x]/4.9 $ ] and @xmath124/4.9 $ ] and probabilities @xmath125 and @xmath123 respectively . the distribution of @xmath112 is obtained in the same way . now @xmath58 = 1 $ ] , @xmath126=10 $ ] and @xmath127)]=10 $ ] . the stability region of fading to is @xmath38<e[g(\bar{h}y ) ] = 22.0 $ ] while that of the other three policies is @xmath38<10 $ ] . however , mean queue length of fading to is larger from the beginning till almost 10 . this is because in fading to , we transmit only when @xmath128 which has a small probability ( @xmath129 ) . [ plot8 ] considers nonlinear @xmath16 with @xmath115 erlang distributed . also , @xmath58=1 , e[g(hy)]=0.62 , e[g(he[y ] ) ] = 0.64 $ ] . now we see that the stability region of unbuffered and greedy is the smallest , then of to and mto while wf and mwf provide the largest region and are stable for @xmath38<0.70 $ ] . mto and mwf provide improvements in mean queue lengths over to and wf . in a sensor network , all the nodes need to transmit their data to a fusion node . thus , for this a natural network to consider is a tree ( @xcite ) . in the present scenario of nodes with energy harvesting sources , selection of a tree can depend on the energy profiles of different nodes . this will be subject of another study . here we assume that an appropriate tree has been formed and will concentrate on the link layer . an important building block for this network is a multiple access channel . in sensor networks contention based ( e.g. , csma ) and contention - free ( tdma / cdma / fdma ) mac protocols are considered suitable ( @xcite , @xcite ) . in fact for estimation of a random field , contention - free protocols are more appropriate . we consider the case where @xmath130 nodes with data queues @xmath131 are sharing a wireless channel . each queue generates its traffic , stores in a queue and transmits as in section [ model ] . also , each node has its own energy harvesting mechanism . the traffic generated at different queues and their energy mechanisms are assumed independent of each other . let @xmath132 and @xmath133 be the sequences corresponding to node @xmath134 . for simplicity we will assume @xmath135 and @xmath136 to be _ iid _ although these assumptions can be weakened as for a single queue . as mentioned at the end of section [ general ] , the energy consumption @xmath133 can be taken care of if we simply replace @xmath137 $ ] by @xmath137 - e[z(i)]$ ] in our algorithms . in the following we do that and write it as @xmath137 $ ] only ( and hence ignore @xmath138 ) . the @xmath130 queues can share the channel in different ways . the stability region of @xmath139 and optimal ( good ) transmit policies depend upon the sharing mechanism used . we consider a few commonly used scenarios in the rest of the paper . the @xmath130 sensor nodes use tdma / orthogonal cdma / fdma / ofdma to transmit . then the @xmath130 queues become independent , decoupled queues and can be considered separately . thus , the transmission policies developed in previous sections for a single queue can be used here . in the following we explain them in the context of tdma . if the queues have to use the channel in a tdma fashion then necessary conditions for stability of the @xmath130 queues are : there exist @xmath140 and @xmath141 such that @xmath142 < \alpha_i \ g_i \ \left ( \frac{e[y(i)]}{\alpha_i } \right ) , \ \ i=1,2 , ... , n , \label{meqn6}\ ] ] where @xmath143 is the energy to bit mapping for @xmath144 . a stable policy for each queue will be as in section [ stability ] : @xmath144 is given @xmath145 fraction of slots ( on a long term basis ) and it uses energy @xmath146 - \epsilon)/ \alpha_i$ ] whenever it transmits . for better delay performance , the slots allocated to different queues should be uniformly spaced . we can improve on the mean delay by using ( [ onestar ] ) . it is possible that more than one set of @xmath147 satisfy the stability condition ( [ meqn6 ] ) . then one should select the values which minimize a cost function , ( say ) weighted sum of mean delays . now we discuss the mac with fading . let @xmath148 be the channel gain process for @xmath144 . it is assumed stationary , ergodic and independent of the fading process for @xmath149 . we discuss opportunistic scheduling for the contention free mac . we will study the csma based algorithms in the next section . if we assume that each of @xmath144 has infinite data backlog , then the policy that maximizes the sum of throughputs for @xmath150 and for symmetric statistics ( i.e. , each @xmath151 has same statistics and all @xmath137 $ ] are same ) is to choose @xmath152 @xmath153 in slot @xmath1 and use @xmath154 via the water - filling formula ( [ fto ] ) with the average power constraint @xmath155 = n e[y(i^*_k)-\epsilon].\ ] ] this is an extension of an algorithm in @xcite to the energy harvesting nodes . a modification of this policy is available in @xcite for asymmetric case . if @xmath16 is linear , then for the symmetric case , a channel is selected only if it has the highest possible gain ( for @xmath95 bounded ) . if more than one channel is in the best state , select one of them with equal probability . although ( [ meqn10 ] ) maximizes throughput , it may be unfair to different queues and may not provide the qos . furthermore , in our setup infinite backlog is not a realistic assumption . without this assumption a throughput optimal policy ( in the class of policies which use constant powers ) is to choose queue @xmath156-\epsilon}{\alpha(i ) } \right ) \right ) \right)\ ] ] and then use @xmath157 - \epsilon ) / \alpha(i^*_k)$ ] . here @xmath158 is the fraction of time slots assigned to @xmath159 . however now we do not know @xmath158 and this may be estimated ( see the end of this section ) . if @xmath158 is replaced with the true value , then stability of the queues in the mac follows from @xcite if the fading states take values in a finite set and the system satisfies the following condition . let there exist a function @xmath160 which picks one of the queues as a function of @xmath161 where @xmath162 - \epsilon}{\alpha_i } \right)$ ] , @xmath163 $ ] and @xmath164 is the stationary distribution of @xmath165 . then if @xmath166 < \sum r_i 1 \ { f(r_1 , ... , r_n)=i \ } \pi ( r_1 , ... , r_n)$ ] for each @xmath134 , the system is stable . this policy tries to satisfy the traffic requirements of different nodes but may not be delay optimal . based on experience in @xcite , a greedy policy @xmath167-\epsilon}{\alpha(i ) } \right),q_k(i ) \right ) \right ) \right)\ ] ] provides better mean delays . however , it is throughput optimal only for symmetric traffic statistics and when @xmath137 = e[y(j)],$ ] for all @xmath168 . but it can be made throughput optimal ( as ( [ meqn11 ] ) ) while still retaining ( partially ) its mean delay performance as follows . choose an appropriately large positive constant @xmath169 . if none of @xmath170 is greater than @xmath169 , use ( [ meqn12 ] ) ; otherwise , on the set @xmath171 , use ( [ meqn11 ] ) . we call this modified greedy policy . the mean delay of the above policies can be further improved , if instead of @xmath172 - \epsilon ) / \alpha(i)$ ] , we use ( [ onestar ] ) . but the stability region remains same . the policies ( [ meqn11 ] ) and ( [ meqn12 ] ) can be further improved if instead of using @xmath173 - \epsilon$ ] , we use waterfilling for @xmath16 in ( [ allert3 ] ) . of course we reduce transmit power as in ( [ onestar ] ) if there is not enough data to transmit . now not only the mean delays reduce but the stability region also enlarges . the policies ( [ meqn11 ] ) , ( [ meqn12 ] ) and modified greedy provide good performance , require minimal information ( only @xmath137 $ ] ) , are easy to implement and have low computational requirements . in addition they naturally adapt to changing traffic and channel conditions . in ( [ meqn11])-([meqn12 ] ) we need @xmath174 to obtain the energy @xmath7 . but unlike for tdma , @xmath175 is not available in these algorithms and depends on the algorithm used . thus , in these algorithms we use a simple variant of the lms ( least mean square ) algorithm ( @xcite ) to estimate @xmath174 : initially start with guess @xmath176 run the algorithm for ( say ) @xmath177 number of slots . each node @xmath134 computes the fraction @xmath178 of slots it gets and recomputes @xmath179 where @xmath180 is a small postive constant . at any time the current estimate of @xmath174 is used by the algorithms . since zigbee and 802.11 use csma , we discuss opportunistic scheduling for csma also . as against ( [ meqn11])-([meqn12 ] ) , this is a completely decentralized algorithm . this is used by zhao and tong @xcite . the basic idea in @xcite is to make the back - off mechanism in a node to be a function of the channel state of that node . the nodes that are to be given priority are given smaller back - off time . this mechanism has also been used in ieee 802.11e to provide priority to voice and video traffic . in this section we take this idea further by also including the effect of queue lengths and power control in deciding the back - off interval as against only the channel state in @xcite . let @xmath181 be a nonincreasing function with values in @xmath182 $ ] where @xmath183 is the maximum allowed back - off time in slots . if @xmath95 is the channel gain in a slot then in @xcite the back - off time is taken to be @xmath184 . in our setup , to use opportunistic scheduling in csma , we use the above mentioned monotonic function @xmath181 on each of the sensor nodes contending for the channel . the @xmath144 uses the back off time of @xmath185-\epsilon)}{\alpha(i ) } \right ) \right).\ ] ] when a node gets the channel , it will transmit a complete packet and use energy per slot as @xmath186 -\epsilon ] / \alpha(i^*_k).\ ] ] now we are making the usual assumption that the channel gains stay constant during the transmission of a packet . we can use ( [ onestar ] ) to improve performance . using the ideas in the last section we can develop better algorithms than ( [ meqn14])-([meqn15 ] ) . indeed , with ( [ meqn14 ] ) , instead of ( [ meqn15 ] ) , we can use waterfilling ( for @xmath16 in ( [ allert3 ] ) ) . we can also improve over ( [ meqn14 ] ) by using , for back - off time of @xmath134th node , @xmath187 - \epsilon}{\alpha(i ) } \right ) \right)\ ] ] which takes care of the traffic requirements of different nodes . we can also use the ( modified ) greedy in ( [ meqn12 ] ) . the @xmath174 in the above algorithms will be computed via lms in ( [ meqn13 ] ) . we will compare the performance of these algorithms via simulations in section [ msimulation ] . an advantage of above algorithms over the algorithms in section [ opportunistic ] are that these are completely decentralized : each node uses only its own queue length , channel state and @xmath137 $ ] to decide when to transmit . the algorithms in section [ opportunistic ] require a central controller ( may be a cluster head ) for implementation . centralized algorithms have also been considered in sensor networks and provide better performance . in this section for simplicity , we simulate the system under symmetric conditions , apply the different algorithms , and compare their performances . we use @xmath188 . the fading of each channel changes from slot to slot independently ; @xmath189 are _ iid _ with values 0.1 , 0.6 , 1.8 and 5 with probabilities 4/12 , 5/12 , 2/12 and 1/12 . the @xmath190 and @xmath191 are iid expontential . the lms ( [ meqn13 ] ) was taken with @xmath192 and the @xmath193s were updated after 30 - 50 slots . for orthogonal channels , under symmetric conditions with 3 queues , average queue lengths are shown in fig . [ orth ] for to ( [ meqn11 ] ) , greedy ( [ meqn12 ] ) , tdma , greedy with water - filling and tdma with water - filling policies . the @xmath189 are _ iid _ exponential with mean 1 . for symmetric conditions , greedy is throughput optimal and hence modified greedy is not implemented . we see that tdma becomes unstable much before the other policies , and that its average queue length is much worse even when it is stable . greedy performs better than to near the stability boundary which is @xmath38=0.39 $ ] . water - filling improves the stability region of tdma as well as greedy . for csma , figs . [ delay ] and [ pl ] show mean delays and packet loss probabilities under symmetric conditions with 10 queues and with normal exponential backoff , zhao - tong @xcite , our policy ( [ meqn16 ] ) and our policy with water - filling ( with @xmath194 and @xmath195 at @xmath196 assumes values 0.1,0.5,1.0,2.2 for time fractions 0.1,0.3,0.4,0.2 ) . we simulated the 10 queues in continuous time . also , @xmath58=1 $ ] and the data packets of unit size arrive at each queue as poisson streams . we see that opportunistic policies improve mean delays substantially . we have considered sensor nodes with energy harvesting sources , deployed for random field estimation . throughput optimal and mean delay optimal energy management policies for single nodes are identified which can make them work in energy neutral operation . next these results are extended to fading channels and when energy at the sensor node is also consumed in sensing and data processing . similarly we can include leakage / wastage of energy when it is stored in the energy buffer and when it is extracted . finally these policies are used to develop efficient mac protocols for such nodes . in particular versions of tdma , opportunistic macs for fading channels and csma are developed . their performance is compared via simulations . it is shown that opportunistic policies can substantially improve the performance . i. f. akyildiz , w. su , y. sankara subramaniam and e. cayirei , a survey on sensor networks " , _ ieee communications magazine _ , vol 40 , 2002 , pp . 102 - 114 . s. asmussen , applied probability and queues " , _ john wiley and sons_,n.y . , s. j. baek , g. veciana and x. su , minimizing energy consumption in large - scale sensor networks through distributed data compression and hierarchical aggregation " , _ ieee jsac _ , vol 22 , 2004 , pp . 1130 - 1140 . d. niyato , e. hossain , m. m. rashid and v. k. bhargava , wireless sensor networks with energy harvesting technologies : a game - theoretic approach to optimal energy management " , _ ieee wireless communications _ , aug . 2007 , pp . 90 - 96 . s. ratnaraj , s. jagannathan and v. rao , optimal energy - delay subnetwork routing protocol for wireless sensor networks " , _ proc . of ieee conf . on networking , sensing and control _ , april 2006 , pp . 787 - 792 . q. zhao and l. tong , opportunistic carrier sensing for energy - efficient information retrieval in sensor networks " , _ eurasip journal on wireless communications and networking _ , vol . 2 , 2005 , pp . 231 - 241 .[/INST] we study sensor networks with energy harvesting nodes . the generated energy at a node can be stored in a buffer . a sensor node periodically senses a random field and generates a packet . these packets are stored in a queue and transmitted using the energy available at that time at the node . for such networks we develop efficient energy management policies . first , for a single node , we obtain policies that are throughput optimal , i.e. , the data queue stays stable for the largest possible data rate . next we obtain energy management policies which minimize the mean delay in the queue . we also compare performance of several easily implementable sub - optimal policies . a greedy policy is identified which , in low snr regime , is throughput optimal and also minimizes mean delay . next using the results for a single node , we develop efficient mac policies . * keywords : * optimal energy management policies , energy harvesting , sensor networks , mac protocols . </s>

Eastern Libya is also being buffeted by strong crosscurrents that intelligence operatives are trying to monitor closely. The killing of Mr. Stevens has ignited public anger against the militias, underscored on Friday when thousands of Libyans took to the streets of Benghazi to demand that the groups be disarmed. The makeup of militias varies widely; some are moderate, while others are ultraconservative Islamists known as Salafis. Advertisement Continue reading the main story “The region’s deeply entrenched Salafi community is undergoing significant upheaval, with debate raging between a current that is amenable to political integration and a more militant strand that opposes democracy,” Frederic Wehrey, a senior policy analyst with the Carnegie Endowment for International Peace who closely follows Libya and visited there recently, wrote in a paper this month, “The Struggle for Security in Eastern Libya.” American intelligence operatives also assisted State Department contractors and Libyan officials in tracking shoulder-fired missiles taken from the former arsenals of the former Libyan Col. Muammar el-Qaddafi’s forces; they aided in efforts to secure Libya’s chemical weapons stockpiles; and they helped train Libya’s new intelligence service, officials said. Senior American officials acknowledged the intelligence setback, but insisted that information was still being collected using a variety of informants on the ground, systems that intercept electronic communications like cellphone conversations and satellite imagery. “The U.S. isn’t close to being blind in Benghazi and eastern Libya,” said an American official. Advertisement Continue reading the main story Spokesmen for the C.I.A., the State Department and the White House declined to comment on the matter on Sunday. Advertisement Continue reading the main story Within months of the start of Libyan revolution in February 2011, the C.I.A. began building a meaningful but covert presence in Benghazi, a locus of the rebel efforts to oust the government of Colonel Qaddafi. Advertisement Continue reading the main story Though the agency has been cooperating with the new post-Qaddafi Libyan intelligence service, the size of the C.I.A.’s presence in Benghazi apparently surprised some Libyan leaders. The deputy prime minister, Mustafa Abushagour, was quoted in The Wall Street Journal last week saying that he learned about some of the delicate American operations in Benghazi only after the attack on the mission, in large part because a surprisingly large number of Americans showed up at the Benghazi airport to be evacuated. Photo “We have no problem with intelligence sharing or gathering, but our sovereignty is also key,” said Mr. Abushagour. The attack has raised questions about the adequacy of security preparations at the two American compounds in Benghazi: the American mission, the main diplomatic facility where Mr. Stevens and another American diplomat died of smoke inhalation after an initial attack, and an annex a half-mile away that encompassed four buildings inside a low-walled compound. Advertisement Continue reading the main story From among these buildings, the C.I.A. personnel carried out their secret missions. The New York Times agreed to withhold locations and details of these operations at the request of Obama administration officials, who said that disclosing such information could jeopardize future sensitive government activities and put at risk American personnel working in dangerous settings. Newsletter Sign Up Continue reading the main story Please verify you're not a robot by clicking the box. Invalid email address. Please re-enter. You must select a newsletter to subscribe to. Sign Up Receive occasional updates and special offers for The New York Times's products and services. Thank you for subscribing. An error has occurred. Please try again later. View all New York Times newsletters. In Benghazi, both compounds were temporary homes in a volatile city teeming with militants, and they were never intended to become permanent diplomatic missions with appropriate security features built into them. Advertisement Continue reading the main story Neither was heavily guarded, and the annex was never intended to be a “safe house,” as initial accounts suggested. Two of the mission’s guards — Tyrone S. Woods and Glen A. Doherty, former members of the Navy SEALs — were killed just outside the villa’s front gate. A mortar round struck the roof of the building where the Americans had scrambled for cover. Secretary of State Hillary Rodham Clinton announced last week the creation of a review board to examine the attacks. The board is to be led by a veteran diplomat and former undersecretary of state, Thomas R. Pickering. Advertisement Continue reading the main story The F.B.I. has sent investigators — many from its New York field office — to Benghazi, but they have been hampered by the city’s tenuous security environment and the fact that they arrived more than a day after the attack occurred, according to senior American officials. Complicating the investigation, the officials said, is that many of the Americans who were evacuated from Benghazi after the attack are now scattered across Europe and the United States. It is also unclear, one of the officials said, whether there was much forensic evidence that could be extracted from the scene of the attacks. Advertisement Continue reading the main story Investigators and intelligence officials are now focusing on the possibility that the attackers were members of Al Qaeda in the Islamic Maghreb, or at least were in communication with the group during the four hours that elapsed between the initial attack at the mission and the second one at the mission’s annex. Representative Mike Rogers, a Michigan Republican who heads the House Intelligence Committee, said on CNN’s “State of the Union” program on Sunday that there was “a high degree of probability that it is an Al Qaeda or Al Qaeda-affiliated group that had a very specific target in mind, and that was to attack the consulate and cause as much harm, chaos and death as possible.” Foreign diplomats say that under security circumstances like those now in Libya, it is generally standard procedure to have a “safe house” in the vicinity of a main diplomatic facility that can be easily defended and evacuated. Advertisement Continue reading the main story “Normally, you try to keep the location of such a safe house secret, but in Benghazi right now, I think this was next to impossible,” Col. Wolfgang Pusztai, who until early August was Austria’s defense attaché to Libya and visited the country every month, wrote in an e-mail. “There are not too many foreigners hanging around, and it is quite easy to track them.” ||||| The Libyan authorities have given armed groups two days to vacate military bases and compounds as they seek to capitalise on the wave of people power that drove an Islamist militia from Benghazi at the weekend. Jihadist militias in Derna, Libya's Islamist stronghold, threw in the towel on Sunday, withdrawing from their stronghold and announcing they were disbanding to avoid a repeat of the scenes in Benghazi in which angry crowds sent armed gunmen fleeing. One of the routed militias was blamed for an attack on the US consulate two weeks ago that left four Americans dead including the ambassador, Chris Stevens. The de facto head of state, Muhammad Magariaf, president of Libya's parliament, met Benghazi politicians and security officials, anxious to fill a security vacuum that has emerged from the weekend violence, in which at least 11 people died. "The army chief Yussef al-Mangoush and Muhammad Magariaf have ordered all illegitimate militias should be removed from compounds and hand over their weapons to the national army," said Adel Othman al-Barasi, a spokesman for the defence ministry, according to Reuters. "A committee made up by the military police has been formed to take over the compounds and the weapons and hand these over to the army." Benghazi's army garrison commander, General Hamad Belkhair, said he was moving military police units into vacated militia bases. "What happened was a big mess," he said of the takeover by protesters of Benghazi's three militia bases on Friday night and Saturday morning. "But it has left the government clearly in control of the streets." Bilal Bettamer, a 22-year-old law student in the city who was one of the organisers of the Benghazi protests, said he was optimistic the militias would be disbanded. "You can't have 100% success in these situations. [But] that's what we wanted – the militias are put on notice and everyone knows now that this country will refuse any extremists and will eventually get rid of them, and become a country that we wanted on 17 February." He condemned the apparent killing of militia guards as a "stupid move" and speculated that pro-Gaddafi elements could be to blame. He even praised the courage of the militias for disbanding, claiming it showed they respected democracy. "Militias are not evil people, they are good people and they have saved Libya before. But it is time for legitimacy to take its place for the police and army. You can't build a country based on militias. "The army are back on the streets. You can see the army and police at night. The collection of individual weapons is beginning right now. They are doing their expected job. They have put small militia on notice to evacuate the neighbourhood. The army got braver. Everyone is telling them, strike with an iron fist." Yet extremists remain a presence: Belkhair himself was kidnapped on Saturday morning by masked gunmen and held for six hours before being released unharmed. He said he thought the group, who did not identify themselves, wanted him to limit the army's role in securing the city. Belkhair and police commanders are uneasily aware that the surge of people power that has swept militias from the streets could degenerate into anarchy, and that he lacks the manpower to impose order. An army unit from Sirte, former stronghold of the late dictator, Muammar Gaddafi, has occupied the compound of the Raffala al-Sahati militia, whose soldiers shot many of the 11 killed in the early hours of Saturday. Investigators are trying to establish who killed six militiamen whose bodies were found, each with a bullet to the head, in a field near the Raffala base. In Derna, a centre for Islamist resistance against the Gaddafi regime, two powerful jihadist formations, Abu Salem and Ansar al-Sharia, have agreed to disband. Commanders of both formations – the latter linked to the group blamed for the killing of Stevens – told Libya's state news agency that they had decided their role was over. In Tripoli, many foreign embassies remain in security lockdown, fearing jihadist units in the capital will seek revenge for the humiliating rout of their comrades in eastern Libya. Benghazi officials say the way is now clear for Washington to deploy an FBI team that is kicking its heels in Tripoli to join the investigation into the death of Stevens, who died from smoke inhalation after the attack on the consulate compound.

– Libya is working to drive out more armed groups after protesters' success against a militia blamed in the death of US ambassador Chris Stevens. Authorities have told "all illegitimate militias" they've got two days to "be removed from compounds and hand over their weapons to the national army," says a defense ministry spokesman. Over the weekend, protesters took over three militia bases; 11 people were killed in the process, the Guardian reports. "What happened was a big mess," says army commander General Hamad Belkhair. "But it has left the government clearly in control of the streets." Some militias are taking heed of the government's warnings, announcing they're calling it quits amid the backlash. Those groups include Ansar al-Sharia, blamed in Stevens' death. But others haven't given up; Belkhair was kidnapped for six hours on Saturday and finally released safely. Meanwhile, the attack on the US consulate earlier this month has created a roadblock for US intelligence efforts: Some dozen CIA agents and contractors were among those evacuated from Benghazi following the attack, the New York Times reports. "It’s a catastrophic intelligence loss," says a US official, even as the region grows more volatile. "We got our eyes poked out."

<s>[INST]Eastern Libya is also being buffeted by strong crosscurrents that intelligence operatives are trying to monitor closely. The killing of Mr. Stevens has ignited public anger against the militias, underscored on Friday when thousands of Libyans took to the streets of Benghazi to demand that the groups be disarmed. The makeup of militias varies widely; some are moderate, while others are ultraconservative Islamists known as Salafis. Advertisement Continue reading the main story “The region’s deeply entrenched Salafi community is undergoing significant upheaval, with debate raging between a current that is amenable to political integration and a more militant strand that opposes democracy,” Frederic Wehrey, a senior policy analyst with the Carnegie Endowment for International Peace who closely follows Libya and visited there recently, wrote in a paper this month, “The Struggle for Security in Eastern Libya.” American intelligence operatives also assisted State Department contractors and Libyan officials in tracking shoulder-fired missiles taken from the former arsenals of the former Libyan Col. Muammar el-Qaddafi’s forces; they aided in efforts to secure Libya’s chemical weapons stockpiles; and they helped train Libya’s new intelligence service, officials said. Senior American officials acknowledged the intelligence setback, but insisted that information was still being collected using a variety of informants on the ground, systems that intercept electronic communications like cellphone conversations and satellite imagery. “The U.S. isn’t close to being blind in Benghazi and eastern Libya,” said an American official. Advertisement Continue reading the main story Spokesmen for the C.I.A., the State Department and the White House declined to comment on the matter on Sunday. Advertisement Continue reading the main story Within months of the start of Libyan revolution in February 2011, the C.I.A. began building a meaningful but covert presence in Benghazi, a locus of the rebel efforts to oust the government of Colonel Qaddafi. Advertisement Continue reading the main story Though the agency has been cooperating with the new post-Qaddafi Libyan intelligence service, the size of the C.I.A.’s presence in Benghazi apparently surprised some Libyan leaders. The deputy prime minister, Mustafa Abushagour, was quoted in The Wall Street Journal last week saying that he learned about some of the delicate American operations in Benghazi only after the attack on the mission, in large part because a surprisingly large number of Americans showed up at the Benghazi airport to be evacuated. Photo “We have no problem with intelligence sharing or gathering, but our sovereignty is also key,” said Mr. Abushagour. The attack has raised questions about the adequacy of security preparations at the two American compounds in Benghazi: the American mission, the main diplomatic facility where Mr. Stevens and another American diplomat died of smoke inhalation after an initial attack, and an annex a half-mile away that encompassed four buildings inside a low-walled compound. Advertisement Continue reading the main story From among these buildings, the C.I.A. personnel carried out their secret missions. The New York Times agreed to withhold locations and details of these operations at the request of Obama administration officials, who said that disclosing such information could jeopardize future sensitive government activities and put at risk American personnel working in dangerous settings. Newsletter Sign Up Continue reading the main story Please verify you're not a robot by clicking the box. Invalid email address. Please re-enter. You must select a newsletter to subscribe to. Sign Up Receive occasional updates and special offers for The New York Times's products and services. Thank you for subscribing. An error has occurred. Please try again later. View all New York Times newsletters. In Benghazi, both compounds were temporary homes in a volatile city teeming with militants, and they were never intended to become permanent diplomatic missions with appropriate security features built into them. Advertisement Continue reading the main story Neither was heavily guarded, and the annex was never intended to be a “safe house,” as initial accounts suggested. Two of the mission’s guards — Tyrone S. Woods and Glen A. Doherty, former members of the Navy SEALs — were killed just outside the villa’s front gate. A mortar round struck the roof of the building where the Americans had scrambled for cover. Secretary of State Hillary Rodham Clinton announced last week the creation of a review board to examine the attacks. The board is to be led by a veteran diplomat and former undersecretary of state, Thomas R. Pickering. Advertisement Continue reading the main story The F.B.I. has sent investigators — many from its New York field office — to Benghazi, but they have been hampered by the city’s tenuous security environment and the fact that they arrived more than a day after the attack occurred, according to senior American officials. Complicating the investigation, the officials said, is that many of the Americans who were evacuated from Benghazi after the attack are now scattered across Europe and the United States. It is also unclear, one of the officials said, whether there was much forensic evidence that could be extracted from the scene of the attacks. Advertisement Continue reading the main story Investigators and intelligence officials are now focusing on the possibility that the attackers were members of Al Qaeda in the Islamic Maghreb, or at least were in communication with the group during the four hours that elapsed between the initial attack at the mission and the second one at the mission’s annex. Representative Mike Rogers, a Michigan Republican who heads the House Intelligence Committee, said on CNN’s “State of the Union” program on Sunday that there was “a high degree of probability that it is an Al Qaeda or Al Qaeda-affiliated group that had a very specific target in mind, and that was to attack the consulate and cause as much harm, chaos and death as possible.” Foreign diplomats say that under security circumstances like those now in Libya, it is generally standard procedure to have a “safe house” in the vicinity of a main diplomatic facility that can be easily defended and evacuated. Advertisement Continue reading the main story “Normally, you try to keep the location of such a safe house secret, but in Benghazi right now, I think this was next to impossible,” Col. Wolfgang Pusztai, who until early August was Austria’s defense attaché to Libya and visited the country every month, wrote in an e-mail. “There are not too many foreigners hanging around, and it is quite easy to track them.” ||||| The Libyan authorities have given armed groups two days to vacate military bases and compounds as they seek to capitalise on the wave of people power that drove an Islamist militia from Benghazi at the weekend. Jihadist militias in Derna, Libya's Islamist stronghold, threw in the towel on Sunday, withdrawing from their stronghold and announcing they were disbanding to avoid a repeat of the scenes in Benghazi in which angry crowds sent armed gunmen fleeing. One of the routed militias was blamed for an attack on the US consulate two weeks ago that left four Americans dead including the ambassador, Chris Stevens. The de facto head of state, Muhammad Magariaf, president of Libya's parliament, met Benghazi politicians and security officials, anxious to fill a security vacuum that has emerged from the weekend violence, in which at least 11 people died. "The army chief Yussef al-Mangoush and Muhammad Magariaf have ordered all illegitimate militias should be removed from compounds and hand over their weapons to the national army," said Adel Othman al-Barasi, a spokesman for the defence ministry, according to Reuters. "A committee made up by the military police has been formed to take over the compounds and the weapons and hand these over to the army." Benghazi's army garrison commander, General Hamad Belkhair, said he was moving military police units into vacated militia bases. "What happened was a big mess," he said of the takeover by protesters of Benghazi's three militia bases on Friday night and Saturday morning. "But it has left the government clearly in control of the streets." Bilal Bettamer, a 22-year-old law student in the city who was one of the organisers of the Benghazi protests, said he was optimistic the militias would be disbanded. "You can't have 100% success in these situations. [But] that's what we wanted – the militias are put on notice and everyone knows now that this country will refuse any extremists and will eventually get rid of them, and become a country that we wanted on 17 February." He condemned the apparent killing of militia guards as a "stupid move" and speculated that pro-Gaddafi elements could be to blame. He even praised the courage of the militias for disbanding, claiming it showed they respected democracy. "Militias are not evil people, they are good people and they have saved Libya before. But it is time for legitimacy to take its place for the police and army. You can't build a country based on militias. "The army are back on the streets. You can see the army and police at night. The collection of individual weapons is beginning right now. They are doing their expected job. They have put small militia on notice to evacuate the neighbourhood. The army got braver. Everyone is telling them, strike with an iron fist." Yet extremists remain a presence: Belkhair himself was kidnapped on Saturday morning by masked gunmen and held for six hours before being released unharmed. He said he thought the group, who did not identify themselves, wanted him to limit the army's role in securing the city. Belkhair and police commanders are uneasily aware that the surge of people power that has swept militias from the streets could degenerate into anarchy, and that he lacks the manpower to impose order. An army unit from Sirte, former stronghold of the late dictator, Muammar Gaddafi, has occupied the compound of the Raffala al-Sahati militia, whose soldiers shot many of the 11 killed in the early hours of Saturday. Investigators are trying to establish who killed six militiamen whose bodies were found, each with a bullet to the head, in a field near the Raffala base. In Derna, a centre for Islamist resistance against the Gaddafi regime, two powerful jihadist formations, Abu Salem and Ansar al-Sharia, have agreed to disband. Commanders of both formations – the latter linked to the group blamed for the killing of Stevens – told Libya's state news agency that they had decided their role was over. In Tripoli, many foreign embassies remain in security lockdown, fearing jihadist units in the capital will seek revenge for the humiliating rout of their comrades in eastern Libya. Benghazi officials say the way is now clear for Washington to deploy an FBI team that is kicking its heels in Tripoli to join the investigation into the death of Stevens, who died from smoke inhalation after the attack on the consulate compound.[/INST]– Libya is working to drive out more armed groups after protesters' success against a militia blamed in the death of US ambassador Chris Stevens. Authorities have told "all illegitimate militias" they've got two days to "be removed from compounds and hand over their weapons to the national army," says a defense ministry spokesman. Over the weekend, protesters took over three militia bases; 11 people were killed in the process, the Guardian reports. "What happened was a big mess," says army commander General Hamad Belkhair. "But it has left the government clearly in control of the streets." Some militias are taking heed of the government's warnings, announcing they're calling it quits amid the backlash. Those groups include Ansar al-Sharia, blamed in Stevens' death. But others haven't given up; Belkhair was kidnapped for six hours on Saturday and finally released safely. Meanwhile, the attack on the US consulate earlier this month has created a roadblock for US intelligence efforts: Some dozen CIA agents and contractors were among those evacuated from Benghazi following the attack, the New York Times reports. "It’s a catastrophic intelligence loss," says a US official, even as the region grows more volatile. "We got our eyes poked out."</s>

chiral perturbation theory ( chpt ) is an efficient tool for the evaluation of hadron observables at low energies ( for a comprehensive introduction to meson and nucleon chpt , see @xcite ) . the predictions of chpt are used in many branches of modern physics from matching of lattice calculations ( for a review see @xcite ) , till the investigations of the nuclei properties ( see e.g. @xcite ) . nowadays , all practically interesting quantities has been calculated at two - loop order ( for the recent status of meson chpt see @xcite , also see the talk given by j.bijnens @xcite ) . however , the straightforward expansion to higher - orders of chpt is meaningless . the main point is the rapidly growing number of low - energy constants ( lecs ) . indeed , in the meson chpt at order @xmath0 the number of lecs is of order of hundred ( depending on the number of active mesons)@xcite . in the nucleon chpt the number of fields and invariant structures grows even faster , and this amount of lecs is reached already at order @xmath1 @xcite . such an enormous amount of lecs can not be fixed in any reasonable way by a recent data . since the straightforward way to the higher precision theoretical predictions is closed , one should investigate other possibilities to improve the chiral perturbation series . one of the promising approach is the evaluation of the leading logarithm ( llog ) part of the chiral expansion . besides the possibility to improve the theoretical estimations for observables , the investigation of llogs grants us a chance to understand the mathematical structure of the theory at high orders of perturbative expansion . in contrast to renormalizable quantum field theories , where , roughly speaking , llog approximation consists in the powering of one - loop diagrams , llogs in non - renormalizable theories are highly non - trivial . the structure of llogs in non - renormalizable theories resembles the structure of the whole perturbative expansion . therefore , observation of any regularities within llog approximation is the reflection of general regularities . in chpt ( as in any non - renormalizable theory ) the evaluation of llog coefficient of any given order implies the evaluation of diagrams at this order . however , this can be done in a relatively efficient way . in this paper we give a short introduction to the calculation of the leading chiral logarithms , and present the results of the recent evaluation of the llog series for the nucleon mass : the first example of llog calculation in the nucleon chpt . in chpt the llog coefficients can be calculated using solely one - loop calculations . this statement was proven in @xcite , and relies on the fact that the llog coefficient is proportional to the main ultraviolet ( uv ) divergency of a diagram . in its own turn , the leading uv divergency of the diagram is composed from the individual divergencies of one - loop subgraphs . in the renormalizable theories , the individual uv divergences of one - loop subgraphs are just multiplied on each other , while in chpt the relation between subgraph s uv divergencies and the leading divergency of a diagram are more involved . there are several sources of complication . first of all , in chpt every one - loop graph is uv divergent . as a result , all possible topologies of diagrams contain llog . this is the main complication point , because there are infinite number of one - loop graphs and all of them should be evaluated in order to obtain the comprehensive llog picture of chpt . second , since the loop - integrals in chpt are dimensional , the individual divergencies of graphs are entangled by the momentum structures . despite its apparent simplicity , this is a serious problem , because it prevents to derive any general relation between leading uv singularity of a graph and individual uv singularities of subgraphs without referring to the particular expressions for graph . in the bosonic chpt this set of problems has been solved in refs.@xcite . the main idea of solution was to reconstruct the llog coefficient by evaluation of the fixed chiral order solution of the system of renormalization group equations on the amplitude and on lecs . instead of giving the formal derivation of this method , which can be found in @xcite , here we present an illustrative description of the route of calculation . the base of the method is the formal solution of the renormalization group equation for an amplitude , which can be written in the form @xcite @xmath2 where @xmath3 is a set of kinematical variables . the operator @xmath4 acts on lecs and defined as @xmath5 where @xmath6 are lec of nth chiral order , @xmath7 is the beta - function of the corresponded lec and the variation over lec is defined as @xmath8 . the action of the operator @xmath4 on lec replaces the lec by its beta - function . on diagrammatic language , this procedure can be illustrated as an insertion of the all possible ( of given chirla order and of given number of external fields ) one - loop graphs on the place of the vertex . the crucial point of the approach is that the lowest order lecs ( lecs of the second chiral order for meson chpt , and lecs of the first and the second chiral orders of nucleon chpt ) have zero beta - function . therefore , the chain of one - loop insertions is finite . ( plot as arrow ) on a vertex effectively inserts the pole contribution of all possible one - loop subgraphs ( inserted loop marked by a dot ) . the repetition of the operation inserts the next subgraph , and so on , until all the vertices of a graph are of the lowest order ( so , no more insertion can be done ) . in this way one recovers the leading pole contribution of sum of all diagrams . some diagrams appear in several brunches of the operational tree ( see e.g. the first diagrams in the first and the second lines ) , this indicates the symmetry of a renormalization procedure and result to a correct multiplier for llog coefficients . the numbers indicate the chiral order of vertices . ] the procedure can be viewed as a graph tree , see fig.1 . the way from the root ( the tree order diagrams ) to branches ( many - loop diagrams ) represents the particular chain of insertions of the one - loop graphs and illustrates the iterative solution of the renormalization group equation ( [ defr ] ) . the consideration of the tree in the opposite way ( from branches to the root ) illustrates the traditional forest formula for the renormalization of a diagram . in this way every step gives a subtraction of a subgraph . one can see that the same multi - loop diagrams appear on the tree several times , this is a reflection of the multiple ways of the subgraph subtractions . important to mention that at every chiral order there are vertices of all possible momentum and isotopic structures whose non - trivially relate to each other in beta - functions . therefore , the chain of insertions ( or subtractions , depending on the point of view ) precisely restores the leading uv singularity of a graph through the known uv singularities of one - loop subgraphs . knowing the leading uv divergency , one easily restores the llog coefficient . the described procedure can be used for the evaluation of the renormalization group logarithms only , i.e. the logarithms of the renormalization scale @xmath9 . the logarithms of momenta and masses should be considered as a finite parts , and do not participate in the logarithmical counting . however , the procedure can be generalized on of any order logarithms by increasing the loop - order of beta - functions . for example , to obtain the next - to - llog coefficient one should use two - loop beta - functions , on the graph - tree that would correspond to the insertion of two - loop graphs in one turn . in some particular models the procedure can be simplified . the great example is the chpt with massless fields . in this case tad - pole diagrams are zero and many branches of the graph - tree lead to zeros ( e.g. in fig.1 only the last two diagrams of the third line are non - zero ) . in this case the infinite set of renormalization group equations can be presented as the closed recursive equation @xcite . the recursive equation has the straightforward interpretation as the llog solution of the joined system of standard restrictions on the pion amplitudes , namely , unitarity , analyticity and crossing symmetry @xcite . such a recursive equations are the convenient tool for the investigation of effective field theories of a very general structure @xcite . the described method has been used for the calculation of llog series for the pion mass , form factors , and scattering lengths @xcite . the calculation can be fully automatized and then the maximum order of calculation is restricted by the computing time . the typical order of calculation is the sixth power of logarithms , which corresponds to the evaluation of six - loop diagrams . for example , the mass of pion in chpt with two active flavors at this order reads @xcite @xmath10 where @xmath11 the llog contribution to the scattering amplitudes is not significant , e.g. see estimations in @xcite . numerically higher orders of llog series give a tiny correction to the first terms and the series is very fast convergent . anyway , the difference between llog and next - to - llog of characteristic energy is much smaller then the difference between the powers of same energy . therefore , the direct practical application of llogs is unreasonable . however , in the case of the chiral expansion for parton distributions at small-@xmath12 ( @xmath13 ) the powers of energies effectively cancel by powers of @xmath12 , and llog approximation is the dominant one @xcite . that leads to the observable effect of the llog resummation in chpt @xcite . the generalization of the scheme on the theories with baryons is straightforward . there are only several complication points that should be specially cared . the first complication is the hierarchy problem of nucleon - pion system , which is the standard problem of the nucleon chpt . nowadays several solution of the problem is known . the most popular are the infrared renormalization scheme @xcite , and the extended - on - mass - shell renormalization scheme @xcite . both these schemes relies on the additional subtractions of the scale - violating terms , as a part of the renormalization procedure . since the additional ( finite ) subtraction do not spoil the renormalization , these schemes can be easily implemented into llog calculations . however , for the first try we found convenient to use somewhat old - fashion heavy baryon chpt ( hbchpt ) , see e.g.@xcite . the advantage of hbchpt for llog calculation is that no extra subtractions should be done , by the price of violation of lorentz invariance on the intermediate steps . the second complication is that in hbchpt ( as in any chpt with nucleon ) there are two lowest order lagrangians . the first chiral order lagrangian , neglecting terms with external fields , reads @xmath14 where @xmath15 is the axial coupling constant , @xmath16 is a spin vector , @xmath17 is the nucleon velocity vector , @xmath18 is the matrix of pion fields , and the field combinations read @xmath19 the second order lagrangian is sensitive to redefinitions of the nucleon field , and in the most standard form reads @xcite @xmath20n_v,\end{aligned}\ ] ] where @xmath21 is the nucleon mass . the addition of the vertices with odd chiral counting does not spoil the general procedure of llog computation , but leads to extra algebra , see details in @xcite . indeed , since every loop increases the chiral counting of a diagrams by at least two , the llog of power @xmath22 is collected from the diagrams of two different scales , @xmath23 and @xmath24 . the third complication is the practical one . due to the presence of the external vector @xmath17 , complicated spin structure , as well as , presence of two initial lagrangians the calculation within hbchpt is dramatically larger in comparison to the meson chpt . it is reflected in every aspect of calculation : the number of diagrams , higher order vertices and the length of the counter terms . these quantities grow rapidly with chiral order . for example , in order to calculate the four - loop llog coefficient for nucleon mass one needs to evaluate nearly @xmath25 one - loop diagrams . the main route of the calculation remains the meson calculation : one should evaluate one - loop beta - function and insert them into amplitude by means of procedure ( [ defr ] ) . in order to obtain the correction to the nucleon mass we evaluate the nucleon propagator , an example of diagram - insertion - chain is shown in fig.2 . one can see that the number of diagrams and their topologies is significantly larger , in comparison to the meson calculation ( see fig.1 ) . however , one can also see some minor simplifications , e.g. the fourth line in fig.2 is ended by zero . it is the reflection of the fact that lagrangians ( [ 3:l0 ] ) and ( [ 3:bkkm ] ) have not counter terms . therefore , the graphs with too many vertices from @xmath26 have larger chiral counting but do not produce llogs . taking into account this fact significantly reduce the number of diagrams to consider . we have performed the calculation of the nucleon propagator and evaluate the nucleon physical mass . the procedure of llog evaluation has been automatized using the computation system form @xcite . within a reasonable computing time we have calculated the llog coefficient and the non - analytical in quark mass llog term up to the fourth power . the results are presented in the form : @xmath27 where @xmath28 is defined in ( [ 2:l_def ] ) . the coefficients up to @xmath29 are presented in the table 1 . this corresponds to the four - loop calculation of llog and five - loop calculation for the terms non - analytical in quark masses . a very strong check of the calculation is performed by parallel calculation with the different parameterizations of the lagrangians . additionally , the coefficients up to @xmath30 agree with known results . the one - loop coefficients @xmath31 are well known , see e.g. @xcite . the two - loop coefficient @xmath32 was first derived in @xcite . the two - loop coefficients @xmath30 and @xmath33 are known from the full two - loop calculation for the nucleon mass performed in the eoms scheme @xcite . ' '' '' @xmath34 & @xmath35 & @xmath36 & @xmath35 + ' '' '' @xmath37 & @xmath38 & @xmath39 & @xmath38 + ' '' '' @xmath40 & @xmath41 & @xmath42 & @xmath43 + ' '' '' @xmath33 & @xmath44 & @xmath45 & @xmath46 + ' '' '' @xmath30 & @xmath47 & @xmath48 & @xmath49 + ' '' '' @xmath50 & @xmath51 & @xmath52 & @xmath53 + ' '' '' @xmath54 & @xmath55 & @xmath56 & @xmath57 + ' '' '' @xmath58 & @xmath59 & @xmath60 & @xmath61 + ' '' '' @xmath62 & @xmath63 & @xmath64 & @xmath65 + ' '' '' @xmath29 & @xmath66 & @xmath67 & @xmath68 + ' '' '' @xmath69 ( * ) & @xmath70 & @xmath71 ( * ) & @xmath72 + ' '' '' @xmath73 ( * * ) & @xmath74 & @xmath75 ( * * ) & @xmath76 + ' '' '' @xmath77 ( * * ) & @xmath78 & & + the calculation of the even coefficients @xmath79 can be significantly simplified by using the conjectures discussed below . so , by neglecting higher powers of @xmath15 during the evaluation of the diagrams , we could also evaluate the five - loop coefficient @xmath69 . adding the further conjecture about the relation with the llog in the pion mass , we can obtain the six and seven - loop coefficients @xmath73 and @xmath77 . however , these coefficients are the result of conjectures and , therefore , in the table 1 they are marked by stars . the obtained result of the straightforward calculation , i.e. the coefficients @xmath80 shows a number of regularities . some of the regularities we can explain easily , while some of them we can not . but we are sure that this regularities are not accidental and are an example of the deep connection of the llog approximation ( in non - renormalizable theories ) with the structure of theory . the most intriguing observation is that the coefficients @xmath81 contains a very particular combination of lecs . the pattern appearing in @xmath81 is not well understood yet . while it is clear why the coupling constant @xmath82 does not participate in the nucleon mass at llog ( because it produces an @xmath83 , which is p - odd ) , we have not found any simple argument why @xmath15 only appears up to order @xmath84 , and what is the special in the combination @xmath85 . from the general point of view , one expects that the llog coefficient should be linear in @xmath86 , but a general polynomial in @xmath15 . because the number of vertices from @xmath87 is restricted to one ( see fig.2 and explanations in the previous section ) , but the number of vertices from @xmath88 is naturally unrestricted . moreover , the expression for the propagator contains all allowed powers of @xmath15 . these powers cancel in the solution of the pole equation on the physical mass . the deeper consideration of these cancelation ( see discussion in @xcite ) hints that that absence of higher powers of @xmath15 in coefficients @xmath81 is a consequence of lorentz invariance , and of the additional subtractions of infrared ( heavy mass ) singularities into renormalization counter terms within hbchpt . however , we have not been able to prove this . supposing that the cancelation of the higher powers of @xmath15 takes place at all orders , one can neglect these powers during the computation of diagrams . this procedure significantly reduces the demands for computer time and allows us to calculate the coefficient @xmath69 . even more intriguing result reveals if one inverts the perturbation series and presents the nucleon mass llog coefficient in terms of the physical pion mass @xmath89 @xmath90 where @xmath91 the coefficients @xmath92 of this expansion are presented in table 1 . one can see that the non - analytical in quark mass terms @xmath94 do not simplify in this form of expansion , while the expressions for the coefficient @xmath95 are significantly simplified . moreover , the combination of lecs @xmath85 completely disappears from the higher order terms . the rest coefficient precisely repeat the llog expansion for @xmath96 . thus , we conjecture the llog part of the expression for the nucleon bare mass via the physical masses _ at all orders _ to be @xmath97 the expression for the physical pion mass is known up to 6-loop order ( [ 2:mphys ] ) , therefore , we can obtain two more llog coefficients for the physical nucleon mass . these are presented in the table 1 and indicated by the double - star marks . as we mentioned earlier , the llog are not necessarily dominant . they do however give an indication of the size of corrections to be expected . to show an example , we plot in fig.3 the absolute value of the individual terms containing @xmath98 of ( [ mainresult ] ) for @xmath93 mev . note the excellent convergence . we have used here one set of inputs for the @xmath86 as determined in @xcite and reasonable values for the other quantities . this work is supported in part by the european community - research infrastructure integrating activity study of strongly interacting matter " ( hadronphysics3 , grant agreement no . 28 3286 ) and the swedish research council grants 621 - 2011 - 5080 and 621 - 2013 - 4287 . s. scherer and m. r. schindler , hep - ph/0505265 . + s. scherer and m. r. schindler , lect . notes phys . * 830 * ( 2012 ) pp.1 . s. aoki , y. aoki , c. bernard , t. blum , g. colangelo , m. della morte , s. du"rr and a. x. el khadra _ et al . _ , eur . j. c * 74 * ( 2014 ) 9 , 2890 [ arxiv:1310.8555 [ hep - lat ] ] . e. epelbaum , h. w. hammer and u. g. meissner , rev . * 81 * ( 2009 ) 1773 [ arxiv:0811.1338 [ nucl - th ] ] . j. bijnens and g. ecker , ann . nucl . part . * 64 * ( 2014 ) 149 [ arxiv:1405.6488 [ hep - ph ] ] . j. bijnens , arxiv:1411.6378 [ hep - ph ] . j. bijnens , g. colangelo and g. ecker , jhep * 9902 * ( 1999 ) 020 [ hep - ph/9902437 ] . n. fettes , u. g. meissner , m. mojzis and s. steininger , annals phys . * 283 * ( 2000 ) 273 [ erratum - ibid . * 288 * ( 2001 ) 249 ] [ hep - ph/0001308 ] . m. bchler and g. colangelo , eur . j. c * 32 * ( 2003 ) 427 [ hep - ph/0309049 ] . n. kivel , m. v. polyakov and a. vladimirov , phys . * 101 * ( 2008 ) 262001 [ arxiv:0809.3236 [ hep - ph ] ] . n. a. kivel , m. v. polyakov and a. a. vladimirov , jetp lett . * 89 * ( 2009 ) 529 [ arxiv:0904.3008 [ hep - ph ] ] . j. bijnens and l. carloni , nucl . b * 827 * ( 2010 ) 237 [ arxiv:0909.5086 [ hep - ph ] ] . j. bijnens and l. carloni , nucl . b * 843 * ( 2011 ) 55 [ arxiv:1008.3499 [ hep - ph ] ] . j. bijnens and a. a. vladimirov , arxiv:1409.6127 [ hep - ph ] . j. koschinski , m. v. polyakov and a. a. vladimirov , phys . d * 82 * ( 2010 ) 014014 [ arxiv:1004.2197 [ hep - ph ] ] . m. v. polyakov and a. a. vladimirov , theor . * 169 * ( 2011 ) 1499 [ arxiv:1012.4205 [ hep - th ] ] . j. bijnens , k. kampf and s. lanz , nucl . b * 860 * ( 2012 ) 245 [ arxiv:1201.2608 [ hep - ph ] ] . j. bijnens , k. kampf and s. lanz , nucl . b * 873 * ( 2013 ) 137 [ arxiv:1303.3125 [ hep - ph ] ] . n. kivel and m. v. polyakov , phys . b * 664 * ( 2008 ) 64 [ arxiv:0707.2208 [ hep - ph ] ] . a. m. moiseeva and a. a. vladimirov , eur . j. a * 49 * ( 2013 ) 23 [ arxiv:1208.1714 [ hep - ph ] ] . i. a. perevalova , m. v. polyakov , a. n. vall and a. a. vladimirov , arxiv:1105.4990 [ hep - ph ] . a. moiseeva and a. a. vladimirov , few body syst . * 55 * ( 2014 ) 389 [ arxiv:1311.3433 [ hep - ph ] ] . v. bernard , n. kaiser , j. kambor and u. g. meissner , nucl . b * 388 * ( 1992 ) 315 . v. bernard , n. kaiser and u. -g . meissner , int . j. mod . e * 4 * ( 1995 ) 193 [ hep - ph/9501384 ] . j. a. m. vermaseren , _ `` new features of form '' _ , math - ph/0010025 . j. a. mcgovern and m. c. birse , phys . b * 446 * ( 1999 ) 300 [ hep - ph/9807384 ] . m. r. schindler , d. djukanovic , j. gegelia and s. scherer , nucl . a * 803 * ( 2008 ) 68 [ arxiv:0707.4296 [ hep - ph ] ] .

we give a short introduction to the calculation of the leading chiral logarithms , and present the results of the recent evaluation of the llog series for the nucleon mass within the heavy baryon theory . the presented results are the first example of llog calculation in the nucleon chpt . we also discuss some regularities observed in the leading logarithmical series for nucleon mass . the talk has been presented at _ quark confinement and hadron spectrum xi_. lu tp 15 - 04 + january 2015 address = department of astronomy and theoretical physics , lund university , + slvegatan 14a , se 223 62 lund , sweden address = department of astronomy and theoretical physics , lund university , + slvegatan 14a , se 223 62 lund , sweden

<s>[INST]chiral perturbation theory ( chpt ) is an efficient tool for the evaluation of hadron observables at low energies ( for a comprehensive introduction to meson and nucleon chpt , see @xcite ) . the predictions of chpt are used in many branches of modern physics from matching of lattice calculations ( for a review see @xcite ) , till the investigations of the nuclei properties ( see e.g. @xcite ) . nowadays , all practically interesting quantities has been calculated at two - loop order ( for the recent status of meson chpt see @xcite , also see the talk given by j.bijnens @xcite ) . however , the straightforward expansion to higher - orders of chpt is meaningless . the main point is the rapidly growing number of low - energy constants ( lecs ) . indeed , in the meson chpt at order @xmath0 the number of lecs is of order of hundred ( depending on the number of active mesons)@xcite . in the nucleon chpt the number of fields and invariant structures grows even faster , and this amount of lecs is reached already at order @xmath1 @xcite . such an enormous amount of lecs can not be fixed in any reasonable way by a recent data . since the straightforward way to the higher precision theoretical predictions is closed , one should investigate other possibilities to improve the chiral perturbation series . one of the promising approach is the evaluation of the leading logarithm ( llog ) part of the chiral expansion . besides the possibility to improve the theoretical estimations for observables , the investigation of llogs grants us a chance to understand the mathematical structure of the theory at high orders of perturbative expansion . in contrast to renormalizable quantum field theories , where , roughly speaking , llog approximation consists in the powering of one - loop diagrams , llogs in non - renormalizable theories are highly non - trivial . the structure of llogs in non - renormalizable theories resembles the structure of the whole perturbative expansion . therefore , observation of any regularities within llog approximation is the reflection of general regularities . in chpt ( as in any non - renormalizable theory ) the evaluation of llog coefficient of any given order implies the evaluation of diagrams at this order . however , this can be done in a relatively efficient way . in this paper we give a short introduction to the calculation of the leading chiral logarithms , and present the results of the recent evaluation of the llog series for the nucleon mass : the first example of llog calculation in the nucleon chpt . in chpt the llog coefficients can be calculated using solely one - loop calculations . this statement was proven in @xcite , and relies on the fact that the llog coefficient is proportional to the main ultraviolet ( uv ) divergency of a diagram . in its own turn , the leading uv divergency of the diagram is composed from the individual divergencies of one - loop subgraphs . in the renormalizable theories , the individual uv divergences of one - loop subgraphs are just multiplied on each other , while in chpt the relation between subgraph s uv divergencies and the leading divergency of a diagram are more involved . there are several sources of complication . first of all , in chpt every one - loop graph is uv divergent . as a result , all possible topologies of diagrams contain llog . this is the main complication point , because there are infinite number of one - loop graphs and all of them should be evaluated in order to obtain the comprehensive llog picture of chpt . second , since the loop - integrals in chpt are dimensional , the individual divergencies of graphs are entangled by the momentum structures . despite its apparent simplicity , this is a serious problem , because it prevents to derive any general relation between leading uv singularity of a graph and individual uv singularities of subgraphs without referring to the particular expressions for graph . in the bosonic chpt this set of problems has been solved in refs.@xcite . the main idea of solution was to reconstruct the llog coefficient by evaluation of the fixed chiral order solution of the system of renormalization group equations on the amplitude and on lecs . instead of giving the formal derivation of this method , which can be found in @xcite , here we present an illustrative description of the route of calculation . the base of the method is the formal solution of the renormalization group equation for an amplitude , which can be written in the form @xcite @xmath2 where @xmath3 is a set of kinematical variables . the operator @xmath4 acts on lecs and defined as @xmath5 where @xmath6 are lec of nth chiral order , @xmath7 is the beta - function of the corresponded lec and the variation over lec is defined as @xmath8 . the action of the operator @xmath4 on lec replaces the lec by its beta - function . on diagrammatic language , this procedure can be illustrated as an insertion of the all possible ( of given chirla order and of given number of external fields ) one - loop graphs on the place of the vertex . the crucial point of the approach is that the lowest order lecs ( lecs of the second chiral order for meson chpt , and lecs of the first and the second chiral orders of nucleon chpt ) have zero beta - function . therefore , the chain of one - loop insertions is finite . ( plot as arrow ) on a vertex effectively inserts the pole contribution of all possible one - loop subgraphs ( inserted loop marked by a dot ) . the repetition of the operation inserts the next subgraph , and so on , until all the vertices of a graph are of the lowest order ( so , no more insertion can be done ) . in this way one recovers the leading pole contribution of sum of all diagrams . some diagrams appear in several brunches of the operational tree ( see e.g. the first diagrams in the first and the second lines ) , this indicates the symmetry of a renormalization procedure and result to a correct multiplier for llog coefficients . the numbers indicate the chiral order of vertices . ] the procedure can be viewed as a graph tree , see fig.1 . the way from the root ( the tree order diagrams ) to branches ( many - loop diagrams ) represents the particular chain of insertions of the one - loop graphs and illustrates the iterative solution of the renormalization group equation ( [ defr ] ) . the consideration of the tree in the opposite way ( from branches to the root ) illustrates the traditional forest formula for the renormalization of a diagram . in this way every step gives a subtraction of a subgraph . one can see that the same multi - loop diagrams appear on the tree several times , this is a reflection of the multiple ways of the subgraph subtractions . important to mention that at every chiral order there are vertices of all possible momentum and isotopic structures whose non - trivially relate to each other in beta - functions . therefore , the chain of insertions ( or subtractions , depending on the point of view ) precisely restores the leading uv singularity of a graph through the known uv singularities of one - loop subgraphs . knowing the leading uv divergency , one easily restores the llog coefficient . the described procedure can be used for the evaluation of the renormalization group logarithms only , i.e. the logarithms of the renormalization scale @xmath9 . the logarithms of momenta and masses should be considered as a finite parts , and do not participate in the logarithmical counting . however , the procedure can be generalized on of any order logarithms by increasing the loop - order of beta - functions . for example , to obtain the next - to - llog coefficient one should use two - loop beta - functions , on the graph - tree that would correspond to the insertion of two - loop graphs in one turn . in some particular models the procedure can be simplified . the great example is the chpt with massless fields . in this case tad - pole diagrams are zero and many branches of the graph - tree lead to zeros ( e.g. in fig.1 only the last two diagrams of the third line are non - zero ) . in this case the infinite set of renormalization group equations can be presented as the closed recursive equation @xcite . the recursive equation has the straightforward interpretation as the llog solution of the joined system of standard restrictions on the pion amplitudes , namely , unitarity , analyticity and crossing symmetry @xcite . such a recursive equations are the convenient tool for the investigation of effective field theories of a very general structure @xcite . the described method has been used for the calculation of llog series for the pion mass , form factors , and scattering lengths @xcite . the calculation can be fully automatized and then the maximum order of calculation is restricted by the computing time . the typical order of calculation is the sixth power of logarithms , which corresponds to the evaluation of six - loop diagrams . for example , the mass of pion in chpt with two active flavors at this order reads @xcite @xmath10 where @xmath11 the llog contribution to the scattering amplitudes is not significant , e.g. see estimations in @xcite . numerically higher orders of llog series give a tiny correction to the first terms and the series is very fast convergent . anyway , the difference between llog and next - to - llog of characteristic energy is much smaller then the difference between the powers of same energy . therefore , the direct practical application of llogs is unreasonable . however , in the case of the chiral expansion for parton distributions at small-@xmath12 ( @xmath13 ) the powers of energies effectively cancel by powers of @xmath12 , and llog approximation is the dominant one @xcite . that leads to the observable effect of the llog resummation in chpt @xcite . the generalization of the scheme on the theories with baryons is straightforward . there are only several complication points that should be specially cared . the first complication is the hierarchy problem of nucleon - pion system , which is the standard problem of the nucleon chpt . nowadays several solution of the problem is known . the most popular are the infrared renormalization scheme @xcite , and the extended - on - mass - shell renormalization scheme @xcite . both these schemes relies on the additional subtractions of the scale - violating terms , as a part of the renormalization procedure . since the additional ( finite ) subtraction do not spoil the renormalization , these schemes can be easily implemented into llog calculations . however , for the first try we found convenient to use somewhat old - fashion heavy baryon chpt ( hbchpt ) , see e.g.@xcite . the advantage of hbchpt for llog calculation is that no extra subtractions should be done , by the price of violation of lorentz invariance on the intermediate steps . the second complication is that in hbchpt ( as in any chpt with nucleon ) there are two lowest order lagrangians . the first chiral order lagrangian , neglecting terms with external fields , reads @xmath14 where @xmath15 is the axial coupling constant , @xmath16 is a spin vector , @xmath17 is the nucleon velocity vector , @xmath18 is the matrix of pion fields , and the field combinations read @xmath19 the second order lagrangian is sensitive to redefinitions of the nucleon field , and in the most standard form reads @xcite @xmath20n_v,\end{aligned}\ ] ] where @xmath21 is the nucleon mass . the addition of the vertices with odd chiral counting does not spoil the general procedure of llog computation , but leads to extra algebra , see details in @xcite . indeed , since every loop increases the chiral counting of a diagrams by at least two , the llog of power @xmath22 is collected from the diagrams of two different scales , @xmath23 and @xmath24 . the third complication is the practical one . due to the presence of the external vector @xmath17 , complicated spin structure , as well as , presence of two initial lagrangians the calculation within hbchpt is dramatically larger in comparison to the meson chpt . it is reflected in every aspect of calculation : the number of diagrams , higher order vertices and the length of the counter terms . these quantities grow rapidly with chiral order . for example , in order to calculate the four - loop llog coefficient for nucleon mass one needs to evaluate nearly @xmath25 one - loop diagrams . the main route of the calculation remains the meson calculation : one should evaluate one - loop beta - function and insert them into amplitude by means of procedure ( [ defr ] ) . in order to obtain the correction to the nucleon mass we evaluate the nucleon propagator , an example of diagram - insertion - chain is shown in fig.2 . one can see that the number of diagrams and their topologies is significantly larger , in comparison to the meson calculation ( see fig.1 ) . however , one can also see some minor simplifications , e.g. the fourth line in fig.2 is ended by zero . it is the reflection of the fact that lagrangians ( [ 3:l0 ] ) and ( [ 3:bkkm ] ) have not counter terms . therefore , the graphs with too many vertices from @xmath26 have larger chiral counting but do not produce llogs . taking into account this fact significantly reduce the number of diagrams to consider . we have performed the calculation of the nucleon propagator and evaluate the nucleon physical mass . the procedure of llog evaluation has been automatized using the computation system form @xcite . within a reasonable computing time we have calculated the llog coefficient and the non - analytical in quark mass llog term up to the fourth power . the results are presented in the form : @xmath27 where @xmath28 is defined in ( [ 2:l_def ] ) . the coefficients up to @xmath29 are presented in the table 1 . this corresponds to the four - loop calculation of llog and five - loop calculation for the terms non - analytical in quark masses . a very strong check of the calculation is performed by parallel calculation with the different parameterizations of the lagrangians . additionally , the coefficients up to @xmath30 agree with known results . the one - loop coefficients @xmath31 are well known , see e.g. @xcite . the two - loop coefficient @xmath32 was first derived in @xcite . the two - loop coefficients @xmath30 and @xmath33 are known from the full two - loop calculation for the nucleon mass performed in the eoms scheme @xcite . ' '' '' @xmath34 & @xmath35 & @xmath36 & @xmath35 + ' '' '' @xmath37 & @xmath38 & @xmath39 & @xmath38 + ' '' '' @xmath40 & @xmath41 & @xmath42 & @xmath43 + ' '' '' @xmath33 & @xmath44 & @xmath45 & @xmath46 + ' '' '' @xmath30 & @xmath47 & @xmath48 & @xmath49 + ' '' '' @xmath50 & @xmath51 & @xmath52 & @xmath53 + ' '' '' @xmath54 & @xmath55 & @xmath56 & @xmath57 + ' '' '' @xmath58 & @xmath59 & @xmath60 & @xmath61 + ' '' '' @xmath62 & @xmath63 & @xmath64 & @xmath65 + ' '' '' @xmath29 & @xmath66 & @xmath67 & @xmath68 + ' '' '' @xmath69 ( * ) & @xmath70 & @xmath71 ( * ) & @xmath72 + ' '' '' @xmath73 ( * * ) & @xmath74 & @xmath75 ( * * ) & @xmath76 + ' '' '' @xmath77 ( * * ) & @xmath78 & & + the calculation of the even coefficients @xmath79 can be significantly simplified by using the conjectures discussed below . so , by neglecting higher powers of @xmath15 during the evaluation of the diagrams , we could also evaluate the five - loop coefficient @xmath69 . adding the further conjecture about the relation with the llog in the pion mass , we can obtain the six and seven - loop coefficients @xmath73 and @xmath77 . however , these coefficients are the result of conjectures and , therefore , in the table 1 they are marked by stars . the obtained result of the straightforward calculation , i.e. the coefficients @xmath80 shows a number of regularities . some of the regularities we can explain easily , while some of them we can not . but we are sure that this regularities are not accidental and are an example of the deep connection of the llog approximation ( in non - renormalizable theories ) with the structure of theory . the most intriguing observation is that the coefficients @xmath81 contains a very particular combination of lecs . the pattern appearing in @xmath81 is not well understood yet . while it is clear why the coupling constant @xmath82 does not participate in the nucleon mass at llog ( because it produces an @xmath83 , which is p - odd ) , we have not found any simple argument why @xmath15 only appears up to order @xmath84 , and what is the special in the combination @xmath85 . from the general point of view , one expects that the llog coefficient should be linear in @xmath86 , but a general polynomial in @xmath15 . because the number of vertices from @xmath87 is restricted to one ( see fig.2 and explanations in the previous section ) , but the number of vertices from @xmath88 is naturally unrestricted . moreover , the expression for the propagator contains all allowed powers of @xmath15 . these powers cancel in the solution of the pole equation on the physical mass . the deeper consideration of these cancelation ( see discussion in @xcite ) hints that that absence of higher powers of @xmath15 in coefficients @xmath81 is a consequence of lorentz invariance , and of the additional subtractions of infrared ( heavy mass ) singularities into renormalization counter terms within hbchpt . however , we have not been able to prove this . supposing that the cancelation of the higher powers of @xmath15 takes place at all orders , one can neglect these powers during the computation of diagrams . this procedure significantly reduces the demands for computer time and allows us to calculate the coefficient @xmath69 . even more intriguing result reveals if one inverts the perturbation series and presents the nucleon mass llog coefficient in terms of the physical pion mass @xmath89 @xmath90 where @xmath91 the coefficients @xmath92 of this expansion are presented in table 1 . one can see that the non - analytical in quark mass terms @xmath94 do not simplify in this form of expansion , while the expressions for the coefficient @xmath95 are significantly simplified . moreover , the combination of lecs @xmath85 completely disappears from the higher order terms . the rest coefficient precisely repeat the llog expansion for @xmath96 . thus , we conjecture the llog part of the expression for the nucleon bare mass via the physical masses _ at all orders _ to be @xmath97 the expression for the physical pion mass is known up to 6-loop order ( [ 2:mphys ] ) , therefore , we can obtain two more llog coefficients for the physical nucleon mass . these are presented in the table 1 and indicated by the double - star marks . as we mentioned earlier , the llog are not necessarily dominant . they do however give an indication of the size of corrections to be expected . to show an example , we plot in fig.3 the absolute value of the individual terms containing @xmath98 of ( [ mainresult ] ) for @xmath93 mev . note the excellent convergence . we have used here one set of inputs for the @xmath86 as determined in @xcite and reasonable values for the other quantities . this work is supported in part by the european community - research infrastructure integrating activity study of strongly interacting matter " ( hadronphysics3 , grant agreement no . 28 3286 ) and the swedish research council grants 621 - 2011 - 5080 and 621 - 2013 - 4287 . s. scherer and m. r. schindler , hep - ph/0505265 . + s. scherer and m. r. schindler , lect . notes phys . * 830 * ( 2012 ) pp.1 . s. aoki , y. aoki , c. bernard , t. blum , g. colangelo , m. della morte , s. du"rr and a. x. el khadra _ et al . _ , eur . j. c * 74 * ( 2014 ) 9 , 2890 [ arxiv:1310.8555 [ hep - lat ] ] . e. epelbaum , h. w. hammer and u. g. meissner , rev . * 81 * ( 2009 ) 1773 [ arxiv:0811.1338 [ nucl - th ] ] . j. bijnens and g. ecker , ann . nucl . part . * 64 * ( 2014 ) 149 [ arxiv:1405.6488 [ hep - ph ] ] . j. bijnens , arxiv:1411.6378 [ hep - ph ] . j. bijnens , g. colangelo and g. ecker , jhep * 9902 * ( 1999 ) 020 [ hep - ph/9902437 ] . n. fettes , u. g. meissner , m. mojzis and s. steininger , annals phys . * 283 * ( 2000 ) 273 [ erratum - ibid . * 288 * ( 2001 ) 249 ] [ hep - ph/0001308 ] . m. bchler and g. colangelo , eur . j. c * 32 * ( 2003 ) 427 [ hep - ph/0309049 ] . n. kivel , m. v. polyakov and a. vladimirov , phys . * 101 * ( 2008 ) 262001 [ arxiv:0809.3236 [ hep - ph ] ] . n. a. kivel , m. v. polyakov and a. a. vladimirov , jetp lett . * 89 * ( 2009 ) 529 [ arxiv:0904.3008 [ hep - ph ] ] . j. bijnens and l. carloni , nucl . b * 827 * ( 2010 ) 237 [ arxiv:0909.5086 [ hep - ph ] ] . j. bijnens and l. carloni , nucl . b * 843 * ( 2011 ) 55 [ arxiv:1008.3499 [ hep - ph ] ] . j. bijnens and a. a. vladimirov , arxiv:1409.6127 [ hep - ph ] . j. koschinski , m. v. polyakov and a. a. vladimirov , phys . d * 82 * ( 2010 ) 014014 [ arxiv:1004.2197 [ hep - ph ] ] . m. v. polyakov and a. a. vladimirov , theor . * 169 * ( 2011 ) 1499 [ arxiv:1012.4205 [ hep - th ] ] . j. bijnens , k. kampf and s. lanz , nucl . b * 860 * ( 2012 ) 245 [ arxiv:1201.2608 [ hep - ph ] ] . j. bijnens , k. kampf and s. lanz , nucl . b * 873 * ( 2013 ) 137 [ arxiv:1303.3125 [ hep - ph ] ] . n. kivel and m. v. polyakov , phys . b * 664 * ( 2008 ) 64 [ arxiv:0707.2208 [ hep - ph ] ] . a. m. moiseeva and a. a. vladimirov , eur . j. a * 49 * ( 2013 ) 23 [ arxiv:1208.1714 [ hep - ph ] ] . i. a. perevalova , m. v. polyakov , a. n. vall and a. a. vladimirov , arxiv:1105.4990 [ hep - ph ] . a. moiseeva and a. a. vladimirov , few body syst . * 55 * ( 2014 ) 389 [ arxiv:1311.3433 [ hep - ph ] ] . v. bernard , n. kaiser , j. kambor and u. g. meissner , nucl . b * 388 * ( 1992 ) 315 . v. bernard , n. kaiser and u. -g . meissner , int . j. mod . e * 4 * ( 1995 ) 193 [ hep - ph/9501384 ] . j. a. m. vermaseren , _ `` new features of form '' _ , math - ph/0010025 . j. a. mcgovern and m. c. birse , phys . b * 446 * ( 1999 ) 300 [ hep - ph/9807384 ] . m. r. schindler , d. djukanovic , j. gegelia and s. scherer , nucl . a * 803 * ( 2008 ) 68 [ arxiv:0707.4296 [ hep - ph ] ] .[/INST] we give a short introduction to the calculation of the leading chiral logarithms , and present the results of the recent evaluation of the llog series for the nucleon mass within the heavy baryon theory . the presented results are the first example of llog calculation in the nucleon chpt . we also discuss some regularities observed in the leading logarithmical series for nucleon mass . the talk has been presented at _ quark confinement and hadron spectrum xi_. lu tp 15 - 04 + january 2015 address = department of astronomy and theoretical physics , lund university , + slvegatan 14a , se 223 62 lund , sweden address = department of astronomy and theoretical physics , lund university , + slvegatan 14a , se 223 62 lund , sweden </s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Personal Retirement Savings Account Act of 1998''. SEC. 2. PERSONAL SOCIAL SECURITY PLUS ACCOUNTS. (a) In General.--Title II of the Social Security Act is amended-- (1) by inserting before section 201 the following: ``Part A--Insurance Benefits''; and (2) by adding at the end the following new part: ``Part B--Personal Social Security Plus Accounts ``annual appropriation of budget surpluses to the social security plus fund for crediting to personal social security plus accounts ``Sec. 251. (a) In General.--At the end of fiscal year 1998 and each fiscal year thereafter, the Secretary of the Treasury shall transfer, from the general fund of the Treasury to the Social Security Plus Fund, an amount equal to 80 percent of the surplus (if any) in the total budget of the United States Government for that fiscal year. ``(b) Allocation of Assets Among Personal Social Security Plus Accounts.--Upon the transfer of an amount to the Social Security Plus Fund at the end of a fiscal year pursuant to subsection (a), the Commissioner of Social Security shall allocate such amount evenly among the personal social security plus accounts then maintained in the Fund by individuals who are eligible individuals for the calendar year ending in such fiscal year and shall credit to each account the amount so allocated. ``(c) Eligible Individual.--For purposes of this part, the term `eligible individual' means, for any calendar year beginning after December 31, 1996, any individual the amount of whose wages paid and self-employment income derived in such year equals, in the aggregate, at least the amount such individual must have in order to be credited with 4 quarters of coverage in such year. ``social security plus fund ``Sec. 252. (a) Establishment.--There is established in the Treasury of the United States a Social Security Plus Fund. Subject to, and to the extent consistent with, the provisions of this part, the Commissioner of Social Security shall exercise the same powers, duties, and responsibilities with respect to the Fund as the powers, duties and responsibilities exercised by the Executive Director with respect to the Thrift Savings Fund. ``(b) Amounts Held by Fund.--The Social Security Plus Fund consists of the sum of all amounts transferred to the Fund under section 251, increased by the total net earnings from investments of sums held in the Fund or reduced by the total net losses from investments of sums held in the Fund, and reduced by the total amount of payments made from the Fund (including payments for administrative expenses). ``(c) Use of Fund.-- ``(1) In general.--The sums in the Social Security Plus Fund are appropriated and shall remain available without fiscal year limitation-- ``(A) to invest under section 254, ``(B) to make distributions under section 255, ``(C) to pay the administrative expenses of this part, and ``(D) to purchase insurance as provided in section 256(b)(2). ``(2) Exclusive purposes.--The sums in the Social Security Plus Fund shall not be appropriated for any purpose other than the purposes specified in this section and may not be used for any other purpose. ``personal social security plus accounts ``Sec. 253. (a) Establishment of Personal Social Security Plus Accounts.--Not later than January 1, 1999, the Commissioner of Social Security shall establish in the Social Security Plus Fund a personal social security plus account for each living individual who has been assigned a social security account number under section 205(c)(2) before such date. The Commissioner shall also establish such an account for each other individual on the date, on or after January 1, 1999, of the issuance to such individual of a social security account number under such section. Amounts in the Social Security Plus Fund shall be credited by the Commissioner to the account in accordance with section 251(b). Each account shall be identified to its account holder by means of the account holder's social security account number. ``(b) Account Balance.--The balance in an individual's personal social security plus account at any time is the excess of-- ``(1) the sum of-- ``(A) all deposits made into the Social Security Plus Fund and credited to the account under section 251(b), and ``(B) the total amount of allocations made to and reductions made in the account pursuant to subsection (c), over ``(2) the amounts paid out of the account with respect to such individual under this part. ``(c) Allocation of Earnings and Losses.--Pursuant to regulations which shall be prescribed by the Commissioner, the Commissioner shall allocate to each account an amount equal to the net earnings and net losses from each investment of sums in the Social Security Plus Fund which are attributable, on a pro rata basis, to sums credited to such account, reduced by an appropriate share of the administrative expenses paid out of the net earnings, as determined by the Commissioner. ``rules governing personal social security plus accounts relating to investment, accounting, reporting, and taxation ``Sec. 254. (a) In General.--Under regulations which shall be prescribed by the Commissioner of Social Security, and subject to the provisions of this part, the provisions of-- ``(1) section 8438 of title 5, United States Code (relating to investment of the Thrift Savings Fund), ``(2) section 8439(b) of such title (relating to engagement of independent qualified public accountant), ``(3) section 8439(c) of such title (relating to periodic statements and summary descriptions of investment options), ``(4) section 8439(d) of such title (relating to assumption of risk), and ``(5) section 8440 of such title (relating to tax treatment of the Thrift Savings Fund), other than subsection (c) thereof, shall apply with respect to the Social Security Plus Fund and accounts maintained in such Fund in the same manner and to the same extent as such provisions relate to the Thrift Savings Fund and personal social security plus accounts maintained in such Fund. ``(b) Related Rules.--For purposes of subsection (a)-- ``(1) the Federal Retirement Thrift Investment Board shall exercise with respect to the Social Security Plus Fund the same powers, duties, and responsibilities as are required to be exercised by the Board under the provisions referred to in subsection (a) with respect to the Thrift Savings Fund, ``(2) the Commissioner of Social Security shall exercise with respect to the Social Security Plus Fund the same powers, duties, and responsibilities as are required to be exercised by the Executive Director under the provisions referred to in subsection (a) with respect to the Thrift Savings Fund, and ``(3) references in such sections 8438 and 8439 to an employee, Member, former employee, or former Member shall be deemed references to an account holder of a social security plus account in the Social Security Plus Fund. ``distributions from personal social security plus accounts ``Sec. 255. (a) In General.--Except as provided in subsections (b) and (c), the balance in a personal social security plus account-- ``(1) shall be distributed to the account holder commencing with the date of the commencement of such account holder's entitlement to old-age insurance benefits under section 202(a), and ``(2) shall be paid, as elected by the account holder (in such form and manner as shall be prescribed in regulations of the Commissioner of Social Security) in the form of-- ``(A) equal annual installments over the life expectancy of the account holder (determined as of the date of the distribution under reasonable actuarial assumptions), or ``(B) otherwise in the form of an immediate annuity (as shall be prescribed in regulations of the Commissioner of Social Security). ``(b) Lump Sum Distributions of Minimal Amounts.-- ``(1) In general.--Notwithstanding subsection (a), if the account holder becomes entitled to old-age insurance benefits under section 202(a) and the balance in the account is $3,500 or less, the Commissioner of Social Security shall pay the balance to the account holder in a single payment. ``(2) Cost-of-living adjustments.--Under regulations of the Commissioner of Social Security, effective January 1 of each calendar year after 1999, the dollar amount referred to in paragraph (1) shall be adjusted annually by the same percentage change as the percentage change then taking effect under section 230. ``fiduciary responsibilities ``Sec 256. (a) In General.--Under regulations of the Secretary of Labor, the provisions of sections 8477 and 8478 of title 5, United States Code, shall apply in connection with the Social Security Plus Fund and the personal social security plus accounts maintained in such Fund in the same manner and to the same extent as such provisions apply in connection with the Thrift Savings Fund and accounts maintained in the Thrift Savings Fund. ``(b) Investigative Authority.--Any authority available to the Secretary of Labor under section 504 of the Employee Retirement Income Security Act of 1974 is hereby made available to the Secretary of Labor, and any officer designated by the Secretary of Labor, to determine whether any person has violated, or is about to violate, any provision applicable under subsection (a). ``(c) Exculpatory Provisions; Insurance.-- ``(1) In general.--Any provision in an agreement or instrument which purports to relieve a fiduciary from responsibility or liability for any responsibility, obligation, or duty under this part shall be void. ``(2) Insurance.--Amounts in the Social Security Plus Fund available for administrative expenses shall be available and may be used at the discretion of the Commissioner of Social Security to purchase insurance to cover potential liability of persons who serve in a fiduciary capacity with respect to the Fund and personal social security plus accounts maintained therein, without regard to whether a policy of insurance permits recourse by the insurer against the fiduciary in the case of a breach of a fiduciary obligation. ``assignment, alienation, and treatment of deceased individuals ``Sec. 257. (a) Assignment and Alienation.--Under regulations which shall be prescribed by the Commissioner of Social Security, rules relating to assignment and alienation applicable under chapter 84 of title 5, United States Code, with respect to amounts held in accounts in the Thrift Savings Fund shall apply with respect to amounts held in personal social security plus accounts in the Social Security Plus Fund. ``(b) Treatment of Accounts of Deceased Individuals.--In the case of a deceased individual who is the account holder with respect to a personal social security plus account and who died before attaining retirement age (as defined in section 216(l)), upon receipt of notification of such individual's death, the Commissioner of Social Security shall close the account and shall transfer the balance in such account to the personal social security plus account of such account holder's surviving spouse or, if there is no such account of a surviving spouse, to the duly appointed legal representative of the estate of the deceased account holder, or if there is no such representative, to the person or persons determined to be entitled thereto under the laws of the domicile of the deceased account holder.

Personal Retirement Savings Account Act of 1998 - Amends title II (Old Age, Survivors and Disability Insurance) (OASDI) of the Social Security Act (SSA) to add a new part B (Personal Social Security Plus Accounts). Establishes in the Treasury a Social Security Plus Fund to hold 80 percent of the surplus (if any) in the Federal budget for each fiscal year for investment in accordance with rules governing the Thrift Savings Plan which shall otherwise govern other Fund operations. Directs the Commissioner of Social Security to establish in the Social Security Plus Fund a personal social security plus account for each living individual who has been assigned a social security number. Requires the Commissioner to allocate: (1) evenly among all personal social security plus accounts the amount transferred annually to the Social Security Plus Fund; as well as (2) an amount equal to the net earnings and net losses from each investment of sums in the Fund. Makes eligible for such an account any individual the amount of whose wages paid and self-employment income derived in the year equals, in the aggregate, at least the amount such individual must have in order to be credited with four quarters of coverage in such year. Requires distribution to an account holder of the balance in a personal social security plus account when the account holder becomes entitled to Old-Age insurance benefits under SSA title II.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Personal Retirement Savings Account Act of 1998''. SEC. 2. PERSONAL SOCIAL SECURITY PLUS ACCOUNTS. (a) In General.--Title II of the Social Security Act is amended-- (1) by inserting before section 201 the following: ``Part A--Insurance Benefits''; and (2) by adding at the end the following new part: ``Part B--Personal Social Security Plus Accounts ``annual appropriation of budget surpluses to the social security plus fund for crediting to personal social security plus accounts ``Sec. 251. (a) In General.--At the end of fiscal year 1998 and each fiscal year thereafter, the Secretary of the Treasury shall transfer, from the general fund of the Treasury to the Social Security Plus Fund, an amount equal to 80 percent of the surplus (if any) in the total budget of the United States Government for that fiscal year. ``(b) Allocation of Assets Among Personal Social Security Plus Accounts.--Upon the transfer of an amount to the Social Security Plus Fund at the end of a fiscal year pursuant to subsection (a), the Commissioner of Social Security shall allocate such amount evenly among the personal social security plus accounts then maintained in the Fund by individuals who are eligible individuals for the calendar year ending in such fiscal year and shall credit to each account the amount so allocated. ``(c) Eligible Individual.--For purposes of this part, the term `eligible individual' means, for any calendar year beginning after December 31, 1996, any individual the amount of whose wages paid and self-employment income derived in such year equals, in the aggregate, at least the amount such individual must have in order to be credited with 4 quarters of coverage in such year. ``social security plus fund ``Sec. 252. (a) Establishment.--There is established in the Treasury of the United States a Social Security Plus Fund. Subject to, and to the extent consistent with, the provisions of this part, the Commissioner of Social Security shall exercise the same powers, duties, and responsibilities with respect to the Fund as the powers, duties and responsibilities exercised by the Executive Director with respect to the Thrift Savings Fund. ``(b) Amounts Held by Fund.--The Social Security Plus Fund consists of the sum of all amounts transferred to the Fund under section 251, increased by the total net earnings from investments of sums held in the Fund or reduced by the total net losses from investments of sums held in the Fund, and reduced by the total amount of payments made from the Fund (including payments for administrative expenses). ``(c) Use of Fund.-- ``(1) In general.--The sums in the Social Security Plus Fund are appropriated and shall remain available without fiscal year limitation-- ``(A) to invest under section 254, ``(B) to make distributions under section 255, ``(C) to pay the administrative expenses of this part, and ``(D) to purchase insurance as provided in section 256(b)(2). ``(2) Exclusive purposes.--The sums in the Social Security Plus Fund shall not be appropriated for any purpose other than the purposes specified in this section and may not be used for any other purpose. ``personal social security plus accounts ``Sec. 253. (a) Establishment of Personal Social Security Plus Accounts.--Not later than January 1, 1999, the Commissioner of Social Security shall establish in the Social Security Plus Fund a personal social security plus account for each living individual who has been assigned a social security account number under section 205(c)(2) before such date. The Commissioner shall also establish such an account for each other individual on the date, on or after January 1, 1999, of the issuance to such individual of a social security account number under such section. Amounts in the Social Security Plus Fund shall be credited by the Commissioner to the account in accordance with section 251(b). Each account shall be identified to its account holder by means of the account holder's social security account number. ``(b) Account Balance.--The balance in an individual's personal social security plus account at any time is the excess of-- ``(1) the sum of-- ``(A) all deposits made into the Social Security Plus Fund and credited to the account under section 251(b), and ``(B) the total amount of allocations made to and reductions made in the account pursuant to subsection (c), over ``(2) the amounts paid out of the account with respect to such individual under this part. ``(c) Allocation of Earnings and Losses.--Pursuant to regulations which shall be prescribed by the Commissioner, the Commissioner shall allocate to each account an amount equal to the net earnings and net losses from each investment of sums in the Social Security Plus Fund which are attributable, on a pro rata basis, to sums credited to such account, reduced by an appropriate share of the administrative expenses paid out of the net earnings, as determined by the Commissioner. ``rules governing personal social security plus accounts relating to investment, accounting, reporting, and taxation ``Sec. 254. (a) In General.--Under regulations which shall be prescribed by the Commissioner of Social Security, and subject to the provisions of this part, the provisions of-- ``(1) section 8438 of title 5, United States Code (relating to investment of the Thrift Savings Fund), ``(2) section 8439(b) of such title (relating to engagement of independent qualified public accountant), ``(3) section 8439(c) of such title (relating to periodic statements and summary descriptions of investment options), ``(4) section 8439(d) of such title (relating to assumption of risk), and ``(5) section 8440 of such title (relating to tax treatment of the Thrift Savings Fund), other than subsection (c) thereof, shall apply with respect to the Social Security Plus Fund and accounts maintained in such Fund in the same manner and to the same extent as such provisions relate to the Thrift Savings Fund and personal social security plus accounts maintained in such Fund. ``(b) Related Rules.--For purposes of subsection (a)-- ``(1) the Federal Retirement Thrift Investment Board shall exercise with respect to the Social Security Plus Fund the same powers, duties, and responsibilities as are required to be exercised by the Board under the provisions referred to in subsection (a) with respect to the Thrift Savings Fund, ``(2) the Commissioner of Social Security shall exercise with respect to the Social Security Plus Fund the same powers, duties, and responsibilities as are required to be exercised by the Executive Director under the provisions referred to in subsection (a) with respect to the Thrift Savings Fund, and ``(3) references in such sections 8438 and 8439 to an employee, Member, former employee, or former Member shall be deemed references to an account holder of a social security plus account in the Social Security Plus Fund. ``distributions from personal social security plus accounts ``Sec. 255. (a) In General.--Except as provided in subsections (b) and (c), the balance in a personal social security plus account-- ``(1) shall be distributed to the account holder commencing with the date of the commencement of such account holder's entitlement to old-age insurance benefits under section 202(a), and ``(2) shall be paid, as elected by the account holder (in such form and manner as shall be prescribed in regulations of the Commissioner of Social Security) in the form of-- ``(A) equal annual installments over the life expectancy of the account holder (determined as of the date of the distribution under reasonable actuarial assumptions), or ``(B) otherwise in the form of an immediate annuity (as shall be prescribed in regulations of the Commissioner of Social Security). ``(b) Lump Sum Distributions of Minimal Amounts.-- ``(1) In general.--Notwithstanding subsection (a), if the account holder becomes entitled to old-age insurance benefits under section 202(a) and the balance in the account is $3,500 or less, the Commissioner of Social Security shall pay the balance to the account holder in a single payment. ``(2) Cost-of-living adjustments.--Under regulations of the Commissioner of Social Security, effective January 1 of each calendar year after 1999, the dollar amount referred to in paragraph (1) shall be adjusted annually by the same percentage change as the percentage change then taking effect under section 230. ``fiduciary responsibilities ``Sec 256. (a) In General.--Under regulations of the Secretary of Labor, the provisions of sections 8477 and 8478 of title 5, United States Code, shall apply in connection with the Social Security Plus Fund and the personal social security plus accounts maintained in such Fund in the same manner and to the same extent as such provisions apply in connection with the Thrift Savings Fund and accounts maintained in the Thrift Savings Fund. ``(b) Investigative Authority.--Any authority available to the Secretary of Labor under section 504 of the Employee Retirement Income Security Act of 1974 is hereby made available to the Secretary of Labor, and any officer designated by the Secretary of Labor, to determine whether any person has violated, or is about to violate, any provision applicable under subsection (a). ``(c) Exculpatory Provisions; Insurance.-- ``(1) In general.--Any provision in an agreement or instrument which purports to relieve a fiduciary from responsibility or liability for any responsibility, obligation, or duty under this part shall be void. ``(2) Insurance.--Amounts in the Social Security Plus Fund available for administrative expenses shall be available and may be used at the discretion of the Commissioner of Social Security to purchase insurance to cover potential liability of persons who serve in a fiduciary capacity with respect to the Fund and personal social security plus accounts maintained therein, without regard to whether a policy of insurance permits recourse by the insurer against the fiduciary in the case of a breach of a fiduciary obligation. ``assignment, alienation, and treatment of deceased individuals ``Sec. 257. (a) Assignment and Alienation.--Under regulations which shall be prescribed by the Commissioner of Social Security, rules relating to assignment and alienation applicable under chapter 84 of title 5, United States Code, with respect to amounts held in accounts in the Thrift Savings Fund shall apply with respect to amounts held in personal social security plus accounts in the Social Security Plus Fund. ``(b) Treatment of Accounts of Deceased Individuals.--In the case of a deceased individual who is the account holder with respect to a personal social security plus account and who died before attaining retirement age (as defined in section 216(l)), upon receipt of notification of such individual's death, the Commissioner of Social Security shall close the account and shall transfer the balance in such account to the personal social security plus account of such account holder's surviving spouse or, if there is no such account of a surviving spouse, to the duly appointed legal representative of the estate of the deceased account holder, or if there is no such representative, to the person or persons determined to be entitled thereto under the laws of the domicile of the deceased account holder.[/INST]Personal Retirement Savings Account Act of 1998 - Amends title II (Old Age, Survivors and Disability Insurance) (OASDI) of the Social Security Act (SSA) to add a new part B (Personal Social Security Plus Accounts). Establishes in the Treasury a Social Security Plus Fund to hold 80 percent of the surplus (if any) in the Federal budget for each fiscal year for investment in accordance with rules governing the Thrift Savings Plan which shall otherwise govern other Fund operations. Directs the Commissioner of Social Security to establish in the Social Security Plus Fund a personal social security plus account for each living individual who has been assigned a social security number. Requires the Commissioner to allocate: (1) evenly among all personal social security plus accounts the amount transferred annually to the Social Security Plus Fund; as well as (2) an amount equal to the net earnings and net losses from each investment of sums in the Fund. Makes eligible for such an account any individual the amount of whose wages paid and self-employment income derived in the year equals, in the aggregate, at least the amount such individual must have in order to be credited with four quarters of coverage in such year. Requires distribution to an account holder of the balance in a personal social security plus account when the account holder becomes entitled to Old-Age insurance benefits under SSA title II.</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Cuba Digital and Telecommunications Advancement Act of 2015'' or the ``Cuba DATA Act''. SEC. 2. EXPORTATION OF CONSUMER COMMUNICATION DEVICES AND TELECOMMUNICATIONS SERVICES TO CUBA. (a) In General.--Notwithstanding any other provision of law, the President may permit any person subject to the jurisdiction of the United States-- (1) to export consumer communication devices and other telecommunications equipment to Cuba; (2) to provide telecommunications services involving Cuba or persons in Cuba; (3) to establish facilities to provide telecommunications services connecting Cuba with another country or to provide telecommunications services in Cuba; (4) to conduct any transaction incident to carrying out an activity described in any of paragraphs (1) through (3); and (5) to enter into, perform, and make and receive payments under a contract with any individual or entity in Cuba with respect to the provision of telecommunications services involving Cuba or persons in Cuba. (b) Report.--Not later than 180 days after the date of the enactment of this Act, and not less frequently than annually thereafter for 4 years, the President shall submit to the Committee on Foreign Relations and the Committee on Appropriations of the Senate and the Committee on Foreign Affairs and the Committee on Appropriations of the House of Representatives a report on-- (1) the percentage of individuals in Cuba who are able to access the Internet and the infrastructure that would be needed in Cuba to reach the goal of increasing that percentage to 50 percent by 2020; (2) the ability of individuals in Cuba, including foreign tourists, to access data through the use of cell phones and the infrastructure that would be needed to bring the capability to access that data to rural and urban population centers in Cuba; (3) the impact of access to telecommunications technology on the development of new businesses, co-ops, and educational opportunities in Cuba; and (4) the impact of the telecommunications equipment and telecommunications services provided under this section on advancing the human rights objectives of the United States and how such equipment and services are being used to advance those objectives. (c) Definitions.--In this section: (1) Consumer communication devices.--The term ``consumer communication devices'' means commodities and software described in section 740.19(b) of title 15, Code of Federal Regulations (or any successor regulation). (2) Person subject to the jurisdiction of the united states.--The term ``person subject to the jurisdiction of the United States'' means-- (A) any individual, wherever located, who is a citizen or resident of the United States; (B) any person located in the United States; (C) any corporation, partnership, association, or other organization organized under the laws of the United States or of any State, territory, possession, or district of the United States; and (D) any corporation, partnership, association, or other organization, wherever organized or doing business, that is owned or controlled by a person described in subparagraph (A), (B), or (C). (3) Telecommunications services.--The term ``telecommunications services'' includes-- (A) data, telephone, telegraph, Internet connectivity, radio, television, news wire feeds, and similar services, regardless of the medium of transmission and including transmission by satellite; (B) services incident to the exchange of communications over the Internet; (C) domain name registration services; and (D) services that are related to consumer communication devices and other telecommunications equipment to install, repair, or replace such devices and equipment. SEC. 3. REPEAL OF CERTAIN AUTHORITIES PREVENTING FINANCING AND MARKET REFORM FOR CUBA. (a) Cuban Democracy Act.-- (1) In general.--Section 1704 of the Cuban Democracy Act of 1992 (22 U.S.C. 6003) is repealed. (2) Conforming amendments.--Section 204 of the Cuban Liberty and Democratic Solidarity (LIBERTAD) Act of 1996 (22 U.S.C. 6064) is amended-- (A) in subsection (b), by amending paragraph (3) to read as follows: ``(3) sections 1705(d) and 1706 of the Cuban Democracy Act of 1992 (22 U.S.C. 6004(d) and 6005);''; and (B) in subsection (d), by amending paragraph (3) to read as follows: ``(3) sections 1705(d) and 1706 of the Cuban Democracy Act of 1992 (22 U.S.C. 6004(d) and 6005) are repealed; and''. (b) Cuban Liberty and Democratic Solidarity Act.-- (1) In general.--Sections 102, 103, 104, 105, and 108 of the Cuban Liberty and Democratic Solidarity (LIBERTAD) Act of 1996 (22 U.S.C. 6032, 6033, 6034, 6035, and 6038) are repealed. (2) Conforming amendment.--Section 109(a) of the Cuban Liberty and Democratic Solidarity (LIBERTAD) Act of 1996 (22 U.S.C. 6039(a)) is amended by striking ``(including section 102 of this Act)''.

Cuba Digital and Telecommunications Advancement Act of 2015 or the Cuba DATA Act This bill authorizes the President to permit any person subject to U.S. jurisdiction to: export consumer communication devices and other telecommunications equipment to Cuba; provide telecommunications services involving Cuba or persons in Cuba; establish facilities to provide telecommunications services connecting Cuba with another country, or to provide telecommunications services in Cuba; conduct any transaction incident to carrying out such activities; and enter into, perform, and make and receive payments under a contract with any individual or entity in Cuba regarding the provision of telecommunications services involving Cuba or persons in Cuba. Repeals or amends specified requirements and prohibitions of: (1) the Cuban Democracy Act of 1992, and (2) the Cuban Liberty and Democratic Solidarity (LIBERTAD) Act of 1996.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Cuba Digital and Telecommunications Advancement Act of 2015'' or the ``Cuba DATA Act''. SEC. 2. EXPORTATION OF CONSUMER COMMUNICATION DEVICES AND TELECOMMUNICATIONS SERVICES TO CUBA. (a) In General.--Notwithstanding any other provision of law, the President may permit any person subject to the jurisdiction of the United States-- (1) to export consumer communication devices and other telecommunications equipment to Cuba; (2) to provide telecommunications services involving Cuba or persons in Cuba; (3) to establish facilities to provide telecommunications services connecting Cuba with another country or to provide telecommunications services in Cuba; (4) to conduct any transaction incident to carrying out an activity described in any of paragraphs (1) through (3); and (5) to enter into, perform, and make and receive payments under a contract with any individual or entity in Cuba with respect to the provision of telecommunications services involving Cuba or persons in Cuba. (b) Report.--Not later than 180 days after the date of the enactment of this Act, and not less frequently than annually thereafter for 4 years, the President shall submit to the Committee on Foreign Relations and the Committee on Appropriations of the Senate and the Committee on Foreign Affairs and the Committee on Appropriations of the House of Representatives a report on-- (1) the percentage of individuals in Cuba who are able to access the Internet and the infrastructure that would be needed in Cuba to reach the goal of increasing that percentage to 50 percent by 2020; (2) the ability of individuals in Cuba, including foreign tourists, to access data through the use of cell phones and the infrastructure that would be needed to bring the capability to access that data to rural and urban population centers in Cuba; (3) the impact of access to telecommunications technology on the development of new businesses, co-ops, and educational opportunities in Cuba; and (4) the impact of the telecommunications equipment and telecommunications services provided under this section on advancing the human rights objectives of the United States and how such equipment and services are being used to advance those objectives. (c) Definitions.--In this section: (1) Consumer communication devices.--The term ``consumer communication devices'' means commodities and software described in section 740.19(b) of title 15, Code of Federal Regulations (or any successor regulation). (2) Person subject to the jurisdiction of the united states.--The term ``person subject to the jurisdiction of the United States'' means-- (A) any individual, wherever located, who is a citizen or resident of the United States; (B) any person located in the United States; (C) any corporation, partnership, association, or other organization organized under the laws of the United States or of any State, territory, possession, or district of the United States; and (D) any corporation, partnership, association, or other organization, wherever organized or doing business, that is owned or controlled by a person described in subparagraph (A), (B), or (C). (3) Telecommunications services.--The term ``telecommunications services'' includes-- (A) data, telephone, telegraph, Internet connectivity, radio, television, news wire feeds, and similar services, regardless of the medium of transmission and including transmission by satellite; (B) services incident to the exchange of communications over the Internet; (C) domain name registration services; and (D) services that are related to consumer communication devices and other telecommunications equipment to install, repair, or replace such devices and equipment. SEC. 3. REPEAL OF CERTAIN AUTHORITIES PREVENTING FINANCING AND MARKET REFORM FOR CUBA. (a) Cuban Democracy Act.-- (1) In general.--Section 1704 of the Cuban Democracy Act of 1992 (22 U.S.C. 6003) is repealed. (2) Conforming amendments.--Section 204 of the Cuban Liberty and Democratic Solidarity (LIBERTAD) Act of 1996 (22 U.S.C. 6064) is amended-- (A) in subsection (b), by amending paragraph (3) to read as follows: ``(3) sections 1705(d) and 1706 of the Cuban Democracy Act of 1992 (22 U.S.C. 6004(d) and 6005);''; and (B) in subsection (d), by amending paragraph (3) to read as follows: ``(3) sections 1705(d) and 1706 of the Cuban Democracy Act of 1992 (22 U.S.C. 6004(d) and 6005) are repealed; and''. (b) Cuban Liberty and Democratic Solidarity Act.-- (1) In general.--Sections 102, 103, 104, 105, and 108 of the Cuban Liberty and Democratic Solidarity (LIBERTAD) Act of 1996 (22 U.S.C. 6032, 6033, 6034, 6035, and 6038) are repealed. (2) Conforming amendment.--Section 109(a) of the Cuban Liberty and Democratic Solidarity (LIBERTAD) Act of 1996 (22 U.S.C. 6039(a)) is amended by striking ``(including section 102 of this Act)''.[/INST]Cuba Digital and Telecommunications Advancement Act of 2015 or the Cuba DATA Act This bill authorizes the President to permit any person subject to U.S. jurisdiction to: export consumer communication devices and other telecommunications equipment to Cuba; provide telecommunications services involving Cuba or persons in Cuba; establish facilities to provide telecommunications services connecting Cuba with another country, or to provide telecommunications services in Cuba; conduct any transaction incident to carrying out such activities; and enter into, perform, and make and receive payments under a contract with any individual or entity in Cuba regarding the provision of telecommunications services involving Cuba or persons in Cuba. Repeals or amends specified requirements and prohibitions of: (1) the Cuban Democracy Act of 1992, and (2) the Cuban Liberty and Democratic Solidarity (LIBERTAD) Act of 1996.</s>

breakthroughs in modern technology have made possible the construction of extremely large interferometers both on the ground and in space for the detection and observation of gravitational waves ( gws ) . several ground - based detectors around the globe have been operational for several years , and are now in the process of being upgraded to achieve even higher sensitivities . these are the ligo and virgo interferometers , which have arm lengths of 4 km and 3 km , respectively , and the geo and tama interferometers with arm lengths of 600 m and 300 m , respectively . these upgraded detectors will operate in the high frequency range of gws of 1 hz to a few khz . a natural limit occurs on decreasing the lower frequency cut - off because it is not practical to increase the arm lengths on ground and also because of the gravity gradient noise which is difficult to eliminate below 1 hz . but , on the other hand , in the cosmos there exist interesting astrophysical gw sources which emit gws below this frequency such as the galactic binaries , massive and super - massive black - hole binaries , etc . if we wish to observe these sources , we need to go to lower frequencies . the solution is to build an interferometer in space , where such noises will be absent and allow the detection of gws in the low frequency regime . the laser interferometer space antenna ( lisa ) mission , and more recent variations of its design [ 13 , 35 ] , is the typical example of a space - based interferometer aiming to detect and study gravitational radiation in the millihertz band . in order to make such observations lisa relied on coherent laser beams exchanged between three identical spacecraft forming a giant ( almost ) equilateral triangle of side 5 10 km to observe and detect low frequency cosmic gws . ground- and space - based detectors will complement each other in the observation of gws in an essential way , analogous to the way optical , radio , x - ray , -ray , etc . observations do for the electromagnetic spectrum . as these detectors begin to make their observations , a new era of gravitational astronomy is on the horizon and a radically different view of the universe the astrophysical sources observable in the mhz band include galactic binaries , extra - galactic super - massive black - hole binaries and coalescences , and stochastic gw background from the early universe . these include galactic and extra galactic stellar mass binaries , and massive and super - massive blackhole binaries . the frequency of the gws emitted by such a system is twice its orbital frequency . population synthesis studies indicate a large number of stellar mass binaries in the frequency range below 23 mhz [ 4 , 34 ] . in the lower frequency range ( 1 mhz ) there is a large number of such unresolvable sources in each of the frequency bins . massive black - hole binaries are interesting both from the astrophysical and theoretical points of view . coalescences of massive black holes from different galaxies after their merger during growth of the present galaxies would provide unique new information on galaxy formation . coalescence of binaries involving intermediate mass black holes could help to understand the formation and growth of massive black holes . the super - massive black - hole binaries are strong emitters of gws and these spectacular events can be detectable beyond red - shift of z = 10 . just as the cosmic microwave background is left over from the big bang , so too should there be a background of gravitational waves . unlike electromagnetic waves , gravitational waves do not interact with matter after a few planck times after the big bang , so they do not thermalize . their spectrum today , therefore , is simply a red - shifted version of the spectrum they formed with , which would throw light on the physical conditions at the epoch of the early universe . interferometric non - resonant detectors of gravitational radiation with frequency content f1 < f < fu ( f1 , fu being respectively the lower and upper frequency cut - offs characterizing the detector s operational bandwidth ) use a coherent train of electromagnetic waves ( of nominal frequency 0 fu ) folded into several beams , and at one or more points where these intersect , monitor relative fluctuations of frequency or phase ( homodyne detection ) . the observed low - frequency fluctuations are due to several causes : frequency variations of the source of the electromagnetic signal about 0,relative motions of the electromagnetic source and the mirrors ( or amplifying transponders ) that do the folding , temporal variations of the index of refraction along the beams , andaccording to general relativity , to any time - variable gravitational fields present , such as the transverse - traceless metric curvature of a passing plane gravitational - wave train . to observe gravitational waves in this way , it is thus necessary to control , or monitor , the other sources of relative frequency fluctuations , and , in the data analysis , to use optimal algorithms based on the different characteristic interferometer responses to gravitational waves ( the signal ) and to the other sources ( the noise ) . by comparing phases of electromagnetic beams referenced to the same frequency generator and propagated along non - parallel equal - length arms , frequency fluctuations of the frequency reference can be removed , and gravitational - wave signals at levels many orders of magnitude lower can be detected . frequency variations of the source of the electromagnetic signal about 0 , relative motions of the electromagnetic source and the mirrors ( or amplifying transponders ) that do the folding , temporal variations of the index of refraction along the beams , and according to general relativity , to any time - variable gravitational fields present , such as the transverse - traceless metric curvature of a passing plane gravitational - wave train . in the present single - spacecraft doppler tracking observations , for instance , many of the noise sources can be either reduced or calibrated by implementing appropriate microwave frequency links and by using specialized electronics , so the fundamental limitation is imposed by the frequency ( time - keeping ) fluctuations inherent to the reference clock that controls the microwave system . hydrogen maser clocks , currently used in doppler tracking experiments , achieve their best performance at about 1000 s integration time , with a fractional frequency stability of a few parts in 10 . this is the reason why these one - arm interferometers in space ( which have one doppler readout and a this integration time is also comparable to the microwave propagation ( or storage ) time 2l / c to spacecraft en route to the outer solar system ( for example l 58 au for the cassini spacecraft ) . low - frequency interferometric gravitational - wave detectors in solar orbits , such as the lisa mission and the currently considered elisa / ngo mission [ 5 , 13 , 35 ] , have been proposed to achieve greater sensitivity to mhz gravitational waves . however , since the armlengths of these space - based interferometers can differ by a few percent , the direct recombination of the two beams at a photo detector will not effectively remove the laser frequency noise . this is because the frequency fluctuations of the laser will be delayed by different amounts within the two arms of unequal length . in order to cancel the laser frequency noise , the time - varying doppler data must be recorded and post - processed to allow for arm - length differences . the data streams will have temporal structure , which can be described as due to many - pulse responses to -function excitations , depending on time - of - flight delays in the response functions of the instrumental doppler noises and in the response to incident plane - parallel , transverse , and traceless gravitational waves . although the theory of tdi can be used by any future space - based interferometer aiming to detect gravitational radiation , this article will focus on its implementation by the lisa mission . each spacecraft was to be equipped with two lasers sending beams to the other two ( 0.03 au away ) while simultaneously measuring the beat frequencies between the local laser and the laser beams received from the other two spacecraft . the analysis of tdi presented in this article will assume a successful prior removal of any first - order doppler beat notes due to relative motions , giving six residual doppler time series as the raw data of a stationary time delay space interferometer . following [ 51 , 2 , 10 ] , we will regard lisa not as constituting one or more conventional michelson interferometers , but rather , in a symmetrical way , a closed array of six one - arm delay lines between the test masses . in this way , during the course of the article , we will show that it is possible to synthesize new data combinations that cancel laser frequency noises , and estimate achievable sensitivities of these combinations in terms of the separate and relatively simple single arm responses both to gravitational wave and instrumental noise ( cf . [ 51 , 2 , 10 ] ) . in contrast to earth - based interferometers , which operate in the long - wavelength limit ( lwl ) ( arm lengths gravitational wavelength c / f0 , where f0 is a characteristic frequency of the gw ) , lisa does not operate in the lwl over much of its frequency band . when the physical scale of a free mass optical interferometer intended to detect gravitational waves is comparable to or larger than the gw wavelength , time delays in the response of the instrument to the waves , and travel times along beams in the instrument , can not be ignored and must be allowed for in computing the detector response used for data interpretation . it is convenient to formulate the instrumental responses in terms of observed differential frequency shifts for short , doppler shifts rather than in terms of phase shifts usually used in interferometry , although of course these data , as functions of time , are inter - convertible . we provide an overview of the physical and historical motivations of tdi . in section 3 we summarize the one - arm doppler transfer functions of an optical beam between two carefully shielded test masses inside each spacecraft resulting from ( i ) frequency fluctuations of the lasers used in transmission and reception , ( ii ) fluctuations due to non - inertial motions of the spacecraft , and ( iii ) beam - pointing fluctuations and shot noise . among these , the dominant noise is from the frequency fluctuations of the lasers and is several orders of magnitude ( perhaps 7 or 8) above the other noises . this noise must be very precisely removed from the data in order to achieve the gw sensitivity at the level set by the remaining doppler noise sources which are at a much lower level and which constitute the noise floor after the laser frequency noise is suppressed . we show that this can be accomplished by shifting and linearly combining the twelve one - way doppler data measured by lisa . the actual procedure can easily be understood in terms of properly defined time - delay operators that act on the one - way doppler measurements . in section 4 we develop a formalism involving the algebra of the time - delay operators which is based on the theory of rings and modules and computational commutative algebra . we show that the space of all possible interferometric combinations canceling the laser frequency noise is a module over the polynomial ring in which the time - delay operators play the role of the indeterminates . in the literature , the module we show that the module can be generated from four generators , so that any data combination canceling the laser frequency noise is simply a linear combination formed from these generators . we would like to emphasize that this is the mathematical structure underlying tdi for lisa . also in section 4 specific interferometric combinations are derived , and their physical interpretations are discussed . the expressions for the sagnac interferometric combinations ( , , , ) are first obtained ; in particular , the symmetric sagnac combination , for which each raw data set needs to be delayed by only a single arm transit time , distinguishes itself against all the other tdi combinations by having a higher order response to gravitational radiation in the lwl when the spacecraft separations are equal . we then express the unequal - arm michelson combinations ( x , y , z ) in terms of the , , , and combinations with further transit time delays . one of these interferometric data combinations would still be available if the links between one pair of spacecraft were lost . other tdi combinations , which rely on only four of the possible six inter - spacecraft doppler measurements ( denoted p , e , and u ) are also presented . they would of course be quite useful in case of potential loss of any two inter - spacecraft doppler measurements . tdi so formulated presumes the spacecraft - to - spacecraft light - travel - times to be constant in time , and independent from being up- or down - links . reduction of data from moving interferometric laser arrays in solar orbit will in fact encounter non - symmetric up- and downlink light time differences that are significant , and need to be accounted for in order to exactly cancel the laser frequency fluctuations [ 44 , 7 , 45 , 41 , 9 ] . in section 5 we show that , by introducing a set of non - commuting time - delay operators , there exists a quite general procedure for deriving generalized tdi combinations that account for the effects of time - dependence of the arms . using this approach it is possible to derive flex - free expression for the unequal - arm michelson combinations x1 , and obtain the generalized expressions for all the tdi combinations . alternatively , a rigorous mathematical formulation can be given in terms of rings and modules . but because of the non - commutativity of operators the polynomial ring is non - commutative . thus the algebraic problem becomes extremely complex and a general solution seems difficult to obtain . but we show that for the special case when one arm of lisa is dysfunctional a plethora of solutions can be found . such a possibility must be envisaged because of reasons such as technical failure or even operating costs . in section 6 we address the question of maximization of the lisa signal - to - noise - ratio ( snr ) to any gravitational - wave signal present in its data . this is done by treating the snr as a functional over the space of all possible tdi combinations . as a simple application of the general formula we have derived , we apply our results to the case of sinusoidal signals randomly polarized and randomly distributed on the celestial sphere . we find that the standard lisa sensitivity figure derived for a single michelson interferometer [ 15 , 38 , 40 ] can be improved by a factor of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2$\end{document } in the low - part of the frequency band , and by more than \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 3$\end{document } in the remaining part of the accessible band . further , we also show that if the location of the gw source is known , then as the source appears to move in the lisa reference frame , it is possible to optimally track the source , by appropriately changing the data combinations during the course of its trajectory [ 38 , 39 ] . as an example of such type of source , , we finally address aspects of tdi of more practical and experimental nature , and provide a list of references where more details about these topics can be found . it is worth mentioning that , as of today , tdi has already gone through several successful experimental tests [ 8 , 32 , 48 , 33 , 25 ] and that it has been endorsed by the elisa / ngo [ 13 , 35 ] project as its baseline technique for achieving its required sensitivity to gravitational radiation . we emphasize that , although this article will use as baseline mission reference the lisa mission , the results here presented can easily be extended to other space mission concepts . equal - arm interferometer detectors of gravitational waves can observe gravitational radiation by canceling the laser frequency fluctuations affecting the light injected into their arms . this is done by comparing phases of split beams propagated along the equal ( but non - parallel ) arms of the detector . the laser frequency fluctuations affecting the two beams experience the same delay within the two equal - length arms and cancel out at the photodetector where relative phases are measured . this way gravitational - wave signals of dimensionless amplitude less than 10 can be observed when using lasers whose frequency stability can be as large as roughly a few parts in 10 . if the arms of the interferometer have different lengths , however , the exact cancellation of the laser frequency fluctuations , say c(t ) , will no longer take place at the photodetector . in fact , the larger the difference between the two arms , the larger will be the magnitude of the laser frequency fluctuations affecting the detector response . if l1 and l2 are the lengths of the two arms , it is easy to see that the amount of laser relative frequency fluctuations remaining in the response is equal to ( units in which the speed of light c = 1 ) 1\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta c(t ) = c(t - 2{l_1 } ) - c(t - 2{l_2}){.}$$\end{document } in the case of a space - based interferometer such as lisa , whose lasers are expected to display relative frequency fluctuations equal to about \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${10^{- 13}}/\sqrt { { \rm{hz}}}$\end{document } in the mhz band , and whose arms will differ by a few percent [ 5 , 13 , 35 ] , eq . ( 1 ) implies the following expression for the amplitude of the fourier components of the uncanceled laser frequency fluctuations ( an over - imposed tilde denotes the operation of fourier transform ) : 2\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\vert \tilde{\delta c}(f)\vert \simeq \vert \tilde c(f)\vert 4\pi f\vert ( { l_1 } - { l_2})\vert { .}$$\end{document } at f = 10 hz , for instance , and assuming l1 l2 0.5 s , the uncanceled fluctuations from the laser are equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$6.3 \times { 10^{- 16}}/\sqrt { { \rm{hz}}}$\end{document}. since the lisa sensitivity goal was about \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${10^{- 20}}/\sqrt { { \rm{hz}}}$\end{document } in this part of the frequency band , it is clear that an alternative experimental approach for canceling the laser frequency fluctuations is needed . a first attempt to solve this problem was presented by faller et al . [ 17 , 19 , 18 ] , and the scheme proposed there can be understood through figure 1 . in this idealized model the two beams exiting the two arms are not made to interfere at a common photodetector . rather , each is made to interfere with the incoming light from the laser at a photodetector , decoupling in this way the phase fluctuations experienced by the two beams in the two arms . now two doppler measurements are available in digital form , and the problem now becomes one of identifying an algorithm for digitally canceling the laser frequency fluctuations from a resulting new data combination . figure 1light from a laser is split into two beams , each injected into an arm formed by pairs of free - falling mirrors . since the length of the two arms , l1 and l2 , are different , now the light beams from the two arms are not recombined at one photo detector . instead each is separately made to interfere with the light that is injected into the arms . two distinct photo detectors are now used , and phase ( or frequency ) fluctuations are then monitored and recorded there . light from a laser is split into two beams , each injected into an arm formed by pairs of free - falling mirrors . since the length of the two arms , l1 and l2 , are different , now the light beams from the two arms are not recombined at one photo detector . instead each is separately made to interfere with the light that is injected into the arms . two distinct photo detectors are now used , and phase ( or frequency ) fluctuations are then monitored and recorded there . the algorithm they first proposed , and refined subsequently in , required processing the two doppler measurements , say y1(t ) and y2(t ) , in the fourier domain . if we denote with h1(t ) , h2(t ) the gravitational - wave signals entering into the doppler data y1 , y2 , respectively , and with n1 , n2 any other remaining noise affecting y1 and y2 , respectively , then the expressions for the doppler observables y1 , y2 can be written in the following form : 3\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${y_1}(t ) = c(t - 2{l_1 } ) - c(t ) + { h_1}(t ) + { n_1}(t),$$\end{document } 4\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${y_2}(t ) = c(t - 2{l_2 } ) - c(t ) + { h_2}(t ) + { n_2}(t){.}$$\end{document } from eqs . ( 3 ) and ( 4 ) it is important to note the characteristic time signature of the random process c(t ) in the doppler responses y1 , y2 . the time signature of the noise c(t ) in y1(t ) , for instance , can be understood by observing that the frequency of the signal received at time t contains laser frequency fluctuations transmitted 2l1 s earlier . by subtracting from the frequency of the received signal the frequency of the signal transmitted at time t , we also subtract the frequency fluctuations c(t ) with the net result shown in eq . the algorithm for canceling the laser noise in the fourier domain suggested in works as follows . if we take an infinitely long fourier transform of the data y1 , the resulting expression of y1 in the fourier domain becomes ( see eq . ( 3 ) ) 5\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\tilde y_1}(f ) = \tilde c(f)[{e^{4\pi i{f^{{l_1 } } } } } - 1 ] + { \tilde h_1}(f ) + { \tilde n_1}(f){.}$$\end{document } if the arm length l1 is known exactly , we can use the y1 data to estimate the laser frequency fluctuations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\tilde c(f)$\end{document}. this can be done by dividing y1 by the transfer function of the laser noise c into the observable y1 itself . by then further multiplying \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\tilde y_1}/[{e^{4\pi if{l_1 } } } - 1]$\end{document } by the transfer function of the laser noise into the other observable \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\tilde y_2}$\end{document } , i.e. , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{e^{4\pi if{l_2 } } } - 1]$\end{document } , and then subtract the resulting expression from \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\tilde y_2}$\end{document } one accomplishes the cancellation of the laser frequency fluctuations . the problem with this procedure is the underlying assumption of being able to take an infinitely long fourier transform of the data . even if one neglects the variation in time of the lisa arms , by taking a finite - length fourier transform of , say , y1(t ) over a time interval t , the resulting transfer function of the laser noise c into y1 no longer will be equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{e^{4\pi if{l_1 } } } - 1]$\end{document}. this can be seen by writing the expression of the finite length fourier transform of y1 in the following way : 6\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\tilde y_1^t \equiv \int\nolimits_{- t}^{+ t } { { y_1 } } ( t){e^{2\pi ift}}dt = \int\nolimits_{- \infty}^{+ \infty } { { y_1 } } ( t)h(t){e^{2\pi ift}}dt,$$\end{document } where we have denoted with h(t ) the function that is equal to 1 in the interval [ t , + t ] , and zero everywhere else . ( 6 ) implies that the finite - length fourier transform \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\tilde y_1^t$\end{document } of y1(t ) is equal to the convolution in the fourier domain of the infinitely long fourier transform of y1(t ) , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\tilde y_1}$\end{document } , with the fourier transform of h(t ) ( i.e. , the sinc function of width 1/t ) . the key point here is that we can no longer use the transfer function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{e^{4\pi if{l_i } } } - 1]$\end{document } , i = 1 , 2 , for estimating the laser noise fluctuations from one of the measured doppler data , without retaining residual laser noise into the combination of the two doppler data y1 , y2 valid in the case of infinite integration time . the amount of residual laser noise remaining in the fourier - based combination described above , as a function of the integration time t and type of window function used , was derived in the appendix of . there it was shown that , in order to suppress the residual laser noise below the lisa sensitivity level identified by secondary noises ( such as proof - mass and optical path noises ) with the use of the fourier - based algorithm an integration time of about six months was needed . a solution to this problem was suggested in , which works entirely in the time - domain . from eqs . ( 3 ) and ( 4 ) we may notice that , by taking the difference of the two doppler data y1(t ) , y2(t ) , the frequency fluctuations of the laser now enter into this new data set in the following way : 7\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${y_1}(t ) - { y_2}(t ) = c(t - 2{l_1 } ) - c(t - 2{l_2 } ) + { h_1}(t ) - { h_2}(t ) + { n_1}(t ) - { n_2}(t){.}$$\end{document } if we now compare how the laser frequency fluctuations enter into eq . ( 3 ) and ( 4 ) , we can further make the following observation . if we time - shift the data y1(t ) by the round trip light time in arm 2 , y1(t 2l2 ) , and subtract from it the data y2(t ) after it has been time - shifted by the round trip light time in arm 1 , y2(t 2l1 ) , we obtain the following data set : 8\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { y_1}(t - 2{l_2 } ) - { y_2}(t - 2{l_1 } ) = c(t - 2{l_1 } ) - c(t - 2{l_2 } ) + { h_1}(t - 2{l_2 } ) - { h_2}(t - 2{l_1})\quad } \\ { + { n_1}(t - 2{l_2 } ) - { n_2}(t - 2{l_1 } ) . } \\ \end{array}$$\end{document } in other words , the laser frequency fluctuations enter into y1(t)y2(t ) and y1(t2l2)y2(t2l1 ) with the same time structure . ( 7 ) we can generate a new data set that does not contain the laser frequency fluctuations c(t ) , 9\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x \equiv [ { y_1}(t ) - { y_2}(t ) ] - [ { y_1}(t - 2{l_2 } ) - { y_2}(t - 2{l_1})]{.}$$\end{document } the expression above of the x combination shows that it is possible to cancel the laser frequency noise in the time domain by properly time - shifting and linearly combining doppler measurements recorded by different doppler readouts . this in essence is what tdi amounts to . in order to gain a better physical understanding of how tdi works , let s rewrite the above x combination in the following form 10\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x = [ { y_1}(t ) + { y_2}(t - 2{l_1 } ) ] - [ { y_2}(t ) + { y_1}(t - 2{l_2})],$$\end{document } where we have simply rearranged the terms in eq . equation ( 10 ) shows that x is the difference of two sums of relative frequency changes , each corresponding to a specific light path ( the continuous and dashed lines in figure 2 ) . the continuous line , corresponding to the first square - bracket term in eq . ( 10 ) , represents a light - beam transmitted from spacecraft 1 and made to bounce once at spacecraft 3 and 2 respectively . since the other beam ( dashed line ) experiences the same overall delay as the first beam ( although by bouncing off spacecraft 2 first and then spacecraft 3 ) when they are recombined they will cancel the laser phase fluctuations exactly , having both experienced the same total delays ( assuming stationary spacecraft ) . for this reason the combination x can be regarded as a synthesized ( via tdi ) zero - area sagnac interferometer , with each beam experiencing a delay equal to ( 2l1 + 2l2 ) . in reality , there are only two beams in each arm ( one in each direction ) and the lines in figure 2 represent the paths of relative frequency changes rather than paths of distinct light beams . figure 2schematic diagram for x , showing that it is a synthesized zero - area sagnac interferometer . schematic diagram for x , showing that it is a synthesized zero - area sagnac interferometer . x and the measurement is made at an o . in the following sections we will further elaborate and generalize tdi to the realistic lisa configuration . the description of tdi for lisa is greatly simplified if we adopt the notation shown in figure 3 , where the overall geometry of the lisa detector is defined . there are three spacecraft , six optical benches , six lasers , six proof - masses , and twelve photodetectors . there are also six phase difference data going clock - wise and counter - clockwise around the lisa triangle . for the moment we will make the simplifying assumption that the array is stationary , i.e. , the back and forth optical paths between pairs of spacecraft are simply equal to their relative distances [ 44 , 7 , 45 , 58 ] . the optical paths are denoted by li , li where the index i corresponds to the opposite spacecraft . the unit vectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\rm{\hat n}}_i}$\end{document } point between pairs of spacecraft , with the orientation indicated . the optical paths are denoted by li , li where the index i corresponds to the opposite spacecraft . the unit vectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\rm{\hat n}}_i}$\end{document } point between pairs of spacecraft , with the orientation indicated . the double index notation recently employed in , where six quantities are involved , is self - evident . however , when algebraic manipulations are involved the following notation seems more convenient to use . the spacecraft are labeled 1 , 2 , 3 and their separating distances are denoted l1 , l2 , l3 , with li being opposite spacecraft i. we orient the vertices 1 , 2 , 3 clockwise in figure 3 . unit vectors between spacecraft are \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\hat n_i}$\end{document } , oriented as indicated in figure 3 . we index the phase difference data to be analyzed as follows : the beam arriving at spacecraft has subscript i and is primed or unprimed depending on whether the beam is traveling clockwise or counter - clockwise ( the sense defined here with reference to figure 3 ) around the lisa triangle , respectively . thus , as seen from the figure , s1 is the phase difference time series measured at reception at spacecraft 1 with transmission from spacecraft 2 ( along l3 ) . similarly , s1 is the phase difference series derived from reception at spacecraft 1 with transmission from spacecraft 3 . the other four one - way phase difference time series from signals exchanged between the spacecraft are obtained by cyclic permutation of the indices : 1 2 3 1 . we also adopt a notation for delayed data streams , which will be convenient later for algebraic manipulations . we define the three time - delay operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i},i = 1,2,3$\end{document } where for any data stream x(t ) 11\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\mathcal{d}_i}x(t ) = x(t - { l_i}),$$\end{document } where li , i = 1 , 2 , 3 , are the light travel times along the three arms of the lisa triangle ( the speed of light c is assumed to be unity in this article ) . thus , for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_{2{s_1}}}(t ) = { s_1}(t - { l_2}),{{\mathcal d}_2}{{\mathcal d}_{3{s_1}}}(t ) = { s_1}(t - { l_2 } - { l_3 } ) = { { \mathcal d}_3}{{\mathcal d}_{2{s_1}}}(t)$\end{document } , etc . if the li are functions of time then the operators no longer commute [ 7 , 58 ] , as will be described in section 4 . six more phase difference series result from laser beams exchanged between adjacent optical benches within each spacecraft ; these are similarly indexed as i , i , i = 1 , 2 , 3 . the proof - mass - plus - optical - bench assemblies for lisa spacecraft number 1 are shown schematically in figure 4 . the photo receivers that generate the data s1 , s1 , 1 , and 1 at spacecraft 1 are shown . the phase fluctuations from the six lasers , which need to be canceled , can be represented by six random processes pi , pi , where pi , pi are the phases of the lasers in spacecraft i on the left and right optical benches , respectively , as shown in the figure . note that this notation is in the same spirit as in [ 57 , 45 ] in which moving spacecraft arrays have been analyzed . figure 4schematic diagram of proof - masses - plus - optical - benches for a lisa spacecraft . the left - hand bench reads out the phase signals s1 and 1 . the right - hand bench analogously reads out s1 and 1 . the random displacements of the two proof masses and two optical benches are indicated ( lower case \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i},{\vec \delta ^{\prime}_i}$\end{document } for the proof masses , upper case \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i}$\end{document } , i for the optical benches ) . schematic diagram of proof - masses - plus - optical - benches for a lisa spacecraft . the random displacements of the two proof masses and two optical benches are indicated ( lower case \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i},{\vec \delta ^{\prime}_i}$\end{document } for the proof masses , upper case \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i}$\end{document } , i for the optical benches ) . we extend the cyclic terminology so that at vertex i , i = 1 , 2 , 3 , the random displacement vectors of the two proof masses are respectively denoted by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i}(t),{\vec \delta ^{\prime}_i}(t)$\end{document } , and the random displacements ( perhaps several orders of magnitude greater ) of their optical benches are correspondingly denoted by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i}(t),\;{\vec \delta ^{\prime}_i}(t)$\end{document } where the primed and unprimed indices correspond to the right and left optical benches , respectively . as pointed out in , the analysis does not assume that pairs of optical benches are rigidly connected , i.e. , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i } \neq { \vec \delta ^{\prime}_i}$\end{document } , in general . we ignore time - delay effects for these signals and will simply denote by i(t ) the phase fluctuations upon transmission through the fibers of the laser beams with frequencies i , and i . the i(t ) phase shifts within a given spacecraft might not be the same for large frequency differences ii for the envisioned frequency differences ( a few hundred mhz ) , however , the remaining fluctuations due to the optical fiber can be neglected . it is also assumed that the phase noise added by the fibers is independent of the direction of light propagation through them . for ease of presentation , in what follows we will assume the center frequencies of the lasers to be the same , and denote this frequency by 0 . the laser phase noise in s3 is therefore equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1}{p_2}(t ) - { p^{\prime}_3}(t)$\end{document}. similarly , since s2 is the phase shift measured on arrival at spacecraft 2 along arm 1 of a signal transmitted from spacecraft 3 , the laser phase noises enter into it with the following time signature : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1}{p^{\prime}_3}(t ) - { p_2}(t)$\end{document}. figure 4 endeavors to make the detailed light paths for these observations clear . an outgoing light beam transmitted to a distant spacecraft is routed from the laser on the local optical bench using mirrors and beam splitters ; this beam does not interact with the local proof mass . conversely , an incoming light beam from a distant spacecraft is bounced off the local proof mass before being reflected onto the photo receiver where it is mixed with light from the laser on that same optical bench . beams between adjacent optical benches within a single spacecraft are bounced off proof masses in the opposite way . light to be transmitted from the laser on an optical bench is first bounced off the proof mass it encloses and then directed to the other optical bench . upon reception it does not interact with the proof mass there , but is directly mixed with local laser light , and again down converted . the expressions for the si , si and i , 1 phase measurements can now be developed from figures 3 and 4 , and they are for the particular lisa configuration in which all the lasers have the same nominal frequency 0 , and the spacecraft are stationary with respect to each other.1 consider the s1(t ) process ( eq . ( 14 ) below ) . the photo receiver on the right bench of spacecraft 1 , which ( in the spacecraft frame ) experiences a time - varying displacement \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta ^{\prime}_1}$\end{document } , measures the phase difference s1 by first mixing the beam from the distant optical bench 3 in direction \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\hat n_2}$\end{document } , and laser phase noise p3 and optical bench motion \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ 3}$\end{document } that have been delayed by propagation along l2 , after one bounce off the proof mass \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\vec \delta ^{\prime}_1})$\end{document } , with the local laser light ( with phase noise p1 ) . since for this simplified configuration no frequency offsets are present , there is of course no need for any heterodyne conversion . in eq . ( 13 ) the 1 measurement results from light originating at the right - bench laser \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({p^{\prime}_1},\;{\vec \delta ^{\prime}_1})$\end{document } , bounced once off the right proof mass \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\vec \delta ^{\prime}_1})$\end{document } , and directed through the fiber ( incurring phase shift 1(t ) ) , to the left bench , where it is mixed with laser light ( p1 ) . the laser noises , the gravitational - wave signals , the optical path noises , and proof - mass and bench noises , enter into the four data streams recorded at vertex 1 according to the following expressions : 12\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_1 } = s_1^{{\rm{gw } } } + s_1^{{\rm{optical}}\;{\rm{path } } } + { \mathcal{d}_3}p_2^\prime - { p_1 } + { \nu _ 0}\left [ { - 2{{\hat n}_3}\cdot{{\vec \delta}_1 } + { { \hat n}_3}\cdot{{\vec \delta}_1 } + { { \hat n}_3}\cdot{\mathcal{d}_3}\vec \delta _ 2^\prime } \right],$$\end{document } 13\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\tau _ 1 } = p_1^\prime - { p_1 } - 2{\nu _ 0}{\hat n_2}\cdot\left({\vec \delta _ 1^\prime - \vec \delta _ 1^\prime } \right ) + { \mu _ 1}{.}$$\end{document } 14\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s_1^\prime = s_1^{\prime { \rm{gw } } } + s_1^{\prime { \rm{optical}}\;{\rm{path } } } + { \mathcal{d}_2}{p_3 } - p_1^\prime + { \nu _ 0}\left [ { 2{{\hat n}_2}\cdot\vec \delta _ 1^\prime - { { \hat n}_2}\cdot\vec \delta _ 1^\prime - { { \hat n}_2}\cdot{\mathcal{d}_2}{{\vec \delta}_3 } } \right],$$\end{document } 15\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\tau _ 1^\prime = { p_1 } - p_1^\prime + 2{\nu _ 0}{\hat n_3}\cdot\left({{{\vec \delta}_1 } - { { \vec \delta}_1 } } \right ) + { \mu _ 1}{.}$$\end{document } eight other relations , for the readouts at vertices 2 and 3 , are given by cyclic permutation of the indices in eqs . ( 12 ) , ( 13 ) , ( 14 ) , and ( 15 ) . the gravitational - wave phase signal components \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$s^{gw}_{i},s\prime^{gw}_{i},i=1,2,3$\end{document } in eqs . ( 12 ) and ( 14 ) are given by integrating with respect to time the eqs . ( 1 ) and ( 2 ) of reference , which relate metric perturbations to optical frequency shifts . the optical path phase noise contributions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$s_{i}^{optical\;path},s\prime_{i}^{optical\;path}$\end{document } which include shot noise from the low snr in the links between the distant spacecraft , can be derived from the corresponding term given in . the i , i measurements will be made with high snr so that for them the shot noise is negligible . in ground - based detectors the arms are chosen to be of equal length so that the laser light experiences identical delay in each arm of the interferometer . the required sensitivity of the instrument can thus only be achieved by near exact cancellation of the laser frequency noise . however , in lisa it is impossible to achieve equal distances between spacecraft , and the laser noise can not be canceled in this way . it is possible to combine the recorded data linearly with suitable time - delays corresponding to the three arm lengths of the giant triangular interferometer so that the laser phase noise is canceled . here we present a systematic method based on modules over polynomial rings which guarantees all the data combinations that cancel both the laser phase and the optical bench motion noises . we first consider the simpler case , where we ignore the optical - bench motion noise and consider only the laser phase noise . we do this because the algebra is somewhat simpler and the method is easy to apply . the simplification amounts to physically considering each spacecraft rigidly carrying the assembly of lasers , beam - splitters , and photodetectors . the two lasers on each spacecraft could be considered to be locked , so effectively there would be only one laser on each spacecraft . this mathematically amounts to setting \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i } = { \vec \delta ^{\prime}_i } = 0$\end{document } and pi = pi . the scheme we describe here for laser phase noise can be extended in a straight - forward way to include optical bench motion noise , which we address in the last part of this section . the data combinations , when only the laser phase noise is considered , consist of the six suitably delayed data streams ( inter - spacecraft ) , the delays being integer multiples of the light travel times between spacecraft , which can be conveniently expressed in terms of polynomials in the three delay operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}$\end{document}. the laser noise cancellation condition puts three constraints on the six polynomials of the delay operators corresponding to the six data streams . the problem , therefore , consists of finding six - tuples of polynomials which satisfy the laser noise cancellation constraints . exist standard methods for obtaining the module , by which we mean methods for obtaining the generators of the module so that the linear combinations of the generators generate the entire module . the procedure first consists of obtaining a grbner basis for the ideal generated by the coefficients appearing in the constraints . this ideal is in the polynomial ring in the variables \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}$\end{document } over the domain of rational numbers ( or integers if one gets rid of the denominators ) . to obtain the grbner basis for the ideal , one may use the buchberger algorithm or use an application such as mathematica . from the grbner basis however , the method does not guarantee a minimal set and we find that a generating set of 4 polynomial six - tuples suffice to generate the required module . the importance of obtaining more data combinations is evident : they provide the necessary redundancy different data combinations produce different transfer functions for gws and the system noises so specific data combinations could be optimal for given astrophysical source parameters in the context of maximizing snr , detection probability , improving parameter estimates , etc . we now only have six data streams si and si , where i = 1 , 2 , 3 . the six data streams with terms containing only the laser frequency noise are 16\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { s_1 } = { \mathcal{d}_3}{p_2 } - { p_1 } , } \\ { s_1^\prime = { \mathcal{d}_2}{p_3 } - { p_1}\ ; } \\ \end{array}$$\end{document } and their cyclic permutations . note that we have intentionally excluded from the data additional phase fluctuations due to the gw signal , and noises such as the optical - path noise , proof - mass noise , etc . since our immediate goal is to cancel the laser frequency noise we have only kept the relevant terms . combining the streams for canceling the laser frequency noise will introduce transfer functions for the other noises and the gw signal . the goal of the analysis is to add suitably delayed beams together so that the laser frequency noise terms add up to zero . this amounts to seeking data combinations that cancel the laser frequency noise . in the notation / formalism that we have invoked , the delay is obtained by applying the operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_k}$\end{document}. to the beams si and si . a delay of k1l1 + k2l2 + k3l3 is represented by the operator \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal d}_1^{{k_1}}{\mathcal d}_2^{k2}{\mathcal d}_3^{{k_3}}$\end{document } acting on the data , where k1 , k2 , and k3 are integers . in general , a polynomial in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_k}$\end{document } , which is a polynomial in three variables , applied to , say , s1 combines the same data stream s1(t ) with different time - delays of the form k1l1 + k2l2 + k3l3 . one must find six polynomials say \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${q_i}({{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}),{q^{\prime}_i}({{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}),\;i = 1,2,3$\end{document } such that 17\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\sum\limits_{i = 1}^3 { { q_i } } { s_i } + q_i^\prime s_i^\prime = 0{.}$$\end{document } the zero on the right - hand side of the above equation signifies zero laser phase noise . this allows us to obtain a matrix operator equation whose solutions are q and q , where qi and qi are written as column vectors . we can similarly express si , si , pi as column vectors s , s , p , respectively . in matrix form eq . ( 16 ) becomes 18\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{s } } = { { \bf{d}}^t}\cdot{\bf{p}},\quad \quad { { \rm{s}}^\prime } = { \bf{d}}\cdot{\bf{p}},$$\end{document } where d is a 3 3 matrix given by 19\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\bf{d } } = \left({\begin{array}{*{20}c } { - 1 } & 0 & { { \mathcal{d}_2 } } \\ { { \mathcal{d}_3 } } & { - 1 } & 0 \\ 0 & { { \mathcal{d}_1 } } & { - 1 } \\ \end{array } } \right){.}$$\end{document } the exponent t represents the transpose of the matrix . ( 17 ) becomes 20\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\bf{q}}^t}\cdot{\bf{s } } + { { \bf{q}}^{\prime t}}\cdot{{\bf{s}}^\prime } = ( { { \bf{q}}^t}\cdot{{\bf{d}}^t } + { { \bf{q}}^{\prime t}}\cdot{\bf{d}})\cdot{\bf{p } } = 0,$$\end{document } where we have taken care to put p on the right - hand side of the operators . since the above equation must be satisfied for an arbitrary vector p , we obtain a matrix equation for the polynomials ( q , q ) : 21\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\bf{q}}^t}\cdot{{\bf{d}}^t } + { { \bf{q}}^\prime}\cdot{\bf{d } } = 0{.}$$\end{document } note that since the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_k}$\end{document}. commute , the order in writing these operators is unimportant . in mathematical terms , the polynomials form a commutative ring . the use of commutative algebra is very conveniently illustrated with the help of the simpler example of the unequal - arm interferometer . here there are only two arms instead of three as we have for lisa , and the mathematics is much simpler and so it easy to see both physically and mathematically how commutative algebra can be applied to this problem of laser phase noise cancellation . the procedure is well known for the unequal - arm interferometer , but here we will describe the same method but in terms of the delay operators that we have introduced . let (t ) denote the laser phase noise entering the laser cavity as shown in figure 5 . consider this light (t ) making a round trip around arm 1 whose length we take to be l1 . if we interfere this phase with the incoming light we get the phase 1(t ) , where 22\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\phi _ 1}(t ) = \phi ( t - 2{l_1 } ) - \phi ( t ) \equiv ( \mathcal{d}_1 ^ 2 - 1)\phi ( t){.}$$\end{document } the second expression we have written in terms of the delay operators . we can do the same for the arm 2 to get another phase 2(t ) , where 23\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\phi _ 2}(t ) = \phi ( t - 2{l_2 } ) - \phi ( t ) \equiv ( \mathcal{d}_2 ^ 2 - 1)\phi ( t){.}$$\end{document } clearly , if l1 l2 , then the difference in phase 2(t ) 1(t ) is not zero and the laser phase noise does not cancel out . however , if one further delays the phases 1(t ) and 2 ( ) and constructs the following combination , 24\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x(t ) = [ { \phi _ 2}(t - 2{l_1 } ) - { \phi _ 2}(t ) ] - [ { \phi _ 1}(t - 2{l_2 } ) - { \phi _ 1}(t)],$$\end{document } then the laser phase noise does cancel out . the beam shown corresponds to the term \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\mathcal d}_2 ^ 2 - 1)({\mathcal d}_1 ^ 2 - 1)\phi ( t)$\end{document } in x(t ) which is first sent around arm 1 followed by arm 2 . the second beam ( not shown ) is first sent around arm 2 and then through arm 1 . the beam shown corresponds to the term \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\mathcal d}_2 ^ 2 - 1)({\mathcal d}_1 ^ 2 - 1)\phi ( t)$\end{document } in x(t ) which is first sent around arm 1 followed by arm 2 . the second beam ( not shown ) is first sent around arm 2 and then through arm 1 . the cancellation of laser frequency noise becomes obvious from the operator algebra in the following way . in the operator notation , 25\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { x(t ) = ( \mathcal{d}_1 ^ 2 - 1){\phi _ 2}(t ) - ( \mathcal{d}_2 ^ 2 - 1){\phi _ 1}(t)\quad \quad \quad \quad \quad \quad \quad } \\ { = [ ( \mathcal{d}_1 ^ 2 - 1)(\mathcal{d}_2 ^ 2 - 1 ) - ( \mathcal{d}_2 ^ 2 - 1)(\mathcal{d}_1 ^ 2 - 1)]\phi ( t ) } \\ { = 0.\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \ ; } \\ \end{array}$$\end{document } from this one immediately sees that just the commutativity of the operators has been used to cancel the laser phase noise . the basic idea was to compute the lowest common multiple ( l.c.m . ) of the polynomials \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal d}_1 ^ 2 - 1$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal d}_2 ^ 2 - 1$\end{document } ( in this case the l.c.m . is just the product , because the polynomials are relatively prime ) and use this fact to construct x(t ) in which the laser phase noise is canceled . in fact we will be using the notion of a grobner basis which is in a sense the generalization of the notion of the greatest common divisor ( gcd ) . since lisa has three spacecraft and six inter - spacecraft beams , the problem of the unequal - arm interferometer only gets technically more complex ; in principle the problem is the same as in this simpler case . thus , the simple operations which were performed here to obtain a laser noise free combination x(t ) are not sufficient and more sophisticated methods need to be adopted from the field of commutative algebra . we merely mention these solutions here ; in the forthcoming text we will discuss them in detail . the solution is given by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$- { { \rm{q}}^{\rm{t } } } = { { \rm{q^{\prime}}}^t } = ( { { \mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3})$\end{document}. the solution is described by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\rm{q}}^t } = - ( 1,{{\mathcal d}_3},{{\mathcal d}_1},{{\mathcal d}_3})$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\rm{q^{\prime}}}^t } = ( 1,{{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_2})$\end{document}. the solutions and are obtained from by cyclically permuting the indices of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_k},{\rm{q}}$\end{document } and q. these solutions are important , because they consist of polynomials with lowest possible degrees and thus are simple . other solutions containing higher degree polynomials can be generated conveniently from these solutions . since the system of equations is linear , linear combinations of these solutions are also solutions to eq . however , it is important to realize that we do not have a vector space here . three independent constraints on a six - tuple do not produce a space which is necessarily generated by three basis elements . this conclusion would follow if the solutions formed a vector space but they do not . the polynomial six - tuple q , q can be multiplied by polynomials in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}$\end{document } ( scalars ) which do not form a field . we , therefore , have a module over the ring of polynomials in the three variables \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}$\end{document}. first we present the general methodology for obtaining the solutions to eq . ( 21 ) and then apply it to eq . ( since the equations are linear , the solutions space is a submodule of the module of six - tuples of polynomials . the module of six - tuples is a free module , i.e. , it has six basis elements that not only generate the module but are linearly independent . a natural choice of the basis is fm = ( 0 , , 1 , , 0 ) with 1 in the m - th place and 0 everywhere else ; m runs from 1 to 6 . the definitions of generation ( spanning ) and linear independence are the same as that for vector spaces . but our interest lies in its submodule which need not be free and need not have just three generators as it would seem if we were dealing with vector spaces . the problem at hand is of finding the generators of this submodule , i.e. , any element of the submodule should be expressible as a linear combination of the generating set . in this way the generators are capable of spanning the full submodule or generating the submodule . in order to achieve our goal , we rewrite eq . ( 21 ) explicitly component - wise : 26\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } + q_1^\prime - { \mathcal{d}_3}q_2^\prime - { \mathcal{d}_2}{q_3 } = 0 , } \\ { { q_2 } + q_2^\prime - { \mathcal{d}_1}q_3^\prime - { \mathcal{d}_3}{q_1 } = 0 , } \\ { { q_3 } + q_3^\prime - { \mathcal{d}_2}q_1^\prime - { \mathcal{d}_1}{q_2 } = 0 . } \\ \end{array}$$\end{document } the first step is to use gaussian elimination to obtain q1 and q2 in terms of q3 , q1 , q2 , q3 , 27\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } = - q_1^\prime + { \mathcal{d}_3}q_2^\prime + { \mathcal{d}_2}{q_3},\quad \quad \quad \quad \quad \quad \quad \quad } \\ { { q_2 } = - q_2^\prime + { \mathcal{d}_1}q_3^\prime + { \mathcal{d}_3}{q_1}\quad \quad \quad \quad \quad \quad \quad \quad \ ; } \\ { = - { \mathcal{d}_3}q_1^\prime - ( 1 - \mathcal{d}_3 ^ 2)q_2^\prime + { \mathcal{d}_1}q_3^\prime + { \mathcal{d}_2}{\mathcal{d}_3}{q_3 } , } \\ \end{array}$$\end{document } and then substitute these values in the third equation to obtain a linear implicit relation between q3 , q1 , q2 , q3 . we then have : 28\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(1 - { \mathcal{d}_1}{\mathcal{d}_2}{\mathcal{d}_3}){q_3 } + ( { \mathcal{d}_1}{\mathcal{d}_3 } - { \mathcal{d}_2})q_1^\prime + { \mathcal{d}_1}(1 - \mathcal{d}_3 ^ 2)q_2^\prime + ( 1 - \mathcal{d}_1 ^ 2)q_3^\prime = 0{.}$$\end{document } obtaining solutions to eq . ( 28 ) amounts to solving the problem since the remaining polynomials q1 , q2 have been expressed in terms of q3 , q1 , q2 , q3 in eq . note that we can not carry on the gaussian elimination process any further , because none of the polynomial coefficients appearing in eq . we will assume that the polynomials have rational coefficients , i.e. , the coefficients belong to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}$\end{document } , the field of the rational numbers . the set of polynomials form a ring the polynomial ring in three variables , which we denote by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r } = { \mathcal q}[{{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}]$\end{document}. the polynomial vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({q_3},{q^{\prime}_1},{q^{\prime}_2},{q^{\prime}_3})\;\;\in \;{{\mathcal r}^4}$\end{document}. the set of solutions to eq . ( 28 ) is just the kernel of the homomorphism \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\varphi \;:{{\mathcal r}^4}\ ; \rightarrow { \mathcal r}$\end{document } , where the polynomial vector ( q3 , q1 , q2 , q3 ) is mapped to the polynomial \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(1 - { { \mathcal d}_1}{{\mathcal d}_2}{{\mathcal d}_3}){q_3}\ ; + ( { { \mathcal d}_1}{{\mathcal d}_3 } - { { \mathcal d}_2}){q^{\prime}_1 } + { { \mathcal d}_1}(1 - { \mathcal d}_3 ^ 2){q^{\prime}_2}\ ; + ( 1 - { \mathcal d}_1 ^ 2){q^{\prime}_3}$\end{document}. thus , the solution space ker is a submodule of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal r}^4}$\end{document}. it is called the module of syzygies . the generators of this module can be obtained from standard methods available in the literature . we briefly outline the method given in the books by becker et al . , and kreuzer and robbiano below . the details have been included in appendix a. the first step is to obtain the grbner basis for the ideal \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } generated by the coefficients in eq . ( 28 ) : 29\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_1 } = 1 - { \mathcal{d}_1}{\mathcal{d}_2}{\mathcal{d}_3},\quad \quad { u_2 } = { \mathcal{d}_1}{\mathcal{d}_3 } - { \mathcal{d}_2},\quad \quad { u_3 } = { \mathcal{d}_1}(1 - \mathcal{d}_3 ^ 2)\;,\quad \quad { u_4 } = 1 - \mathcal{d}_1 ^ 2{.}$$\end{document } the ideal \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } consists of linear combinations of the form viui where vi , i = 1 , , 4 are polynomials in the ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r}$\end{document}. there can be several sets of generators for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document}. a grbner basis is a set of generators which is there are several ways to look at the theory of grbner basis . one way is the following : suppose we are given polynomials g1 , g2 , , gm in one variable over say \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}$\end{document } and we would like to know whether another polynomial f belongs to the ideal generated by the g s . a good way to decide the issue would be to first compute the gcd g of g1 , g2 , , gm and check whether f is a multiple of g. one can achieve this by doing the long division of f by g and checking whether the remainder is zero . all this is possible because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}[x]$\end{document } is a euclidean domain and also a principle ideal domain ( pid ) wherein any ideal is generated by a single element . therefore we have essentially just one polynomial the gcd which generates the ideal generated by g1 , g2 , , gm . the ring of integers or the ring of polynomials in one variable over any field are examples of pids whose ideals are generated by single elements . however , when we consider more general rings ( not pids ) like the one we are dealing with here , we do not have a single gcd but a set of several polynomials which generates an ideal in general . a grbner basis of an ideal can be thought of as a generalization of the gcd . in the univariate case grbner basis theory generalizes these ideas to multivariate polynomials which are neither euclidean rings nor pids . since there is in general not a single generator for an ideal , grbner basis theory comes up with the idea of dividing a polynomial with a set of polynomials , the set of generators of the ideal , so that by successive divisions by the polynomials in this generating set of the given polynomial , the remainder becomes zero . clearly , those special generating sets that do possess this property ( and they exist ! ) are called grbner bases . in order for a division to be carried out in a sensible manner , an order must be put on the ring of polynomials , so that the final remainder after every division is strictly smaller than each of the divisors in the generating set . a natural order exists on the ring of integers or on the polynomial ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}(x)$\end{document } ; the degree of the polynomial decides the order in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}(x)$\end{document}. however , even for polynomials in two variables there is no natural order a priori ( is x + y greater or smaller than x + y ? ) . but one can , by hand as it were , put an order on such a ring by saying x y , where is an order , called the lexicographical order . we follow this type of order , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1 } \gg { { \mathcal d}_2 } \gg { { \mathcal d}_3}$\end{document } and ordering polynomials by considering their highest degree terms . it is possible to put different orderings on a given ring which then produce different grbner bases . small elements so that division is possible and every element of the ideal when divided by the grbner basis elements leaves zero remainder , i.e. , every element modulo the grbner basis reduces to zero . in the literature , there exists a well - known algorithm called the buchberger algorithm , which may be used to obtain the grbner basis for a given set of polynomials in the ring . so a grbner basis of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } can be obtained from the generators ui given in eq . it is essentially again a generalization of the usual long division that we perform on univariate polynomials . mathematica yields a 3-element grbner basis \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal g}$\end{document } for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } : 30\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mathcal{g } = \{\mathcal{d}_3 ^ 2 - 1,\mathcal{d}_2 ^ 2 - 1,{\mathcal{d}_1 } - { \mathcal{d}_2}{\mathcal{d}_3}\ } { .}$$\end{document } one can easily check that all the ui of eq . ( 29 ) are linear combinations of the polynomials in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal g}$\end{document } and hence \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal g}$\end{document } generates \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document}. one also observes that the elements look small in the order mentioned above . however , one can satisfy oneself that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal g}$\end{document } is a grbner basis by using the standard methods available in the literature . one method consists of computing the s - polynomials ( see appendix a ) for all the pairs of the grbner basis elements and checking whether these reduce to zero modulo \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal g}$\end{document}. this grbner basis of the ideal \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } is then used to obtain the generators for the module of syzygies . note that although the grbner basis depends on the order we choose among the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_k}$\end{document } , the module itself is independent of the order . the generating set for the module is obtained by further following the procedure in the literature [ 3 , 29 ] . these generators do not form a minimal set and there are relations between them ; in fact this method does not guarantee a minimum set of generators . these generators can be expressed as linear combinations of , , , and also in terms of x , x , x , x given below in eq . the importance in obtaining the seven generators is that the standard theorems guarantee that these seven generators do in fact generate the required module . therefore , from this proven set of generators we can check whether a particular set is in fact a generating set . alternatively , we may use a software package called macaulay 2 which directly calculates the generators given the eqs . again , macaulay s algorithm does not yield a minimal set ; we can express the last two generators in terms of the first four . below we list this smaller set of four generators in the order x = ( q1 , q2 , q3 , q1 , q2 , q3 ) : 31\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { x^{(1 ) } } = ( { \mathcal{d}_2 } - { \mathcal{d}_1}{\mathcal{d}_3},0,1 - \mathcal{d}_3 ^ 2,0,\;{\mathcal{d}_2}{\mathcal{d}_3 } - { \mathcal{d}_1},\;\mathcal{d}_3 ^ 2 - 1 ) , } \\ { { x^{(2 ) } } = ( - { \mathcal{d}_1},\ ; - { \mathcal{d}_2},\ ; - { \mathcal{d}_3},\;{\mathcal{d}_1},\;{\mathcal{d}_2},\;{\mathcal{d}_3}),\quad \quad \quad \quad \quad \ ; } \\ { { x^{(3 ) } } = ( - 1,\ ; - { \mathcal{d}_3},\ ; - { \mathcal{d}_1}{\mathcal{d}_3},1,\;{\mathcal{d}_1}{\mathcal{d}_2},\;{\mathcal{d}_2}),\quad \quad \quad \quad \;\ ; } \\ { { x^{(4 ) } } = ( - { \mathcal{d}_1}{\mathcal{d}_2},\ ; - 1,\ ; - { \mathcal{d}_1},\;{\mathcal{d}_3},1,\;{\mathcal{d}_2}{\mathcal{d}_3}).\quad \quad \quad \quad \;\;\ , } \\ \end{array}$$\end{document } note that the last three generators are just x = , x = , x = . an extra generator x is needed to generate all the solutions . another set of generators which may be useful for further work is a grbner basis of a module . the concept of a grbner basis of an ideal can be extended to that of a grbner basis of a submodule of ( k[x1 , x2 , , xn ] ) where k is a field , since a module over the polynomial ring can be considered as generalization of an ideal in a polynomial ring . just as in the case of an ideal , a grbner basis for a module is a generating set with special properties . for the module under consideration we obtain a grbner basis using macaulay 2 : 32\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { g^{(1 ) } } = ( - { \mathcal{d}_1},\ ; - { \mathcal{d}_2},\ ; - { \mathcal{d}_3},\;{\mathcal{d}_1},\;{\mathcal{d}_2},\;{\mathcal{d}_3}),\quad \quad \quad \quad \quad \ , } \\ { { g^{(2 ) } } = ( { \mathcal{d}_2 } - { \mathcal{d}_1}{\mathcal{d}_3},0,1 - \mathcal{d}_3 ^ 2,0,\;{\mathcal{d}_2}{\mathcal{d}_3 } - { \mathcal{d}_1},\;\mathcal{d}_3 ^ 2 - 1),\ , } \\ { { g^{(3 ) } } = ( - { \mathcal{d}_1}{\mathcal{d}_2},\ ; - 1,\ ; - { \mathcal{d}_1},\;{\mathcal{d}_3},1,\;{\mathcal{d}_2}{\mathcal{d}_3}),\quad \quad \quad \quad \quad \ ; } \\ { { g^{(4 ) } } = ( - 1,\ ; - { \mathcal{d}_3},\ ; - { \mathcal{d}_1}{\mathcal{d}_3},1,\;{\mathcal{d}_1}{\mathcal{d}_2},\;{\mathcal{d}_2}),\quad \quad \quad \quad \quad } \\ { { g^{(5 ) } } = ( { \mathcal{d}_3}(1 - \mathcal{d}_1 ^ 2),\;\mathcal{d}_3 ^ 2 - 1,0,0,1 - \mathcal{d}_1 ^ 2,\;{\mathcal{d}_1}(\mathcal{d}_3 ^ 2 - 1 ) ) . } \\ \end{array}$$\end{document } note that in this grbner basis g = = x , g = x , g = = x , g = = x. only g is the new generator . another set of generators are just , , , and . this can be checked using macaulay 2 , or one can relate , , , and to the generators x , a = 1 , 2 , 3 , 4 , by polynomial matrices . in appendix b , we express the seven generators we obtained following the literature , in terms of , , , and . also we express , , , and in terms of x. this proves that all these sets generate the required module of syzygies . the question now arises as to which set of generators we should choose which facilitates further analysis . also we would prefer low degree polynomials to appear in the generators so as to avoid cancellation of leading terms in the polynomials . by these two criteria we may choose x or , , , . however , , , , possess the additional property that this set is left invariant under a cyclic permutation of indices 1 , 2 , 3 . it is found that this set is more convenient to use because of this symmetry . there are now twelve doppler data streams which have to be combined in an appropriate manner in order to cancel the noise from the laser as well as from the motion of the optical benches . as in the previous case of canceling laser phase noise , here too , we keep the relevant terms only , namely those terms containing laser phase noise and optical bench motion noise . we then have the following expressions for the four data streams on spacecraft 1 : 33\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_1 } = { \mathcal{d}_3}\left [ { p_2^\prime + { \nu _ 0}{{{\bf{\hat n}}}_3}\cdot\vec \delta _ 2^\prime } \right ] - \left [ { { p_1 } - { \nu _ 0}{{{\bf{\hat n}}}_3}\cdot{{\vec \delta}_1 } } \right],$$\end{document } 34\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s_1^\prime = { \mathcal{d}_2}\left [ { { p_3 } - { \nu _ 0}{{{\bf{\hat n}}}_2}\cdot{{\vec \delta}_3 } } \right ] - \left [ { p_1^\prime + { \nu _ 0}{{{\bf{\hat n}}}_2}\cdot\vec \delta _ 1^\prime } \right],$$\end{document } 35\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\tau _ 1 } = p_1^\prime - { p_1 } + 2{\nu _ 0}{{\bf{\hat n}}_2}\cdot\vec \delta _ 1^\prime + { \mu _ 1},$$\end{document } 36\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\tau _ 1^\prime = { p_1 } - p_1^\prime - 2{\nu _ 0}{{\bf{\hat n}}_3}\cdot{\vec \delta _ 1 } + { \mu _ 1}{.}$$\end{document } the other eight data streams on spacecraft 2 and 3 are obtained by cyclic permutations of the indices in the above equations . in order to simplify the derivation of the expressions canceling the optical bench noises ( 35 ) , we can rewriting the resulting expression ( and those obtained from it by permutation of the spacecraft indices ) in the following form : 37\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${z_1 } \equiv { 1 \over 2}({\tau _ 1 } - \tau _ 1^\prime ) = \phi _ 1^\prime - { \phi _ 1},$$\end{document } where 1 , 1 are defined as 38\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { \phi _ 1^\prime \equiv p_1^\prime + { \nu _ 0}{{{\bf{\hat n}}}_2}\cdot\vec \delta _ 1^\prime , } \\ { { \phi _ 1 } \equiv { p_1 } - { \nu _ 0}{{{\bf{\hat n}}}_3}\cdot{{\vec \delta}_1 } , } \\ \end{array}$$\end{document } the importance in defining these combinations is that the expressions for the data streams si , si simplify into the following form : 39\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { s_1 } = { \mathcal{d}_3}\phi _ 2^\prime - { \phi _ 1 } , } \\ { s_1^\prime = { \mathcal{d}_2}{\phi _ 3 } - \phi _ 1^\prime . } \\ \end{array}$$\end{document } if we now combine the si , si , and zi in the following way , 40\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 1 } \equiv { s_1 } - { \mathcal{d}_3}{z_2 } = { \mathcal{d}_3}{\phi _ 2 } - { \phi _ 1},\quad \quad { \eta _ { 1^\prime } } \equiv { s_{1^\prime } } + { z_1 } = { \mathcal{d}_2}{\phi _ 3 } - { \phi _ 1},$$\end{document } 41\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 2 } \equiv { s_2 } - { \mathcal{d}_1}{z_3 } = { \mathcal{d}_1}{\phi _ 3 } - { \phi _ 2},\quad \quad { \eta _ { 2^\prime } } \equiv { s_{2^\prime } } + { z_2 } = { \mathcal{d}_3}{\phi _ 1 } - { \phi _ 2},$$\end{document } 42\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 3 } \equiv { s_3 } - { \mathcal{d}_2}{z_1 } = { \mathcal{d}_2}{\phi _ 1 } - { \phi _ 3},\quad \quad { \eta _ { 3^\prime } } \equiv { s_{3^\prime } } + { z_3 } = { \mathcal{d}_1}{\phi _ 2 } - { \phi _ 3},$$\end{document } we have just reduced the problem of canceling of six laser and six optical bench noises to the equivalent problem of removing the three random processes 1 , 2 , and 3 from the six linear combinations i , i of the one - way measurements si , si , and zi . by comparing the equations above to eq . ( 16 ) for the simpler configuration with only three lasers , analyzed in the previous sections 4.1 to 4.4 , we see that they are identical in form . it is important to notice that the four interferometric combinations ( , , , ) , which can be used as a basis for generating the entire tdi space , are actually synthesized sagnac interferometers . this can be seen by rewriting the expression for , for instance , in the following form , 43\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\alpha = [ { \eta _ { 1^\prime } } + { \mathcal{d}_2}{\eta _ { 3^\prime } } + { \mathcal{d}_1}{\mathcal{d}_2}{\eta _ { 2^\prime } } ] - [ { \eta _ 1 } + { \mathcal{d}_3}{\eta _ 2 } + { \mathcal{d}_1}{\mathcal{d}_3}{\eta _ 3}],$$\end{document } and noticing that the first square bracket on the right - hand side of eq . ( 43 ) contains a combination of one - way measurements describing a light beam propagating clockwise around the array , while the other terms in the second square - bracket give the equivalent of another beam propagating counter - clockwise around the constellation . contrary to , , and , can not be visualized as the difference ( or interference ) of two synthesized beams . however , it should still be regarded as a sagnac combination since there exists a time - delay relationship between it and , , and : 44\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\zeta - { \mathcal{d}_1}{\mathcal{d}_2}{\mathcal{d}_3}\zeta = { \mathcal{d}_1}\alpha - { \mathcal{d}_2}{\mathcal{d}_3}\alpha + { \mathcal{d}_2}\beta - { \mathcal{d}_3}{\mathcal{d}_1}\beta + { \mathcal{d}_3}\gamma - { \mathcal{d}_1}{\mathcal{d}_2}\gamma { .}$$\end{document } as a consequence of the time - structure of this relationship , has been called the symmetrized sagnac combination . by using the four generators , it is possible to construct several other interferometric combinations , such as the unequal - arm michelson ( x , y , z ) , the beacons ( p , q , r ) , the monitors ( e , f , g ) , and the relays ( u , v , w ) . contrary to the sagnac combinations , these only use four of the six data combinations i , i . these observables can be written in terms of the sagnac observables ( , , , ) in the following way , 45\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { \mathcal{d}_1}x = { \mathcal{d}_2}{\mathcal{d}_3}\alpha - { \mathcal{d}_2}\beta - { d_3}\gamma + \zeta , } \\ { p = \zeta - { \mathcal{d}_1}\alpha , \quad \quad \quad \quad \quad } \\ { e = \alpha - { \mathcal{d}_1}\zeta , \quad \quad \quad \quad \quad } \\ { u = { \mathcal{d}_1}\gamma - \beta , \quad \quad \quad \quad \quad } \\ \end{array}$$\end{document } as it is easy to verify by substituting the expressions for the sagnac combinations into the above equations . figure 6schematic diagrams of the unequal - arm michelson , monitor , beacon , and relay combinations . these tdi combinations rely only on four of the six one - way doppler measurements , as illustrated here . schematic diagrams of the unequal - arm michelson , monitor , beacon , and relay combinations . these tdi combinations rely only on four of the six one - way doppler measurements , as illustrated here . in the case of the combination x , in particular , by writing it in the following form , 46\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x = [ ( { \eta _ { 1^\prime } } + { \mathcal{d}_2}{\eta _ 3 } ) + { \mathcal{d}_2}{\mathcal{d}_2}({\eta _ 1 } + { \mathcal{d}_3}{\eta _ 2 } ) ] - [ ( { \eta _ 1 } + { \mathcal{d}_3}{\eta _ { 2^\prime } } ) + { \mathcal{d}_3}{\mathcal{d}_3}({\eta _ { 1^\prime } } + { \mathcal{d}_2}{\eta _ 3})],$$\end{document } one can notice ( as pointed out in and ) that this combination can be visualized as the difference of two sums of phase measurements , each corresponding to a specific light path from a laser onboard spacecraft 1 having phase noise 1 . the first square - bracket term in eq . ( 46 ) represents a synthesized light - beam transmitted from spacecraft 1 and made to bounce once at spacecraft 2 and 3 , respectively . the second square - bracket term instead corresponds to another beam also originating from the same laser , experiencing the same overall delay as the first beam , but bouncing off spacecraft 3 first and then spacecraft 2 . when they are recombined they will cancel the laser phase fluctuations exactly , having both experienced the same total delay ( assuming stationary spacecraft ) . the x combinations should therefore be regarded as the response of a zero - area sagnac interferometer . the rotational motion of the lisa array results in a difference of the light travel times in the two directions around a sagnac circuit [ 44 , 7 ] . two time delays along each arm must be used , say li and li for clockwise or counter - clockwise propagation as they enter in any of the tdi combinations . furthermore , since li and li not only differ from one another but can be time dependent ( they flex ) , it was shown that the first generation tdi combinations do not completely cancel the laser phase noise ( at least with present laser stability requirements ) , which can enter at a level above the secondary noises . for lisa , and assuming \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\dot l_i } \simeq \;10{\rm{m / s}}$\end{document } , the estimated magnitude of the remaining frequency fluctuations from the laser can be about 30 times larger than the level set by the secondary noise sources in the center of the frequency band . in order to solve this potential problem , it has been shown that there exist new tdi combinations that are immune to first order shearing ( flexing , or constant rate of change of delay times ) . these combinations can be derived by using the time - delay operators formalism introduced in the previous section 4 , although one has to keep in mind that now these operators no longer commute . in order to derive the new , flex - free tdi combinations we will start by taking specific combinations of the one - way data entering in each of the expressions derived in the previous section 4 . note , however , that now the expressions for the -measurements assume the following form 47\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 1 } = { \mathcal{d}_3}{\phi _ 2 } - { \phi _ 1},\quad \quad { \eta _ { 1^\prime } } = { \mathcal{d}_{2^\prime}}{\phi _ 3 } - { \phi _ 1},$$\end{document } 48\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 2 } = { \mathcal{d}_1}{\phi _ 3 } - { \phi _ 2},\quad \quad { \eta _ { 2^\prime } } = { \mathcal{d}_{3^\prime}}{\phi _ 1 } - { \phi _ 2},$$\end{document } 49\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 3 } = { \mathcal{d}_2}{\phi _ 1 } - { \phi _ 3},\quad \quad { \eta _ { 3^\prime } } = { \mathcal{d}_{1^\prime}}{\phi _ 2 } - { \phi _ 3},$$\end{document } where the i , i = 1 , 2 , 3 measurements are as given in eq . the new tdi combinations are chosen in such a way so as to retain only one of the three noises i , i = 1 , 2 , 3 , if possible . in this way we can then implement an iterative procedure based on the use of these basic combinations and of time - delay operators , to cancel the laser noises after dropping terms that are quadratic in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\dot l / c$\end{document } or linear in the accelerations . this iterative time - delay method , to first order in the velocity , is illustrated abstractly as follows . given a function of time = (t ) , time delay by li is now denoted either with the standard comma notation or by applying the delay operator \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i}$\end{document } introduced in the previous section 4 , 50\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\mathcal{d}_i}\psi = { \psi _ { , i } } \equiv \psi ( t - { l_i}(t)){.}$$\end{document } we then impose a second time delay li(t ) : 51\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \mathcal d}_j}{{\mathcal d}_i}\psi = { \psi _ { ; ij } } \equiv \psi ( t - { l_j}(t ) - { l_i}(t - { l_j}(t)))\quad \,\ , } \\ { \quad \quad \quad \quad \quad \simeq \psi ( t - { l_j}(t ) - { l_i}(t ) + { { \dot l}_i}(t){l_j } ) } \\ { \quad \quad \quad \quad \ , \simeq { \psi _ { , ij } } + { { \dot \psi}_{,ij}}{{\dot l}_i}{l_j}.\quad \quad \quad \quad \quad } \\ \end{array}$$\end{document } a third time delay lk(t ) gives 52\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { \mathcal{d}_k}{\mathcal{d}_j}{\mathcal{d}_i}\psi = { \psi _ { ; ijk } } = \psi ( t - { l_k}(t ) - { l_j}(t - { l_k}(t ) ) - { l_i}(t - { l_k}(t ) - { l_j}(t - { l_k}(t ) ) ) ) } \\ { \simeq { \psi _ { , ijk } } + { { \dot \psi}_{,ijk}}\left [ { { { \dot l}_i}({l_j } + { l_k } ) + { { \dot l}_j}{l_k } } \right],\quad \quad \;\ ; } \\ \end{array}$$\end{document } and so on , recursively ; each delay generates a first - order correction proportional to its rate of change times the sum of all delays coming after it in the subscripts . commas have now been replaced with semicolons , to remind us that we consider moving arrays . when the sum of these corrections to the terms of a data combination vanishes , the combination is called flex - free . also , note that each delay operator \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i}$\end{document } has a unique inverse \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d_i^{- 1}$\end{document } , whose expression can be derived by requiring that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d_i^{- 1}{{\mathcal d}_i } = i$\end{document } , and neglecting quadratic and higher order velocity terms . its action on a time series (t ) is 53\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d_i^{- 1}\psi ( t ) \equiv \psi ( t + { l_i}(t + { l_i})){.}$$\end{document } note that this is not like an advance operator one might expect , since it advances not by li(t ) but rather li(t + li ) . the unequal - arm michelson combination relies on the four measurements 1 , 1 , 2 , and 3 . note that the two combinations 1 + 2,3 , 1 + 3,2 represent the two synthesized two - way data measured onboard spacecraft 1 , and can be written in the following form ( see eqs . ( 47 ) , ( 48 ) , and ( 49 ) for deriving the following synthesized two - way measurements ) 54\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 1 } + { \eta _ { 2^\prime,3 } } = ( { \mathcal{d}_3}{\mathcal{d}_{3^\prime } } - i){\phi _ 1},$$\end{document } 55\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ { { 1^\prime } } } + { \eta _ { 3,{2^\prime } } } = ( { \mathcal{d}_{{2^\prime}}}{\mathcal{d}_2 } - i){\phi _ 1},$$\end{document } where is the identity operator . since in the stationary case any pairs of these operators commute , i.e. , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i}{{\mathcal d}_{{j^\prime } } } - { { \mathcal d}_{{j^\prime}}}{{\mathcal d}_i } = 0$\end{document } , from eqs . ( 54 ) and ( 55 ) it is easy to derive the following expression for the unequal - arm interferometric combination x which eliminates 1 : 56\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x = [ { \mathcal{d}_{{2^\prime}}}{\mathcal{d}_2 } - i]({\eta _ 1 } + { \eta _ { { 2^\prime},3 } } ) - [ ( { \mathcal{d}_3}{\mathcal{d}_{{3^\prime } } } - i)]({\eta _ { { 1^\prime } } } + { \eta _ { 3,{2^\prime}}}){.}$$\end{document } if , on the other hand , the time - delays depend on time , the expression of the unequal - arm michelson combination above no longer cancels 1 . in order to derive the new expression for the unequal - arm interferometer that accounts for flexing , let us first consider the following two combinations of the one - way measurements entering into the x observable given in eq . ( 56 ) : 57\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[({\eta _ { { 1^\prime } } } + { \eta _ { 3;{2^\prime } } } ) + { ( { \eta _ 1 } + { \eta _ { { 2^\prime};3}})_{;{{22}^\prime } } } ] = [ { d_{{2^\prime}}}{d_2}{d_3}{d_{{3^\prime } } } - i]{\phi _ 1},$$\end{document } 58\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[({\eta _ 1 } + { \eta _ { { 2^\prime};3 } } ) + { ( { \eta _ { { 1^\prime } } } + { \eta _ { 3;{2^\prime}}})_{;{3^\prime}3 } } ] = [ { d_3}{d_{{3^\prime}}}{d_{{2^\prime}}}{d_2 } - i]{\phi _ 1}{.}$$\end{document } using eqs . ( 57 ) and ( 58 ) , we can use the delay technique again to finally derive the following expression for the new unequal - arm michelson combination x1 that accounts for the flexing effect : 59\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { x_1 } = [ { d_{{2^\prime}}}{d_2}{d_3}{d_{{3^\prime } } } - i][({\eta _ 1 } + { \eta _ { { 2^\prime};{3^\prime } } } ) + { { ( { \eta _ { { 1^\prime } } } + { \eta _ { 3;{2^\prime}}})}_{;{3^\prime}3}}]\quad \quad \quad } \\ { - [ { d_3}{d_{{3^\prime}}}{d_{{2^\prime}}}{d_2 } - i][({\eta _ { { 1^\prime } } } + { \eta _ { 3,\cdot{2^\prime } } } ) + { { ( { \eta _ 1 } + { \eta _ { { 2^\prime};3}})}_{;{{22}^\prime } } } ] . } \\ \end{array}$$\end{document } as usual , x2 and x3 are obtained by cyclic permutation of the spacecraft indices . this expression is readily shown to be laser - noise - free to first order of spacecraft separation velocities \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\dot l_i}$\end{document } : it is flex - free . in the above section 5.1 , we have used the same symbol x for the unequal - arm michelson combination for both the rotating ( i.e. , constant delay times ) and stationary cases . this emphasizes that , for this tdi combination ( and , as we will see below , also for all the combinations including only four links ) the forms of the equations do not change going from systems at rest to the rotating case . one needs only distinguish between the time - of - flight variations in the clockwise and counter - clockwise senses ( primed and unprimed delays ) . in the case of the sagnac variables ( , , , ) , however , this is not the case as it is easy to understand on simple physical grounds . in the case of for instance , light originating from spacecraft 1 is simultaneously sent around the array on clockwise and counter - clockwise loops , and the two returning beams are then recombined . if the array is rotating , the two beams experience a different delay ( the sagnac effect ) , preventing the noise 1 from canceling in the combination . in order to find the solution to this problem let us first rewrite in such a way to explicitly emphasize what it does : attempts to remove the same fluctuations affecting two beams that have been made to propagated clockwise and counter - clockwise around the array , 60\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\alpha = [ { \eta _ { { 1^\prime } } } + { \mathcal{d}_{{2^\prime}}}{\eta _ { { 3^\prime } } } + { \mathcal{d}_{{1^\prime}}}{\mathcal{d}_{{2^\prime}}}{\eta _ { { 2^\prime } } } ] - [ { \eta _ 1 } + { \mathcal{d}_3}{\eta _ 2 } + { \mathcal{d}_1}{\mathcal{d}_3}{\eta _ 2}],$$\end{document } where we have accounted for clockwise and counter - clockwise light delays . it is straight - forward to verify that this combination no longer cancels the laser and optical bench noises . if , however , we expand the two terms inside the square - brackets on the right - hand side of eq . ( 60 ) we find that they are equal to 61\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{\eta _ { { 1^\prime } } } + { \mathcal{d}_{{2^\prime}}}{\eta _ { { 3^\prime } } } + { \mathcal{d}_{{1^\prime}}}{\mathcal{d}_{{2^\prime}}}{\eta _ { { 2^\prime } } } ] = [ { \mathcal{d}_{{2^\prime}}}{\mathcal{d}_{{1^\prime}}}{\mathcal{d}_{{3^\prime } } } - i]{\phi _ 1}$$\end{document } 62\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{\eta _ 1 } + { \mathcal{d}_3}{\eta _ 2 } + { \mathcal{d}_1}{\mathcal{d}_3}{\eta _ 2 } ] = [ { \mathcal{d}_3}{\mathcal{d}_1}{\mathcal{d}_2 } - i]{\phi _ 1}{.}$$\end{document } if we now apply our iterative scheme to the combinations given in eq . ( 62 ) we finally get the expression for the sagnac combination 1 that is unaffected by laser noise in presence of rotation , 63\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\alpha _ 1 } = [ { \mathcal{d}_3}{\mathcal{d}_1}{\mathcal{d}_2 } - i][{\eta _ { { 1^\prime } } } + { \mathcal{d}_{{2^\prime}}}{\eta _ { { 3^\prime } } } + { \mathcal{d}_{{1^\prime}}}{\mathcal{d}_{{2^\prime}}}{\eta _ { { 2^\prime } } } ] - [ { \mathcal{d}_{{2^\prime}}}{\mathcal{d}_{{1^\prime}}}{\mathcal{d}_{{3^\prime } } } - i][{\eta _ 1 } + { \mathcal{d}_3}{\eta _ 2 } + { \mathcal{d}_1}{\mathcal{d}_3}{\eta _ 2}]{.}$$\end{document } if the delay - times are also time - dependent , we find that the residual laser noise remaining into the combination 1 is actually equal to 64\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\dot \phi _ { 1,{{1231}^\prime}{2^\prime}{3^\prime}}}\left [ { \left({{{\dot l}_1 } + { { \dot l}_2 } + { { \dot l}_3 } } \right)\left({l_1^\prime + l_2^\prime + l_3^\prime } \right ) - \left({\dot l_1^\prime + \dot l_2^\prime + \dot l_3^\prime } \right)({l_1 } + { l_2 } + { l_3 } ) } \right]{.}$$\end{document } fortunately , although first order in the relative velocities , the residual is small , as it involves the difference of the clockwise and counter - clockwise rates of change of the propagation delays on the same circuit . for lisa , the remaining laser phase noises in i , i = 1 , 2 , 3 , are several orders of magnitude below the secondary noises . in the case of , however , the rotation of the array breaks the symmetry and therefore its uniqueness . however , there still exist three generalized tdi laser - noise - free data combinations that have properties very similar to , and which can be used for the same scientific purposes . these combinations , which we call ( 1 , 2 , 3 ) , can be derived by applying again our time - delay operator approach . let us consider the following combination of the i , i measurements , each being delayed only once : 65\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ { 3,3 } } - { \eta _ { { 3^\prime},3 } } + { \eta _ { 1,{1^\prime } } } = [ { d_3}{d_2 } - { d_{{1^\prime}}}]{\phi _ 1},$$\end{document } 66\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ { { 1^\prime},1 } } - { \eta _ { 2,{2^\prime } } } + { \eta _ { { 2^\prime},{2^\prime } } } = [ { d_{{3^\prime}}}{d_{{2^\prime } } } - { d_1}]{\phi _ 1},$$\end{document } where we have used the commutativity property of the delay operators in order to cancel the 2 and 3 terms . since both sides of the two equations above contain only the 1 noise , 1 is found by the following expression : 67\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\zeta _ 1 } = [ { d_{{3^\prime}}}{d_{{2^\prime } } } - { d_1}]({\eta _ { 3,3 } } - { \eta _ { { 3^\prime},3 } } + { \eta _ { 1,{1^\prime } } } ) - [ { d_2}{d_3 } - { d_{{1^\prime}}}]({\eta _ { { 1^\prime},1 } } - { \eta _ { 2,{2^\prime } } } + { \eta _ { { 2^\prime},{2^\prime}}}){.}$$\end{document } if the light - times in the arms are equal in the clockwise and counter - clockwise senses ( e.g. , no rotation ) there is no distinction between primed and unprimed delay times . in this case , 1 is related to our original symmetric sagnac by 1 = ,23 ,1 . thusm for the lisa case ( arm length difference < 1% ) , the snr of 1 will be the same as the snr of . if the delay - times also change with time , the perfect cancellation of the laser noises is no longer achieved in the ( 1 , 2 , 3 ) combinations . however , it has been shown in that the magnitude of the residual laser noises in these combinations are significantly smaller than the lisa secondary system noises , making their effects entirely negligible . the expressions for the monitor , beacon , and relay combinations , accounting for the rotation and flexing of the lisa array , have been derived in the literature by applying the time - delay iterative procedure highlighted in this section . we present a mathematical formulation of the second - generation tdi , which generalizes the one presented in section 4 for stationary lisa . although a full solution as in the case of stationary lisa seems difficult to obtain , significant progress can be made . there is , however , a case in between the 1st and 2nd generation tdi , called modified first - generation tdi , in which only the sagnac effect is considered [ 7 , 44 ] . in this case the up - down links are unequal while the delay - times remain constant . the mathematical formulation of section 4 can be extended in a straight - forward way where now the six time - delays \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_{{i^\prime}}}$\end{document } must be taken into account . the corresponding module of syzygies can be constructed over this larger polynomial ring . when the arms are allowed to flex , that is , the operators themselves are functions of time , the operators no longer commute . since lot of the discussion has been covered in the previous subsections we just describe the algebraic formulation . the equation eq . ( 26 ) generalizes in two ways : ( 1 ) we need to consider now six operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_{{i^\prime}}}$\end{document } , and ( 2 ) we need to take into account the non - commutativity of the operators the order of the operators is important . accordingly eq . ( 26 ) generalizes to , 68\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } + q_1^\prime - q_2^\prime { \mathcal{d}_{{3^\prime } } } - { q_3}{\mathcal{d}_2 } = 0 , } \\ { { q_2 } + q_2^\prime - q_3^\prime { \mathcal{d}_{{1^\prime } } } - { q_1}{\mathcal{d}_3 } = 0 , } \\ { { q_3 } + q_3^\prime - q_1^\prime { \mathcal{d}_{{2^\prime } } } - { q_2}{\mathcal{d}_1 } = 0 . } \\ \end{array}$$\end{document } eliminating q1 and q2 from the three eqs . ( 68 ) while respecting the order of the variables we get : 69\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${q_3}(1 - { \mathcal{d}_2}{\mathcal{d}_3}{\mathcal{d}_1 } ) + q_1^\prime ( { \mathcal{d}_{{2^\prime } } } - { \mathcal{d}_3}{\mathcal{d}_1 } ) + q_2^\prime ( { \mathcal{d}_{{3^\prime}}}{\mathcal{d}_3 } - 1){\mathcal{d}_1 } + q_3^\prime ( { \mathcal{d}_{{1^\prime}}}{\mathcal{d}_1 } - 1 ) = 0{.}$$\end{document } the polynomial ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}({{\mathcal d}_i},{{\mathcal d}_{{i^\prime } } } ) \equiv { \mathcal k}$\end{document } , is non - commutative , of polynomials in the six variables \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i},{{\mathcal d}_{{i^\prime}}}$\end{document } and coefficients in the rational field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}$\end{document}. the polynomial vectors ( qi , qi ) satisfying the above equations form a left module over \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal k}$\end{document}. a left module means that one can multiply a solution ( qi , qi ) from the left by any polynomial in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal k}$\end{document } , then it is also a solution to the eqs . ( 68 ) and , therefore , in the module the module of noise - free tdi observables . for details see . if we follow on the lines of the commutative case , the first step would be to find a grbner basis for the ideal generated by the coefficients appearing in eq . ( 69 ) , namely , the set of polynomials \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{1 - { { \mathcal d}_2}{{\mathcal d}_3}{{\mathcal d}_1},{{\mathcal d}_{{2^\prime } } } - { { \mathcal d}_3}{{\mathcal d}_1},({{\mathcal d}_{{3^\prime}}}{{\mathcal d}_3 } - 1){{\mathcal d}_1},{{\mathcal d}_{{1^\prime}}}{{\mathcal d}_1 } - 1\ } $ \end{document}. although we may be able to apply non - commutative grbner basis methods , the general solution seems quite difficult . however , simplifications are possible because of the inherent symmetries in the problem and so the ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal k}$\end{document } can be quotiented by a certain ideal , simplifying the algebraic problem . we describe below how this can achieved with the help of certain commutators . in general , a commutator of two operators x , y is defined as the operator [ x , y ] = xy yx . in our situation x and y are strings of operators built up of the operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${d_1},{d_2},{d_3},{d_{{1^\prime}}},{d_{{2^\prime}}},{d_{{3^\prime}}}$\end{document}. for example , in the sagnac combination the following commutator occurs : 70\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{d_1}{d_2}{d_3},{d_{{1^\prime}}}{d_{{2^\prime}}}{d_{{3^\prime } } } ] \equiv { d_1}{d_2}{d_3}{d_{{1^\prime}}}{d_{{2^\prime}}}{d_{{3^\prime } } } - { d_{{1^\prime}}}{d_{{2^\prime}}}{d_{{3^\prime}}}{d_1}{d_2}{d_3}{.}$$\end{document } here x = d1 d2 d3 and y = d1 d2 d3. this commutator leads to the residual noise term given in eq . ( 64 ) and which happens to be small . in the context of the reasonably optimized model of lisa we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l \sim { 10^{- 6}}{\rm{m/}}{{\rm{s}}^2}$\end{document } and thus , even if one considers say 20 successive optical paths , that is , about t 330 s of light travel time , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\delta { t^2}\ddot l \sim 0.1\;{\rm{m}}$\end{document}. this is well below few meters and thus can be neglected in the residual laser noise computation . moreover , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\dot l^2}$\end{document } terms ( and higher order ) can be dropped since they are of the order of 10 ( they come with a factor 1/c ) , which is much smaller than 1 part in 10 , which is the level at which the laser frequency noise must be canceled . thus , we keep terms only to the first degree in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\dot l$\end{document } and also neglect higher time derivative terms in l. the result for the sagnac combination can be generalized . in order to simplify notation we write xk or ym for the time - delay operators , where k , m = 1 , 2 , , n and n 2 , that is , xk or ym are any of the operators d1 , d2 , d3 , d1 , d2 , d3. then a commutator is : 71\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{x_1}{x_2 } \ldots { x_n},\;{y_1}{y_2 } \ldots { y_n } ] = { x_1}{x_2 } \ldots { x_n}{y_1}{y_2 } \ldots { y_n } - { y_1}{y_2 } \ldots { y_n}{x_1}{x_2 } \ldots { x_n}{.}$$\end{document } up to the order of approximation we are working in we compute the effect of the commutator on the phase (t ) : 72\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { [ { x_1}{x_2 } \ldots { x_n},\;{y_1}{y_2 } \ldots { y_n}]\phi ( t)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { = \left({\sum\limits_{k = 1}^n { { l_{{x_k } } } } \sum\limits_{m = 1}^n { { { \dot l}_{{y_m } } } } - \sum\limits_{m = 1}^n { { l_{{y_m } } } } \sum\limits_{k = 1}^n { { { \dot l}_{{x_k } } } } } \right)\dot \phi \left({t - \sum\limits_{k = 1}^n { { l_{{x_k } } } } - \sum\limits_{m = 1}^n { { l_{{y_m } } } } } \right ) . } \\ \end{array}$$\end{document } note that the lhs acts on (t ) , while the right - hand side multiplies \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\dot \phi $ \end{document } at an appropriately delayed time . for the sagnac combination also the notation on the rhs is obvious : if for some k , we have , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${x_k } = { { \mathcal d}_{{2^\prime}}}$\end{document } say , then \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${l_{{x_k } } } = { l\prime_2}$\end{document } and so on ; the same holds for ym for a given m. from this equation it immediately follows that if the operators y1 , y2 , , yn are a permutation of the operators x1 , x2 , , xn , then the commutator , 73\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{x_1}{x_2 } \ldots { x_n},\;{y_1}{y_2 } \ldots { y_n } ] = 0,$$\end{document } up to the order we are working in . if y1 yn is a permutation of x1 xn then both polynomials trace the same links , except that the nodes ( spacecraft ) of the links are taken in different orders . if the armlengths were constant , the path - lengths would be identical and the commutator would be zero . but here , by neglecting \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l$\end{document } terms and those of higher orders , we have effectively assumed that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\dot l_s}$\end{document } are constant , so the increments also cancel out , resulting in a vanishing commutator . these vanishing commutators ( in the approximation we are working in ) can be used to simplify the algebra . we first construct the ideal \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } generated by the commutators such as those given by eq . . then we quotient the ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal k}$\end{document } by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } , thereby constructing a smaller ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal k}/{\mathcal u } \equiv \bar { \mathcal k}$\end{document}. this ring is smaller because it has fewer distinct terms in a polynomial . although , this reduces the complexity of the problem , a full solution to the tdi problem is still lacking . in the following section 5.4 , we will consider the case where we have only two arms of lisa in operation , that is one arm is nonfunctional . we must envisage the possibility that not all optical links of lisa can be operating at all times for various reasons like technical failure for instance or even the operating costs . an analysis covering the scientific capabilities achievable by lisa in the eventuality of loosing one and two links has been discussed in . here we obtain the tdi combinations when one entire arm becomes dysfunctional . we arbitrarily choose the non - functional arm to be the one connecting s / c 2 and s / c 3 . this means from our labeling that the polynomials are now restricted to only the four operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_2},{{\mathcal d}_{{2^\prime}}},{{\mathcal d}_3},{{\mathcal d}_{{3^\prime}}}$\end{document } and we can set the polynomials q2 = q3 = 0 . ( 68 ) considerably because the last two equations reduce to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$q_2^\prime = { q_1}{{\mathcal d}_3}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${q_3 } = q_1^\prime{{\mathcal d}_{{2^\prime}}}$\end{document}. substituting these in the first equation gives just one equation : 74\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${q_1}(1 - { \mathcal{d}_3}{\mathcal{d}_{{3^\prime } } } ) + q_1^\prime ( 1 - { \mathcal{d}_{{2^\prime}}}{\mathcal{d}_2 } ) = 0,$$\end{document } if we can solve this equation for q1 , q1 then the full polynomial vector can be obtained because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$q_2^\prime = { q_1}{{\mathcal d}_3}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${q_3 } = q_1^\prime{{\mathcal d}_{{2^\prime}}}$\end{document}. it is clear that solutions are of the michelson type . also notice that the coefficients of this equation has the operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a = { { \mathcal d}_3}{{\mathcal d}_{{3^\prime}}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$b = { { \mathcal d}_{{2^\prime}}}{{\mathcal d}_2}$\end{document } occurring in them . so the solutions q1 , q1 too will be in terms of a and b only . physically , the operators a and b correspond to round trips . this solution in terms of a , b is : 75\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } = 1 - b - ba + a{b^2},\quad \ ; } \\ { q_1^\prime = - ( 1 - a - ab + b{a^2 } ) . } \\ \end{array}$$\end{document } writing , 76\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta = { q_1}(1 - a ) + q_1^\prime ( 1 - b),$$\end{document } we get for eq . ( 75 ) , = [ ba , ab ] , which is a commutator that vanishes since ab is a permutation of ba . thus , it is an element of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } and eq . what we would like to emphasize is that there are more solutions of this type in fact there are infinite number of such solutions . note that these are of degree 3 in a and b. the commutator corresponding to this solution is = [ ba , ab ] = bab aba and is of degree 4 . one solution is : 77\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } = 1 - b - ba + a{b^2 } - b{a^2}b + a{b^2}ab + a{b^2}aba - b{a^2}ba{b^2},\quad \ ; } \\ { q_1^\prime = - ( 1 - a - ab + b{a^2 } - a{b^2}a + b{a^2}ba + b{a^2}bab - a{b^2}ab{a^2 } ) , } \\ \end{array}$$\end{document } whose commutator is : 78\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta = \;[ab2a,\;b{a^2}b]{.}$$\end{document } the second solution is : 79\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } = 1 + a - { b^2 } - { b^2}a - { b^2}{a^2 } - { b^2}{a^3 } + { a^2}{b^4 } + { a^2}{b^4}a\quad } \\ { = ( 1 - { b^2 } - { b^2}{a^2 } + { a^2}{b^4})(1 + a),\quad \quad \quad \quad \quad \quad \ ; } \\ { q_1^\prime = - ( 1 + b - { a^2 } - { a^2}b - { a^2}{b^2 } - { a^2}{b^3 } + { b^2}{a^4 } + { b^2}{a^4}b ) } \\ { = - ( 1 - { a^2 } - { a^2}{b^2 } + { b^2}{a^4})(1 + b),\quad \quad \quad \quad \quad \;\ ; } \\ \end{array}$$\end{document } whose commutator is = [ b a , a a ] . this solution is given by : 80\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } = 1 - b + ab - bab - baba + aba{b^2 } - bab{a^2}b + aba{b^2}ab,\quad \;\ ; } \\ { q_1^\prime = - ( 1 - a + ba - aba - abab + bab{a^2 } - aba{b^2}a + bab{a^2}ba ) . } \\ if we call the degree of the commutators as 4 where n = 1 , 2 , , then the solutions q1 , q1 are of degree 4n 1 . the cases mentioned above , correspond to n = 1 and n = 2 . the general formula for the number of commutators of degree 4n is cn1 . so at n = 3 we have 10 commutators and so as many solutions q1 , q1 of degree 11 . these are the degrees of polynomials of q1 , q1 in the operators a , b. but for the full polynomial vector , which has q2 and q3 , we need to go over to the operators expressed in terms of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i},{{\mathcal d}_{{i^\prime}}}$\end{document}. then the degree of each of the q1 , q1 is doubled to 8n 2 , while q2 and q3 are each of degree 8n 1 . thus , for a general value of , the solution contains polynomials of maximum degree 8n 1 in the time - delay operators . from the mathematical point of view however the family of solutions is sufficiently rich , because we can form linear combinations of these solutions and they also are solutions . from the physical point of view , since terms in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\dot l^2}$\end{document } and higher orders have been neglected , a limit on the degree of the polynomial solutions arises . that is up to certain degree of the polynomials , we can safely assume the commutators to vanish . but as the degree of the polynomials increases it is not possible to neglect these higher order terms any longer and then such a limit becomes important . the limit is essentially set by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l$\end{document}. we now investigate this limit and make a very rough estimate of it . as mentioned earlier , the lisa model in gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l \sim { 10^{- 6}}{\rm{m/}}{{\rm{s}}^2}$\end{document}. from \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l$\end{document } we compute the error in l , namely , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\delta l \sim { 1 \over 2}\delta { t^2}\ddot l$\end{document}. if we allow the error to be no more than say 10 meters , then we find t 4500 s. since each time - delay is about 16.7 s for lisa , the number of successive time - delays is about 270 . if we set the limit more stringently at l 1 m , then the highest degree of the polynomial reduces to about 80 , which means one can go up to n = 10 . thus , there are a large number of tdi observables available to do the physics . some remarks are in order : a geometric combinatorial approach was adopted in where several solutions were presented . the algebraic approach has the advantage of easy manipulation of data streams , although some geometrical insight could be at a premium.another important aspect is the gw response of such tdi observables . the gw response to a tdi observable may be calculated in the simplest way by assuming equal arms ( the possible differences in lengths would be sensitive to frequencies outside the lisa bandwidth ) . this leads in the fourier domain to polynomials in the same phase factor from which the signal to noise ratio can be found . a comprehensive and generic treatment of the responses of second - generation tdi observables can be found in . the algebraic approach has the advantage of easy manipulation of data streams , although some geometrical insight could be at a premium . the gw response to a tdi observable may be calculated in the simplest way by assuming equal arms ( the possible differences in lengths would be sensitive to frequencies outside the lisa bandwidth ) . this leads in the fourier domain to polynomials in the same phase factor from which the signal to noise ratio can be found . a comprehensive and generic treatment of the responses of second - generation tdi observables can be found in . all the above interferometric combinations have been shown to individually have rather different sensitivities , as a consequence of their different responses to gravitational radiation and system noises . since lisa has the capability of simultaneously observing a gravitational - wave signal with many different interferometric combinations ( all having different antenna patterns and noises ) , we should no longer regard lisa as a single detector system but rather as an array of gravitational - wave detectors working in coincidence . this suggests that the lisa sensitivity could be improved by optimally combining elements of the tdi space . before proceeding with this idea , however , let us consider again the so - called second - generation tdi sagnac observables : ( 1 , 2 , 3 ) . the expressions of the gravitational - wave signal and the secondary noise sources entering into 1 will in general be different from those entering into , the corresponding sagnac observable derived under the assumption of a stationary lisa array [ 2 , 15 ] . however , the other remaining , secondary noises in lisa are so much smaller , and the rotation and systematic velocities in lisa are so intrinsically small , that index permutation may still be done for them . it is therefore easy to derive the following relationship between the signal and secondary noises in 1 , and those entering into the stationary tdi combination [ 45 , 58 ] , 81\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\alpha _ 1}\;(t)\ ; \simeq \alpha ( t ) - \alpha ( t - { l_1 } - { l_2 } - { l_3}),$$\end{document } where li , i = 1 , 2 , 3 , are the unequal - arm lengths of the stationary lisa array . equation ( 81 ) implies that any data analysis procedure and algorithm that will be implemented for the second - generation tdi combinations can actually be derived by considering the corresponding first - generation tdi combinations . for this reason , from now on we will focus our attention on the gravitational - wave responses of the first - generation tdi observables ( , , , ) . as a consequence of these considerations , we can still regard ( , , , ) as the generators of the tdi space , and write the most general expression for an element of the tdi space , (f ) , as a linear combination of the fourier transforms of the four generators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\tilde \alpha , \tilde \beta , \tilde \gamma , \tilde \zeta)$\end{document } , 82\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\eta ( f ) \equiv { a_1}(f,\vec \lambda)\tilde \alpha ( f ) + { a_2}(f,\vec \lambda)\tilde \beta ( f ) + { a_3}(f,\vec \lambda)\tilde \gamma ( f ) + { a_4}(f,\vec \lambda)\tilde \zeta ( f),$$\end{document } where the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{a_i}(f,\vec \lambda)\ } _ { i = 1}^4$\end{document } are arbitrary complex functions of the fourier frequency f , and of a vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\vec \lambda $ \end{document } containing parameters characterizing the gravitational - wave signal ( source location in the sky , waveform parameters , etc . ) and the noises affecting the four responses ( noise levels , their correlations , etc . ) . for a given choice of the four functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{a_i}\ } _ { i = 1,}^4\eta $ \end{document } gives an element of the functional space of interferometric combinations generated by ( , , , ) . our goal is therefore to identify , for a given gravitational - wave signal , the four functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{a_i}\ } _ { i = 1}^4$\end{document } that maximize the signal - to - noise ratio \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_\eta ^2$\end{document } of the combination , 83\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{snr}}_\eta ^2 = \int\nolimits_{{f_1}}^{{f_{\rm{u } } } } { { { { { \left\vert { { a_1}{{\tilde \alpha}_{\rm{s } } } + { a_2}{{\tilde \beta}_{\rm{s } } } + { a_3}{{\tilde \gamma}_{\rm{s } } } + { a_4}{{\tilde \zeta}_{\rm{s } } } } \right\vert}^2 } } \over { \left\langle { { { \left\vert { { a_1}{{\tilde \alpha}_{\rm{n } } } + { a_2}{{\tilde \beta}_{\rm{n } } } + { a_3}{{\tilde \gamma}_{\rm{n } } } + { a_4}{\zeta _ { \rm{n } } } } \right\vert}^2 } } \right\rangle } } } df{.}$$\end{document } in eq . ( 83 ) the subscripts s and n refer to the signal and the noise parts of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\tilde \alpha , \tilde \beta , \tilde \gamma , \tilde \zeta)$\end{document } , respectively , the angle brackets represent noise ensemble averages , and the interval of integration ( f1 , fu ) corresponds to the frequency band accessible by lisa . before proceeding with the maximization of the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_\eta ^2$\end{document } we may notice from eq . ( 44 ) that the fourier transform of the totally symmetric sagnac combination , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\tilde \zeta $ \end{document } , multiplied by the transfer function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$1 - { e^{2\pi if({l_1 } + { l_2 } + l3)}}$\end{document } can be written as a linear combination of the fourier transforms of the remaining three generators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\tilde \alpha , \tilde \beta , \tilde \gamma)$\end{document}. since the signal - to - noise ratio of and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(1 - { e^{2\pi if({l_1 } + { l_2 } + { l_3})}})\eta $ \end{document } are equal , we may conclude that the optimization of the signal - to - noise ratio of can be performed only on the three observables , , . this implies the following redefined expression for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_\eta ^2$\end{document } : 84\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{snr}}_\eta ^2 = \int\nolimits_{{f_1}}^{{f_{\rm{u } } } } { { { { { \left\vert { { a_1}{{\tilde \alpha}_{\rm{s } } } + { a_2}{{\tilde \beta}_{\rm{s } } } + { a_3}{{\tilde \gamma}_{\rm{s } } } } \right\vert}^2 } } \over { \left\langle { { { \left\vert { { a_1}{{\tilde \alpha}_{\rm{n } } } + { a_2}{{\tilde \beta}_{\rm{n } } } + { a_3}{{\tilde \gamma}_{\rm{n } } } } \right\vert}^2 } } \right\rangle } } } df{.}$$\end{document } the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_\eta ^2$\end{document } can be regarded as a functional over the space of the three complex functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{a_i}\ } _ { i = 1}^3$\end{document } , and the particular set of complex functions that extremize it can of course be derived by solving the associated set of euler - lagrange equations . in order to make the derivation of the optimal snr easier , let us first denote by x and x the two vectors of the signals \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\tilde \alpha _ { \rm{s}}},{\tilde \beta _ { \rm{s}}},{\tilde \gamma _ { \rm{s}}})$\end{document } and the noises \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\tilde \alpha let us also define a to be the vector of the three functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{a_i}\ } _ { i = 1}^3$\end{document } , and denote with c the hermitian , non - singular , correlation matrix of the vector random process xn , 85\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${({\bf{c}})_{rt } } \equiv \left\langle { { \rm{x}}_r^{(n)}{\rm{x}}_t^{(n)\ast } } \right\rangle { .}$$\end{document } if we finally define ( a)ij to be the components of the hermitian matrix \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{x}}_i^{({\rm{s}})}{\rm{x}}_j^{({\rm{s } } ) \ast}$\end{document } , we can rewrite \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_\eta ^2$\end{document } in the following form , 86\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{snr}}_\eta ^2 = \int\nolimits_{{f_1}}^{{f_{\rm{u } } } } { { { { { \bf{a}}_i}{{\bf{a}}_{ij}}{\bf{a}}_j^\ast } \over { { { \bf{a}}_r}{{\bf{c}}_{rt}}{\bf{a}}_t^\ast } } } df,$$\end{document } where we have adopted the usual convention of summation over repeated indices . since the noise correlation matrix c is non - singular , and the integrand is positive definite or null , the stationary values of the signal - to - noise ratio will be attained at the stationary values of the integrand , which are given by solving the following set of equations ( and their complex conjugated expressions ) : 87\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\partial \over { \partial { { \bf{a}}_k}}}\left [ { { { { { \bf{a}}_i}{{\bf{a}}_{ij}}{\bf{a}}_j^\ast } \over { { { \bf{a}}_r}{{\bf{c}}_{rt}}{\bf{a}}_t^\ast } } } \right ] = 0,\quad \quad k = 1,2,3{.}$$\end{document } after taking the partial derivatives , eq . ( 87 ) can be rewritten in the following form , 88\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${({{\bf{c}}^{- 1}})_{ir}}{({\bf{a}})_{rj}}{({{\bf{a}}^\ast})_j } = \left [ { { { { { \bf{a}}_p}{{\bf{a}}_{pq}}{\bf{a}}_q^\ast } \over { { { \bf{a}}_l}{{\bf{c}}_{lm}}{\bf{a}}_m^\ast } } } \right]{({{\bf{a}}^\ast})_i},\quad \quad i = 1,2,3,$$\end{document } which tells us that the stationary values of the signal - to - noise ratio of are equal to the eigenvalues of the the matrix c a. the result in eq . ( 87 ) is well known in the theory of quadratic forms , and it is called rayleigh s principle [ 36 , 42 ] . in order now to identify the eigenvalues of the matrix c a , we first notice that the 3 3 matrix a has rank 1 . this implies that the matrix c a has also rank 1 , as it is easy to verify . therefore two of its three eigenvalues are equal to zero , while the remaining non - zero eigenvalue represents the solution we are looking for . the analytic expression of the third eigenvalue can be obtained by using the property that the trace of the 3 3 matrix c a is equal to the sum of its three eigenvalues , and in our case to the eigenvalue we are looking for . from these considerations we derive the following expression for the optimized signal - to - noise ratio \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_{\eta \;{\rm{opt}}}^2$\end{document } : 89\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{snr}}_{\eta \;{\rm{opt}}}^2 = \int\nolimits_{{f_1}}^{{f_{\rm{u } } } } { { \bf{x}}_i^{({\rm{s}})\ast } } { ( { { \bf{c}}^{- 1}})_{ij}}{\bf{x}}_j^{({\rm{s}})}df{.}$$\end{document } we can summarize the results derived in this section , which are given by eqs . ( 84 ) and ( 89 ) , in the following way : among all possible interferometric combinations lisa will be able to synthesize with its four generators , , , , the particular combination giving maximum signal - to - noise ratio can be obtained by using only three of them , namely ( , , ).the expression of the optimal signal - to - noise ratio given by eq . ( 89 ) implies that lisa should be regarded as a network of three interferometer detectors of gravitational radiation ( of responses ( , , ) ) working in coincidence [ 20 , 40 ] . among all possible interferometric combinations lisa will be able to synthesize with its four generators , , , , the particular combination giving maximum signal - to - noise ratio can be obtained by using only three of them , namely ( , , ) . ( 89 ) implies that lisa should be regarded as a network of three interferometer detectors of gravitational radiation ( of responses ( , , ) ) working in coincidence [ 20 , 40 ] . as an application of eq . ( 89 ) , here we calculate the sensitivity that lisa can reach when observing sinusoidal signals uniformly distributed on the celestial sphere and of random polarization . in order to calculate the optimal signal - to - noise ratio we will also need to use a specific expression for the noise correlation matrix c. as a simplification , we will assume the lisa arm lengths to be equal to their nominal value l = 16.67 s , the optical - path noises to be equal and uncorrelated to each other , and finally the noises due to the proof - mass noises to be also equal , uncorrelated to each other and to the optical - path noises . under these assumptions the correlation matrix becomes real , its three diagonal elements are equal , and all the off - diagonal terms are equal to each other , as it is easy to verify by direct calculation . the noise correlation matrix c is therefore uniquely identified by two real functions s and s in the following way : 90\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\bf{c } } = \left({\begin{array}{*{20}c } { { s_\alpha } } & { { s_{\alpha \beta } } } & { { s_{\alpha \beta } } } \\ { { s_{\alpha \beta } } } & { { s_\alpha } } & { { s_{\alpha \beta } } } \\ { { s_{\alpha \beta } } } & { { s_{\alpha \beta } } } & { { s_\alpha } } \\ \end{array } } \right){.}$$\end{document } the expression of the optimal signal - to - noise ratio assumes a rather simple form if we diagonalize this correlation matrix by properly choosing a new basis . there exists an orthogonal transformation of the generators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\tilde \alpha , \tilde \beta , \tilde \gamma)$\end{document } , which will transform the optimal signal - to - noise ratio into the sum of the signal - to - noise ratios of the transformed three interferometric combinations . the expressions of the three eigenvalues \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{\mu _ i}\ } _ { i = 1}^3$\end{document } ( which are real ) of the noise correlation matrix c can easily be found by using the algebraic manipulator mathematica , and they are equal to 91\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\mu _ 1 } = { \mu _ 2 } = { s_\alpha } - { s_{\alpha \beta}},\quad \quad { \mu _ 3 } = { s_\alpha } + 2{s_{\alpha \beta}}{.}$$\end{document } note that two of the three real eigenvalues , ( 1 , 2 ) , are equal . this implies that the eigenvector associated to 3 is orthogonal to the two - dimensional space generated by the eigenvalue 1 , while any chosen pair of eigenvectors corresponding to 1 will not necessarily be orthogonal . this inconvenience can be avoided by choosing an arbitrary set of vectors in this two - dimensional space , and by ortho - normalizing them . after some simple algebra , we have derived the following three ortho - normalized eigenvectors : 92\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\bf{v}}_1 } = { 1 \over { \sqrt 2}}(- 1,0,1)\quad \quad { { \bf{v}}_2 } = { 1 \over { \sqrt 6}}(1,\ ; - 2,1)\quad \quad { { \bf{v}}_3 } = { 1 \over { \sqrt 3}}(1,1,1){.}$$\end{document } equation ( 92 ) implies the following three linear combinations of the generators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\tilde \alpha , \tilde \beta , \tilde \gamma)$\end{document } : 93\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a = { 1 \over { \sqrt 2}}(\tilde \gamma - \tilde \alpha)\quad \quad e = { 1 \over { \sqrt 6}}\left({\tilde \alpha - 2\tilde \beta + \tilde \gamma } \right)\quad \quad t = { 1 \over { \sqrt 3}}\left({\tilde \alpha + \tilde \beta + \tilde \gamma } \right),$$\end{document } where a , e , and t are italicized to indicate that these are orthogonal modes . although the expressions for the modes a and e depend on our particular choice for the two eigenvectors ( v1 , v2 ) , it is clear from our earlier considerations that the value of the optimal signal - to - noise ratio is unaffected by such a choice . from eq . ( 93 ) it is also easy to verify that the noise correlation matrix of these three combinations is diagonal , and that its non - zero elements are indeed equal to the eigenvalues given in eq . ( 91 ) . in order to calculate the sensitivity corresponding to the expression of the optimal signal - to - noise ratio , we have proceeded similarly to what was done in [ 2 , 15 ] , and described in more detail in . we assume an equal - arm lisa ( l = 16.67 s ) , and take the one - sided spectra of proof mass and aggregate optical - path - noises ( on a single link ) , expressed as fractional frequency fluctuation spectra , to be \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$s_y^{{\rm{proof}}\,{\rm{mass } } } = 2.5 \times { 10^{- 48}}{[f/1\,{\rm{hz}}]^{- 2}}\,{\rm{h}}{{\rm{z}}^{- 1}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$s_y^{{\rm{optical}}\,{\rm{path } } } = 1.8 \times { 10^{- 37}}{[f/1\,{\rm{hz}}]^2}\,{\rm{h}}{{\rm{z}}^{- 1}}$\end{document } , respectively ( see [ 15 , 5 ] ) . we also assume that aggregate optical path noise has the same transfer function as shot noise . the optimum snr is the square root of the sum of the squares of the snrs of the three orthogonal modes ( a , e , t ) . to compare with previous sensitivity curves of a single lisa michelson interferometer , we construct the snrs as a function of fourier frequency for sinusoidal waves from sources uniformly distributed on the celestial sphere . to produce the snr of each of the ( a , e , t ) modes we need the gravitational - wave response and the noise response as a function of fourier frequency . we build up the gravitational - wave responses of the three modes ( a , e , t ) from the gravitational - wave responses of ( , , ) . for 7000 fourier frequencies in the 10 hz to 1 hz lisa band , we produce the fourier transforms of the gravitational - wave response of ( , , ) from the formulas in [ 2 , 56 ] . the averaging over source directions ( uniformly distributed on the celestial sphere ) and polarization states ( uniformly distributed on the poincar sphere ) is performed via a monte carlo method . from the fourier transforms of the ( , , ) responses at each frequency , we construct the fourier transforms of ( a , e , t ) . we then square and average to compute the mean - squared responses of ( a , e , t ) at that frequency from 10 realizations of ( source position , polarization state ) pairs . we adopt the following terminology : we refer to a single element of the module as a data combination , while a function of the elements of the module , such as taking the maximum over several data combinations in the module or squaring and adding data combinations belonging to the module , is called as an observable . the important point to note is that the laser frequency noise is also suppressed for the observable although it may not be an element of the module . the noise spectra of ( a , e , t ) are determined from the raw spectra of proof - mass and optical - path noises , and the transfer functions of these noises to ( a , e , t ) . using the transfer functions given in , the resulting spectra are equal to 94\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { s_a}(f ) = { s_e}(f ) = 16{{\sin}^2}(\pi fl)[3 + 2\cos ( 2\pi fl ) + \cos ( 4\pi fl)]s_y^{{\rm{proof}}\;{\rm{mass}}}(f)\quad \;\;\ ; } \\ { + 8{{\sin}^2}(\pi fl)[2 + \cos ( 2\pi fl)]s_y^{{\rm{optical}}\;{\rm{path}}}(f ) , } \\ \end{array}$$\end{document } 95\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_t}(f ) = 2{[1 + 2\cos ( 2\pi fl)]^2}[4{\sin ^2}(\pi fl)s_y^{{\rm{proof}}\;{\rm{mass } } } + s_y^{{\rm{optical}}\;{\rm{path}}}(f)]{.}$$\end{document } let the amplitude of the sinusoidal gravitational wave be h. the snr for , e.g. , a , snra , at each frequency f is equal to h times the ratio of the root - mean - squared gravitational - wave response at that frequency divided by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt { { s_a}(f)b } $ \end{document } , where b is the bandwidth conventionally taken to be equal to 1 cycle per year . finally , if we take the reciprocal of snra/ and multiply it by 5 to get the conventional snr = 5 sensitivity criterion , we obtain the sensitivity curve for this combination , which can then be compared against the corresponding sensitivity curve for the equal - arm michelson interferometer . in figure 7 we show the sensitivity curve for the lisa equal - arm michelson response ( snr = 5 ) as a function of the fourier frequency , and the sensitivity curve from the optimum weighting of the data described above : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$5h/\sqrt { { \rm{snr}}_a^2 + { \rm{snr}}_e^2 + { \rm{snr}}_t^2 } $ \end{document}. the snrs were computed for a bandwidth of 1 cycle / year . note that at frequencies where the lisa michelson combination has best sensitivity , the improvement in signal - to - noise ratio provided by the optimal observable is slightly larger than \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2 $ \end{document}. figure 7the lisa michelson sensitivity curve ( snr = 5 ) and the sensitivity curve for the optimal combination of the data , both as a function of fourier frequency . the integration time is equal to one year , and lisa is assumed to have a nominal armlength l = 16.67 s. the lisa michelson sensitivity curve ( snr = 5 ) and the sensitivity curve for the optimal combination of the data , both as a function of fourier frequency . the integration time is equal to one year , and lisa is assumed to have a nominal armlength l = 16.67 s. in figure 8 we plot the ratio between the optimal snr and the snr of a single michelson interferometer . in the long - wavelength limit , the snr improvement is \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2 $ \end{document}. for fourier frequencies greater than or about equal to 1/l , the snr improvement is larger and varies with the frequency , showing an average value of about \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 3 $ \end{document}. in particular , for bands of frequencies centered on integer multiples of 1/l , snrt contributes strongly and the aggregate snr in these bands can be greater than 2 . figure 8the optimal snr divided by the snr of a single michelson interferometer , as a function of the fourier frequency f. the sensitivity gain in the low - frequency band is equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2 $ \end{document } , while it can get larger than 2 at selected frequencies in the high - frequency region of the accessible band . the integration time has been assumed to be one year , and the proof mass and optical path noise spectra are the nominal ones . the optimal snr divided by the snr of a single michelson interferometer , as a function of the fourier frequency f. the sensitivity gain in the low - frequency band is equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2 $ \end{document } , while it can get larger than 2 at selected frequencies in the high - frequency region of the accessible band . the integration time has been assumed to be one year , and the proof mass and optical path noise spectra are the nominal ones . see the main body of the paper for a quantitative discussion of this point . in order to better understand the contribution from the three different combinations to the optimal combination of the three generators , in figure 9 we plot the signal - to - noise ratios of ( a , e , t ) as well as the optimal signal - to - noise ratio . for an assumed h = 10 , the snrs of the three modes are plotted versus frequency . for the equal - arm case computed here , the snrs of a and e are equal across the band . in the long wavelength region of the band , modes a and e have snrs much greater than mode t , where its contribution to the total snr is negligible . at higher frequencies , however , the t combination has snr greater than or comparable to the other modes and can dominate the snr improvement at selected frequencies . figure 9the snrs of the three combinations ( a , e , t ) and their sum as a function of the fourier frequency f. the snrs of a and e are equal over the entire frequency band . the snr of t is significantly smaller than the other two in the low part of the frequency band , while is comparable to ( and at times larger than ) the snr of the other two in the high - frequency region . see text for a complete discussion . the snrs of the three combinations ( a , e , t ) and their sum as a function of the fourier frequency f. the snrs of a and e are equal over the entire frequency band . the snr of t is significantly smaller than the other two in the low part of the frequency band , while is comparable to ( and at times larger than ) the snr of the other two in the high - frequency region . see text for a complete discussion . binaries are important sources for lisa and therefore the analysis of such sources is of major importance . one such class is of massive or super - massive binaries whose individual masses could range from 10m to 10m and which could be up to a few gpc away . another class of interest are known binaries within our own galaxy whose individual masses are of the order of a solar mass but are just at a distance of a few kpc or less . here it is assumed that the direction of the source is known , which is so for known binaries in our galaxy . however , even for such binaries , the inclination angle of the plane of the orbit of the binary is either poorly estimated or unknown . the optimization problem is now posed differently : the snr is optimized after averaging over the polarizations of the binary signals , so the results obtained are optimal on the average , that is , the source is tracked with an observable which is optimal on the average . for computing the average , a uniform distribution for the direction of the orbital angular momentum of the binary is assumed . when the binary masses are of the order of a solar mass and the signal typically has a frequency of a few mhz , the gw frequency of the binary may be taken to be constant over the period of observation , which is typically taken to be of the order of an year . a complete calculation of the signal matrix and the optimization procedure of snr is given in . here we briefly mention the main points and the final results . a source fixed in the solar system barycentric reference frame in the direction ( b , b ) but as the lisa constellation moves along its heliocentric orbit , the apparent direction ( l , l ) of the source in the lisa reference frame ( xl , yl , zl ) changes with time . the lisa reference frame ( xl , yl , zl ) has been defined in as follows : the origin lies at the center of the lisa triangle and the plane of lisa coincides with the ( xl , yl ) plane with spacecraft 2 lying on the xl axis . figure ( 10 ) displays this apparent motion for a source lying in the ecliptic plane , that is with b = 90 and b = 0. the source in the lisa reference frame describes a figure of 8 . optimizing the snr amounts to tracking the source with an optimal observable as the source apparently moves in the lisa reference frame . figure 10apparent position of the source in the sky as seen from lisa frame for ( b = 90 , b = 0 ) . the track of the source for a period of one year is shown on the unit sphere in the lisa reference frame . apparent position of the source in the sky as seen from lisa frame for ( b = 90 , b = 0 ) . the track of the source for a period of one year is shown on the unit sphere in the lisa reference frame . since an average has been taken over the orientation of the orbital plane of the binary or equivalently over the polarizations , the signal matrix a is now of rank 2 instead of rank 1 as compared with the application in the previous section 6.1 . the mutually orthogonal data combinations a , e , t are convenient in carrying out the computations because in this case as well , they simultaneously diagonalize the signal and the noise covariance matrix . the optimization problem now reduces to an eigenvalue problem with the eigenvalues being the squares of the snrs . there are two eigen - vectors which are labeled as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ { + , \times}}$\end{document } belonging to two non - zero eigenvalues . the two snrs are labelled as snr+ and snr , corresponding to the two orthogonal ( thus statistically independent ) eigenvectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ { + , \times}}$\end{document}. as was done in the previous section 6.1 f the two snrs can be squared and added to yield a network snr , which is defined through the equation 96\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{snr}}_{{\rm{network}}}^2 = { \rm{snr } } _ the third eigenvalue is zero and the corresponding eigenvector orthogonal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ \times}$\end{document } gives zero signal . the eigenvectors and the snrs are functions of the apparent source direction parameters ( l , l ) in the lisa reference frame , which in turn are functions of time . the eigenvectors optimally track the source as it moves in the lisa reference frame . assuming an observation period of an year , the snrs are integrated over this period of time . figure 11sensitivity curves for the observables : michelson , max[x , y , z ] , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } , and network for the source direction ( b = 90 , b = 0 ) . sensitivity curves for the observables : michelson , max[x , y , z ] , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } , and network for the source direction ( b = 90 , b = 0 ) . it shows the sensitivity curves of the following observables : the michelson combination x ( faint solid curve).the observable obtained by taking the maximum sensitivity among x , y , and z for each direction , where y and z are the michelson observables corresponding to the remaining two pairs of arms of lisa . this maximum is denoted by max[x , y , z ] ( dash - dotted curve ) and is operationally given by switching the combinations x , y , z so that the best sensitivity is achieved.the eigen - combination \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } which has the best sensitivity among all data combinations ( dashed curve).the network observable ( solid curve ) . the michelson combination x ( faint solid curve ) . the observable obtained by taking the maximum sensitivity among x , y , and z for each direction , where y and z are the michelson observables corresponding to the remaining two pairs of arms of lisa . this maximum is denoted by max[x , y , z ] ( dash - dotted curve ) and is operationally given by switching the combinations x , y , z so that the best sensitivity is achieved . the eigen - combination \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } which has the best sensitivity among all data combinations ( dashed curve ) . it is observed that the sensitivity over the band - width of lisa increases as one goes from observable 1 to 4 . also it is seen that the max[x , y , z ] does not do much better than x. this is because for the source direction chosen b = 90 , x is reasonably well oriented and switching to y and z combinations does not improve the sensitivity significantly . however , the network and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } observables show significant improvement in sensitivity over both x and max[x , y , z ] . this is the typical behavior and the sensitivity curves ( except ) do not show much variations for other source directions and the plots are similar . also it may be fair to compare the optimal sensitivities with max[x , y , z ] rather than x. this comparison of sensitivities is shown in figure 12 , where the network and the eigen - combinations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ { + , \times}}$\end{document } are compared with max[x , y , z ] . figure 12ratios of the sensitivities of the observables network , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ { + , \times}}$\end{document } with max[x , y , z ] for the source direction b = 90 , b = 0. ratios of the sensitivities of the observables network , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ { + , \times}}$\end{document } with max[x , y , z ] for the source direction b = 90 , b = 0. defining 97\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\kappa _ a}(f ) = { { { \rm{sn}}{{\rm{r}}_a}(f ) } \over { { \rm{sn}}{{\rm{r}}_{\max [ x , y , z]}}(f)}},$$\end{document } where the subscript a stands for network or + , , and snrmax[x , y , z ] is the snr of the observable max[x , y , z ] , the ratios of sensitivities are plotted over the lisa band - width . the improvement in sensitivity for the network observable is about 34% at low frequencies and rises to nearly 90% at about 20 mhz , while at the same time the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } combination shows improvement of 12% at low frequencies rising to over 50% at about 20 mhz . it is clear that the suppression of the laser phase fluctuations by more than nine orders of magnitude with the use of tdi is a very challenging experimental task . it requires developing and building subsystems capable of unprecedented accuracy and precision levels , and test their end - to - end performance in a laboratory environment that naturally precludes the availability of 5 10 km delay lines ! in what follows we will address some aspects related to the experimental implementation of tdi , and derive the performance specifications for the subsystems involved . we will not address , however , any of the experimental aspects related to the verification of tdi in a laboratory environment . [ 8 , 32 ] , spero et al . , and mitryk et al . it is easy to see that a successful implementation of tdi requires : accurate knowledge of the time shifts , li(t ) , li(t ) i = 1 , 2 , 3 , to be applied to the heterodyne measurements si(t ) , si(t ) , i(t ) , i(t ) i = 1 , 2 , 3;accurate synchronization among the three clocks onboard the three spacecraft as these are used for time - stamping the recorded heterodyne phase measurements;sampling time stability ( i.e. , clock stability ) for successfully suppressing the laser noise to the desired level;an accurate reconstruction algorithm of the phase measurements corresponding to the required time delays as these in general will not be equal to integer multiples of the sampling time;a phase meter capable of a very large dynamic range in order to suppress the laser noise to the required level while still preserving the phase fluctuations induced by a gravitational - wave signal in the tdi combinations . in the following subsections , we will quantitatively address the issues listed above , and provide the reader with a related list of references where more details can be found . accurate knowledge of the time shifts , li(t ) , li(t ) i = 1 , 2 , 3 , to be applied to the heterodyne measurements si(t ) , si(t ) , i(t ) , i(t ) i = 1 , 2 , 3 ; accurate synchronization among the three clocks onboard the three spacecraft as these are used for time - stamping the recorded heterodyne phase measurements ; sampling time stability ( i.e. , clock stability ) for successfully suppressing the laser noise to the desired level ; an accurate reconstruction algorithm of the phase measurements corresponding to the required time delays as these in general will not be equal to integer multiples of the sampling time ; a phase meter capable of a very large dynamic range in order to suppress the laser noise to the required level while still preserving the phase fluctuations induced by a gravitational - wave signal in the tdi combinations . the tdi combinations described in the previous sections ( whether of the first- or second - generation ) rely on the assumption of knowing the time - delays with infinite accuracy to exactly cancel the laser noise . since the six delays will in fact be known only within the accuracies li , li i = 1 , 2 , 3 , the cancellation of the laser frequency fluctuations in , for instance , the combinations ( , , , ) will no longer be exact . in order to estimate the magnitude of the laser fluctuations remaining in these data sets , let us define \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\hat l_i}\;,{\hat l\prime_i}\;i = 1,2,3$\end{document } to be the estimated time - delays . they are related to the true delays li , li i = 1 , 2 , 3 , and the accuracies li , li i = 1 , 2 , 3 through the following expressions 98\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\hat l_i } = { l_i } + \delta { l_i},\quad \quad i = 1,2,3,$$\end{document } and similarly for the primed delays . in what follows we will limit our derivation of the time - delays accuracies to only the first - generation tdi combinations and treat the three common delays li , i = 1 , 2 , 3 as constants equal to 16.7 light - seconds . we will also assume to know with infinite accuracies and precisions all the remaining physical quantities ( listed at the beginning of section 7 ) that are needed to successfully synthesize the tdi generators . ( 98 ) into the expression for the tdi combination , for instance , ( eq . ( 43 ) ) and expand it to first order in li , it is easy to derive the following approximate expression for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\hat \alpha ( t)$\end{document } , which now will show a non - zero contribution from the laser noises 99\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\hat \alpha ( t ) \simeq \alpha ( t ) + [ { \dot \phi _ { 2,12 } } - { \dot \phi _ { 3,13}}]\delta { l_1 } + [ { \dot \phi _ { 3,2 } } - { \dot \phi _ { 1,123}}]\delta { l_2 } + [ { \dot \phi _ { 1,123 } } - { \dot \phi _ { 2,3}}]\delta { l_3},$$\end{document } where the symbol denotes time derivative . time - delay interferometry can be considered effective if the magnitude of the remaining fluctuations from the lasers are much smaller than the fluctuations due to the remaining ( proof mass and optical path ) noises entering (t ) . let us assume the laser phase fluctuations to be uncorrelated to each other , their one - sided power spectral densities to be equal , the three armlengths to differ by a few percent , and the three armlength accuracies also to be equal . by requiring the magnitude of the remaining laser noises to be smaller than the secondary noise sources , it is straightforward to derive , from eq . ( 99 ) and the expressions for the noise spectrum of the tdi combination given in , the following constraint on the common armlength accuracy l 100\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\vert \delta { l_\alpha}\vert \ll { 1 \over { \sqrt { 32 } \pi f}}\sqrt { { { [ 8{{\sin}^2}(3\pi fl ) + 16{{\sin}^2}(\pi fl)]{s^{{\rm{proof}}\;{\rm{mass}}}}(f ) + { s^{{\rm{optical}}\;{\rm{path}}}}(f ) } \over { { s_\phi}(f)}}},$$\end{document } with similar inequalities also holding for and . here s , s , s are the onesided power spectral densities of the relative frequency fluctuations of a stabilized laser , a single proof mass , and a single - link optical path respectively . if we take them to be equal to the following functions of the fourier frequency f [ 53 , 15 ] 101\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_\phi}(f ) = { 10^{- 28}}{f^{- 2/3 } } + 6.3 \times { 10^{- 37}}\;{f^{- 3.4}}\;{\rm{h}}{{\rm{z}}^{- 1}}$$\end{document } 102\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s^{{\rm{proof}}\;{\rm{mass}}}}(f ) = 2.5 \times { 10^{- 48}}\;{f^{- 2}}\;{\rm{h}}{{\rm{z}}^{- 1}}$$\end{document } 103\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s^{{\rm{optical}}\;{\rm{path}}}}(f ) = 1.8 \times { 10^{- 37}}{f^2}\;{\rm{h}}{{\rm{z}}^{- 1}}$$\end{document } ( where f is in hz ) , we find that the right - hand side of the inequality given by eq . ( 100 ) reaches its minimum of about 30 meters at the fourier frequency fmin = 1.0 10 hz , over the assumed ( 10,1 ) hz lisa band . this implies that , if the armlength knowledge l can be made much smaller than 30 meters , the magnitude of the residual laser noise affecting the combination can be regarded as negligible over the entire frequency band . this reflects the fact that the armlength accuracy is a decreasing function of the frequency . for instance , at 10 hz the armlength accuracy goes up by almost an order of magnitude to about 155 meters . a perturbation analysis similar to the one described above can be performed for , resulting into the following inequality for the required delay accuracy , l 104\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\vert \delta { l_\zeta}\vert \ll { 1 \over { 2\pi f}}\sqrt { { { 4{{\sin}^2}(\pi fl){s^{{\rm{proof}}\;{\rm{mass}}}}(f ) + { s^{{\rm{optical}}\;{\rm{path}}}}(f ) } \over { { s_\phi}(f ) } } } { .}$$\end{document } equation ( 104 ) implies a minimum of the function on the right - hand side equal to about 16 meters at the fourier frequency fmin = 1.0 10 hz , while at 10 hz the armlength accuracy goes up to 154 meters . armlength accuracies at the centimeters level have already been demonstrated in the laboratory [ 16 , 50 , 64 , 26 ] , making us confident that the required level of time - delays accuracy will be available . in relation to the accuracies derived above , it is interesting to calculate the time scales during which the armlengths will change by an amount equal to the accuracies themselves . this identifies the minimum time required before updating the armlength values in the tdi combinations . that the relative longitudinal speeds between the three pairs of spacecraft , during approximately the first year of the lisa mission , can be written in the following approximate form 105\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${v_{i , j}}(t ) = v_{i , j}^{(0)}\sin \left({{{2\pi t } \over { { t_{i , j } } } } } \right)\quad \quad ( i,\;j ) = ( 1,2);(1,3);(2,3),$$\end{document } where we have denoted with ( 1 , 2 ) , ( 1 , 3 ) , ( 2 , 3 ) the three possible spacecraft pairs , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{i , j}^{(0)}$\end{document } is a constant velocity , and ti , j is the period for the pair ( i , j ) . in reference it has also been shown that the lisa trajectory can be selected in such a way that two of the three arms rates of change are essentially equal during the first year of the mission . following reference , we will assume \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{1,2}^{(0 ) } = v_{1,3}^{(0 ) } \neq v_{2,3}^{(0)}$\end{document } , with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{1,2}^{(0 ) } = 1\;{\rm{m / s,}}\;v_{2,3}^{(0 ) } = 13\;{\rm{m / s,}}\;{t_{1,2}}\ ; = { t_{1,3 } } \approx 4$\end{document } months , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${t_{2,3 } } \approx 1$\end{document } year . from eq . ( 105 ) it is easy to derive the variation of each armlength , for example l3(t ) , as a function of the time and the time scale t during which it takes place 106\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta { l_3}(t ) = v_{1,2}^{(0)}\sin \left({{{2\pi t } \over { { t_{1,2 } } } } } \right)\delta t{.}$$\end{document } equation ( 106 ) implies that a variation in armlength l3 10 m can take place during different time scales , depending on when during the mission this change takes place . for instance , if t t1,2 we find that the armlength l3 changes by more than its accuracy ( 10 m ) after a time t = 2.3 10 s. if however t t1,2/4 , the armlength will change by the same amount after only t 10 s instead . as this value is less than the one - way - light - time , one might argue that the measured time - delay will not represent well enough the delay that needs to be applied in the tdi combinations at that particular time . one way to address this problem is to treat the delays in the tdi combinations as parameters to be determined by a non - linear least - squares procedure , in which the minimum of the minimizer is achieved at the correct delays since that the laser noise will exactly cancel there in the tdi combinations . such a technique , which was named time - delay interferometric ranging ( tdir ) , requires a starting point in the time - delays space in order to implement the minimization , and it will work quite effectively jointly with the ranging data available onboard . the effectiveness of the tdi data combinations requires the clocks onboard the three spacecraft to be synchronized . in what follows we will identify the minimum level of off - synchronization among the clocks that can be tolerated . in order to proceed with our analysis we will treat one of the three clocks ( say the clock onboard spacecraft 1 ) as the master clock defining the time for lisa , while the other two to be synchronized to it . the relativistic ( sagnac ) time - delay effect due to the fact that the lisa trajectory is a combination of two rotations , each with a period of one year , will have to be accounted for in the synchronization procedure and , as has already been discussed earlier , will be accounted for within the second - generation formulation of tdi . here , for simplicity , we will analyze an idealized non - rotating constellation in order to get a sense of the required level of clocks synchronization . let us denote by t2 , t3 , the time accuracies ( time - offsets ) for the clocks onboard spacecraft 2 and 3 respectively . if t is the time onboard spacecraft 1 , then what is believed to be time t onboard spacecraft 2 and 3 is actually equal to the following times 107\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\hat t_2 } = t + \delta { t_2},$$\end{document } 108\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\hat t_3 } = t + \delta { t_3}{.}$$\end{document } if we now substitute eqs . ( 107 and 108 ) into the tdi combination , for instance , and expand it to first order in ti , i = 2 , 3 , it is easy to derive the following approximate expression for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\hat \zeta ( t)$\end{document } , which shows the following non - zero contribution from the laser noises 109\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\hat \zeta ( t ) \simeq \zeta ( t ) + [ { \dot \phi _ { 1,23 } } - { \dot \phi _ { 3,12 } } + { \dot \phi _ { 2,13 } } - { \dot \phi _ { 2,13}}]\delta { t_2 } + [ { \dot \phi _ { 2,13 } } - { \dot \phi _ { 1,23 } } + { \dot \phi _ { 3,12 } } - { \dot \phi _ { 3,12}}]\delta { t_3}{.}$$\end{document } by requiring again the magnitude of the remaining fluctuations from the lasers to be smaller than the fluctuations due to the other ( secondary ) noise sources affecting (t ) , it is possible to derive an upper limit for the accuracies of the synchronization of the clocks . if we assume again the three laser phase fluctuations to be uncorrelated to each other , their one - sided power spectral densities to be equal , the three armlengths to differ by a few percent , and the two time - offsets magnitudes to be equal , by requiring the magnitude of the remaining laser noises to be smaller than the secondary noise sources it is easy to derive the following constraint on the time synchronization accuracy t 110\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\vert \delta { t_\zeta}\vert \ll { 1 \over { 2\pi f}}\sqrt { { { 12{{\sin}^2}(\pi fl){s^{{\rm{proof}}\;{\rm{mass}}}}(f ) + 3\;{s^{{\rm{optical}}\;{\rm{path}}}}(f ) } \over { 4\;{s_\phi}(f)}}},$$\end{document } with s , s , s again as given in eqs . ( 110 ) reaches its minimum of about 47 nanoseconds at the fourier frequency fmin = 1.0 10 hz . this means that clocks synchronized at a level of accuracy significantly better than 47 nanoseconds will result into a residual laser noise that is much smaller than the secondary noise sources entering into the combination . an analysis similar to the one described above can be performed for the remaining generators ( , , ) . for them we find that the corresponding inequality for the accuracy in the synchronization of the clocks is now equal to 111\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\vert \delta { t_\alpha}\vert \leq { 1 \over { 2\pi f}}\sqrt { { { [ 4{{\sin}^2}(3\pi fl ) + 8{{\sin}^2}(\pi fl)]{s^{{\rm{proof}}\;{\rm{mass}}}}(f ) + 3\;{s^{{\rm{optical}}\;{\rm{path}}}}(f ) } \over { 4\;{s_\phi}(f)}}},$$\end{document } with equal expressions holding also for and . the function on the right - hand side of eq . ( 111 ) has a minimum equal to 88 nanoseconds at the fourier frequency fmin = 1.0 10 hz . as for the armlength accuracies , also the timing accuracy requirements become less stringent at higher frequencies . at 10 hz , for instance , the timing accuracy for and , , go up to 446 and 500 ns respectively . as a final note , a required clock synchronizations of about 40 ns derived in this section translates into a ranging accuracy of 12 meters , which has been experimentally shown to be easily achievable [ 16 , 50 , 64 , 26 ] . the sampling times of all the measurements needed for synthesizing the tdi combinations will not be constant , due to the intrinsic timing jitters of the onboard measuring system . among all the subsystems involved in the data measuring process , the onboard clock is expected to be the dominant source of time jitter in the sampled data . presently existing space qualified clocks can achieve an allan standard deviation of about 10 for integration times from 1 to 10 000 seconds . this timing stability translates into a time jitter of about 10 seconds over a period of 1 second . a perturbation analysis including the three sampling time jitters due to the three clocks shows that any laser phase fluctuations remaining in the four tdi generators will also be proportional to the sampling time jitters . since the latter are approximately four orders of magnitude smaller than the armlength and clocks synchronization accuracies derived earlier , we conclude that the magnitude of laser noise residual into the tdi combinations due to the sampling time jitters is negligible . the derivations of the time - delays and clocks synchronization accuracies highlighted earlier presumed the availability of the phase measurement samples at the required time - delays . since this condition will not be true in general , as the time - delays used by the tdi combinations will not be equal to integer - multiples of the sampling time , with a sampling rate of , let us say , 10 hz , the time delays could be off their correct values by a tenth of a second , way more than the 10 nanoseconds time - delays and clocks synchronization accuracies estimated above . earlier suggestions for addressing this problem envisioned sampling the data at very - high rates ( perhaps of the order of hundreds of mhz ) , so reducing the additional error to the estimated time - delays to a few nanoseconds . although in principle such a solution would allow us to suppress the residual laser noise to the required level , it would create an insurmountable problem for transmitting the science data to the ground due to the limited space - to - ground data rates . an alternate scheme for obtaining the phase measurement points needed by tdi envisioned sampling the phase measurements at the required delayed times . this scheme naturally requires knowledge of the time - delays and synchronization of the clocks at the required accuracy levels during data acquisition . although such a procedure could be feasible in principle , it would still leave open the possibility of irreversible corruption of the tdi combinations in the eventuality of performance degradation in the ranging and clock synchronization procedures . given that the data will need to be sampled at a rate of 10 hz , an alternative options is to implement an interpolation scheme for reconstructing the required data points from the sampled measurements . an analysis based on the implementation of the truncated shannon formula , however , showed that several months of data were required in order to reconstruct the phase samples at the estimated time - delays with a sufficiently high accuracy . this conclusion implied that several months ( at the beginning and end ) of the entire data records measured by lisa would be of no use , resulting into a significant mission science degradation . although the truncated shannon formula was proved to be impracticable for reconstructing phase samples at the required time - delays , it was then recognized that a more efficient and accurate interpolation technique could be adopted . in what follows , we provide a brief account of this data processing technique , which is known as fractional - delay filtering let s write the truncated shannon formula for the delayed sample , yn(n d ) , which we want to construct by filtering the sampled data y(n ) 112\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${y_n}(n - d ) = \sum\limits_{j = - n}^n { y(n + j)\;{\rm{sinc}}(d - j),}$$\end{document } where , as usual , sinc(x ) sin(x)/x , and n is an integer at which the shannon formula has been truncated to . as pointed out in , although the truncated shannon formula is optimal in the least - squares sense , the sinc - function that appears in it is far from being ideal in reconstructing the transfer function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${e^{2\pi ifd/{f_s}}}$\end{document } , where fs is the sampling frequency . in fact , over the lisa observational band the sinc - function displays significant ringing , which can only be suppressed by taking n very large ( as the error , , decays slowly as 1/n ) . it was estimated that , in order to achieve an < 10 , an n 10 is needed . if , however , we give up on the requirement of minimizing the error in the least - squares sense and replace it with a mini - max criterion error applied to the absolute value of the difference between the ideal transfer function ( i.e. , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${e^{2\pi ifd/{f_s}}}$\end{document } ) and a modified sinc - function , we will be able to achieve a rapid convergence while suppressing the ringing effects associated with the sinc function . one way to achieve this result is to modify the shannon formula by multiplying the sinc - function by a window - function , w(j ) , in the following way 113\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${y_n}(n - d ) = \sum\limits_{j = - n}^n { y(n + j)w(j)\;{\rm{sinc}}(d - j),}$$\end{document } where w(j ) smoothly decays to zero at j = n . in several windows were tested , and the resulting values of n needed to accurately reconstruct the desired delayed samples were estimated , both on theoretical and numerically grounds . it was found that , with windows belonging to the family of lagrange polynomials a delayed sample could be reconstructed by using n 25 samples while achieving a mini - max error < 10 between the ideal transfer function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${e^{2\pi ifd/{f_s}}}$\end{document } , and the kernel of the modified truncated shannon formula . it has been shown that the maximum of the ratio between the amplitudes of the laser and the secondary phase fluctuations occurs at the lower end of the lisa bandwidth ( i.e. , 0.1 mhz ) and it is equal to about 10 . this corresponds to the minimum dynamic range for the phasemeters to correctly measure the laser fluctuations and the weaker ( gravitational - wave ) signals simultaneously . an additional safety factor of 10 should be sufficient to avoid saturation if the noises are well described by gaussian statistics . in terms of requirements on the digital signal processing subsystem , this dynamic range implies that approximately 36 bits are needed when combining the signals in tdi , only to bridge the gap between laser frequency noise and the other noises and gravitational - wave signals . more bits might be necessary to provide enough information to efficiently filter the data when extracting weak gravitational - wave signals embedded into noise . the phasemeters will be the onboard instrument that will perform the phase measurements containing the gravitational signals . they will also need to simultaneously measure the time - delays to be applied to the tdi combinations via ranging tones over - imposed on the laser beams exchanged by the spacecraft . and they will need to have the capability of simultaneously measure additional side - band tones that are required for the calibration of the onboard ultra - stable oscillator used in the down - conversion of heterodyned carrier signal [ 57 , 27 ] . work toward the realization of a phasemeter capable of meeting these very stringent performance and operational requirements has aggressively been performed both in the united states and in europe [ 43 , 23 , 22 , 6 , 63 ] , and we refer the reader interested in the technical details associated with the development studies of such device to the above references and those therein . in this article we have summarized the use of tdi for canceling the laser phase noise from heterodyne phase measurements performed by a constellation of three spacecraft tracking each other along arms of unequal length . underlying the tdi technique is the mathematical structure of the theory of grbner basis and the algebra of modules over polynomial rings . these methods have been motivated and illustrated with the simple example of an unequal - arm interferometer in order to give a physical insight of tdi . here , these methods have been rigorously applied to the idealized case of a stationary interferometer such as the lisa mission . this allowed us to derive the generators of the module from which the entire tdi data set can be obtained ; they can be extended in a straight - forward way to more than three spacecraft for possible future mission concepts . the stationary lisa case was used as a propaedeutical introduction to the physical motivation of tdi , and for further extending it to the realistic lisa configuration of free - falling spacecraft orbiting around the sun . the tdi data combinations canceling laser phase noise in this general case are referred to as second - generation tdi , and they contain twice as many terms as their corresponding first - generation combinations valid for the stationary configuration . as a data analysis application we have shown that it is possible to identify specific tdi combinations that will allow lisa to achieve optimal sensitivity to gravitational radiation [ 38 , 40 , 39 ] . the resulting improvement in sensitivity over that of an unequal - arm michelson interferometer , in the case of monochromatic signals randomly distributed over the celestial sphere and of random polarization , is non - negligible . we have found this to be equal to a factor of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2 $ \end{document } in the low - part of the frequency band , and slightly more than \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 3 $ \end{document } in the high - part of the lisa band . the snr for binaries whose location in the sky is known , but their polarization is not , can also be optimized , and the degree of improvement depends on the location of the source in the sky . we also addressed several experimental aspects of tdi , and emphasized that it has already been successfully tested experimentally [ 8 , 32 , 48 , 33 ] . as of the writing of this second edition of our living review article , it is very gratifying to see how much tdi has matured since the publishing of its first version . the purpose of this second edition review of tdi was to provide the basic mathematical tools and knowledge of the current experimental results needed for working on future tdi projects . we hope to have accomplished this goal , and that others will be stimulated to work in this fascinating field of research .

equal - arm detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms . this is because the noise in the laser light is common to both arms , experiencing exactly the same delay , and thus cancels when it is differenced at the photo detector . in this situation , much lower level secondary noises then set the overall performance . if , however , the two arms have different lengths ( as will necessarily be the case with space - borne interferometers ) , the laser noise experiences different delays in the two arms and will hence not directly cancel at the detector . in order to solve this problem , a technique involving heterodyne interferometry with unequal arm lengths and independent phase - difference readouts has been proposed . it relies on properly time - shifting and linearly combining independent doppler measurements , and for this reason it has been called time - delay interferometry ( tdi).this article provides an overview of the theory , mathematical foundations , and experimental aspects associated with the implementation of tdi . although emphasis on the application of tdi to the laser interferometer space antenna ( lisa ) mission appears throughout this article , tdi can be incorporated into the design of any future space - based mission aiming to search for gravitational waves via interferometric measurements . we have purposely left out all theoretical aspects that data analysts will need to account for when analyzing the tdi data combinations .

<s>[INST]breakthroughs in modern technology have made possible the construction of extremely large interferometers both on the ground and in space for the detection and observation of gravitational waves ( gws ) . several ground - based detectors around the globe have been operational for several years , and are now in the process of being upgraded to achieve even higher sensitivities . these are the ligo and virgo interferometers , which have arm lengths of 4 km and 3 km , respectively , and the geo and tama interferometers with arm lengths of 600 m and 300 m , respectively . these upgraded detectors will operate in the high frequency range of gws of 1 hz to a few khz . a natural limit occurs on decreasing the lower frequency cut - off because it is not practical to increase the arm lengths on ground and also because of the gravity gradient noise which is difficult to eliminate below 1 hz . but , on the other hand , in the cosmos there exist interesting astrophysical gw sources which emit gws below this frequency such as the galactic binaries , massive and super - massive black - hole binaries , etc . if we wish to observe these sources , we need to go to lower frequencies . the solution is to build an interferometer in space , where such noises will be absent and allow the detection of gws in the low frequency regime . the laser interferometer space antenna ( lisa ) mission , and more recent variations of its design [ 13 , 35 ] , is the typical example of a space - based interferometer aiming to detect and study gravitational radiation in the millihertz band . in order to make such observations lisa relied on coherent laser beams exchanged between three identical spacecraft forming a giant ( almost ) equilateral triangle of side 5 10 km to observe and detect low frequency cosmic gws . ground- and space - based detectors will complement each other in the observation of gws in an essential way , analogous to the way optical , radio , x - ray , -ray , etc . observations do for the electromagnetic spectrum . as these detectors begin to make their observations , a new era of gravitational astronomy is on the horizon and a radically different view of the universe the astrophysical sources observable in the mhz band include galactic binaries , extra - galactic super - massive black - hole binaries and coalescences , and stochastic gw background from the early universe . these include galactic and extra galactic stellar mass binaries , and massive and super - massive blackhole binaries . the frequency of the gws emitted by such a system is twice its orbital frequency . population synthesis studies indicate a large number of stellar mass binaries in the frequency range below 23 mhz [ 4 , 34 ] . in the lower frequency range ( 1 mhz ) there is a large number of such unresolvable sources in each of the frequency bins . massive black - hole binaries are interesting both from the astrophysical and theoretical points of view . coalescences of massive black holes from different galaxies after their merger during growth of the present galaxies would provide unique new information on galaxy formation . coalescence of binaries involving intermediate mass black holes could help to understand the formation and growth of massive black holes . the super - massive black - hole binaries are strong emitters of gws and these spectacular events can be detectable beyond red - shift of z = 10 . just as the cosmic microwave background is left over from the big bang , so too should there be a background of gravitational waves . unlike electromagnetic waves , gravitational waves do not interact with matter after a few planck times after the big bang , so they do not thermalize . their spectrum today , therefore , is simply a red - shifted version of the spectrum they formed with , which would throw light on the physical conditions at the epoch of the early universe . interferometric non - resonant detectors of gravitational radiation with frequency content f1 < f < fu ( f1 , fu being respectively the lower and upper frequency cut - offs characterizing the detector s operational bandwidth ) use a coherent train of electromagnetic waves ( of nominal frequency 0 fu ) folded into several beams , and at one or more points where these intersect , monitor relative fluctuations of frequency or phase ( homodyne detection ) . the observed low - frequency fluctuations are due to several causes : frequency variations of the source of the electromagnetic signal about 0,relative motions of the electromagnetic source and the mirrors ( or amplifying transponders ) that do the folding , temporal variations of the index of refraction along the beams , andaccording to general relativity , to any time - variable gravitational fields present , such as the transverse - traceless metric curvature of a passing plane gravitational - wave train . to observe gravitational waves in this way , it is thus necessary to control , or monitor , the other sources of relative frequency fluctuations , and , in the data analysis , to use optimal algorithms based on the different characteristic interferometer responses to gravitational waves ( the signal ) and to the other sources ( the noise ) . by comparing phases of electromagnetic beams referenced to the same frequency generator and propagated along non - parallel equal - length arms , frequency fluctuations of the frequency reference can be removed , and gravitational - wave signals at levels many orders of magnitude lower can be detected . frequency variations of the source of the electromagnetic signal about 0 , relative motions of the electromagnetic source and the mirrors ( or amplifying transponders ) that do the folding , temporal variations of the index of refraction along the beams , and according to general relativity , to any time - variable gravitational fields present , such as the transverse - traceless metric curvature of a passing plane gravitational - wave train . in the present single - spacecraft doppler tracking observations , for instance , many of the noise sources can be either reduced or calibrated by implementing appropriate microwave frequency links and by using specialized electronics , so the fundamental limitation is imposed by the frequency ( time - keeping ) fluctuations inherent to the reference clock that controls the microwave system . hydrogen maser clocks , currently used in doppler tracking experiments , achieve their best performance at about 1000 s integration time , with a fractional frequency stability of a few parts in 10 . this is the reason why these one - arm interferometers in space ( which have one doppler readout and a this integration time is also comparable to the microwave propagation ( or storage ) time 2l / c to spacecraft en route to the outer solar system ( for example l 58 au for the cassini spacecraft ) . low - frequency interferometric gravitational - wave detectors in solar orbits , such as the lisa mission and the currently considered elisa / ngo mission [ 5 , 13 , 35 ] , have been proposed to achieve greater sensitivity to mhz gravitational waves . however , since the armlengths of these space - based interferometers can differ by a few percent , the direct recombination of the two beams at a photo detector will not effectively remove the laser frequency noise . this is because the frequency fluctuations of the laser will be delayed by different amounts within the two arms of unequal length . in order to cancel the laser frequency noise , the time - varying doppler data must be recorded and post - processed to allow for arm - length differences . the data streams will have temporal structure , which can be described as due to many - pulse responses to -function excitations , depending on time - of - flight delays in the response functions of the instrumental doppler noises and in the response to incident plane - parallel , transverse , and traceless gravitational waves . although the theory of tdi can be used by any future space - based interferometer aiming to detect gravitational radiation , this article will focus on its implementation by the lisa mission . each spacecraft was to be equipped with two lasers sending beams to the other two ( 0.03 au away ) while simultaneously measuring the beat frequencies between the local laser and the laser beams received from the other two spacecraft . the analysis of tdi presented in this article will assume a successful prior removal of any first - order doppler beat notes due to relative motions , giving six residual doppler time series as the raw data of a stationary time delay space interferometer . following [ 51 , 2 , 10 ] , we will regard lisa not as constituting one or more conventional michelson interferometers , but rather , in a symmetrical way , a closed array of six one - arm delay lines between the test masses . in this way , during the course of the article , we will show that it is possible to synthesize new data combinations that cancel laser frequency noises , and estimate achievable sensitivities of these combinations in terms of the separate and relatively simple single arm responses both to gravitational wave and instrumental noise ( cf . [ 51 , 2 , 10 ] ) . in contrast to earth - based interferometers , which operate in the long - wavelength limit ( lwl ) ( arm lengths gravitational wavelength c / f0 , where f0 is a characteristic frequency of the gw ) , lisa does not operate in the lwl over much of its frequency band . when the physical scale of a free mass optical interferometer intended to detect gravitational waves is comparable to or larger than the gw wavelength , time delays in the response of the instrument to the waves , and travel times along beams in the instrument , can not be ignored and must be allowed for in computing the detector response used for data interpretation . it is convenient to formulate the instrumental responses in terms of observed differential frequency shifts for short , doppler shifts rather than in terms of phase shifts usually used in interferometry , although of course these data , as functions of time , are inter - convertible . we provide an overview of the physical and historical motivations of tdi . in section 3 we summarize the one - arm doppler transfer functions of an optical beam between two carefully shielded test masses inside each spacecraft resulting from ( i ) frequency fluctuations of the lasers used in transmission and reception , ( ii ) fluctuations due to non - inertial motions of the spacecraft , and ( iii ) beam - pointing fluctuations and shot noise . among these , the dominant noise is from the frequency fluctuations of the lasers and is several orders of magnitude ( perhaps 7 or 8) above the other noises . this noise must be very precisely removed from the data in order to achieve the gw sensitivity at the level set by the remaining doppler noise sources which are at a much lower level and which constitute the noise floor after the laser frequency noise is suppressed . we show that this can be accomplished by shifting and linearly combining the twelve one - way doppler data measured by lisa . the actual procedure can easily be understood in terms of properly defined time - delay operators that act on the one - way doppler measurements . in section 4 we develop a formalism involving the algebra of the time - delay operators which is based on the theory of rings and modules and computational commutative algebra . we show that the space of all possible interferometric combinations canceling the laser frequency noise is a module over the polynomial ring in which the time - delay operators play the role of the indeterminates . in the literature , the module we show that the module can be generated from four generators , so that any data combination canceling the laser frequency noise is simply a linear combination formed from these generators . we would like to emphasize that this is the mathematical structure underlying tdi for lisa . also in section 4 specific interferometric combinations are derived , and their physical interpretations are discussed . the expressions for the sagnac interferometric combinations ( , , , ) are first obtained ; in particular , the symmetric sagnac combination , for which each raw data set needs to be delayed by only a single arm transit time , distinguishes itself against all the other tdi combinations by having a higher order response to gravitational radiation in the lwl when the spacecraft separations are equal . we then express the unequal - arm michelson combinations ( x , y , z ) in terms of the , , , and combinations with further transit time delays . one of these interferometric data combinations would still be available if the links between one pair of spacecraft were lost . other tdi combinations , which rely on only four of the possible six inter - spacecraft doppler measurements ( denoted p , e , and u ) are also presented . they would of course be quite useful in case of potential loss of any two inter - spacecraft doppler measurements . tdi so formulated presumes the spacecraft - to - spacecraft light - travel - times to be constant in time , and independent from being up- or down - links . reduction of data from moving interferometric laser arrays in solar orbit will in fact encounter non - symmetric up- and downlink light time differences that are significant , and need to be accounted for in order to exactly cancel the laser frequency fluctuations [ 44 , 7 , 45 , 41 , 9 ] . in section 5 we show that , by introducing a set of non - commuting time - delay operators , there exists a quite general procedure for deriving generalized tdi combinations that account for the effects of time - dependence of the arms . using this approach it is possible to derive flex - free expression for the unequal - arm michelson combinations x1 , and obtain the generalized expressions for all the tdi combinations . alternatively , a rigorous mathematical formulation can be given in terms of rings and modules . but because of the non - commutativity of operators the polynomial ring is non - commutative . thus the algebraic problem becomes extremely complex and a general solution seems difficult to obtain . but we show that for the special case when one arm of lisa is dysfunctional a plethora of solutions can be found . such a possibility must be envisaged because of reasons such as technical failure or even operating costs . in section 6 we address the question of maximization of the lisa signal - to - noise - ratio ( snr ) to any gravitational - wave signal present in its data . this is done by treating the snr as a functional over the space of all possible tdi combinations . as a simple application of the general formula we have derived , we apply our results to the case of sinusoidal signals randomly polarized and randomly distributed on the celestial sphere . we find that the standard lisa sensitivity figure derived for a single michelson interferometer [ 15 , 38 , 40 ] can be improved by a factor of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2$\end{document } in the low - part of the frequency band , and by more than \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 3$\end{document } in the remaining part of the accessible band . further , we also show that if the location of the gw source is known , then as the source appears to move in the lisa reference frame , it is possible to optimally track the source , by appropriately changing the data combinations during the course of its trajectory [ 38 , 39 ] . as an example of such type of source , , we finally address aspects of tdi of more practical and experimental nature , and provide a list of references where more details about these topics can be found . it is worth mentioning that , as of today , tdi has already gone through several successful experimental tests [ 8 , 32 , 48 , 33 , 25 ] and that it has been endorsed by the elisa / ngo [ 13 , 35 ] project as its baseline technique for achieving its required sensitivity to gravitational radiation . we emphasize that , although this article will use as baseline mission reference the lisa mission , the results here presented can easily be extended to other space mission concepts . equal - arm interferometer detectors of gravitational waves can observe gravitational radiation by canceling the laser frequency fluctuations affecting the light injected into their arms . this is done by comparing phases of split beams propagated along the equal ( but non - parallel ) arms of the detector . the laser frequency fluctuations affecting the two beams experience the same delay within the two equal - length arms and cancel out at the photodetector where relative phases are measured . this way gravitational - wave signals of dimensionless amplitude less than 10 can be observed when using lasers whose frequency stability can be as large as roughly a few parts in 10 . if the arms of the interferometer have different lengths , however , the exact cancellation of the laser frequency fluctuations , say c(t ) , will no longer take place at the photodetector . in fact , the larger the difference between the two arms , the larger will be the magnitude of the laser frequency fluctuations affecting the detector response . if l1 and l2 are the lengths of the two arms , it is easy to see that the amount of laser relative frequency fluctuations remaining in the response is equal to ( units in which the speed of light c = 1 ) 1\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta c(t ) = c(t - 2{l_1 } ) - c(t - 2{l_2}){.}$$\end{document } in the case of a space - based interferometer such as lisa , whose lasers are expected to display relative frequency fluctuations equal to about \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${10^{- 13}}/\sqrt { { \rm{hz}}}$\end{document } in the mhz band , and whose arms will differ by a few percent [ 5 , 13 , 35 ] , eq . ( 1 ) implies the following expression for the amplitude of the fourier components of the uncanceled laser frequency fluctuations ( an over - imposed tilde denotes the operation of fourier transform ) : 2\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\vert \tilde{\delta c}(f)\vert \simeq \vert \tilde c(f)\vert 4\pi f\vert ( { l_1 } - { l_2})\vert { .}$$\end{document } at f = 10 hz , for instance , and assuming l1 l2 0.5 s , the uncanceled fluctuations from the laser are equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$6.3 \times { 10^{- 16}}/\sqrt { { \rm{hz}}}$\end{document}. since the lisa sensitivity goal was about \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${10^{- 20}}/\sqrt { { \rm{hz}}}$\end{document } in this part of the frequency band , it is clear that an alternative experimental approach for canceling the laser frequency fluctuations is needed . a first attempt to solve this problem was presented by faller et al . [ 17 , 19 , 18 ] , and the scheme proposed there can be understood through figure 1 . in this idealized model the two beams exiting the two arms are not made to interfere at a common photodetector . rather , each is made to interfere with the incoming light from the laser at a photodetector , decoupling in this way the phase fluctuations experienced by the two beams in the two arms . now two doppler measurements are available in digital form , and the problem now becomes one of identifying an algorithm for digitally canceling the laser frequency fluctuations from a resulting new data combination . figure 1light from a laser is split into two beams , each injected into an arm formed by pairs of free - falling mirrors . since the length of the two arms , l1 and l2 , are different , now the light beams from the two arms are not recombined at one photo detector . instead each is separately made to interfere with the light that is injected into the arms . two distinct photo detectors are now used , and phase ( or frequency ) fluctuations are then monitored and recorded there . light from a laser is split into two beams , each injected into an arm formed by pairs of free - falling mirrors . since the length of the two arms , l1 and l2 , are different , now the light beams from the two arms are not recombined at one photo detector . instead each is separately made to interfere with the light that is injected into the arms . two distinct photo detectors are now used , and phase ( or frequency ) fluctuations are then monitored and recorded there . the algorithm they first proposed , and refined subsequently in , required processing the two doppler measurements , say y1(t ) and y2(t ) , in the fourier domain . if we denote with h1(t ) , h2(t ) the gravitational - wave signals entering into the doppler data y1 , y2 , respectively , and with n1 , n2 any other remaining noise affecting y1 and y2 , respectively , then the expressions for the doppler observables y1 , y2 can be written in the following form : 3\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${y_1}(t ) = c(t - 2{l_1 } ) - c(t ) + { h_1}(t ) + { n_1}(t),$$\end{document } 4\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${y_2}(t ) = c(t - 2{l_2 } ) - c(t ) + { h_2}(t ) + { n_2}(t){.}$$\end{document } from eqs . ( 3 ) and ( 4 ) it is important to note the characteristic time signature of the random process c(t ) in the doppler responses y1 , y2 . the time signature of the noise c(t ) in y1(t ) , for instance , can be understood by observing that the frequency of the signal received at time t contains laser frequency fluctuations transmitted 2l1 s earlier . by subtracting from the frequency of the received signal the frequency of the signal transmitted at time t , we also subtract the frequency fluctuations c(t ) with the net result shown in eq . the algorithm for canceling the laser noise in the fourier domain suggested in works as follows . if we take an infinitely long fourier transform of the data y1 , the resulting expression of y1 in the fourier domain becomes ( see eq . ( 3 ) ) 5\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\tilde y_1}(f ) = \tilde c(f)[{e^{4\pi i{f^{{l_1 } } } } } - 1 ] + { \tilde h_1}(f ) + { \tilde n_1}(f){.}$$\end{document } if the arm length l1 is known exactly , we can use the y1 data to estimate the laser frequency fluctuations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\tilde c(f)$\end{document}. this can be done by dividing y1 by the transfer function of the laser noise c into the observable y1 itself . by then further multiplying \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\tilde y_1}/[{e^{4\pi if{l_1 } } } - 1]$\end{document } by the transfer function of the laser noise into the other observable \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\tilde y_2}$\end{document } , i.e. , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{e^{4\pi if{l_2 } } } - 1]$\end{document } , and then subtract the resulting expression from \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\tilde y_2}$\end{document } one accomplishes the cancellation of the laser frequency fluctuations . the problem with this procedure is the underlying assumption of being able to take an infinitely long fourier transform of the data . even if one neglects the variation in time of the lisa arms , by taking a finite - length fourier transform of , say , y1(t ) over a time interval t , the resulting transfer function of the laser noise c into y1 no longer will be equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{e^{4\pi if{l_1 } } } - 1]$\end{document}. this can be seen by writing the expression of the finite length fourier transform of y1 in the following way : 6\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\tilde y_1^t \equiv \int\nolimits_{- t}^{+ t } { { y_1 } } ( t){e^{2\pi ift}}dt = \int\nolimits_{- \infty}^{+ \infty } { { y_1 } } ( t)h(t){e^{2\pi ift}}dt,$$\end{document } where we have denoted with h(t ) the function that is equal to 1 in the interval [ t , + t ] , and zero everywhere else . ( 6 ) implies that the finite - length fourier transform \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\tilde y_1^t$\end{document } of y1(t ) is equal to the convolution in the fourier domain of the infinitely long fourier transform of y1(t ) , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\tilde y_1}$\end{document } , with the fourier transform of h(t ) ( i.e. , the sinc function of width 1/t ) . the key point here is that we can no longer use the transfer function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$[{e^{4\pi if{l_i } } } - 1]$\end{document } , i = 1 , 2 , for estimating the laser noise fluctuations from one of the measured doppler data , without retaining residual laser noise into the combination of the two doppler data y1 , y2 valid in the case of infinite integration time . the amount of residual laser noise remaining in the fourier - based combination described above , as a function of the integration time t and type of window function used , was derived in the appendix of . there it was shown that , in order to suppress the residual laser noise below the lisa sensitivity level identified by secondary noises ( such as proof - mass and optical path noises ) with the use of the fourier - based algorithm an integration time of about six months was needed . a solution to this problem was suggested in , which works entirely in the time - domain . from eqs . ( 3 ) and ( 4 ) we may notice that , by taking the difference of the two doppler data y1(t ) , y2(t ) , the frequency fluctuations of the laser now enter into this new data set in the following way : 7\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${y_1}(t ) - { y_2}(t ) = c(t - 2{l_1 } ) - c(t - 2{l_2 } ) + { h_1}(t ) - { h_2}(t ) + { n_1}(t ) - { n_2}(t){.}$$\end{document } if we now compare how the laser frequency fluctuations enter into eq . ( 3 ) and ( 4 ) , we can further make the following observation . if we time - shift the data y1(t ) by the round trip light time in arm 2 , y1(t 2l2 ) , and subtract from it the data y2(t ) after it has been time - shifted by the round trip light time in arm 1 , y2(t 2l1 ) , we obtain the following data set : 8\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { y_1}(t - 2{l_2 } ) - { y_2}(t - 2{l_1 } ) = c(t - 2{l_1 } ) - c(t - 2{l_2 } ) + { h_1}(t - 2{l_2 } ) - { h_2}(t - 2{l_1})\quad } \\ { + { n_1}(t - 2{l_2 } ) - { n_2}(t - 2{l_1 } ) . } \\ \end{array}$$\end{document } in other words , the laser frequency fluctuations enter into y1(t)y2(t ) and y1(t2l2)y2(t2l1 ) with the same time structure . ( 7 ) we can generate a new data set that does not contain the laser frequency fluctuations c(t ) , 9\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x \equiv [ { y_1}(t ) - { y_2}(t ) ] - [ { y_1}(t - 2{l_2 } ) - { y_2}(t - 2{l_1})]{.}$$\end{document } the expression above of the x combination shows that it is possible to cancel the laser frequency noise in the time domain by properly time - shifting and linearly combining doppler measurements recorded by different doppler readouts . this in essence is what tdi amounts to . in order to gain a better physical understanding of how tdi works , let s rewrite the above x combination in the following form 10\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x = [ { y_1}(t ) + { y_2}(t - 2{l_1 } ) ] - [ { y_2}(t ) + { y_1}(t - 2{l_2})],$$\end{document } where we have simply rearranged the terms in eq . equation ( 10 ) shows that x is the difference of two sums of relative frequency changes , each corresponding to a specific light path ( the continuous and dashed lines in figure 2 ) . the continuous line , corresponding to the first square - bracket term in eq . ( 10 ) , represents a light - beam transmitted from spacecraft 1 and made to bounce once at spacecraft 3 and 2 respectively . since the other beam ( dashed line ) experiences the same overall delay as the first beam ( although by bouncing off spacecraft 2 first and then spacecraft 3 ) when they are recombined they will cancel the laser phase fluctuations exactly , having both experienced the same total delays ( assuming stationary spacecraft ) . for this reason the combination x can be regarded as a synthesized ( via tdi ) zero - area sagnac interferometer , with each beam experiencing a delay equal to ( 2l1 + 2l2 ) . in reality , there are only two beams in each arm ( one in each direction ) and the lines in figure 2 represent the paths of relative frequency changes rather than paths of distinct light beams . figure 2schematic diagram for x , showing that it is a synthesized zero - area sagnac interferometer . schematic diagram for x , showing that it is a synthesized zero - area sagnac interferometer . x and the measurement is made at an o . in the following sections we will further elaborate and generalize tdi to the realistic lisa configuration . the description of tdi for lisa is greatly simplified if we adopt the notation shown in figure 3 , where the overall geometry of the lisa detector is defined . there are three spacecraft , six optical benches , six lasers , six proof - masses , and twelve photodetectors . there are also six phase difference data going clock - wise and counter - clockwise around the lisa triangle . for the moment we will make the simplifying assumption that the array is stationary , i.e. , the back and forth optical paths between pairs of spacecraft are simply equal to their relative distances [ 44 , 7 , 45 , 58 ] . the optical paths are denoted by li , li where the index i corresponds to the opposite spacecraft . the unit vectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\rm{\hat n}}_i}$\end{document } point between pairs of spacecraft , with the orientation indicated . the optical paths are denoted by li , li where the index i corresponds to the opposite spacecraft . the unit vectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\rm{\hat n}}_i}$\end{document } point between pairs of spacecraft , with the orientation indicated . the double index notation recently employed in , where six quantities are involved , is self - evident . however , when algebraic manipulations are involved the following notation seems more convenient to use . the spacecraft are labeled 1 , 2 , 3 and their separating distances are denoted l1 , l2 , l3 , with li being opposite spacecraft i. we orient the vertices 1 , 2 , 3 clockwise in figure 3 . unit vectors between spacecraft are \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\hat n_i}$\end{document } , oriented as indicated in figure 3 . we index the phase difference data to be analyzed as follows : the beam arriving at spacecraft has subscript i and is primed or unprimed depending on whether the beam is traveling clockwise or counter - clockwise ( the sense defined here with reference to figure 3 ) around the lisa triangle , respectively . thus , as seen from the figure , s1 is the phase difference time series measured at reception at spacecraft 1 with transmission from spacecraft 2 ( along l3 ) . similarly , s1 is the phase difference series derived from reception at spacecraft 1 with transmission from spacecraft 3 . the other four one - way phase difference time series from signals exchanged between the spacecraft are obtained by cyclic permutation of the indices : 1 2 3 1 . we also adopt a notation for delayed data streams , which will be convenient later for algebraic manipulations . we define the three time - delay operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i},i = 1,2,3$\end{document } where for any data stream x(t ) 11\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\mathcal{d}_i}x(t ) = x(t - { l_i}),$$\end{document } where li , i = 1 , 2 , 3 , are the light travel times along the three arms of the lisa triangle ( the speed of light c is assumed to be unity in this article ) . thus , for example , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_{2{s_1}}}(t ) = { s_1}(t - { l_2}),{{\mathcal d}_2}{{\mathcal d}_{3{s_1}}}(t ) = { s_1}(t - { l_2 } - { l_3 } ) = { { \mathcal d}_3}{{\mathcal d}_{2{s_1}}}(t)$\end{document } , etc . if the li are functions of time then the operators no longer commute [ 7 , 58 ] , as will be described in section 4 . six more phase difference series result from laser beams exchanged between adjacent optical benches within each spacecraft ; these are similarly indexed as i , i , i = 1 , 2 , 3 . the proof - mass - plus - optical - bench assemblies for lisa spacecraft number 1 are shown schematically in figure 4 . the photo receivers that generate the data s1 , s1 , 1 , and 1 at spacecraft 1 are shown . the phase fluctuations from the six lasers , which need to be canceled , can be represented by six random processes pi , pi , where pi , pi are the phases of the lasers in spacecraft i on the left and right optical benches , respectively , as shown in the figure . note that this notation is in the same spirit as in [ 57 , 45 ] in which moving spacecraft arrays have been analyzed . figure 4schematic diagram of proof - masses - plus - optical - benches for a lisa spacecraft . the left - hand bench reads out the phase signals s1 and 1 . the right - hand bench analogously reads out s1 and 1 . the random displacements of the two proof masses and two optical benches are indicated ( lower case \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i},{\vec \delta ^{\prime}_i}$\end{document } for the proof masses , upper case \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i}$\end{document } , i for the optical benches ) . schematic diagram of proof - masses - plus - optical - benches for a lisa spacecraft . the random displacements of the two proof masses and two optical benches are indicated ( lower case \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i},{\vec \delta ^{\prime}_i}$\end{document } for the proof masses , upper case \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i}$\end{document } , i for the optical benches ) . we extend the cyclic terminology so that at vertex i , i = 1 , 2 , 3 , the random displacement vectors of the two proof masses are respectively denoted by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i}(t),{\vec \delta ^{\prime}_i}(t)$\end{document } , and the random displacements ( perhaps several orders of magnitude greater ) of their optical benches are correspondingly denoted by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i}(t),\;{\vec \delta ^{\prime}_i}(t)$\end{document } where the primed and unprimed indices correspond to the right and left optical benches , respectively . as pointed out in , the analysis does not assume that pairs of optical benches are rigidly connected , i.e. , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i } \neq { \vec \delta ^{\prime}_i}$\end{document } , in general . we ignore time - delay effects for these signals and will simply denote by i(t ) the phase fluctuations upon transmission through the fibers of the laser beams with frequencies i , and i . the i(t ) phase shifts within a given spacecraft might not be the same for large frequency differences ii for the envisioned frequency differences ( a few hundred mhz ) , however , the remaining fluctuations due to the optical fiber can be neglected . it is also assumed that the phase noise added by the fibers is independent of the direction of light propagation through them . for ease of presentation , in what follows we will assume the center frequencies of the lasers to be the same , and denote this frequency by 0 . the laser phase noise in s3 is therefore equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1}{p_2}(t ) - { p^{\prime}_3}(t)$\end{document}. similarly , since s2 is the phase shift measured on arrival at spacecraft 2 along arm 1 of a signal transmitted from spacecraft 3 , the laser phase noises enter into it with the following time signature : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1}{p^{\prime}_3}(t ) - { p_2}(t)$\end{document}. figure 4 endeavors to make the detailed light paths for these observations clear . an outgoing light beam transmitted to a distant spacecraft is routed from the laser on the local optical bench using mirrors and beam splitters ; this beam does not interact with the local proof mass . conversely , an incoming light beam from a distant spacecraft is bounced off the local proof mass before being reflected onto the photo receiver where it is mixed with light from the laser on that same optical bench . beams between adjacent optical benches within a single spacecraft are bounced off proof masses in the opposite way . light to be transmitted from the laser on an optical bench is first bounced off the proof mass it encloses and then directed to the other optical bench . upon reception it does not interact with the proof mass there , but is directly mixed with local laser light , and again down converted . the expressions for the si , si and i , 1 phase measurements can now be developed from figures 3 and 4 , and they are for the particular lisa configuration in which all the lasers have the same nominal frequency 0 , and the spacecraft are stationary with respect to each other.1 consider the s1(t ) process ( eq . ( 14 ) below ) . the photo receiver on the right bench of spacecraft 1 , which ( in the spacecraft frame ) experiences a time - varying displacement \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta ^{\prime}_1}$\end{document } , measures the phase difference s1 by first mixing the beam from the distant optical bench 3 in direction \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\hat n_2}$\end{document } , and laser phase noise p3 and optical bench motion \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ 3}$\end{document } that have been delayed by propagation along l2 , after one bounce off the proof mass \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\vec \delta ^{\prime}_1})$\end{document } , with the local laser light ( with phase noise p1 ) . since for this simplified configuration no frequency offsets are present , there is of course no need for any heterodyne conversion . in eq . ( 13 ) the 1 measurement results from light originating at the right - bench laser \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({p^{\prime}_1},\;{\vec \delta ^{\prime}_1})$\end{document } , bounced once off the right proof mass \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\vec \delta ^{\prime}_1})$\end{document } , and directed through the fiber ( incurring phase shift 1(t ) ) , to the left bench , where it is mixed with laser light ( p1 ) . the laser noises , the gravitational - wave signals , the optical path noises , and proof - mass and bench noises , enter into the four data streams recorded at vertex 1 according to the following expressions : 12\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_1 } = s_1^{{\rm{gw } } } + s_1^{{\rm{optical}}\;{\rm{path } } } + { \mathcal{d}_3}p_2^\prime - { p_1 } + { \nu _ 0}\left [ { - 2{{\hat n}_3}\cdot{{\vec \delta}_1 } + { { \hat n}_3}\cdot{{\vec \delta}_1 } + { { \hat n}_3}\cdot{\mathcal{d}_3}\vec \delta _ 2^\prime } \right],$$\end{document } 13\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\tau _ 1 } = p_1^\prime - { p_1 } - 2{\nu _ 0}{\hat n_2}\cdot\left({\vec \delta _ 1^\prime - \vec \delta _ 1^\prime } \right ) + { \mu _ 1}{.}$$\end{document } 14\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s_1^\prime = s_1^{\prime { \rm{gw } } } + s_1^{\prime { \rm{optical}}\;{\rm{path } } } + { \mathcal{d}_2}{p_3 } - p_1^\prime + { \nu _ 0}\left [ { 2{{\hat n}_2}\cdot\vec \delta _ 1^\prime - { { \hat n}_2}\cdot\vec \delta _ 1^\prime - { { \hat n}_2}\cdot{\mathcal{d}_2}{{\vec \delta}_3 } } \right],$$\end{document } 15\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\tau _ 1^\prime = { p_1 } - p_1^\prime + 2{\nu _ 0}{\hat n_3}\cdot\left({{{\vec \delta}_1 } - { { \vec \delta}_1 } } \right ) + { \mu _ 1}{.}$$\end{document } eight other relations , for the readouts at vertices 2 and 3 , are given by cyclic permutation of the indices in eqs . ( 12 ) , ( 13 ) , ( 14 ) , and ( 15 ) . the gravitational - wave phase signal components \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$s^{gw}_{i},s\prime^{gw}_{i},i=1,2,3$\end{document } in eqs . ( 12 ) and ( 14 ) are given by integrating with respect to time the eqs . ( 1 ) and ( 2 ) of reference , which relate metric perturbations to optical frequency shifts . the optical path phase noise contributions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$s_{i}^{optical\;path},s\prime_{i}^{optical\;path}$\end{document } which include shot noise from the low snr in the links between the distant spacecraft , can be derived from the corresponding term given in . the i , i measurements will be made with high snr so that for them the shot noise is negligible . in ground - based detectors the arms are chosen to be of equal length so that the laser light experiences identical delay in each arm of the interferometer . the required sensitivity of the instrument can thus only be achieved by near exact cancellation of the laser frequency noise . however , in lisa it is impossible to achieve equal distances between spacecraft , and the laser noise can not be canceled in this way . it is possible to combine the recorded data linearly with suitable time - delays corresponding to the three arm lengths of the giant triangular interferometer so that the laser phase noise is canceled . here we present a systematic method based on modules over polynomial rings which guarantees all the data combinations that cancel both the laser phase and the optical bench motion noises . we first consider the simpler case , where we ignore the optical - bench motion noise and consider only the laser phase noise . we do this because the algebra is somewhat simpler and the method is easy to apply . the simplification amounts to physically considering each spacecraft rigidly carrying the assembly of lasers , beam - splitters , and photodetectors . the two lasers on each spacecraft could be considered to be locked , so effectively there would be only one laser on each spacecraft . this mathematically amounts to setting \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \delta _ i } = { \vec \delta ^{\prime}_i } = 0$\end{document } and pi = pi . the scheme we describe here for laser phase noise can be extended in a straight - forward way to include optical bench motion noise , which we address in the last part of this section . the data combinations , when only the laser phase noise is considered , consist of the six suitably delayed data streams ( inter - spacecraft ) , the delays being integer multiples of the light travel times between spacecraft , which can be conveniently expressed in terms of polynomials in the three delay operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}$\end{document}. the laser noise cancellation condition puts three constraints on the six polynomials of the delay operators corresponding to the six data streams . the problem , therefore , consists of finding six - tuples of polynomials which satisfy the laser noise cancellation constraints . exist standard methods for obtaining the module , by which we mean methods for obtaining the generators of the module so that the linear combinations of the generators generate the entire module . the procedure first consists of obtaining a grbner basis for the ideal generated by the coefficients appearing in the constraints . this ideal is in the polynomial ring in the variables \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}$\end{document } over the domain of rational numbers ( or integers if one gets rid of the denominators ) . to obtain the grbner basis for the ideal , one may use the buchberger algorithm or use an application such as mathematica . from the grbner basis however , the method does not guarantee a minimal set and we find that a generating set of 4 polynomial six - tuples suffice to generate the required module . the importance of obtaining more data combinations is evident : they provide the necessary redundancy different data combinations produce different transfer functions for gws and the system noises so specific data combinations could be optimal for given astrophysical source parameters in the context of maximizing snr , detection probability , improving parameter estimates , etc . we now only have six data streams si and si , where i = 1 , 2 , 3 . the six data streams with terms containing only the laser frequency noise are 16\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { s_1 } = { \mathcal{d}_3}{p_2 } - { p_1 } , } \\ { s_1^\prime = { \mathcal{d}_2}{p_3 } - { p_1}\ ; } \\ \end{array}$$\end{document } and their cyclic permutations . note that we have intentionally excluded from the data additional phase fluctuations due to the gw signal , and noises such as the optical - path noise , proof - mass noise , etc . since our immediate goal is to cancel the laser frequency noise we have only kept the relevant terms . combining the streams for canceling the laser frequency noise will introduce transfer functions for the other noises and the gw signal . the goal of the analysis is to add suitably delayed beams together so that the laser frequency noise terms add up to zero . this amounts to seeking data combinations that cancel the laser frequency noise . in the notation / formalism that we have invoked , the delay is obtained by applying the operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_k}$\end{document}. to the beams si and si . a delay of k1l1 + k2l2 + k3l3 is represented by the operator \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal d}_1^{{k_1}}{\mathcal d}_2^{k2}{\mathcal d}_3^{{k_3}}$\end{document } acting on the data , where k1 , k2 , and k3 are integers . in general , a polynomial in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_k}$\end{document } , which is a polynomial in three variables , applied to , say , s1 combines the same data stream s1(t ) with different time - delays of the form k1l1 + k2l2 + k3l3 . one must find six polynomials say \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${q_i}({{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}),{q^{\prime}_i}({{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}),\;i = 1,2,3$\end{document } such that 17\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\sum\limits_{i = 1}^3 { { q_i } } { s_i } + q_i^\prime s_i^\prime = 0{.}$$\end{document } the zero on the right - hand side of the above equation signifies zero laser phase noise . this allows us to obtain a matrix operator equation whose solutions are q and q , where qi and qi are written as column vectors . we can similarly express si , si , pi as column vectors s , s , p , respectively . in matrix form eq . ( 16 ) becomes 18\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{s } } = { { \bf{d}}^t}\cdot{\bf{p}},\quad \quad { { \rm{s}}^\prime } = { \bf{d}}\cdot{\bf{p}},$$\end{document } where d is a 3 3 matrix given by 19\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\bf{d } } = \left({\begin{array}{*{20}c } { - 1 } & 0 & { { \mathcal{d}_2 } } \\ { { \mathcal{d}_3 } } & { - 1 } & 0 \\ 0 & { { \mathcal{d}_1 } } & { - 1 } \\ \end{array } } \right){.}$$\end{document } the exponent t represents the transpose of the matrix . ( 17 ) becomes 20\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\bf{q}}^t}\cdot{\bf{s } } + { { \bf{q}}^{\prime t}}\cdot{{\bf{s}}^\prime } = ( { { \bf{q}}^t}\cdot{{\bf{d}}^t } + { { \bf{q}}^{\prime t}}\cdot{\bf{d}})\cdot{\bf{p } } = 0,$$\end{document } where we have taken care to put p on the right - hand side of the operators . since the above equation must be satisfied for an arbitrary vector p , we obtain a matrix equation for the polynomials ( q , q ) : 21\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\bf{q}}^t}\cdot{{\bf{d}}^t } + { { \bf{q}}^\prime}\cdot{\bf{d } } = 0{.}$$\end{document } note that since the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_k}$\end{document}. commute , the order in writing these operators is unimportant . in mathematical terms , the polynomials form a commutative ring . the use of commutative algebra is very conveniently illustrated with the help of the simpler example of the unequal - arm interferometer . here there are only two arms instead of three as we have for lisa , and the mathematics is much simpler and so it easy to see both physically and mathematically how commutative algebra can be applied to this problem of laser phase noise cancellation . the procedure is well known for the unequal - arm interferometer , but here we will describe the same method but in terms of the delay operators that we have introduced . let (t ) denote the laser phase noise entering the laser cavity as shown in figure 5 . consider this light (t ) making a round trip around arm 1 whose length we take to be l1 . if we interfere this phase with the incoming light we get the phase 1(t ) , where 22\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\phi _ 1}(t ) = \phi ( t - 2{l_1 } ) - \phi ( t ) \equiv ( \mathcal{d}_1 ^ 2 - 1)\phi ( t){.}$$\end{document } the second expression we have written in terms of the delay operators . we can do the same for the arm 2 to get another phase 2(t ) , where 23\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\phi _ 2}(t ) = \phi ( t - 2{l_2 } ) - \phi ( t ) \equiv ( \mathcal{d}_2 ^ 2 - 1)\phi ( t){.}$$\end{document } clearly , if l1 l2 , then the difference in phase 2(t ) 1(t ) is not zero and the laser phase noise does not cancel out . however , if one further delays the phases 1(t ) and 2 ( ) and constructs the following combination , 24\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x(t ) = [ { \phi _ 2}(t - 2{l_1 } ) - { \phi _ 2}(t ) ] - [ { \phi _ 1}(t - 2{l_2 } ) - { \phi _ 1}(t)],$$\end{document } then the laser phase noise does cancel out . the beam shown corresponds to the term \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\mathcal d}_2 ^ 2 - 1)({\mathcal d}_1 ^ 2 - 1)\phi ( t)$\end{document } in x(t ) which is first sent around arm 1 followed by arm 2 . the second beam ( not shown ) is first sent around arm 2 and then through arm 1 . the beam shown corresponds to the term \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\mathcal d}_2 ^ 2 - 1)({\mathcal d}_1 ^ 2 - 1)\phi ( t)$\end{document } in x(t ) which is first sent around arm 1 followed by arm 2 . the second beam ( not shown ) is first sent around arm 2 and then through arm 1 . the cancellation of laser frequency noise becomes obvious from the operator algebra in the following way . in the operator notation , 25\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { x(t ) = ( \mathcal{d}_1 ^ 2 - 1){\phi _ 2}(t ) - ( \mathcal{d}_2 ^ 2 - 1){\phi _ 1}(t)\quad \quad \quad \quad \quad \quad \quad } \\ { = [ ( \mathcal{d}_1 ^ 2 - 1)(\mathcal{d}_2 ^ 2 - 1 ) - ( \mathcal{d}_2 ^ 2 - 1)(\mathcal{d}_1 ^ 2 - 1)]\phi ( t ) } \\ { = 0.\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \ ; } \\ \end{array}$$\end{document } from this one immediately sees that just the commutativity of the operators has been used to cancel the laser phase noise . the basic idea was to compute the lowest common multiple ( l.c.m . ) of the polynomials \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal d}_1 ^ 2 - 1$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal d}_2 ^ 2 - 1$\end{document } ( in this case the l.c.m . is just the product , because the polynomials are relatively prime ) and use this fact to construct x(t ) in which the laser phase noise is canceled . in fact we will be using the notion of a grobner basis which is in a sense the generalization of the notion of the greatest common divisor ( gcd ) . since lisa has three spacecraft and six inter - spacecraft beams , the problem of the unequal - arm interferometer only gets technically more complex ; in principle the problem is the same as in this simpler case . thus , the simple operations which were performed here to obtain a laser noise free combination x(t ) are not sufficient and more sophisticated methods need to be adopted from the field of commutative algebra . we merely mention these solutions here ; in the forthcoming text we will discuss them in detail . the solution is given by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$- { { \rm{q}}^{\rm{t } } } = { { \rm{q^{\prime}}}^t } = ( { { \mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3})$\end{document}. the solution is described by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\rm{q}}^t } = - ( 1,{{\mathcal d}_3},{{\mathcal d}_1},{{\mathcal d}_3})$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\rm{q^{\prime}}}^t } = ( 1,{{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_2})$\end{document}. the solutions and are obtained from by cyclically permuting the indices of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_k},{\rm{q}}$\end{document } and q. these solutions are important , because they consist of polynomials with lowest possible degrees and thus are simple . other solutions containing higher degree polynomials can be generated conveniently from these solutions . since the system of equations is linear , linear combinations of these solutions are also solutions to eq . however , it is important to realize that we do not have a vector space here . three independent constraints on a six - tuple do not produce a space which is necessarily generated by three basis elements . this conclusion would follow if the solutions formed a vector space but they do not . the polynomial six - tuple q , q can be multiplied by polynomials in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}$\end{document } ( scalars ) which do not form a field . we , therefore , have a module over the ring of polynomials in the three variables \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}$\end{document}. first we present the general methodology for obtaining the solutions to eq . ( 21 ) and then apply it to eq . ( since the equations are linear , the solutions space is a submodule of the module of six - tuples of polynomials . the module of six - tuples is a free module , i.e. , it has six basis elements that not only generate the module but are linearly independent . a natural choice of the basis is fm = ( 0 , , 1 , , 0 ) with 1 in the m - th place and 0 everywhere else ; m runs from 1 to 6 . the definitions of generation ( spanning ) and linear independence are the same as that for vector spaces . but our interest lies in its submodule which need not be free and need not have just three generators as it would seem if we were dealing with vector spaces . the problem at hand is of finding the generators of this submodule , i.e. , any element of the submodule should be expressible as a linear combination of the generating set . in this way the generators are capable of spanning the full submodule or generating the submodule . in order to achieve our goal , we rewrite eq . ( 21 ) explicitly component - wise : 26\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } + q_1^\prime - { \mathcal{d}_3}q_2^\prime - { \mathcal{d}_2}{q_3 } = 0 , } \\ { { q_2 } + q_2^\prime - { \mathcal{d}_1}q_3^\prime - { \mathcal{d}_3}{q_1 } = 0 , } \\ { { q_3 } + q_3^\prime - { \mathcal{d}_2}q_1^\prime - { \mathcal{d}_1}{q_2 } = 0 . } \\ \end{array}$$\end{document } the first step is to use gaussian elimination to obtain q1 and q2 in terms of q3 , q1 , q2 , q3 , 27\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } = - q_1^\prime + { \mathcal{d}_3}q_2^\prime + { \mathcal{d}_2}{q_3},\quad \quad \quad \quad \quad \quad \quad \quad } \\ { { q_2 } = - q_2^\prime + { \mathcal{d}_1}q_3^\prime + { \mathcal{d}_3}{q_1}\quad \quad \quad \quad \quad \quad \quad \quad \ ; } \\ { = - { \mathcal{d}_3}q_1^\prime - ( 1 - \mathcal{d}_3 ^ 2)q_2^\prime + { \mathcal{d}_1}q_3^\prime + { \mathcal{d}_2}{\mathcal{d}_3}{q_3 } , } \\ \end{array}$$\end{document } and then substitute these values in the third equation to obtain a linear implicit relation between q3 , q1 , q2 , q3 . we then have : 28\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$(1 - { \mathcal{d}_1}{\mathcal{d}_2}{\mathcal{d}_3}){q_3 } + ( { \mathcal{d}_1}{\mathcal{d}_3 } - { \mathcal{d}_2})q_1^\prime + { \mathcal{d}_1}(1 - \mathcal{d}_3 ^ 2)q_2^\prime + ( 1 - \mathcal{d}_1 ^ 2)q_3^\prime = 0{.}$$\end{document } obtaining solutions to eq . ( 28 ) amounts to solving the problem since the remaining polynomials q1 , q2 have been expressed in terms of q3 , q1 , q2 , q3 in eq . note that we can not carry on the gaussian elimination process any further , because none of the polynomial coefficients appearing in eq . we will assume that the polynomials have rational coefficients , i.e. , the coefficients belong to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}$\end{document } , the field of the rational numbers . the set of polynomials form a ring the polynomial ring in three variables , which we denote by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r } = { \mathcal q}[{{\mathcal d}_1},{{\mathcal d}_2},{{\mathcal d}_3}]$\end{document}. the polynomial vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({q_3},{q^{\prime}_1},{q^{\prime}_2},{q^{\prime}_3})\;\;\in \;{{\mathcal r}^4}$\end{document}. the set of solutions to eq . ( 28 ) is just the kernel of the homomorphism \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\varphi \;:{{\mathcal r}^4}\ ; \rightarrow { \mathcal r}$\end{document } , where the polynomial vector ( q3 , q1 , q2 , q3 ) is mapped to the polynomial \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(1 - { { \mathcal d}_1}{{\mathcal d}_2}{{\mathcal d}_3}){q_3}\ ; + ( { { \mathcal d}_1}{{\mathcal d}_3 } - { { \mathcal d}_2}){q^{\prime}_1 } + { { \mathcal d}_1}(1 - { \mathcal d}_3 ^ 2){q^{\prime}_2}\ ; + ( 1 - { \mathcal d}_1 ^ 2){q^{\prime}_3}$\end{document}. thus , the solution space ker is a submodule of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal r}^4}$\end{document}. it is called the module of syzygies . the generators of this module can be obtained from standard methods available in the literature . we briefly outline the method given in the books by becker et al . , and kreuzer and robbiano below . the details have been included in appendix a. the first step is to obtain the grbner basis for the ideal \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } generated by the coefficients in eq . ( 28 ) : 29\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${u_1 } = 1 - { \mathcal{d}_1}{\mathcal{d}_2}{\mathcal{d}_3},\quad \quad { u_2 } = { \mathcal{d}_1}{\mathcal{d}_3 } - { \mathcal{d}_2},\quad \quad { u_3 } = { \mathcal{d}_1}(1 - \mathcal{d}_3 ^ 2)\;,\quad \quad { u_4 } = 1 - \mathcal{d}_1 ^ 2{.}$$\end{document } the ideal \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } consists of linear combinations of the form viui where vi , i = 1 , , 4 are polynomials in the ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal r}$\end{document}. there can be several sets of generators for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document}. a grbner basis is a set of generators which is there are several ways to look at the theory of grbner basis . one way is the following : suppose we are given polynomials g1 , g2 , , gm in one variable over say \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}$\end{document } and we would like to know whether another polynomial f belongs to the ideal generated by the g s . a good way to decide the issue would be to first compute the gcd g of g1 , g2 , , gm and check whether f is a multiple of g. one can achieve this by doing the long division of f by g and checking whether the remainder is zero . all this is possible because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}[x]$\end{document } is a euclidean domain and also a principle ideal domain ( pid ) wherein any ideal is generated by a single element . therefore we have essentially just one polynomial the gcd which generates the ideal generated by g1 , g2 , , gm . the ring of integers or the ring of polynomials in one variable over any field are examples of pids whose ideals are generated by single elements . however , when we consider more general rings ( not pids ) like the one we are dealing with here , we do not have a single gcd but a set of several polynomials which generates an ideal in general . a grbner basis of an ideal can be thought of as a generalization of the gcd . in the univariate case grbner basis theory generalizes these ideas to multivariate polynomials which are neither euclidean rings nor pids . since there is in general not a single generator for an ideal , grbner basis theory comes up with the idea of dividing a polynomial with a set of polynomials , the set of generators of the ideal , so that by successive divisions by the polynomials in this generating set of the given polynomial , the remainder becomes zero . clearly , those special generating sets that do possess this property ( and they exist ! ) are called grbner bases . in order for a division to be carried out in a sensible manner , an order must be put on the ring of polynomials , so that the final remainder after every division is strictly smaller than each of the divisors in the generating set . a natural order exists on the ring of integers or on the polynomial ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}(x)$\end{document } ; the degree of the polynomial decides the order in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}(x)$\end{document}. however , even for polynomials in two variables there is no natural order a priori ( is x + y greater or smaller than x + y ? ) . but one can , by hand as it were , put an order on such a ring by saying x y , where is an order , called the lexicographical order . we follow this type of order , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_1 } \gg { { \mathcal d}_2 } \gg { { \mathcal d}_3}$\end{document } and ordering polynomials by considering their highest degree terms . it is possible to put different orderings on a given ring which then produce different grbner bases . small elements so that division is possible and every element of the ideal when divided by the grbner basis elements leaves zero remainder , i.e. , every element modulo the grbner basis reduces to zero . in the literature , there exists a well - known algorithm called the buchberger algorithm , which may be used to obtain the grbner basis for a given set of polynomials in the ring . so a grbner basis of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } can be obtained from the generators ui given in eq . it is essentially again a generalization of the usual long division that we perform on univariate polynomials . mathematica yields a 3-element grbner basis \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal g}$\end{document } for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } : 30\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\mathcal{g } = \{\mathcal{d}_3 ^ 2 - 1,\mathcal{d}_2 ^ 2 - 1,{\mathcal{d}_1 } - { \mathcal{d}_2}{\mathcal{d}_3}\ } { .}$$\end{document } one can easily check that all the ui of eq . ( 29 ) are linear combinations of the polynomials in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal g}$\end{document } and hence \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal g}$\end{document } generates \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document}. one also observes that the elements look small in the order mentioned above . however , one can satisfy oneself that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal g}$\end{document } is a grbner basis by using the standard methods available in the literature . one method consists of computing the s - polynomials ( see appendix a ) for all the pairs of the grbner basis elements and checking whether these reduce to zero modulo \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal g}$\end{document}. this grbner basis of the ideal \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } is then used to obtain the generators for the module of syzygies . note that although the grbner basis depends on the order we choose among the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_k}$\end{document } , the module itself is independent of the order . the generating set for the module is obtained by further following the procedure in the literature [ 3 , 29 ] . these generators do not form a minimal set and there are relations between them ; in fact this method does not guarantee a minimum set of generators . these generators can be expressed as linear combinations of , , , and also in terms of x , x , x , x given below in eq . the importance in obtaining the seven generators is that the standard theorems guarantee that these seven generators do in fact generate the required module . therefore , from this proven set of generators we can check whether a particular set is in fact a generating set . alternatively , we may use a software package called macaulay 2 which directly calculates the generators given the eqs . again , macaulay s algorithm does not yield a minimal set ; we can express the last two generators in terms of the first four . below we list this smaller set of four generators in the order x = ( q1 , q2 , q3 , q1 , q2 , q3 ) : 31\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { x^{(1 ) } } = ( { \mathcal{d}_2 } - { \mathcal{d}_1}{\mathcal{d}_3},0,1 - \mathcal{d}_3 ^ 2,0,\;{\mathcal{d}_2}{\mathcal{d}_3 } - { \mathcal{d}_1},\;\mathcal{d}_3 ^ 2 - 1 ) , } \\ { { x^{(2 ) } } = ( - { \mathcal{d}_1},\ ; - { \mathcal{d}_2},\ ; - { \mathcal{d}_3},\;{\mathcal{d}_1},\;{\mathcal{d}_2},\;{\mathcal{d}_3}),\quad \quad \quad \quad \quad \ ; } \\ { { x^{(3 ) } } = ( - 1,\ ; - { \mathcal{d}_3},\ ; - { \mathcal{d}_1}{\mathcal{d}_3},1,\;{\mathcal{d}_1}{\mathcal{d}_2},\;{\mathcal{d}_2}),\quad \quad \quad \quad \;\ ; } \\ { { x^{(4 ) } } = ( - { \mathcal{d}_1}{\mathcal{d}_2},\ ; - 1,\ ; - { \mathcal{d}_1},\;{\mathcal{d}_3},1,\;{\mathcal{d}_2}{\mathcal{d}_3}).\quad \quad \quad \quad \;\;\ , } \\ \end{array}$$\end{document } note that the last three generators are just x = , x = , x = . an extra generator x is needed to generate all the solutions . another set of generators which may be useful for further work is a grbner basis of a module . the concept of a grbner basis of an ideal can be extended to that of a grbner basis of a submodule of ( k[x1 , x2 , , xn ] ) where k is a field , since a module over the polynomial ring can be considered as generalization of an ideal in a polynomial ring . just as in the case of an ideal , a grbner basis for a module is a generating set with special properties . for the module under consideration we obtain a grbner basis using macaulay 2 : 32\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { g^{(1 ) } } = ( - { \mathcal{d}_1},\ ; - { \mathcal{d}_2},\ ; - { \mathcal{d}_3},\;{\mathcal{d}_1},\;{\mathcal{d}_2},\;{\mathcal{d}_3}),\quad \quad \quad \quad \quad \ , } \\ { { g^{(2 ) } } = ( { \mathcal{d}_2 } - { \mathcal{d}_1}{\mathcal{d}_3},0,1 - \mathcal{d}_3 ^ 2,0,\;{\mathcal{d}_2}{\mathcal{d}_3 } - { \mathcal{d}_1},\;\mathcal{d}_3 ^ 2 - 1),\ , } \\ { { g^{(3 ) } } = ( - { \mathcal{d}_1}{\mathcal{d}_2},\ ; - 1,\ ; - { \mathcal{d}_1},\;{\mathcal{d}_3},1,\;{\mathcal{d}_2}{\mathcal{d}_3}),\quad \quad \quad \quad \quad \ ; } \\ { { g^{(4 ) } } = ( - 1,\ ; - { \mathcal{d}_3},\ ; - { \mathcal{d}_1}{\mathcal{d}_3},1,\;{\mathcal{d}_1}{\mathcal{d}_2},\;{\mathcal{d}_2}),\quad \quad \quad \quad \quad } \\ { { g^{(5 ) } } = ( { \mathcal{d}_3}(1 - \mathcal{d}_1 ^ 2),\;\mathcal{d}_3 ^ 2 - 1,0,0,1 - \mathcal{d}_1 ^ 2,\;{\mathcal{d}_1}(\mathcal{d}_3 ^ 2 - 1 ) ) . } \\ \end{array}$$\end{document } note that in this grbner basis g = = x , g = x , g = = x , g = = x. only g is the new generator . another set of generators are just , , , and . this can be checked using macaulay 2 , or one can relate , , , and to the generators x , a = 1 , 2 , 3 , 4 , by polynomial matrices . in appendix b , we express the seven generators we obtained following the literature , in terms of , , , and . also we express , , , and in terms of x. this proves that all these sets generate the required module of syzygies . the question now arises as to which set of generators we should choose which facilitates further analysis . also we would prefer low degree polynomials to appear in the generators so as to avoid cancellation of leading terms in the polynomials . by these two criteria we may choose x or , , , . however , , , , possess the additional property that this set is left invariant under a cyclic permutation of indices 1 , 2 , 3 . it is found that this set is more convenient to use because of this symmetry . there are now twelve doppler data streams which have to be combined in an appropriate manner in order to cancel the noise from the laser as well as from the motion of the optical benches . as in the previous case of canceling laser phase noise , here too , we keep the relevant terms only , namely those terms containing laser phase noise and optical bench motion noise . we then have the following expressions for the four data streams on spacecraft 1 : 33\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_1 } = { \mathcal{d}_3}\left [ { p_2^\prime + { \nu _ 0}{{{\bf{\hat n}}}_3}\cdot\vec \delta _ 2^\prime } \right ] - \left [ { { p_1 } - { \nu _ 0}{{{\bf{\hat n}}}_3}\cdot{{\vec \delta}_1 } } \right],$$\end{document } 34\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$s_1^\prime = { \mathcal{d}_2}\left [ { { p_3 } - { \nu _ 0}{{{\bf{\hat n}}}_2}\cdot{{\vec \delta}_3 } } \right ] - \left [ { p_1^\prime + { \nu _ 0}{{{\bf{\hat n}}}_2}\cdot\vec \delta _ 1^\prime } \right],$$\end{document } 35\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\tau _ 1 } = p_1^\prime - { p_1 } + 2{\nu _ 0}{{\bf{\hat n}}_2}\cdot\vec \delta _ 1^\prime + { \mu _ 1},$$\end{document } 36\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\tau _ 1^\prime = { p_1 } - p_1^\prime - 2{\nu _ 0}{{\bf{\hat n}}_3}\cdot{\vec \delta _ 1 } + { \mu _ 1}{.}$$\end{document } the other eight data streams on spacecraft 2 and 3 are obtained by cyclic permutations of the indices in the above equations . in order to simplify the derivation of the expressions canceling the optical bench noises ( 35 ) , we can rewriting the resulting expression ( and those obtained from it by permutation of the spacecraft indices ) in the following form : 37\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${z_1 } \equiv { 1 \over 2}({\tau _ 1 } - \tau _ 1^\prime ) = \phi _ 1^\prime - { \phi _ 1},$$\end{document } where 1 , 1 are defined as 38\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { \phi _ 1^\prime \equiv p_1^\prime + { \nu _ 0}{{{\bf{\hat n}}}_2}\cdot\vec \delta _ 1^\prime , } \\ { { \phi _ 1 } \equiv { p_1 } - { \nu _ 0}{{{\bf{\hat n}}}_3}\cdot{{\vec \delta}_1 } , } \\ \end{array}$$\end{document } the importance in defining these combinations is that the expressions for the data streams si , si simplify into the following form : 39\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { s_1 } = { \mathcal{d}_3}\phi _ 2^\prime - { \phi _ 1 } , } \\ { s_1^\prime = { \mathcal{d}_2}{\phi _ 3 } - \phi _ 1^\prime . } \\ \end{array}$$\end{document } if we now combine the si , si , and zi in the following way , 40\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 1 } \equiv { s_1 } - { \mathcal{d}_3}{z_2 } = { \mathcal{d}_3}{\phi _ 2 } - { \phi _ 1},\quad \quad { \eta _ { 1^\prime } } \equiv { s_{1^\prime } } + { z_1 } = { \mathcal{d}_2}{\phi _ 3 } - { \phi _ 1},$$\end{document } 41\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 2 } \equiv { s_2 } - { \mathcal{d}_1}{z_3 } = { \mathcal{d}_1}{\phi _ 3 } - { \phi _ 2},\quad \quad { \eta _ { 2^\prime } } \equiv { s_{2^\prime } } + { z_2 } = { \mathcal{d}_3}{\phi _ 1 } - { \phi _ 2},$$\end{document } 42\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 3 } \equiv { s_3 } - { \mathcal{d}_2}{z_1 } = { \mathcal{d}_2}{\phi _ 1 } - { \phi _ 3},\quad \quad { \eta _ { 3^\prime } } \equiv { s_{3^\prime } } + { z_3 } = { \mathcal{d}_1}{\phi _ 2 } - { \phi _ 3},$$\end{document } we have just reduced the problem of canceling of six laser and six optical bench noises to the equivalent problem of removing the three random processes 1 , 2 , and 3 from the six linear combinations i , i of the one - way measurements si , si , and zi . by comparing the equations above to eq . ( 16 ) for the simpler configuration with only three lasers , analyzed in the previous sections 4.1 to 4.4 , we see that they are identical in form . it is important to notice that the four interferometric combinations ( , , , ) , which can be used as a basis for generating the entire tdi space , are actually synthesized sagnac interferometers . this can be seen by rewriting the expression for , for instance , in the following form , 43\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\alpha = [ { \eta _ { 1^\prime } } + { \mathcal{d}_2}{\eta _ { 3^\prime } } + { \mathcal{d}_1}{\mathcal{d}_2}{\eta _ { 2^\prime } } ] - [ { \eta _ 1 } + { \mathcal{d}_3}{\eta _ 2 } + { \mathcal{d}_1}{\mathcal{d}_3}{\eta _ 3}],$$\end{document } and noticing that the first square bracket on the right - hand side of eq . ( 43 ) contains a combination of one - way measurements describing a light beam propagating clockwise around the array , while the other terms in the second square - bracket give the equivalent of another beam propagating counter - clockwise around the constellation . contrary to , , and , can not be visualized as the difference ( or interference ) of two synthesized beams . however , it should still be regarded as a sagnac combination since there exists a time - delay relationship between it and , , and : 44\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\zeta - { \mathcal{d}_1}{\mathcal{d}_2}{\mathcal{d}_3}\zeta = { \mathcal{d}_1}\alpha - { \mathcal{d}_2}{\mathcal{d}_3}\alpha + { \mathcal{d}_2}\beta - { \mathcal{d}_3}{\mathcal{d}_1}\beta + { \mathcal{d}_3}\gamma - { \mathcal{d}_1}{\mathcal{d}_2}\gamma { .}$$\end{document } as a consequence of the time - structure of this relationship , has been called the symmetrized sagnac combination . by using the four generators , it is possible to construct several other interferometric combinations , such as the unequal - arm michelson ( x , y , z ) , the beacons ( p , q , r ) , the monitors ( e , f , g ) , and the relays ( u , v , w ) . contrary to the sagnac combinations , these only use four of the six data combinations i , i . these observables can be written in terms of the sagnac observables ( , , , ) in the following way , 45\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { \mathcal{d}_1}x = { \mathcal{d}_2}{\mathcal{d}_3}\alpha - { \mathcal{d}_2}\beta - { d_3}\gamma + \zeta , } \\ { p = \zeta - { \mathcal{d}_1}\alpha , \quad \quad \quad \quad \quad } \\ { e = \alpha - { \mathcal{d}_1}\zeta , \quad \quad \quad \quad \quad } \\ { u = { \mathcal{d}_1}\gamma - \beta , \quad \quad \quad \quad \quad } \\ \end{array}$$\end{document } as it is easy to verify by substituting the expressions for the sagnac combinations into the above equations . figure 6schematic diagrams of the unequal - arm michelson , monitor , beacon , and relay combinations . these tdi combinations rely only on four of the six one - way doppler measurements , as illustrated here . schematic diagrams of the unequal - arm michelson , monitor , beacon , and relay combinations . these tdi combinations rely only on four of the six one - way doppler measurements , as illustrated here . in the case of the combination x , in particular , by writing it in the following form , 46\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x = [ ( { \eta _ { 1^\prime } } + { \mathcal{d}_2}{\eta _ 3 } ) + { \mathcal{d}_2}{\mathcal{d}_2}({\eta _ 1 } + { \mathcal{d}_3}{\eta _ 2 } ) ] - [ ( { \eta _ 1 } + { \mathcal{d}_3}{\eta _ { 2^\prime } } ) + { \mathcal{d}_3}{\mathcal{d}_3}({\eta _ { 1^\prime } } + { \mathcal{d}_2}{\eta _ 3})],$$\end{document } one can notice ( as pointed out in and ) that this combination can be visualized as the difference of two sums of phase measurements , each corresponding to a specific light path from a laser onboard spacecraft 1 having phase noise 1 . the first square - bracket term in eq . ( 46 ) represents a synthesized light - beam transmitted from spacecraft 1 and made to bounce once at spacecraft 2 and 3 , respectively . the second square - bracket term instead corresponds to another beam also originating from the same laser , experiencing the same overall delay as the first beam , but bouncing off spacecraft 3 first and then spacecraft 2 . when they are recombined they will cancel the laser phase fluctuations exactly , having both experienced the same total delay ( assuming stationary spacecraft ) . the x combinations should therefore be regarded as the response of a zero - area sagnac interferometer . the rotational motion of the lisa array results in a difference of the light travel times in the two directions around a sagnac circuit [ 44 , 7 ] . two time delays along each arm must be used , say li and li for clockwise or counter - clockwise propagation as they enter in any of the tdi combinations . furthermore , since li and li not only differ from one another but can be time dependent ( they flex ) , it was shown that the first generation tdi combinations do not completely cancel the laser phase noise ( at least with present laser stability requirements ) , which can enter at a level above the secondary noises . for lisa , and assuming \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\dot l_i } \simeq \;10{\rm{m / s}}$\end{document } , the estimated magnitude of the remaining frequency fluctuations from the laser can be about 30 times larger than the level set by the secondary noise sources in the center of the frequency band . in order to solve this potential problem , it has been shown that there exist new tdi combinations that are immune to first order shearing ( flexing , or constant rate of change of delay times ) . these combinations can be derived by using the time - delay operators formalism introduced in the previous section 4 , although one has to keep in mind that now these operators no longer commute . in order to derive the new , flex - free tdi combinations we will start by taking specific combinations of the one - way data entering in each of the expressions derived in the previous section 4 . note , however , that now the expressions for the -measurements assume the following form 47\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 1 } = { \mathcal{d}_3}{\phi _ 2 } - { \phi _ 1},\quad \quad { \eta _ { 1^\prime } } = { \mathcal{d}_{2^\prime}}{\phi _ 3 } - { \phi _ 1},$$\end{document } 48\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 2 } = { \mathcal{d}_1}{\phi _ 3 } - { \phi _ 2},\quad \quad { \eta _ { 2^\prime } } = { \mathcal{d}_{3^\prime}}{\phi _ 1 } - { \phi _ 2},$$\end{document } 49\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 3 } = { \mathcal{d}_2}{\phi _ 1 } - { \phi _ 3},\quad \quad { \eta _ { 3^\prime } } = { \mathcal{d}_{1^\prime}}{\phi _ 2 } - { \phi _ 3},$$\end{document } where the i , i = 1 , 2 , 3 measurements are as given in eq . the new tdi combinations are chosen in such a way so as to retain only one of the three noises i , i = 1 , 2 , 3 , if possible . in this way we can then implement an iterative procedure based on the use of these basic combinations and of time - delay operators , to cancel the laser noises after dropping terms that are quadratic in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\dot l / c$\end{document } or linear in the accelerations . this iterative time - delay method , to first order in the velocity , is illustrated abstractly as follows . given a function of time = (t ) , time delay by li is now denoted either with the standard comma notation or by applying the delay operator \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i}$\end{document } introduced in the previous section 4 , 50\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\mathcal{d}_i}\psi = { \psi _ { , i } } \equiv \psi ( t - { l_i}(t)){.}$$\end{document } we then impose a second time delay li(t ) : 51\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { { \mathcal d}_j}{{\mathcal d}_i}\psi = { \psi _ { ; ij } } \equiv \psi ( t - { l_j}(t ) - { l_i}(t - { l_j}(t)))\quad \,\ , } \\ { \quad \quad \quad \quad \quad \simeq \psi ( t - { l_j}(t ) - { l_i}(t ) + { { \dot l}_i}(t){l_j } ) } \\ { \quad \quad \quad \quad \ , \simeq { \psi _ { , ij } } + { { \dot \psi}_{,ij}}{{\dot l}_i}{l_j}.\quad \quad \quad \quad \quad } \\ \end{array}$$\end{document } a third time delay lk(t ) gives 52\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { \mathcal{d}_k}{\mathcal{d}_j}{\mathcal{d}_i}\psi = { \psi _ { ; ijk } } = \psi ( t - { l_k}(t ) - { l_j}(t - { l_k}(t ) ) - { l_i}(t - { l_k}(t ) - { l_j}(t - { l_k}(t ) ) ) ) } \\ { \simeq { \psi _ { , ijk } } + { { \dot \psi}_{,ijk}}\left [ { { { \dot l}_i}({l_j } + { l_k } ) + { { \dot l}_j}{l_k } } \right],\quad \quad \;\ ; } \\ \end{array}$$\end{document } and so on , recursively ; each delay generates a first - order correction proportional to its rate of change times the sum of all delays coming after it in the subscripts . commas have now been replaced with semicolons , to remind us that we consider moving arrays . when the sum of these corrections to the terms of a data combination vanishes , the combination is called flex - free . also , note that each delay operator \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i}$\end{document } has a unique inverse \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d_i^{- 1}$\end{document } , whose expression can be derived by requiring that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$d_i^{- 1}{{\mathcal d}_i } = i$\end{document } , and neglecting quadratic and higher order velocity terms . its action on a time series (t ) is 53\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$d_i^{- 1}\psi ( t ) \equiv \psi ( t + { l_i}(t + { l_i})){.}$$\end{document } note that this is not like an advance operator one might expect , since it advances not by li(t ) but rather li(t + li ) . the unequal - arm michelson combination relies on the four measurements 1 , 1 , 2 , and 3 . note that the two combinations 1 + 2,3 , 1 + 3,2 represent the two synthesized two - way data measured onboard spacecraft 1 , and can be written in the following form ( see eqs . ( 47 ) , ( 48 ) , and ( 49 ) for deriving the following synthesized two - way measurements ) 54\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ 1 } + { \eta _ { 2^\prime,3 } } = ( { \mathcal{d}_3}{\mathcal{d}_{3^\prime } } - i){\phi _ 1},$$\end{document } 55\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ { { 1^\prime } } } + { \eta _ { 3,{2^\prime } } } = ( { \mathcal{d}_{{2^\prime}}}{\mathcal{d}_2 } - i){\phi _ 1},$$\end{document } where is the identity operator . since in the stationary case any pairs of these operators commute , i.e. , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i}{{\mathcal d}_{{j^\prime } } } - { { \mathcal d}_{{j^\prime}}}{{\mathcal d}_i } = 0$\end{document } , from eqs . ( 54 ) and ( 55 ) it is easy to derive the following expression for the unequal - arm interferometric combination x which eliminates 1 : 56\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$x = [ { \mathcal{d}_{{2^\prime}}}{\mathcal{d}_2 } - i]({\eta _ 1 } + { \eta _ { { 2^\prime},3 } } ) - [ ( { \mathcal{d}_3}{\mathcal{d}_{{3^\prime } } } - i)]({\eta _ { { 1^\prime } } } + { \eta _ { 3,{2^\prime}}}){.}$$\end{document } if , on the other hand , the time - delays depend on time , the expression of the unequal - arm michelson combination above no longer cancels 1 . in order to derive the new expression for the unequal - arm interferometer that accounts for flexing , let us first consider the following two combinations of the one - way measurements entering into the x observable given in eq . ( 56 ) : 57\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[({\eta _ { { 1^\prime } } } + { \eta _ { 3;{2^\prime } } } ) + { ( { \eta _ 1 } + { \eta _ { { 2^\prime};3}})_{;{{22}^\prime } } } ] = [ { d_{{2^\prime}}}{d_2}{d_3}{d_{{3^\prime } } } - i]{\phi _ 1},$$\end{document } 58\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[({\eta _ 1 } + { \eta _ { { 2^\prime};3 } } ) + { ( { \eta _ { { 1^\prime } } } + { \eta _ { 3;{2^\prime}}})_{;{3^\prime}3 } } ] = [ { d_3}{d_{{3^\prime}}}{d_{{2^\prime}}}{d_2 } - i]{\phi _ 1}{.}$$\end{document } using eqs . ( 57 ) and ( 58 ) , we can use the delay technique again to finally derive the following expression for the new unequal - arm michelson combination x1 that accounts for the flexing effect : 59\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { x_1 } = [ { d_{{2^\prime}}}{d_2}{d_3}{d_{{3^\prime } } } - i][({\eta _ 1 } + { \eta _ { { 2^\prime};{3^\prime } } } ) + { { ( { \eta _ { { 1^\prime } } } + { \eta _ { 3;{2^\prime}}})}_{;{3^\prime}3}}]\quad \quad \quad } \\ { - [ { d_3}{d_{{3^\prime}}}{d_{{2^\prime}}}{d_2 } - i][({\eta _ { { 1^\prime } } } + { \eta _ { 3,\cdot{2^\prime } } } ) + { { ( { \eta _ 1 } + { \eta _ { { 2^\prime};3}})}_{;{{22}^\prime } } } ] . } \\ \end{array}$$\end{document } as usual , x2 and x3 are obtained by cyclic permutation of the spacecraft indices . this expression is readily shown to be laser - noise - free to first order of spacecraft separation velocities \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\dot l_i}$\end{document } : it is flex - free . in the above section 5.1 , we have used the same symbol x for the unequal - arm michelson combination for both the rotating ( i.e. , constant delay times ) and stationary cases . this emphasizes that , for this tdi combination ( and , as we will see below , also for all the combinations including only four links ) the forms of the equations do not change going from systems at rest to the rotating case . one needs only distinguish between the time - of - flight variations in the clockwise and counter - clockwise senses ( primed and unprimed delays ) . in the case of the sagnac variables ( , , , ) , however , this is not the case as it is easy to understand on simple physical grounds . in the case of for instance , light originating from spacecraft 1 is simultaneously sent around the array on clockwise and counter - clockwise loops , and the two returning beams are then recombined . if the array is rotating , the two beams experience a different delay ( the sagnac effect ) , preventing the noise 1 from canceling in the combination . in order to find the solution to this problem let us first rewrite in such a way to explicitly emphasize what it does : attempts to remove the same fluctuations affecting two beams that have been made to propagated clockwise and counter - clockwise around the array , 60\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\alpha = [ { \eta _ { { 1^\prime } } } + { \mathcal{d}_{{2^\prime}}}{\eta _ { { 3^\prime } } } + { \mathcal{d}_{{1^\prime}}}{\mathcal{d}_{{2^\prime}}}{\eta _ { { 2^\prime } } } ] - [ { \eta _ 1 } + { \mathcal{d}_3}{\eta _ 2 } + { \mathcal{d}_1}{\mathcal{d}_3}{\eta _ 2}],$$\end{document } where we have accounted for clockwise and counter - clockwise light delays . it is straight - forward to verify that this combination no longer cancels the laser and optical bench noises . if , however , we expand the two terms inside the square - brackets on the right - hand side of eq . ( 60 ) we find that they are equal to 61\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{\eta _ { { 1^\prime } } } + { \mathcal{d}_{{2^\prime}}}{\eta _ { { 3^\prime } } } + { \mathcal{d}_{{1^\prime}}}{\mathcal{d}_{{2^\prime}}}{\eta _ { { 2^\prime } } } ] = [ { \mathcal{d}_{{2^\prime}}}{\mathcal{d}_{{1^\prime}}}{\mathcal{d}_{{3^\prime } } } - i]{\phi _ 1}$$\end{document } 62\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{\eta _ 1 } + { \mathcal{d}_3}{\eta _ 2 } + { \mathcal{d}_1}{\mathcal{d}_3}{\eta _ 2 } ] = [ { \mathcal{d}_3}{\mathcal{d}_1}{\mathcal{d}_2 } - i]{\phi _ 1}{.}$$\end{document } if we now apply our iterative scheme to the combinations given in eq . ( 62 ) we finally get the expression for the sagnac combination 1 that is unaffected by laser noise in presence of rotation , 63\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\alpha _ 1 } = [ { \mathcal{d}_3}{\mathcal{d}_1}{\mathcal{d}_2 } - i][{\eta _ { { 1^\prime } } } + { \mathcal{d}_{{2^\prime}}}{\eta _ { { 3^\prime } } } + { \mathcal{d}_{{1^\prime}}}{\mathcal{d}_{{2^\prime}}}{\eta _ { { 2^\prime } } } ] - [ { \mathcal{d}_{{2^\prime}}}{\mathcal{d}_{{1^\prime}}}{\mathcal{d}_{{3^\prime } } } - i][{\eta _ 1 } + { \mathcal{d}_3}{\eta _ 2 } + { \mathcal{d}_1}{\mathcal{d}_3}{\eta _ 2}]{.}$$\end{document } if the delay - times are also time - dependent , we find that the residual laser noise remaining into the combination 1 is actually equal to 64\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\dot \phi _ { 1,{{1231}^\prime}{2^\prime}{3^\prime}}}\left [ { \left({{{\dot l}_1 } + { { \dot l}_2 } + { { \dot l}_3 } } \right)\left({l_1^\prime + l_2^\prime + l_3^\prime } \right ) - \left({\dot l_1^\prime + \dot l_2^\prime + \dot l_3^\prime } \right)({l_1 } + { l_2 } + { l_3 } ) } \right]{.}$$\end{document } fortunately , although first order in the relative velocities , the residual is small , as it involves the difference of the clockwise and counter - clockwise rates of change of the propagation delays on the same circuit . for lisa , the remaining laser phase noises in i , i = 1 , 2 , 3 , are several orders of magnitude below the secondary noises . in the case of , however , the rotation of the array breaks the symmetry and therefore its uniqueness . however , there still exist three generalized tdi laser - noise - free data combinations that have properties very similar to , and which can be used for the same scientific purposes . these combinations , which we call ( 1 , 2 , 3 ) , can be derived by applying again our time - delay operator approach . let us consider the following combination of the i , i measurements , each being delayed only once : 65\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ { 3,3 } } - { \eta _ { { 3^\prime},3 } } + { \eta _ { 1,{1^\prime } } } = [ { d_3}{d_2 } - { d_{{1^\prime}}}]{\phi _ 1},$$\end{document } 66\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\eta _ { { 1^\prime},1 } } - { \eta _ { 2,{2^\prime } } } + { \eta _ { { 2^\prime},{2^\prime } } } = [ { d_{{3^\prime}}}{d_{{2^\prime } } } - { d_1}]{\phi _ 1},$$\end{document } where we have used the commutativity property of the delay operators in order to cancel the 2 and 3 terms . since both sides of the two equations above contain only the 1 noise , 1 is found by the following expression : 67\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\zeta _ 1 } = [ { d_{{3^\prime}}}{d_{{2^\prime } } } - { d_1}]({\eta _ { 3,3 } } - { \eta _ { { 3^\prime},3 } } + { \eta _ { 1,{1^\prime } } } ) - [ { d_2}{d_3 } - { d_{{1^\prime}}}]({\eta _ { { 1^\prime},1 } } - { \eta _ { 2,{2^\prime } } } + { \eta _ { { 2^\prime},{2^\prime}}}){.}$$\end{document } if the light - times in the arms are equal in the clockwise and counter - clockwise senses ( e.g. , no rotation ) there is no distinction between primed and unprimed delay times . in this case , 1 is related to our original symmetric sagnac by 1 = ,23 ,1 . thusm for the lisa case ( arm length difference < 1% ) , the snr of 1 will be the same as the snr of . if the delay - times also change with time , the perfect cancellation of the laser noises is no longer achieved in the ( 1 , 2 , 3 ) combinations . however , it has been shown in that the magnitude of the residual laser noises in these combinations are significantly smaller than the lisa secondary system noises , making their effects entirely negligible . the expressions for the monitor , beacon , and relay combinations , accounting for the rotation and flexing of the lisa array , have been derived in the literature by applying the time - delay iterative procedure highlighted in this section . we present a mathematical formulation of the second - generation tdi , which generalizes the one presented in section 4 for stationary lisa . although a full solution as in the case of stationary lisa seems difficult to obtain , significant progress can be made . there is , however , a case in between the 1st and 2nd generation tdi , called modified first - generation tdi , in which only the sagnac effect is considered [ 7 , 44 ] . in this case the up - down links are unequal while the delay - times remain constant . the mathematical formulation of section 4 can be extended in a straight - forward way where now the six time - delays \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_{{i^\prime}}}$\end{document } must be taken into account . the corresponding module of syzygies can be constructed over this larger polynomial ring . when the arms are allowed to flex , that is , the operators themselves are functions of time , the operators no longer commute . since lot of the discussion has been covered in the previous subsections we just describe the algebraic formulation . the equation eq . ( 26 ) generalizes in two ways : ( 1 ) we need to consider now six operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_{{i^\prime}}}$\end{document } , and ( 2 ) we need to take into account the non - commutativity of the operators the order of the operators is important . accordingly eq . ( 26 ) generalizes to , 68\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } + q_1^\prime - q_2^\prime { \mathcal{d}_{{3^\prime } } } - { q_3}{\mathcal{d}_2 } = 0 , } \\ { { q_2 } + q_2^\prime - q_3^\prime { \mathcal{d}_{{1^\prime } } } - { q_1}{\mathcal{d}_3 } = 0 , } \\ { { q_3 } + q_3^\prime - q_1^\prime { \mathcal{d}_{{2^\prime } } } - { q_2}{\mathcal{d}_1 } = 0 . } \\ \end{array}$$\end{document } eliminating q1 and q2 from the three eqs . ( 68 ) while respecting the order of the variables we get : 69\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${q_3}(1 - { \mathcal{d}_2}{\mathcal{d}_3}{\mathcal{d}_1 } ) + q_1^\prime ( { \mathcal{d}_{{2^\prime } } } - { \mathcal{d}_3}{\mathcal{d}_1 } ) + q_2^\prime ( { \mathcal{d}_{{3^\prime}}}{\mathcal{d}_3 } - 1){\mathcal{d}_1 } + q_3^\prime ( { \mathcal{d}_{{1^\prime}}}{\mathcal{d}_1 } - 1 ) = 0{.}$$\end{document } the polynomial ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}({{\mathcal d}_i},{{\mathcal d}_{{i^\prime } } } ) \equiv { \mathcal k}$\end{document } , is non - commutative , of polynomials in the six variables \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i},{{\mathcal d}_{{i^\prime}}}$\end{document } and coefficients in the rational field \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal q}$\end{document}. the polynomial vectors ( qi , qi ) satisfying the above equations form a left module over \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal k}$\end{document}. a left module means that one can multiply a solution ( qi , qi ) from the left by any polynomial in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal k}$\end{document } , then it is also a solution to the eqs . ( 68 ) and , therefore , in the module the module of noise - free tdi observables . for details see . if we follow on the lines of the commutative case , the first step would be to find a grbner basis for the ideal generated by the coefficients appearing in eq . ( 69 ) , namely , the set of polynomials \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{1 - { { \mathcal d}_2}{{\mathcal d}_3}{{\mathcal d}_1},{{\mathcal d}_{{2^\prime } } } - { { \mathcal d}_3}{{\mathcal d}_1},({{\mathcal d}_{{3^\prime}}}{{\mathcal d}_3 } - 1){{\mathcal d}_1},{{\mathcal d}_{{1^\prime}}}{{\mathcal d}_1 } - 1\ } $ \end{document}. although we may be able to apply non - commutative grbner basis methods , the general solution seems quite difficult . however , simplifications are possible because of the inherent symmetries in the problem and so the ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal k}$\end{document } can be quotiented by a certain ideal , simplifying the algebraic problem . we describe below how this can achieved with the help of certain commutators . in general , a commutator of two operators x , y is defined as the operator [ x , y ] = xy yx . in our situation x and y are strings of operators built up of the operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${d_1},{d_2},{d_3},{d_{{1^\prime}}},{d_{{2^\prime}}},{d_{{3^\prime}}}$\end{document}. for example , in the sagnac combination the following commutator occurs : 70\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{d_1}{d_2}{d_3},{d_{{1^\prime}}}{d_{{2^\prime}}}{d_{{3^\prime } } } ] \equiv { d_1}{d_2}{d_3}{d_{{1^\prime}}}{d_{{2^\prime}}}{d_{{3^\prime } } } - { d_{{1^\prime}}}{d_{{2^\prime}}}{d_{{3^\prime}}}{d_1}{d_2}{d_3}{.}$$\end{document } here x = d1 d2 d3 and y = d1 d2 d3. this commutator leads to the residual noise term given in eq . ( 64 ) and which happens to be small . in the context of the reasonably optimized model of lisa we have \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l \sim { 10^{- 6}}{\rm{m/}}{{\rm{s}}^2}$\end{document } and thus , even if one considers say 20 successive optical paths , that is , about t 330 s of light travel time , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\delta { t^2}\ddot l \sim 0.1\;{\rm{m}}$\end{document}. this is well below few meters and thus can be neglected in the residual laser noise computation . moreover , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\dot l^2}$\end{document } terms ( and higher order ) can be dropped since they are of the order of 10 ( they come with a factor 1/c ) , which is much smaller than 1 part in 10 , which is the level at which the laser frequency noise must be canceled . thus , we keep terms only to the first degree in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\dot l$\end{document } and also neglect higher time derivative terms in l. the result for the sagnac combination can be generalized . in order to simplify notation we write xk or ym for the time - delay operators , where k , m = 1 , 2 , , n and n 2 , that is , xk or ym are any of the operators d1 , d2 , d3 , d1 , d2 , d3. then a commutator is : 71\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{x_1}{x_2 } \ldots { x_n},\;{y_1}{y_2 } \ldots { y_n } ] = { x_1}{x_2 } \ldots { x_n}{y_1}{y_2 } \ldots { y_n } - { y_1}{y_2 } \ldots { y_n}{x_1}{x_2 } \ldots { x_n}{.}$$\end{document } up to the order of approximation we are working in we compute the effect of the commutator on the phase (t ) : 72\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { [ { x_1}{x_2 } \ldots { x_n},\;{y_1}{y_2 } \ldots { y_n}]\phi ( t)\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ { = \left({\sum\limits_{k = 1}^n { { l_{{x_k } } } } \sum\limits_{m = 1}^n { { { \dot l}_{{y_m } } } } - \sum\limits_{m = 1}^n { { l_{{y_m } } } } \sum\limits_{k = 1}^n { { { \dot l}_{{x_k } } } } } \right)\dot \phi \left({t - \sum\limits_{k = 1}^n { { l_{{x_k } } } } - \sum\limits_{m = 1}^n { { l_{{y_m } } } } } \right ) . } \\ \end{array}$$\end{document } note that the lhs acts on (t ) , while the right - hand side multiplies \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\dot \phi $ \end{document } at an appropriately delayed time . for the sagnac combination also the notation on the rhs is obvious : if for some k , we have , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${x_k } = { { \mathcal d}_{{2^\prime}}}$\end{document } say , then \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${l_{{x_k } } } = { l\prime_2}$\end{document } and so on ; the same holds for ym for a given m. from this equation it immediately follows that if the operators y1 , y2 , , yn are a permutation of the operators x1 , x2 , , xn , then the commutator , 73\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$[{x_1}{x_2 } \ldots { x_n},\;{y_1}{y_2 } \ldots { y_n } ] = 0,$$\end{document } up to the order we are working in . if y1 yn is a permutation of x1 xn then both polynomials trace the same links , except that the nodes ( spacecraft ) of the links are taken in different orders . if the armlengths were constant , the path - lengths would be identical and the commutator would be zero . but here , by neglecting \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l$\end{document } terms and those of higher orders , we have effectively assumed that \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\dot l_s}$\end{document } are constant , so the increments also cancel out , resulting in a vanishing commutator . these vanishing commutators ( in the approximation we are working in ) can be used to simplify the algebra . we first construct the ideal \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } generated by the commutators such as those given by eq . . then we quotient the ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal k}$\end{document } by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } , thereby constructing a smaller ring \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal k}/{\mathcal u } \equiv \bar { \mathcal k}$\end{document}. this ring is smaller because it has fewer distinct terms in a polynomial . although , this reduces the complexity of the problem , a full solution to the tdi problem is still lacking . in the following section 5.4 , we will consider the case where we have only two arms of lisa in operation , that is one arm is nonfunctional . we must envisage the possibility that not all optical links of lisa can be operating at all times for various reasons like technical failure for instance or even the operating costs . an analysis covering the scientific capabilities achievable by lisa in the eventuality of loosing one and two links has been discussed in . here we obtain the tdi combinations when one entire arm becomes dysfunctional . we arbitrarily choose the non - functional arm to be the one connecting s / c 2 and s / c 3 . this means from our labeling that the polynomials are now restricted to only the four operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_2},{{\mathcal d}_{{2^\prime}}},{{\mathcal d}_3},{{\mathcal d}_{{3^\prime}}}$\end{document } and we can set the polynomials q2 = q3 = 0 . ( 68 ) considerably because the last two equations reduce to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$q_2^\prime = { q_1}{{\mathcal d}_3}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${q_3 } = q_1^\prime{{\mathcal d}_{{2^\prime}}}$\end{document}. substituting these in the first equation gives just one equation : 74\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${q_1}(1 - { \mathcal{d}_3}{\mathcal{d}_{{3^\prime } } } ) + q_1^\prime ( 1 - { \mathcal{d}_{{2^\prime}}}{\mathcal{d}_2 } ) = 0,$$\end{document } if we can solve this equation for q1 , q1 then the full polynomial vector can be obtained because \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$q_2^\prime = { q_1}{{\mathcal d}_3}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${q_3 } = q_1^\prime{{\mathcal d}_{{2^\prime}}}$\end{document}. it is clear that solutions are of the michelson type . also notice that the coefficients of this equation has the operators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$a = { { \mathcal d}_3}{{\mathcal d}_{{3^\prime}}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$b = { { \mathcal d}_{{2^\prime}}}{{\mathcal d}_2}$\end{document } occurring in them . so the solutions q1 , q1 too will be in terms of a and b only . physically , the operators a and b correspond to round trips . this solution in terms of a , b is : 75\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } = 1 - b - ba + a{b^2},\quad \ ; } \\ { q_1^\prime = - ( 1 - a - ab + b{a^2 } ) . } \\ \end{array}$$\end{document } writing , 76\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta = { q_1}(1 - a ) + q_1^\prime ( 1 - b),$$\end{document } we get for eq . ( 75 ) , = [ ba , ab ] , which is a commutator that vanishes since ab is a permutation of ba . thus , it is an element of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\mathcal u}$\end{document } and eq . what we would like to emphasize is that there are more solutions of this type in fact there are infinite number of such solutions . note that these are of degree 3 in a and b. the commutator corresponding to this solution is = [ ba , ab ] = bab aba and is of degree 4 . one solution is : 77\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } = 1 - b - ba + a{b^2 } - b{a^2}b + a{b^2}ab + a{b^2}aba - b{a^2}ba{b^2},\quad \ ; } \\ { q_1^\prime = - ( 1 - a - ab + b{a^2 } - a{b^2}a + b{a^2}ba + b{a^2}bab - a{b^2}ab{a^2 } ) , } \\ \end{array}$$\end{document } whose commutator is : 78\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta = \;[ab2a,\;b{a^2}b]{.}$$\end{document } the second solution is : 79\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } = 1 + a - { b^2 } - { b^2}a - { b^2}{a^2 } - { b^2}{a^3 } + { a^2}{b^4 } + { a^2}{b^4}a\quad } \\ { = ( 1 - { b^2 } - { b^2}{a^2 } + { a^2}{b^4})(1 + a),\quad \quad \quad \quad \quad \quad \ ; } \\ { q_1^\prime = - ( 1 + b - { a^2 } - { a^2}b - { a^2}{b^2 } - { a^2}{b^3 } + { b^2}{a^4 } + { b^2}{a^4}b ) } \\ { = - ( 1 - { a^2 } - { a^2}{b^2 } + { b^2}{a^4})(1 + b),\quad \quad \quad \quad \quad \;\ ; } \\ \end{array}$$\end{document } whose commutator is = [ b a , a a ] . this solution is given by : 80\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { q_1 } = 1 - b + ab - bab - baba + aba{b^2 } - bab{a^2}b + aba{b^2}ab,\quad \;\ ; } \\ { q_1^\prime = - ( 1 - a + ba - aba - abab + bab{a^2 } - aba{b^2}a + bab{a^2}ba ) . } \\ if we call the degree of the commutators as 4 where n = 1 , 2 , , then the solutions q1 , q1 are of degree 4n 1 . the cases mentioned above , correspond to n = 1 and n = 2 . the general formula for the number of commutators of degree 4n is cn1 . so at n = 3 we have 10 commutators and so as many solutions q1 , q1 of degree 11 . these are the degrees of polynomials of q1 , q1 in the operators a , b. but for the full polynomial vector , which has q2 and q3 , we need to go over to the operators expressed in terms of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${{\mathcal d}_i},{{\mathcal d}_{{i^\prime}}}$\end{document}. then the degree of each of the q1 , q1 is doubled to 8n 2 , while q2 and q3 are each of degree 8n 1 . thus , for a general value of , the solution contains polynomials of maximum degree 8n 1 in the time - delay operators . from the mathematical point of view however the family of solutions is sufficiently rich , because we can form linear combinations of these solutions and they also are solutions . from the physical point of view , since terms in \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\dot l^2}$\end{document } and higher orders have been neglected , a limit on the degree of the polynomial solutions arises . that is up to certain degree of the polynomials , we can safely assume the commutators to vanish . but as the degree of the polynomials increases it is not possible to neglect these higher order terms any longer and then such a limit becomes important . the limit is essentially set by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l$\end{document}. we now investigate this limit and make a very rough estimate of it . as mentioned earlier , the lisa model in gives \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l \sim { 10^{- 6}}{\rm{m/}}{{\rm{s}}^2}$\end{document}. from \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\ddot l$\end{document } we compute the error in l , namely , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\delta l \sim { 1 \over 2}\delta { t^2}\ddot l$\end{document}. if we allow the error to be no more than say 10 meters , then we find t 4500 s. since each time - delay is about 16.7 s for lisa , the number of successive time - delays is about 270 . if we set the limit more stringently at l 1 m , then the highest degree of the polynomial reduces to about 80 , which means one can go up to n = 10 . thus , there are a large number of tdi observables available to do the physics . some remarks are in order : a geometric combinatorial approach was adopted in where several solutions were presented . the algebraic approach has the advantage of easy manipulation of data streams , although some geometrical insight could be at a premium.another important aspect is the gw response of such tdi observables . the gw response to a tdi observable may be calculated in the simplest way by assuming equal arms ( the possible differences in lengths would be sensitive to frequencies outside the lisa bandwidth ) . this leads in the fourier domain to polynomials in the same phase factor from which the signal to noise ratio can be found . a comprehensive and generic treatment of the responses of second - generation tdi observables can be found in . the algebraic approach has the advantage of easy manipulation of data streams , although some geometrical insight could be at a premium . the gw response to a tdi observable may be calculated in the simplest way by assuming equal arms ( the possible differences in lengths would be sensitive to frequencies outside the lisa bandwidth ) . this leads in the fourier domain to polynomials in the same phase factor from which the signal to noise ratio can be found . a comprehensive and generic treatment of the responses of second - generation tdi observables can be found in . all the above interferometric combinations have been shown to individually have rather different sensitivities , as a consequence of their different responses to gravitational radiation and system noises . since lisa has the capability of simultaneously observing a gravitational - wave signal with many different interferometric combinations ( all having different antenna patterns and noises ) , we should no longer regard lisa as a single detector system but rather as an array of gravitational - wave detectors working in coincidence . this suggests that the lisa sensitivity could be improved by optimally combining elements of the tdi space . before proceeding with this idea , however , let us consider again the so - called second - generation tdi sagnac observables : ( 1 , 2 , 3 ) . the expressions of the gravitational - wave signal and the secondary noise sources entering into 1 will in general be different from those entering into , the corresponding sagnac observable derived under the assumption of a stationary lisa array [ 2 , 15 ] . however , the other remaining , secondary noises in lisa are so much smaller , and the rotation and systematic velocities in lisa are so intrinsically small , that index permutation may still be done for them . it is therefore easy to derive the following relationship between the signal and secondary noises in 1 , and those entering into the stationary tdi combination [ 45 , 58 ] , 81\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\alpha _ 1}\;(t)\ ; \simeq \alpha ( t ) - \alpha ( t - { l_1 } - { l_2 } - { l_3}),$$\end{document } where li , i = 1 , 2 , 3 , are the unequal - arm lengths of the stationary lisa array . equation ( 81 ) implies that any data analysis procedure and algorithm that will be implemented for the second - generation tdi combinations can actually be derived by considering the corresponding first - generation tdi combinations . for this reason , from now on we will focus our attention on the gravitational - wave responses of the first - generation tdi observables ( , , , ) . as a consequence of these considerations , we can still regard ( , , , ) as the generators of the tdi space , and write the most general expression for an element of the tdi space , (f ) , as a linear combination of the fourier transforms of the four generators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\tilde \alpha , \tilde \beta , \tilde \gamma , \tilde \zeta)$\end{document } , 82\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\eta ( f ) \equiv { a_1}(f,\vec \lambda)\tilde \alpha ( f ) + { a_2}(f,\vec \lambda)\tilde \beta ( f ) + { a_3}(f,\vec \lambda)\tilde \gamma ( f ) + { a_4}(f,\vec \lambda)\tilde \zeta ( f),$$\end{document } where the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{a_i}(f,\vec \lambda)\ } _ { i = 1}^4$\end{document } are arbitrary complex functions of the fourier frequency f , and of a vector \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\vec \lambda $ \end{document } containing parameters characterizing the gravitational - wave signal ( source location in the sky , waveform parameters , etc . ) and the noises affecting the four responses ( noise levels , their correlations , etc . ) . for a given choice of the four functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{a_i}\ } _ { i = 1,}^4\eta $ \end{document } gives an element of the functional space of interferometric combinations generated by ( , , , ) . our goal is therefore to identify , for a given gravitational - wave signal , the four functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{a_i}\ } _ { i = 1}^4$\end{document } that maximize the signal - to - noise ratio \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_\eta ^2$\end{document } of the combination , 83\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{snr}}_\eta ^2 = \int\nolimits_{{f_1}}^{{f_{\rm{u } } } } { { { { { \left\vert { { a_1}{{\tilde \alpha}_{\rm{s } } } + { a_2}{{\tilde \beta}_{\rm{s } } } + { a_3}{{\tilde \gamma}_{\rm{s } } } + { a_4}{{\tilde \zeta}_{\rm{s } } } } \right\vert}^2 } } \over { \left\langle { { { \left\vert { { a_1}{{\tilde \alpha}_{\rm{n } } } + { a_2}{{\tilde \beta}_{\rm{n } } } + { a_3}{{\tilde \gamma}_{\rm{n } } } + { a_4}{\zeta _ { \rm{n } } } } \right\vert}^2 } } \right\rangle } } } df{.}$$\end{document } in eq . ( 83 ) the subscripts s and n refer to the signal and the noise parts of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\tilde \alpha , \tilde \beta , \tilde \gamma , \tilde \zeta)$\end{document } , respectively , the angle brackets represent noise ensemble averages , and the interval of integration ( f1 , fu ) corresponds to the frequency band accessible by lisa . before proceeding with the maximization of the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_\eta ^2$\end{document } we may notice from eq . ( 44 ) that the fourier transform of the totally symmetric sagnac combination , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\tilde \zeta $ \end{document } , multiplied by the transfer function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$1 - { e^{2\pi if({l_1 } + { l_2 } + l3)}}$\end{document } can be written as a linear combination of the fourier transforms of the remaining three generators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\tilde \alpha , \tilde \beta , \tilde \gamma)$\end{document}. since the signal - to - noise ratio of and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(1 - { e^{2\pi if({l_1 } + { l_2 } + { l_3})}})\eta $ \end{document } are equal , we may conclude that the optimization of the signal - to - noise ratio of can be performed only on the three observables , , . this implies the following redefined expression for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_\eta ^2$\end{document } : 84\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{snr}}_\eta ^2 = \int\nolimits_{{f_1}}^{{f_{\rm{u } } } } { { { { { \left\vert { { a_1}{{\tilde \alpha}_{\rm{s } } } + { a_2}{{\tilde \beta}_{\rm{s } } } + { a_3}{{\tilde \gamma}_{\rm{s } } } } \right\vert}^2 } } \over { \left\langle { { { \left\vert { { a_1}{{\tilde \alpha}_{\rm{n } } } + { a_2}{{\tilde \beta}_{\rm{n } } } + { a_3}{{\tilde \gamma}_{\rm{n } } } } \right\vert}^2 } } \right\rangle } } } df{.}$$\end{document } the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_\eta ^2$\end{document } can be regarded as a functional over the space of the three complex functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{a_i}\ } _ { i = 1}^3$\end{document } , and the particular set of complex functions that extremize it can of course be derived by solving the associated set of euler - lagrange equations . in order to make the derivation of the optimal snr easier , let us first denote by x and x the two vectors of the signals \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\tilde \alpha _ { \rm{s}}},{\tilde \beta _ { \rm{s}}},{\tilde \gamma _ { \rm{s}}})$\end{document } and the noises \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$({\tilde \alpha let us also define a to be the vector of the three functions \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{a_i}\ } _ { i = 1}^3$\end{document } , and denote with c the hermitian , non - singular , correlation matrix of the vector random process xn , 85\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${({\bf{c}})_{rt } } \equiv \left\langle { { \rm{x}}_r^{(n)}{\rm{x}}_t^{(n)\ast } } \right\rangle { .}$$\end{document } if we finally define ( a)ij to be the components of the hermitian matrix \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{x}}_i^{({\rm{s}})}{\rm{x}}_j^{({\rm{s } } ) \ast}$\end{document } , we can rewrite \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_\eta ^2$\end{document } in the following form , 86\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{snr}}_\eta ^2 = \int\nolimits_{{f_1}}^{{f_{\rm{u } } } } { { { { { \bf{a}}_i}{{\bf{a}}_{ij}}{\bf{a}}_j^\ast } \over { { { \bf{a}}_r}{{\bf{c}}_{rt}}{\bf{a}}_t^\ast } } } df,$$\end{document } where we have adopted the usual convention of summation over repeated indices . since the noise correlation matrix c is non - singular , and the integrand is positive definite or null , the stationary values of the signal - to - noise ratio will be attained at the stationary values of the integrand , which are given by solving the following set of equations ( and their complex conjugated expressions ) : 87\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\partial \over { \partial { { \bf{a}}_k}}}\left [ { { { { { \bf{a}}_i}{{\bf{a}}_{ij}}{\bf{a}}_j^\ast } \over { { { \bf{a}}_r}{{\bf{c}}_{rt}}{\bf{a}}_t^\ast } } } \right ] = 0,\quad \quad k = 1,2,3{.}$$\end{document } after taking the partial derivatives , eq . ( 87 ) can be rewritten in the following form , 88\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${({{\bf{c}}^{- 1}})_{ir}}{({\bf{a}})_{rj}}{({{\bf{a}}^\ast})_j } = \left [ { { { { { \bf{a}}_p}{{\bf{a}}_{pq}}{\bf{a}}_q^\ast } \over { { { \bf{a}}_l}{{\bf{c}}_{lm}}{\bf{a}}_m^\ast } } } \right]{({{\bf{a}}^\ast})_i},\quad \quad i = 1,2,3,$$\end{document } which tells us that the stationary values of the signal - to - noise ratio of are equal to the eigenvalues of the the matrix c a. the result in eq . ( 87 ) is well known in the theory of quadratic forms , and it is called rayleigh s principle [ 36 , 42 ] . in order now to identify the eigenvalues of the matrix c a , we first notice that the 3 3 matrix a has rank 1 . this implies that the matrix c a has also rank 1 , as it is easy to verify . therefore two of its three eigenvalues are equal to zero , while the remaining non - zero eigenvalue represents the solution we are looking for . the analytic expression of the third eigenvalue can be obtained by using the property that the trace of the 3 3 matrix c a is equal to the sum of its three eigenvalues , and in our case to the eigenvalue we are looking for . from these considerations we derive the following expression for the optimized signal - to - noise ratio \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\rm{snr}}_{\eta \;{\rm{opt}}}^2$\end{document } : 89\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{snr}}_{\eta \;{\rm{opt}}}^2 = \int\nolimits_{{f_1}}^{{f_{\rm{u } } } } { { \bf{x}}_i^{({\rm{s}})\ast } } { ( { { \bf{c}}^{- 1}})_{ij}}{\bf{x}}_j^{({\rm{s}})}df{.}$$\end{document } we can summarize the results derived in this section , which are given by eqs . ( 84 ) and ( 89 ) , in the following way : among all possible interferometric combinations lisa will be able to synthesize with its four generators , , , , the particular combination giving maximum signal - to - noise ratio can be obtained by using only three of them , namely ( , , ).the expression of the optimal signal - to - noise ratio given by eq . ( 89 ) implies that lisa should be regarded as a network of three interferometer detectors of gravitational radiation ( of responses ( , , ) ) working in coincidence [ 20 , 40 ] . among all possible interferometric combinations lisa will be able to synthesize with its four generators , , , , the particular combination giving maximum signal - to - noise ratio can be obtained by using only three of them , namely ( , , ) . ( 89 ) implies that lisa should be regarded as a network of three interferometer detectors of gravitational radiation ( of responses ( , , ) ) working in coincidence [ 20 , 40 ] . as an application of eq . ( 89 ) , here we calculate the sensitivity that lisa can reach when observing sinusoidal signals uniformly distributed on the celestial sphere and of random polarization . in order to calculate the optimal signal - to - noise ratio we will also need to use a specific expression for the noise correlation matrix c. as a simplification , we will assume the lisa arm lengths to be equal to their nominal value l = 16.67 s , the optical - path noises to be equal and uncorrelated to each other , and finally the noises due to the proof - mass noises to be also equal , uncorrelated to each other and to the optical - path noises . under these assumptions the correlation matrix becomes real , its three diagonal elements are equal , and all the off - diagonal terms are equal to each other , as it is easy to verify by direct calculation . the noise correlation matrix c is therefore uniquely identified by two real functions s and s in the following way : 90\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\bf{c } } = \left({\begin{array}{*{20}c } { { s_\alpha } } & { { s_{\alpha \beta } } } & { { s_{\alpha \beta } } } \\ { { s_{\alpha \beta } } } & { { s_\alpha } } & { { s_{\alpha \beta } } } \\ { { s_{\alpha \beta } } } & { { s_{\alpha \beta } } } & { { s_\alpha } } \\ \end{array } } \right){.}$$\end{document } the expression of the optimal signal - to - noise ratio assumes a rather simple form if we diagonalize this correlation matrix by properly choosing a new basis . there exists an orthogonal transformation of the generators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\tilde \alpha , \tilde \beta , \tilde \gamma)$\end{document } , which will transform the optimal signal - to - noise ratio into the sum of the signal - to - noise ratios of the transformed three interferometric combinations . the expressions of the three eigenvalues \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\{{\mu _ i}\ } _ { i = 1}^3$\end{document } ( which are real ) of the noise correlation matrix c can easily be found by using the algebraic manipulator mathematica , and they are equal to 91\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\mu _ 1 } = { \mu _ 2 } = { s_\alpha } - { s_{\alpha \beta}},\quad \quad { \mu _ 3 } = { s_\alpha } + 2{s_{\alpha \beta}}{.}$$\end{document } note that two of the three real eigenvalues , ( 1 , 2 ) , are equal . this implies that the eigenvector associated to 3 is orthogonal to the two - dimensional space generated by the eigenvalue 1 , while any chosen pair of eigenvectors corresponding to 1 will not necessarily be orthogonal . this inconvenience can be avoided by choosing an arbitrary set of vectors in this two - dimensional space , and by ortho - normalizing them . after some simple algebra , we have derived the following three ortho - normalized eigenvectors : 92\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${{\bf{v}}_1 } = { 1 \over { \sqrt 2}}(- 1,0,1)\quad \quad { { \bf{v}}_2 } = { 1 \over { \sqrt 6}}(1,\ ; - 2,1)\quad \quad { { \bf{v}}_3 } = { 1 \over { \sqrt 3}}(1,1,1){.}$$\end{document } equation ( 92 ) implies the following three linear combinations of the generators \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$(\tilde \alpha , \tilde \beta , \tilde \gamma)$\end{document } : 93\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$a = { 1 \over { \sqrt 2}}(\tilde \gamma - \tilde \alpha)\quad \quad e = { 1 \over { \sqrt 6}}\left({\tilde \alpha - 2\tilde \beta + \tilde \gamma } \right)\quad \quad t = { 1 \over { \sqrt 3}}\left({\tilde \alpha + \tilde \beta + \tilde \gamma } \right),$$\end{document } where a , e , and t are italicized to indicate that these are orthogonal modes . although the expressions for the modes a and e depend on our particular choice for the two eigenvectors ( v1 , v2 ) , it is clear from our earlier considerations that the value of the optimal signal - to - noise ratio is unaffected by such a choice . from eq . ( 93 ) it is also easy to verify that the noise correlation matrix of these three combinations is diagonal , and that its non - zero elements are indeed equal to the eigenvalues given in eq . ( 91 ) . in order to calculate the sensitivity corresponding to the expression of the optimal signal - to - noise ratio , we have proceeded similarly to what was done in [ 2 , 15 ] , and described in more detail in . we assume an equal - arm lisa ( l = 16.67 s ) , and take the one - sided spectra of proof mass and aggregate optical - path - noises ( on a single link ) , expressed as fractional frequency fluctuation spectra , to be \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$s_y^{{\rm{proof}}\,{\rm{mass } } } = 2.5 \times { 10^{- 48}}{[f/1\,{\rm{hz}}]^{- 2}}\,{\rm{h}}{{\rm{z}}^{- 1}}$\end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$s_y^{{\rm{optical}}\,{\rm{path } } } = 1.8 \times { 10^{- 37}}{[f/1\,{\rm{hz}}]^2}\,{\rm{h}}{{\rm{z}}^{- 1}}$\end{document } , respectively ( see [ 15 , 5 ] ) . we also assume that aggregate optical path noise has the same transfer function as shot noise . the optimum snr is the square root of the sum of the squares of the snrs of the three orthogonal modes ( a , e , t ) . to compare with previous sensitivity curves of a single lisa michelson interferometer , we construct the snrs as a function of fourier frequency for sinusoidal waves from sources uniformly distributed on the celestial sphere . to produce the snr of each of the ( a , e , t ) modes we need the gravitational - wave response and the noise response as a function of fourier frequency . we build up the gravitational - wave responses of the three modes ( a , e , t ) from the gravitational - wave responses of ( , , ) . for 7000 fourier frequencies in the 10 hz to 1 hz lisa band , we produce the fourier transforms of the gravitational - wave response of ( , , ) from the formulas in [ 2 , 56 ] . the averaging over source directions ( uniformly distributed on the celestial sphere ) and polarization states ( uniformly distributed on the poincar sphere ) is performed via a monte carlo method . from the fourier transforms of the ( , , ) responses at each frequency , we construct the fourier transforms of ( a , e , t ) . we then square and average to compute the mean - squared responses of ( a , e , t ) at that frequency from 10 realizations of ( source position , polarization state ) pairs . we adopt the following terminology : we refer to a single element of the module as a data combination , while a function of the elements of the module , such as taking the maximum over several data combinations in the module or squaring and adding data combinations belonging to the module , is called as an observable . the important point to note is that the laser frequency noise is also suppressed for the observable although it may not be an element of the module . the noise spectra of ( a , e , t ) are determined from the raw spectra of proof - mass and optical - path noises , and the transfer functions of these noises to ( a , e , t ) . using the transfer functions given in , the resulting spectra are equal to 94\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\begin{array}{*{20}c } { { s_a}(f ) = { s_e}(f ) = 16{{\sin}^2}(\pi fl)[3 + 2\cos ( 2\pi fl ) + \cos ( 4\pi fl)]s_y^{{\rm{proof}}\;{\rm{mass}}}(f)\quad \;\;\ ; } \\ { + 8{{\sin}^2}(\pi fl)[2 + \cos ( 2\pi fl)]s_y^{{\rm{optical}}\;{\rm{path}}}(f ) , } \\ \end{array}$$\end{document } 95\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_t}(f ) = 2{[1 + 2\cos ( 2\pi fl)]^2}[4{\sin ^2}(\pi fl)s_y^{{\rm{proof}}\;{\rm{mass } } } + s_y^{{\rm{optical}}\;{\rm{path}}}(f)]{.}$$\end{document } let the amplitude of the sinusoidal gravitational wave be h. the snr for , e.g. , a , snra , at each frequency f is equal to h times the ratio of the root - mean - squared gravitational - wave response at that frequency divided by \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt { { s_a}(f)b } $ \end{document } , where b is the bandwidth conventionally taken to be equal to 1 cycle per year . finally , if we take the reciprocal of snra/ and multiply it by 5 to get the conventional snr = 5 sensitivity criterion , we obtain the sensitivity curve for this combination , which can then be compared against the corresponding sensitivity curve for the equal - arm michelson interferometer . in figure 7 we show the sensitivity curve for the lisa equal - arm michelson response ( snr = 5 ) as a function of the fourier frequency , and the sensitivity curve from the optimum weighting of the data described above : \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$5h/\sqrt { { \rm{snr}}_a^2 + { \rm{snr}}_e^2 + { \rm{snr}}_t^2 } $ \end{document}. the snrs were computed for a bandwidth of 1 cycle / year . note that at frequencies where the lisa michelson combination has best sensitivity , the improvement in signal - to - noise ratio provided by the optimal observable is slightly larger than \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2 $ \end{document}. figure 7the lisa michelson sensitivity curve ( snr = 5 ) and the sensitivity curve for the optimal combination of the data , both as a function of fourier frequency . the integration time is equal to one year , and lisa is assumed to have a nominal armlength l = 16.67 s. the lisa michelson sensitivity curve ( snr = 5 ) and the sensitivity curve for the optimal combination of the data , both as a function of fourier frequency . the integration time is equal to one year , and lisa is assumed to have a nominal armlength l = 16.67 s. in figure 8 we plot the ratio between the optimal snr and the snr of a single michelson interferometer . in the long - wavelength limit , the snr improvement is \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2 $ \end{document}. for fourier frequencies greater than or about equal to 1/l , the snr improvement is larger and varies with the frequency , showing an average value of about \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 3 $ \end{document}. in particular , for bands of frequencies centered on integer multiples of 1/l , snrt contributes strongly and the aggregate snr in these bands can be greater than 2 . figure 8the optimal snr divided by the snr of a single michelson interferometer , as a function of the fourier frequency f. the sensitivity gain in the low - frequency band is equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2 $ \end{document } , while it can get larger than 2 at selected frequencies in the high - frequency region of the accessible band . the integration time has been assumed to be one year , and the proof mass and optical path noise spectra are the nominal ones . the optimal snr divided by the snr of a single michelson interferometer , as a function of the fourier frequency f. the sensitivity gain in the low - frequency band is equal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2 $ \end{document } , while it can get larger than 2 at selected frequencies in the high - frequency region of the accessible band . the integration time has been assumed to be one year , and the proof mass and optical path noise spectra are the nominal ones . see the main body of the paper for a quantitative discussion of this point . in order to better understand the contribution from the three different combinations to the optimal combination of the three generators , in figure 9 we plot the signal - to - noise ratios of ( a , e , t ) as well as the optimal signal - to - noise ratio . for an assumed h = 10 , the snrs of the three modes are plotted versus frequency . for the equal - arm case computed here , the snrs of a and e are equal across the band . in the long wavelength region of the band , modes a and e have snrs much greater than mode t , where its contribution to the total snr is negligible . at higher frequencies , however , the t combination has snr greater than or comparable to the other modes and can dominate the snr improvement at selected frequencies . figure 9the snrs of the three combinations ( a , e , t ) and their sum as a function of the fourier frequency f. the snrs of a and e are equal over the entire frequency band . the snr of t is significantly smaller than the other two in the low part of the frequency band , while is comparable to ( and at times larger than ) the snr of the other two in the high - frequency region . see text for a complete discussion . the snrs of the three combinations ( a , e , t ) and their sum as a function of the fourier frequency f. the snrs of a and e are equal over the entire frequency band . the snr of t is significantly smaller than the other two in the low part of the frequency band , while is comparable to ( and at times larger than ) the snr of the other two in the high - frequency region . see text for a complete discussion . binaries are important sources for lisa and therefore the analysis of such sources is of major importance . one such class is of massive or super - massive binaries whose individual masses could range from 10m to 10m and which could be up to a few gpc away . another class of interest are known binaries within our own galaxy whose individual masses are of the order of a solar mass but are just at a distance of a few kpc or less . here it is assumed that the direction of the source is known , which is so for known binaries in our galaxy . however , even for such binaries , the inclination angle of the plane of the orbit of the binary is either poorly estimated or unknown . the optimization problem is now posed differently : the snr is optimized after averaging over the polarizations of the binary signals , so the results obtained are optimal on the average , that is , the source is tracked with an observable which is optimal on the average . for computing the average , a uniform distribution for the direction of the orbital angular momentum of the binary is assumed . when the binary masses are of the order of a solar mass and the signal typically has a frequency of a few mhz , the gw frequency of the binary may be taken to be constant over the period of observation , which is typically taken to be of the order of an year . a complete calculation of the signal matrix and the optimization procedure of snr is given in . here we briefly mention the main points and the final results . a source fixed in the solar system barycentric reference frame in the direction ( b , b ) but as the lisa constellation moves along its heliocentric orbit , the apparent direction ( l , l ) of the source in the lisa reference frame ( xl , yl , zl ) changes with time . the lisa reference frame ( xl , yl , zl ) has been defined in as follows : the origin lies at the center of the lisa triangle and the plane of lisa coincides with the ( xl , yl ) plane with spacecraft 2 lying on the xl axis . figure ( 10 ) displays this apparent motion for a source lying in the ecliptic plane , that is with b = 90 and b = 0. the source in the lisa reference frame describes a figure of 8 . optimizing the snr amounts to tracking the source with an optimal observable as the source apparently moves in the lisa reference frame . figure 10apparent position of the source in the sky as seen from lisa frame for ( b = 90 , b = 0 ) . the track of the source for a period of one year is shown on the unit sphere in the lisa reference frame . apparent position of the source in the sky as seen from lisa frame for ( b = 90 , b = 0 ) . the track of the source for a period of one year is shown on the unit sphere in the lisa reference frame . since an average has been taken over the orientation of the orbital plane of the binary or equivalently over the polarizations , the signal matrix a is now of rank 2 instead of rank 1 as compared with the application in the previous section 6.1 . the mutually orthogonal data combinations a , e , t are convenient in carrying out the computations because in this case as well , they simultaneously diagonalize the signal and the noise covariance matrix . the optimization problem now reduces to an eigenvalue problem with the eigenvalues being the squares of the snrs . there are two eigen - vectors which are labeled as \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ { + , \times}}$\end{document } belonging to two non - zero eigenvalues . the two snrs are labelled as snr+ and snr , corresponding to the two orthogonal ( thus statistically independent ) eigenvectors \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ { + , \times}}$\end{document}. as was done in the previous section 6.1 f the two snrs can be squared and added to yield a network snr , which is defined through the equation 96\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\rm{snr}}_{{\rm{network}}}^2 = { \rm{snr } } _ the third eigenvalue is zero and the corresponding eigenvector orthogonal to \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ \times}$\end{document } gives zero signal . the eigenvectors and the snrs are functions of the apparent source direction parameters ( l , l ) in the lisa reference frame , which in turn are functions of time . the eigenvectors optimally track the source as it moves in the lisa reference frame . assuming an observation period of an year , the snrs are integrated over this period of time . figure 11sensitivity curves for the observables : michelson , max[x , y , z ] , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } , and network for the source direction ( b = 90 , b = 0 ) . sensitivity curves for the observables : michelson , max[x , y , z ] , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } , and network for the source direction ( b = 90 , b = 0 ) . it shows the sensitivity curves of the following observables : the michelson combination x ( faint solid curve).the observable obtained by taking the maximum sensitivity among x , y , and z for each direction , where y and z are the michelson observables corresponding to the remaining two pairs of arms of lisa . this maximum is denoted by max[x , y , z ] ( dash - dotted curve ) and is operationally given by switching the combinations x , y , z so that the best sensitivity is achieved.the eigen - combination \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } which has the best sensitivity among all data combinations ( dashed curve).the network observable ( solid curve ) . the michelson combination x ( faint solid curve ) . the observable obtained by taking the maximum sensitivity among x , y , and z for each direction , where y and z are the michelson observables corresponding to the remaining two pairs of arms of lisa . this maximum is denoted by max[x , y , z ] ( dash - dotted curve ) and is operationally given by switching the combinations x , y , z so that the best sensitivity is achieved . the eigen - combination \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } which has the best sensitivity among all data combinations ( dashed curve ) . it is observed that the sensitivity over the band - width of lisa increases as one goes from observable 1 to 4 . also it is seen that the max[x , y , z ] does not do much better than x. this is because for the source direction chosen b = 90 , x is reasonably well oriented and switching to y and z combinations does not improve the sensitivity significantly . however , the network and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } observables show significant improvement in sensitivity over both x and max[x , y , z ] . this is the typical behavior and the sensitivity curves ( except ) do not show much variations for other source directions and the plots are similar . also it may be fair to compare the optimal sensitivities with max[x , y , z ] rather than x. this comparison of sensitivities is shown in figure 12 , where the network and the eigen - combinations \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ { + , \times}}$\end{document } are compared with max[x , y , z ] . figure 12ratios of the sensitivities of the observables network , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ { + , \times}}$\end{document } with max[x , y , z ] for the source direction b = 90 , b = 0. ratios of the sensitivities of the observables network , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ { + , \times}}$\end{document } with max[x , y , z ] for the source direction b = 90 , b = 0. defining 97\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\kappa _ a}(f ) = { { { \rm{sn}}{{\rm{r}}_a}(f ) } \over { { \rm{sn}}{{\rm{r}}_{\max [ x , y , z]}}(f)}},$$\end{document } where the subscript a stands for network or + , , and snrmax[x , y , z ] is the snr of the observable max[x , y , z ] , the ratios of sensitivities are plotted over the lisa band - width . the improvement in sensitivity for the network observable is about 34% at low frequencies and rises to nearly 90% at about 20 mhz , while at the same time the \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\vec \upsilon _ + } $ \end{document } combination shows improvement of 12% at low frequencies rising to over 50% at about 20 mhz . it is clear that the suppression of the laser phase fluctuations by more than nine orders of magnitude with the use of tdi is a very challenging experimental task . it requires developing and building subsystems capable of unprecedented accuracy and precision levels , and test their end - to - end performance in a laboratory environment that naturally precludes the availability of 5 10 km delay lines ! in what follows we will address some aspects related to the experimental implementation of tdi , and derive the performance specifications for the subsystems involved . we will not address , however , any of the experimental aspects related to the verification of tdi in a laboratory environment . [ 8 , 32 ] , spero et al . , and mitryk et al . it is easy to see that a successful implementation of tdi requires : accurate knowledge of the time shifts , li(t ) , li(t ) i = 1 , 2 , 3 , to be applied to the heterodyne measurements si(t ) , si(t ) , i(t ) , i(t ) i = 1 , 2 , 3;accurate synchronization among the three clocks onboard the three spacecraft as these are used for time - stamping the recorded heterodyne phase measurements;sampling time stability ( i.e. , clock stability ) for successfully suppressing the laser noise to the desired level;an accurate reconstruction algorithm of the phase measurements corresponding to the required time delays as these in general will not be equal to integer multiples of the sampling time;a phase meter capable of a very large dynamic range in order to suppress the laser noise to the required level while still preserving the phase fluctuations induced by a gravitational - wave signal in the tdi combinations . in the following subsections , we will quantitatively address the issues listed above , and provide the reader with a related list of references where more details can be found . accurate knowledge of the time shifts , li(t ) , li(t ) i = 1 , 2 , 3 , to be applied to the heterodyne measurements si(t ) , si(t ) , i(t ) , i(t ) i = 1 , 2 , 3 ; accurate synchronization among the three clocks onboard the three spacecraft as these are used for time - stamping the recorded heterodyne phase measurements ; sampling time stability ( i.e. , clock stability ) for successfully suppressing the laser noise to the desired level ; an accurate reconstruction algorithm of the phase measurements corresponding to the required time delays as these in general will not be equal to integer multiples of the sampling time ; a phase meter capable of a very large dynamic range in order to suppress the laser noise to the required level while still preserving the phase fluctuations induced by a gravitational - wave signal in the tdi combinations . the tdi combinations described in the previous sections ( whether of the first- or second - generation ) rely on the assumption of knowing the time - delays with infinite accuracy to exactly cancel the laser noise . since the six delays will in fact be known only within the accuracies li , li i = 1 , 2 , 3 , the cancellation of the laser frequency fluctuations in , for instance , the combinations ( , , , ) will no longer be exact . in order to estimate the magnitude of the laser fluctuations remaining in these data sets , let us define \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${\hat l_i}\;,{\hat l\prime_i}\;i = 1,2,3$\end{document } to be the estimated time - delays . they are related to the true delays li , li i = 1 , 2 , 3 , and the accuracies li , li i = 1 , 2 , 3 through the following expressions 98\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\hat l_i } = { l_i } + \delta { l_i},\quad \quad i = 1,2,3,$$\end{document } and similarly for the primed delays . in what follows we will limit our derivation of the time - delays accuracies to only the first - generation tdi combinations and treat the three common delays li , i = 1 , 2 , 3 as constants equal to 16.7 light - seconds . we will also assume to know with infinite accuracies and precisions all the remaining physical quantities ( listed at the beginning of section 7 ) that are needed to successfully synthesize the tdi generators . ( 98 ) into the expression for the tdi combination , for instance , ( eq . ( 43 ) ) and expand it to first order in li , it is easy to derive the following approximate expression for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\hat \alpha ( t)$\end{document } , which now will show a non - zero contribution from the laser noises 99\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\hat \alpha ( t ) \simeq \alpha ( t ) + [ { \dot \phi _ { 2,12 } } - { \dot \phi _ { 3,13}}]\delta { l_1 } + [ { \dot \phi _ { 3,2 } } - { \dot \phi _ { 1,123}}]\delta { l_2 } + [ { \dot \phi _ { 1,123 } } - { \dot \phi _ { 2,3}}]\delta { l_3},$$\end{document } where the symbol denotes time derivative . time - delay interferometry can be considered effective if the magnitude of the remaining fluctuations from the lasers are much smaller than the fluctuations due to the remaining ( proof mass and optical path ) noises entering (t ) . let us assume the laser phase fluctuations to be uncorrelated to each other , their one - sided power spectral densities to be equal , the three armlengths to differ by a few percent , and the three armlength accuracies also to be equal . by requiring the magnitude of the remaining laser noises to be smaller than the secondary noise sources , it is straightforward to derive , from eq . ( 99 ) and the expressions for the noise spectrum of the tdi combination given in , the following constraint on the common armlength accuracy l 100\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\vert \delta { l_\alpha}\vert \ll { 1 \over { \sqrt { 32 } \pi f}}\sqrt { { { [ 8{{\sin}^2}(3\pi fl ) + 16{{\sin}^2}(\pi fl)]{s^{{\rm{proof}}\;{\rm{mass}}}}(f ) + { s^{{\rm{optical}}\;{\rm{path}}}}(f ) } \over { { s_\phi}(f)}}},$$\end{document } with similar inequalities also holding for and . here s , s , s are the onesided power spectral densities of the relative frequency fluctuations of a stabilized laser , a single proof mass , and a single - link optical path respectively . if we take them to be equal to the following functions of the fourier frequency f [ 53 , 15 ] 101\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s_\phi}(f ) = { 10^{- 28}}{f^{- 2/3 } } + 6.3 \times { 10^{- 37}}\;{f^{- 3.4}}\;{\rm{h}}{{\rm{z}}^{- 1}}$$\end{document } 102\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s^{{\rm{proof}}\;{\rm{mass}}}}(f ) = 2.5 \times { 10^{- 48}}\;{f^{- 2}}\;{\rm{h}}{{\rm{z}}^{- 1}}$$\end{document } 103\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${s^{{\rm{optical}}\;{\rm{path}}}}(f ) = 1.8 \times { 10^{- 37}}{f^2}\;{\rm{h}}{{\rm{z}}^{- 1}}$$\end{document } ( where f is in hz ) , we find that the right - hand side of the inequality given by eq . ( 100 ) reaches its minimum of about 30 meters at the fourier frequency fmin = 1.0 10 hz , over the assumed ( 10,1 ) hz lisa band . this implies that , if the armlength knowledge l can be made much smaller than 30 meters , the magnitude of the residual laser noise affecting the combination can be regarded as negligible over the entire frequency band . this reflects the fact that the armlength accuracy is a decreasing function of the frequency . for instance , at 10 hz the armlength accuracy goes up by almost an order of magnitude to about 155 meters . a perturbation analysis similar to the one described above can be performed for , resulting into the following inequality for the required delay accuracy , l 104\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\vert \delta { l_\zeta}\vert \ll { 1 \over { 2\pi f}}\sqrt { { { 4{{\sin}^2}(\pi fl){s^{{\rm{proof}}\;{\rm{mass}}}}(f ) + { s^{{\rm{optical}}\;{\rm{path}}}}(f ) } \over { { s_\phi}(f ) } } } { .}$$\end{document } equation ( 104 ) implies a minimum of the function on the right - hand side equal to about 16 meters at the fourier frequency fmin = 1.0 10 hz , while at 10 hz the armlength accuracy goes up to 154 meters . armlength accuracies at the centimeters level have already been demonstrated in the laboratory [ 16 , 50 , 64 , 26 ] , making us confident that the required level of time - delays accuracy will be available . in relation to the accuracies derived above , it is interesting to calculate the time scales during which the armlengths will change by an amount equal to the accuracies themselves . this identifies the minimum time required before updating the armlength values in the tdi combinations . that the relative longitudinal speeds between the three pairs of spacecraft , during approximately the first year of the lisa mission , can be written in the following approximate form 105\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${v_{i , j}}(t ) = v_{i , j}^{(0)}\sin \left({{{2\pi t } \over { { t_{i , j } } } } } \right)\quad \quad ( i,\;j ) = ( 1,2);(1,3);(2,3),$$\end{document } where we have denoted with ( 1 , 2 ) , ( 1 , 3 ) , ( 2 , 3 ) the three possible spacecraft pairs , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{i , j}^{(0)}$\end{document } is a constant velocity , and ti , j is the period for the pair ( i , j ) . in reference it has also been shown that the lisa trajectory can be selected in such a way that two of the three arms rates of change are essentially equal during the first year of the mission . following reference , we will assume \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{1,2}^{(0 ) } = v_{1,3}^{(0 ) } \neq v_{2,3}^{(0)}$\end{document } , with \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$v_{1,2}^{(0 ) } = 1\;{\rm{m / s,}}\;v_{2,3}^{(0 ) } = 13\;{\rm{m / s,}}\;{t_{1,2}}\ ; = { t_{1,3 } } \approx 4$\end{document } months , and \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${t_{2,3 } } \approx 1$\end{document } year . from eq . ( 105 ) it is easy to derive the variation of each armlength , for example l3(t ) , as a function of the time and the time scale t during which it takes place 106\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\delta { l_3}(t ) = v_{1,2}^{(0)}\sin \left({{{2\pi t } \over { { t_{1,2 } } } } } \right)\delta t{.}$$\end{document } equation ( 106 ) implies that a variation in armlength l3 10 m can take place during different time scales , depending on when during the mission this change takes place . for instance , if t t1,2 we find that the armlength l3 changes by more than its accuracy ( 10 m ) after a time t = 2.3 10 s. if however t t1,2/4 , the armlength will change by the same amount after only t 10 s instead . as this value is less than the one - way - light - time , one might argue that the measured time - delay will not represent well enough the delay that needs to be applied in the tdi combinations at that particular time . one way to address this problem is to treat the delays in the tdi combinations as parameters to be determined by a non - linear least - squares procedure , in which the minimum of the minimizer is achieved at the correct delays since that the laser noise will exactly cancel there in the tdi combinations . such a technique , which was named time - delay interferometric ranging ( tdir ) , requires a starting point in the time - delays space in order to implement the minimization , and it will work quite effectively jointly with the ranging data available onboard . the effectiveness of the tdi data combinations requires the clocks onboard the three spacecraft to be synchronized . in what follows we will identify the minimum level of off - synchronization among the clocks that can be tolerated . in order to proceed with our analysis we will treat one of the three clocks ( say the clock onboard spacecraft 1 ) as the master clock defining the time for lisa , while the other two to be synchronized to it . the relativistic ( sagnac ) time - delay effect due to the fact that the lisa trajectory is a combination of two rotations , each with a period of one year , will have to be accounted for in the synchronization procedure and , as has already been discussed earlier , will be accounted for within the second - generation formulation of tdi . here , for simplicity , we will analyze an idealized non - rotating constellation in order to get a sense of the required level of clocks synchronization . let us denote by t2 , t3 , the time accuracies ( time - offsets ) for the clocks onboard spacecraft 2 and 3 respectively . if t is the time onboard spacecraft 1 , then what is believed to be time t onboard spacecraft 2 and 3 is actually equal to the following times 107\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\hat t_2 } = t + \delta { t_2},$$\end{document } 108\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${\hat t_3 } = t + \delta { t_3}{.}$$\end{document } if we now substitute eqs . ( 107 and 108 ) into the tdi combination , for instance , and expand it to first order in ti , i = 2 , 3 , it is easy to derive the following approximate expression for \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\hat \zeta ( t)$\end{document } , which shows the following non - zero contribution from the laser noises 109\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\hat \zeta ( t ) \simeq \zeta ( t ) + [ { \dot \phi _ { 1,23 } } - { \dot \phi _ { 3,12 } } + { \dot \phi _ { 2,13 } } - { \dot \phi _ { 2,13}}]\delta { t_2 } + [ { \dot \phi _ { 2,13 } } - { \dot \phi _ { 1,23 } } + { \dot \phi _ { 3,12 } } - { \dot \phi _ { 3,12}}]\delta { t_3}{.}$$\end{document } by requiring again the magnitude of the remaining fluctuations from the lasers to be smaller than the fluctuations due to the other ( secondary ) noise sources affecting (t ) , it is possible to derive an upper limit for the accuracies of the synchronization of the clocks . if we assume again the three laser phase fluctuations to be uncorrelated to each other , their one - sided power spectral densities to be equal , the three armlengths to differ by a few percent , and the two time - offsets magnitudes to be equal , by requiring the magnitude of the remaining laser noises to be smaller than the secondary noise sources it is easy to derive the following constraint on the time synchronization accuracy t 110\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\vert \delta { t_\zeta}\vert \ll { 1 \over { 2\pi f}}\sqrt { { { 12{{\sin}^2}(\pi fl){s^{{\rm{proof}}\;{\rm{mass}}}}(f ) + 3\;{s^{{\rm{optical}}\;{\rm{path}}}}(f ) } \over { 4\;{s_\phi}(f)}}},$$\end{document } with s , s , s again as given in eqs . ( 110 ) reaches its minimum of about 47 nanoseconds at the fourier frequency fmin = 1.0 10 hz . this means that clocks synchronized at a level of accuracy significantly better than 47 nanoseconds will result into a residual laser noise that is much smaller than the secondary noise sources entering into the combination . an analysis similar to the one described above can be performed for the remaining generators ( , , ) . for them we find that the corresponding inequality for the accuracy in the synchronization of the clocks is now equal to 111\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$$\vert \delta { t_\alpha}\vert \leq { 1 \over { 2\pi f}}\sqrt { { { [ 4{{\sin}^2}(3\pi fl ) + 8{{\sin}^2}(\pi fl)]{s^{{\rm{proof}}\;{\rm{mass}}}}(f ) + 3\;{s^{{\rm{optical}}\;{\rm{path}}}}(f ) } \over { 4\;{s_\phi}(f)}}},$$\end{document } with equal expressions holding also for and . the function on the right - hand side of eq . ( 111 ) has a minimum equal to 88 nanoseconds at the fourier frequency fmin = 1.0 10 hz . as for the armlength accuracies , also the timing accuracy requirements become less stringent at higher frequencies . at 10 hz , for instance , the timing accuracy for and , , go up to 446 and 500 ns respectively . as a final note , a required clock synchronizations of about 40 ns derived in this section translates into a ranging accuracy of 12 meters , which has been experimentally shown to be easily achievable [ 16 , 50 , 64 , 26 ] . the sampling times of all the measurements needed for synthesizing the tdi combinations will not be constant , due to the intrinsic timing jitters of the onboard measuring system . among all the subsystems involved in the data measuring process , the onboard clock is expected to be the dominant source of time jitter in the sampled data . presently existing space qualified clocks can achieve an allan standard deviation of about 10 for integration times from 1 to 10 000 seconds . this timing stability translates into a time jitter of about 10 seconds over a period of 1 second . a perturbation analysis including the three sampling time jitters due to the three clocks shows that any laser phase fluctuations remaining in the four tdi generators will also be proportional to the sampling time jitters . since the latter are approximately four orders of magnitude smaller than the armlength and clocks synchronization accuracies derived earlier , we conclude that the magnitude of laser noise residual into the tdi combinations due to the sampling time jitters is negligible . the derivations of the time - delays and clocks synchronization accuracies highlighted earlier presumed the availability of the phase measurement samples at the required time - delays . since this condition will not be true in general , as the time - delays used by the tdi combinations will not be equal to integer - multiples of the sampling time , with a sampling rate of , let us say , 10 hz , the time delays could be off their correct values by a tenth of a second , way more than the 10 nanoseconds time - delays and clocks synchronization accuracies estimated above . earlier suggestions for addressing this problem envisioned sampling the data at very - high rates ( perhaps of the order of hundreds of mhz ) , so reducing the additional error to the estimated time - delays to a few nanoseconds . although in principle such a solution would allow us to suppress the residual laser noise to the required level , it would create an insurmountable problem for transmitting the science data to the ground due to the limited space - to - ground data rates . an alternate scheme for obtaining the phase measurement points needed by tdi envisioned sampling the phase measurements at the required delayed times . this scheme naturally requires knowledge of the time - delays and synchronization of the clocks at the required accuracy levels during data acquisition . although such a procedure could be feasible in principle , it would still leave open the possibility of irreversible corruption of the tdi combinations in the eventuality of performance degradation in the ranging and clock synchronization procedures . given that the data will need to be sampled at a rate of 10 hz , an alternative options is to implement an interpolation scheme for reconstructing the required data points from the sampled measurements . an analysis based on the implementation of the truncated shannon formula , however , showed that several months of data were required in order to reconstruct the phase samples at the estimated time - delays with a sufficiently high accuracy . this conclusion implied that several months ( at the beginning and end ) of the entire data records measured by lisa would be of no use , resulting into a significant mission science degradation . although the truncated shannon formula was proved to be impracticable for reconstructing phase samples at the required time - delays , it was then recognized that a more efficient and accurate interpolation technique could be adopted . in what follows , we provide a brief account of this data processing technique , which is known as fractional - delay filtering let s write the truncated shannon formula for the delayed sample , yn(n d ) , which we want to construct by filtering the sampled data y(n ) 112\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${y_n}(n - d ) = \sum\limits_{j = - n}^n { y(n + j)\;{\rm{sinc}}(d - j),}$$\end{document } where , as usual , sinc(x ) sin(x)/x , and n is an integer at which the shannon formula has been truncated to . as pointed out in , although the truncated shannon formula is optimal in the least - squares sense , the sinc - function that appears in it is far from being ideal in reconstructing the transfer function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${e^{2\pi ifd/{f_s}}}$\end{document } , where fs is the sampling frequency . in fact , over the lisa observational band the sinc - function displays significant ringing , which can only be suppressed by taking n very large ( as the error , , decays slowly as 1/n ) . it was estimated that , in order to achieve an < 10 , an n 10 is needed . if , however , we give up on the requirement of minimizing the error in the least - squares sense and replace it with a mini - max criterion error applied to the absolute value of the difference between the ideal transfer function ( i.e. , \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${e^{2\pi ifd/{f_s}}}$\end{document } ) and a modified sinc - function , we will be able to achieve a rapid convergence while suppressing the ringing effects associated with the sinc function . one way to achieve this result is to modify the shannon formula by multiplying the sinc - function by a window - function , w(j ) , in the following way 113\documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$${y_n}(n - d ) = \sum\limits_{j = - n}^n { y(n + j)w(j)\;{\rm{sinc}}(d - j),}$$\end{document } where w(j ) smoothly decays to zero at j = n . in several windows were tested , and the resulting values of n needed to accurately reconstruct the desired delayed samples were estimated , both on theoretical and numerically grounds . it was found that , with windows belonging to the family of lagrange polynomials a delayed sample could be reconstructed by using n 25 samples while achieving a mini - max error < 10 between the ideal transfer function \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}${e^{2\pi ifd/{f_s}}}$\end{document } , and the kernel of the modified truncated shannon formula . it has been shown that the maximum of the ratio between the amplitudes of the laser and the secondary phase fluctuations occurs at the lower end of the lisa bandwidth ( i.e. , 0.1 mhz ) and it is equal to about 10 . this corresponds to the minimum dynamic range for the phasemeters to correctly measure the laser fluctuations and the weaker ( gravitational - wave ) signals simultaneously . an additional safety factor of 10 should be sufficient to avoid saturation if the noises are well described by gaussian statistics . in terms of requirements on the digital signal processing subsystem , this dynamic range implies that approximately 36 bits are needed when combining the signals in tdi , only to bridge the gap between laser frequency noise and the other noises and gravitational - wave signals . more bits might be necessary to provide enough information to efficiently filter the data when extracting weak gravitational - wave signals embedded into noise . the phasemeters will be the onboard instrument that will perform the phase measurements containing the gravitational signals . they will also need to simultaneously measure the time - delays to be applied to the tdi combinations via ranging tones over - imposed on the laser beams exchanged by the spacecraft . and they will need to have the capability of simultaneously measure additional side - band tones that are required for the calibration of the onboard ultra - stable oscillator used in the down - conversion of heterodyned carrier signal [ 57 , 27 ] . work toward the realization of a phasemeter capable of meeting these very stringent performance and operational requirements has aggressively been performed both in the united states and in europe [ 43 , 23 , 22 , 6 , 63 ] , and we refer the reader interested in the technical details associated with the development studies of such device to the above references and those therein . in this article we have summarized the use of tdi for canceling the laser phase noise from heterodyne phase measurements performed by a constellation of three spacecraft tracking each other along arms of unequal length . underlying the tdi technique is the mathematical structure of the theory of grbner basis and the algebra of modules over polynomial rings . these methods have been motivated and illustrated with the simple example of an unequal - arm interferometer in order to give a physical insight of tdi . here , these methods have been rigorously applied to the idealized case of a stationary interferometer such as the lisa mission . this allowed us to derive the generators of the module from which the entire tdi data set can be obtained ; they can be extended in a straight - forward way to more than three spacecraft for possible future mission concepts . the stationary lisa case was used as a propaedeutical introduction to the physical motivation of tdi , and for further extending it to the realistic lisa configuration of free - falling spacecraft orbiting around the sun . the tdi data combinations canceling laser phase noise in this general case are referred to as second - generation tdi , and they contain twice as many terms as their corresponding first - generation combinations valid for the stationary configuration . as a data analysis application we have shown that it is possible to identify specific tdi combinations that will allow lisa to achieve optimal sensitivity to gravitational radiation [ 38 , 40 , 39 ] . the resulting improvement in sensitivity over that of an unequal - arm michelson interferometer , in the case of monochromatic signals randomly distributed over the celestial sphere and of random polarization , is non - negligible . we have found this to be equal to a factor of \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 2 $ \end{document } in the low - part of the frequency band , and slightly more than \documentclass[12pt]{minimal } \usepackage{amsmath } \usepackage{wasysym } \usepackage{amsfonts } \usepackage{amssymb } \usepackage{amsbsy } \usepackage{mathrsfs } \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt } \begin{document}$\sqrt 3 $ \end{document } in the high - part of the lisa band . the snr for binaries whose location in the sky is known , but their polarization is not , can also be optimized , and the degree of improvement depends on the location of the source in the sky . we also addressed several experimental aspects of tdi , and emphasized that it has already been successfully tested experimentally [ 8 , 32 , 48 , 33 ] . as of the writing of this second edition of our living review article , it is very gratifying to see how much tdi has matured since the publishing of its first version . the purpose of this second edition review of tdi was to provide the basic mathematical tools and knowledge of the current experimental results needed for working on future tdi projects . we hope to have accomplished this goal , and that others will be stimulated to work in this fascinating field of research .[/INST]equal - arm detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms . this is because the noise in the laser light is common to both arms , experiencing exactly the same delay , and thus cancels when it is differenced at the photo detector . in this situation , much lower level secondary noises then set the overall performance . if , however , the two arms have different lengths ( as will necessarily be the case with space - borne interferometers ) , the laser noise experiences different delays in the two arms and will hence not directly cancel at the detector . in order to solve this problem , a technique involving heterodyne interferometry with unequal arm lengths and independent phase - difference readouts has been proposed . it relies on properly time - shifting and linearly combining independent doppler measurements , and for this reason it has been called time - delay interferometry ( tdi).this article provides an overview of the theory , mathematical foundations , and experimental aspects associated with the implementation of tdi . although emphasis on the application of tdi to the laser interferometer space antenna ( lisa ) mission appears throughout this article , tdi can be incorporated into the design of any future space - based mission aiming to search for gravitational waves via interferometric measurements . we have purposely left out all theoretical aspects that data analysts will need to account for when analyzing the tdi data combinations .</s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Train the Future Act''. SEC. 2. ENCOURAGING MENTORS TO TRAIN THE FUTURE. (a) Early Distributions From Qualified Retirement Plans.--Section 72(t)(2) of the Internal Revenue Code of 1986 is amended-- (1) in subparagraph (A)-- (A) by striking ``or'' at the end of clause (vii); (B) by striking the period at the end of clause (viii) and inserting ``, or''; and (C) by adding at the end the following new clause: ``(ix) made to an employee who is serving as a mentor.''; and (2) by adding at the end the following new subparagraph: ``(H) Distributions to mentors.--For purposes of this paragraph, the term `mentor' means an individual who-- ``(i) has attained 55 years of age, ``(ii) is not separated from their employment with a company, corporation, or institution of higher education, ``(iii) in accordance with such requirements and standards as the Secretary determines to be necessary, has substantially reduced their hours of employment with their employer, with the individual to be engaged in mentoring activities described in clause (iv) for not less than 20 percent of the hours of employment after such reduction, and ``(iv) is responsible for the training and education of employees or students in an area of expertise for which the individual has a professional credential, certificate, or degree.''. (b) Distributions During Working Retirement.--Paragraph (36) of section 401(a) of the Internal Revenue Code of 1986 is amended to read as follows: ``(36) Distributions during working retirement.-- ``(A) In general.--A trust forming part of a pension plan shall not be treated as failing to constitute a qualified trust under this section solely because the plan provides that a distribution may be made from such trust to an employee who-- ``(i) has attained age 62 and who is not separated from employment at the time of such distribution, or ``(ii) subject to subparagraph (B), is serving as a mentor (as such term is defined in section 72(t)(2)(H)). ``(B) Limitation on distributions to mentors.--For purposes of subparagraph (A)(ii), the amount of the distribution made to an employee who is serving as a mentor shall not be greater than the amount equal to the product obtained by multiplying-- ``(i) the amount of the distribution that would have been payable to the employee if such employee had separated from employment instead of reducing their hours of employment with their employer and engaging in mentoring activities, in accordance with clauses (iii) and (iv) of section 72(t)(2)(H), by ``(ii) the percentage equal to the quotient obtained by dividing-- ``(I) the sum of-- ``(aa) the number of hours per pay period by which the employee's hours of employment are reduced, and ``(bb) the number of hours of employment that such employee is engaging in mentoring activities, by ``(II) the total number of hours per pay period worked by the employee before such reduction in hours of employment.''. (c) ERISA.--Subparagraph (A) of section 3(2) of the Employee Retirement Income Security Act of 1974 (29 U.S.C. 1002(2)) is amended by striking the period at the end and inserting the following: ``, or solely because such distribution is made to an employee who is serving as a mentor (as such term is defined in section 72(t)(2)(H) of the Internal Revenue Code of 1986).''. (d) Application.--The amendments made by this section shall apply to distributions made in taxable years beginning after December 31, 2015.

Train the Future Act This bill amends the Internal Revenue Code to allow an early distribution, without penalty, from a qualified retirement plan to an employee who is serving as a mentor. The bill defines &quot;mentor&quot; as a working individual who: (1) has attained age 55; (2) works reduced hours and engages in mentoring activities for at least 20% of such hours; and (3) is responsible for the training and education of employees or students in an area of expertise for which such individual has a professional credential, certificate, or degree.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Train the Future Act''. SEC. 2. ENCOURAGING MENTORS TO TRAIN THE FUTURE. (a) Early Distributions From Qualified Retirement Plans.--Section 72(t)(2) of the Internal Revenue Code of 1986 is amended-- (1) in subparagraph (A)-- (A) by striking ``or'' at the end of clause (vii); (B) by striking the period at the end of clause (viii) and inserting ``, or''; and (C) by adding at the end the following new clause: ``(ix) made to an employee who is serving as a mentor.''; and (2) by adding at the end the following new subparagraph: ``(H) Distributions to mentors.--For purposes of this paragraph, the term `mentor' means an individual who-- ``(i) has attained 55 years of age, ``(ii) is not separated from their employment with a company, corporation, or institution of higher education, ``(iii) in accordance with such requirements and standards as the Secretary determines to be necessary, has substantially reduced their hours of employment with their employer, with the individual to be engaged in mentoring activities described in clause (iv) for not less than 20 percent of the hours of employment after such reduction, and ``(iv) is responsible for the training and education of employees or students in an area of expertise for which the individual has a professional credential, certificate, or degree.''. (b) Distributions During Working Retirement.--Paragraph (36) of section 401(a) of the Internal Revenue Code of 1986 is amended to read as follows: ``(36) Distributions during working retirement.-- ``(A) In general.--A trust forming part of a pension plan shall not be treated as failing to constitute a qualified trust under this section solely because the plan provides that a distribution may be made from such trust to an employee who-- ``(i) has attained age 62 and who is not separated from employment at the time of such distribution, or ``(ii) subject to subparagraph (B), is serving as a mentor (as such term is defined in section 72(t)(2)(H)). ``(B) Limitation on distributions to mentors.--For purposes of subparagraph (A)(ii), the amount of the distribution made to an employee who is serving as a mentor shall not be greater than the amount equal to the product obtained by multiplying-- ``(i) the amount of the distribution that would have been payable to the employee if such employee had separated from employment instead of reducing their hours of employment with their employer and engaging in mentoring activities, in accordance with clauses (iii) and (iv) of section 72(t)(2)(H), by ``(ii) the percentage equal to the quotient obtained by dividing-- ``(I) the sum of-- ``(aa) the number of hours per pay period by which the employee's hours of employment are reduced, and ``(bb) the number of hours of employment that such employee is engaging in mentoring activities, by ``(II) the total number of hours per pay period worked by the employee before such reduction in hours of employment.''. (c) ERISA.--Subparagraph (A) of section 3(2) of the Employee Retirement Income Security Act of 1974 (29 U.S.C. 1002(2)) is amended by striking the period at the end and inserting the following: ``, or solely because such distribution is made to an employee who is serving as a mentor (as such term is defined in section 72(t)(2)(H) of the Internal Revenue Code of 1986).''. (d) Application.--The amendments made by this section shall apply to distributions made in taxable years beginning after December 31, 2015.[/INST]Train the Future Act This bill amends the Internal Revenue Code to allow an early distribution, without penalty, from a qualified retirement plan to an employee who is serving as a mentor. The bill defines &quot;mentor&quot; as a working individual who: (1) has attained age 55; (2) works reduced hours and engages in mentoring activities for at least 20% of such hours; and (3) is responsible for the training and education of employees or students in an area of expertise for which such individual has a professional credential, certificate, or degree. </s>

the recently proven shuffle conjecture asserts a formula for the bigraded frobenius character of the module of diagonal harmonics in terms of a macdonald eigenoperator and the combinatorics of parking functions @xcite . the delta conjecture is a still - open generalization of the shuffle conjecture due to haglund , remmel , and wilson @xcite . this paper proves combinatorial results about statistics on ordered set partitions to obtain a specialization of the delta conjecture . we begin by reviewing the delta conjecture and then turn our attention to combinatorics ( where it will remain for the rest of the paper ) . let @xmath0 denote the ring of symmetric functions in the variable set @xmath1 with coefficients in the field @xmath2 . for any partition @xmath3 , let @xmath4 denote the corresponding modified macdonald symmetric function ; it is known that @xmath5 is a basis for @xmath0 . for any symmetric function @xmath6 , define the _ delta operator _ @xmath7 to be the macdonald eigenoperator given by @xmath8 \tilde{h}_{\mu}.\ ] ] here we are using the plethystic shorthand @xmath9 = f ( \dots , q^{i-1 } t^{j-1 } , \dots ) $ ] , where @xmath10 ranges over the matrix coordinates of all cells @xmath11 in the ( english ) young diagram of @xmath3 . for example , suppose @xmath12 is the partition whose young diagram is shown below . we have that @xmath13 \tilde{h}_{(3,2,1 ) } = f(q , q^2 , t , qt , t^2 ) \tilde{h}_{(3,2,1)},\ ] ] where we implicitly set @xmath14 in @xmath15 for all @xmath16 . @xmath17 & @xmath18 & @xmath19 @xmath20 & @xmath21 @xmath22 let @xmath23 denote the elementary symmetric function of degree @xmath24 . the delta conjecture ( ( * ? ? ? * conjecture 1.1 ) ) asserts a combinatorial formula for the application of @xmath25 to @xmath26 for all nonnegative integers @xmath27 . _ ( the delta conjecture ) _ for any integers @xmath28 , @xmath29 \\ & = \{z^{n - k-1}\ } \left [ \sum_{p \in \mathcal{ld}_n } q^{\mathrm{dinv}(p ) } t^{\mathrm{area}(p ) } \prod_{i \in \mathrm{val}(p ) } \left ( 1 + z / t^{d_i(p ) + 1 } \right ) x^p \right].\end{aligned}\ ] ] here the operator @xmath30 extracts the coefficient of @xmath31 . we will not need the set @xmath32 of labeled dyck paths , nor the statistics @xmath33 , @xmath34 , @xmath35 , @xmath36 , and @xmath37 that they carry ; for details on these objects see @xcite . for our purposes it will be enough to know that the delta conjecture asserts an equality of quasisymmetric functions in @xmath1 with coefficients depending on the parameters @xmath18 and @xmath20 . the two right hand sides of the delta conjecture display two quasisymmetric functions . following @xcite , we name these quantities as follows . @xmath38 , \\ { { \mathrm { val}}}_{n , k}(x ; q , t ) & : = \{z^{n - k-1}\ } \left [ \sum_{p \in \mathcal{ld}_n } q^{\mathrm{dinv}(p ) } t^{\mathrm{area}(p ) } \prod_{i \in \mathrm{val}(p ) } \left ( 1 + z / t^{d_i(p ) + 1 } \right ) x^p \right].\end{aligned}\ ] ] the notation here reflects the combinatorics ; @xmath39 is governed by rises of dyck paths and @xmath40 is governed by valleys of dyck paths ; see @xcite for details . when @xmath41 , the delta conjecture specializes to the shuffle conjecture of haglund , haiman , remmel , loehr , and ulyanov @xcite . the shuffle conjecture gives an expansion of the symmetric function @xmath42 into the fundamental basis of quasisymmetric functions , and therefore an expansion of the bigraded frobenius character of the module of diagonal harmonics into this quasisymmetric basis . it is an open problem to find a nice representation theoretic interpretation of @xmath43 for general @xmath27 . carlsson and mellit proved the shuffle conjecture using a dazzling and groundbreaking array of plethystic operators and combinatorial techniques @xcite . however , the delta conjecture remains open for general @xmath27 . various special cases of the delta conjecture were proven in @xcite . one of these special cases is as follows ; it concerns setting one of the variables @xmath44 equal to zero . [ delta - q - t - zero - hrw ] ( ( * ? ? ? * theorem 4.1 ) ) the coefficients of the monomial quasisymmetric function @xmath45 are equal in each of the following : @xmath46 not included in theorem [ delta - q - t - zero - hrw ] is the expression @xmath47 . in section [ words ] below , we will add it in by proving the following result . [ valley - function - equality ] for all @xmath28 , we have the equality @xmath48 consequently , we can append @xmath47 to the list in theorem [ delta - q - t - zero - hrw ] . theorem [ valley - function - equality ] proves a conjecture of a. t. wilson ( * ? ? ? * conjecture 1 ) as well as a related conjecture of haglund , remmel , and wilson ( * ? ? ? * conjecture 4.1 ) . our proof of theorem [ valley - function - equality ] will rely on equidistribution results for statistics on ordered set partitions and ordered multiset partitions which generalize statistics on permutations and words . let @xmath49 be any word in the alphabet @xmath50 . the _ inversion number _ of @xmath51 is @xmath52 a _ descent _ of @xmath51 is an index @xmath53 such that @xmath54 . the _ descent set _ of @xmath51 is @xmath55 finally , the _ major index _ of @xmath51 is @xmath56 the study of statistics on words ( and in particular permutations in the symmetric group @xmath57 on @xmath58 : = \{1 , 2 , \dots , n\}$ ] ) is a major facet of enumerative combinatorics . one of the foundational results on permutations statistics is due to macmahon @xcite ; in 1915 he proved that @xmath59!_q,\ ] ] where @xmath58!_q : = [ n]_q [ n-1]_q \cdots [ 1]_q$ ] and @xmath60_q : = 1 + q + \cdots + q^{r-1}$ ] . in his honor , any permutation statistic which shares this distribution is called _ mahonian_. in @xcite it was proven that @xmath39 and @xmath40 at @xmath61 or @xmath62 can be written using generalizations of permutation and word statistics to statistics on ordered set partitions and ordered multiset partitions . the result for @xmath63 is as follows . [ valley - interpretation ] ( @xcite ) for all @xmath28 , we have the equalities @xmath64 the outer sums in theorem [ valley - interpretation ] are over all weak compositions @xmath65 of @xmath66 . the inner sums in theorem [ valley - interpretation ] are over all @xmath67-block ordered multiset partitions @xmath3 of the multiset @xmath68 . the entries @xmath69 and @xmath70 appearing in the exponents are generalizations to ordered multiset partitions of the inversion and major index statistic on words . theorem [ valley - function - equality ] is therefore equivalent to proving that @xmath71 for any @xmath72 . this will be demonstrated in section [ words ] . the inversion statistic @xmath69 on ordered multiset partitions was studied by steingrmsson @xcite ( under the name @xmath73 ) and has received a fair amount of attention @xcite . the minimaj statistic @xmath70 is newer ; it first appeared in @xcite . given an ordered multiset partition @xmath3 , one considers the set of words @xmath74 obtained by permuting letters within the blocks of @xmath3 . for example , if @xmath75 , then @xmath76 the number @xmath70 is defined to be the minimum of the major index statistic over the set @xmath74 . in this example , we have @xmath77 so that @xmath78 . the rest of the paper is organized as follows . in * section [ permutations ] * we will study the @xmath79 and @xmath80 statistics on ordered set partitions . we will prove that they have the same distribution on ordered set partitions with a fixed shape , and calculate this distribution @xmath81 explicitly . the polynomials @xmath81 are nonstandard @xmath18-analogs of the multinomial coefficients @xmath82 . in * section [ words ] * we generalize from permutations and ordered set partitions to words and ordered multiset partitions . we will see that the theory of @xmath79 and @xmath80 behaves differently in the presence of repeated letters . in particular , these statistics are _ not _ equidistributed on ordered multiset partitions of the same weight and shape . on the other hand , these statistics _ are _ equidistributed on ordered multiset partitions of the same weight and with a fixed number of blocks . in * section [ colored ] * we generalize in another direction to colored permutations and colored ordered set partitions . as in the uncolored case , we will see that the statistics @xmath79 and @xmath80 share the same distribution on these sets . in fact , we will prove that this distribution is a natural generalization @xmath83_q)^n f_{n,\alpha}(q^r)$ ] of the polynomial @xmath81 . however , we will see that attempting to mimic the arguments of section [ permutations ] in the presence of colors results in a seemingly difficult polynomial identity ( proposition [ polynomial - identity ] ) . we close in * section [ closing ] * with some algebraic questions regarding the polynomial @xmath81 . a natural generalization of permutations is given by ordered set partitions . an _ ordered set partition _ @xmath84 of @xmath58 $ ] is a sequence @xmath85 of nonempty subsets of @xmath58 $ ] ( called _ blocks _ ) such that @xmath58 = b_1 \uplus \dots \uplus b_k$ ] . the sequence of cardinalities @xmath86 is called the _ shape _ of @xmath84 , so an ordered set partition of shape @xmath87 is just a permutation in @xmath57 . for example , we have that @xmath88 is an ordered set partition of @xmath89 $ ] with @xmath90 blocks and shape @xmath91 . we will adopt the shorthand of writing ordered set partitions @xmath92 by using vertical bars to demarcate blocks and writing entries within blocks in increasing order . our example ordered set partition is therefore @xmath93 recall that a _ weak composition of @xmath66 _ is a finite sequence @xmath94 of nonnegative integers satisfying @xmath95 . we say that @xmath96 . a _ composition of @xmath66 _ is a weak composition of @xmath66 without any zeros . we use the notation @xmath97 to mean that @xmath98 is a weak composition of @xmath66 and @xmath99 to mean that @xmath98 is a composition of @xmath66 . for any @xmath100 and @xmath99 , we introduce the following families of ordered set partitions : @xmath101 $ } \ } , \\ { { \mathcal{op}}}_{n , k } & : = \ { \text{all ordered set partitions of $ [ n]$ with $ k$ blocks } \ } , \\ { { \mathcal{op}}}_{n , \alpha } & : = \ { \text{all ordered set partitions of $ [ n]$ of shape $ \alpha$ } \}.\end{aligned}\ ] ] let @xmath102 be an ordered set partition . an _ inversion _ of @xmath84 is a pair @xmath103 such that @xmath104 and @xmath105 for some @xmath106 . the _ inversion count _ @xmath107 is the number of inversions of @xmath84 . for example , the inversions of @xmath108 are @xmath109 and @xmath110 and we have @xmath111 . the @xmath79 statistic on ordered set partitions was introduced by steingrmsson @xcite . for @xmath112 , let @xmath113 be the set of permutations in @xmath57 obtained by rearranging letters within the blocks of @xmath84 . for example , we have @xmath114 as @xmath84 varies over @xmath115 , the sets @xmath113 are precisely the parabolic cosets of the symmetric group @xmath57 . as in section [ introduction ] , we set @xmath116 for example , we have @xmath117 for any @xmath100 and @xmath99 , we introduce the generating functions for @xmath79 and @xmath80 . @xmath118 it will be convenient to consider permutations and words which carry a segmentation . formally , a _ @xmath119-segmented permutation _ of size @xmath66 is a pair @xmath120 where @xmath121 and @xmath99 has @xmath96 . we write @xmath120 by inserting dots between just after the positions @xmath122 of @xmath123 , resulting in a figure @xmath124 \cdot \pi[2 ] \cdot \ldots \cdot \pi[k]$ ] . the words @xmath125 , \pi[2 ] , \dots , \pi[k]$ ] are called the _ segments _ of @xmath120 . for example , we have that @xmath126 is a @xmath127-segmented permutation of size @xmath128 . we represent this pair as @xmath129 \cdot \pi[2 ] \cdot \pi[3 ] \cdot \pi[4 ] = 627 \cdot 3 \cdot 189 \cdot 45\ ] ] and we have the segments @xmath129 = 627 , \pi[2 ] = 3 , \pi[3 ] = 189 , \pi[4 ] = 45.\ ] ] for any permutation statistic @xmath130 , we have a natural extension of @xmath130 to segmented permutations given by forgetting the segmentation ; that is @xmath131 the role played by segmentation will be minor in this section , but segmentation will become very important in section [ words ] when we allow repetition of letters . segmented permutations can be used to give an alternative characterization of @xmath80 . in particular , we define a map @xmath132 as follows . [ segment - pi - map ] let @xmath133 . we define @xmath134 \cdot \pi[2 ] \cdot \ldots \cdot \pi[k]$ ] by the following recursive procedure . for @xmath135 , write @xmath136 * let the @xmath137 segment @xmath138 $ ] be the letters of @xmath139 written in increasing order : @xmath140 : = j_1^{(k ) } j_2^{(k ) } \cdots j_{\alpha_k}^{(k)}.\ ] ] * for @xmath141 , assume that the segment @xmath142 $ ] has been defined . let @xmath143 be the first letter in @xmath142 $ ] and let @xmath144 be the maximum index such that @xmath145 ( where we set @xmath146 ) . define the @xmath147 segment @xmath148 $ ] to be the sequence @xmath149 : = j_{m+1}^{(i ) } j_{m+2}^{(i ) } \cdots j_{\alpha_i}^{(i ) } j_1^{(i ) } j_2^{(i ) } \cdots j_m^{(i)}.\ ] ] for example , we have @xmath150 observe that if @xmath151 , we have that @xmath152 . the following alternative formulation of @xmath80 is easy to see ; its proof is left to the reader . [ minimaj - alternative ] let @xmath112 be an ordered set partition of @xmath58 $ ] and let @xmath151 . the major index statistic @xmath153 achieves a unique minimum value on @xmath113 , and this value is achieved at @xmath123 . in particular , we have @xmath154 for example , we may calculate @xmath155 given any sequence @xmath156 of nonempty , finite , and pairwise disjoint sets of integers , define the _ standardization _ @xmath157 to be the unique ordered set partition of @xmath158 $ ] which is order isomorphic to @xmath156 . for example , we have @xmath159 the @xmath80 statistic satisfies the following ` compression ' property . [ compress ] let @xmath160 be an ordered set partition . we have @xmath161 we have that @xmath162 coincides with @xmath134 \cdot \pi[2 ] \cdot \dots \cdot \pi[k]$ ] , except that its terminal segment @xmath138 $ ] is shortened to its first letter . moreover , the segment @xmath138 $ ] does not contain any descents . now apply lemma [ minimaj - alternative ] . for example , we have @xmath163 for a composition @xmath165 with @xmath96 , let @xmath81 be the following polynomial : @xmath166 for example , if @xmath167 we have @xmath168 \times \left [ { 1 \choose 1 } + { 2 \choose 1 } q + \cdots + { 6 \choose 1 } q^5 \right].\end{aligned}\ ] ] at the extremes , we have that @xmath169 and @xmath170!_q$ ] . we have that @xmath171 is the multinomial coefficient @xmath172 , but for general @xmath98 the polynomial @xmath81 is _ not _ the standard @xmath18-multinomial @xmath173!_q}{[\alpha_1]!_q \cdots [ \alpha_k]!_q}$ ] . in this subsection we will prove that @xmath174 coincides with both @xmath175 and @xmath176 . the strategy is to show that these three polynomials obey the same recursion . let @xmath177 act on permutations in @xmath57 by decrementing every letter by @xmath178 modulo @xmath66 . for example , if @xmath179 we have @xmath180 the following simple lemma will be crucial . [ cycle - major - permutations ] let @xmath181 and assume @xmath182 . we have @xmath183 the action of @xmath184 on @xmath123 preserves the descent set , except that the descent just before @xmath178 moves a single unit to the right . decrementing by @xmath178 modulo @xmath66 also defines an action of @xmath185 on ordered set partitions of @xmath58 $ ] . moreover , we have an action of @xmath185 on segmented permutations given by preserving segmentation : @xmath186 recall the map @xmath123 of definition [ segment - pi - map ] from ordered set partitions to segmented words . although @xmath123 does not commute with the action of @xmath185 in general , we have commutativity when we restrict to ordered set partitions whose terminal block size is @xmath178 . [ cycle - commute - permutations ] let @xmath187 and suppose that @xmath188 . let @xmath189 . we have that @xmath190 let @xmath191 be the block of @xmath84 containing @xmath178 . write the segments of @xmath192 and @xmath193 as @xmath134 \cdot \pi[2 ] \cdot \ldots \cdot \pi[k]$ ] and @xmath194 \cdot \pi'[2 ] \cdot \ldots \cdot \pi'[k]$ ] . we want to show that @xmath148 = c.\pi'[i]$ ] for all @xmath195 . this is true when @xmath196 because @xmath188 . definition [ segment - pi - map ] makes it clear that @xmath148 = c.\pi'[i]$ ] for @xmath197 . if @xmath198 = j_{m+1 } j_{m+2 } \dots j_{\alpha_{i_0 } } 1 j_2 \dots j_m$ ] , we see that @xmath199 = ( j_{m+1}-1 ) ( j_{m+2}-1 ) \dots ( j_{\alpha_{i_0}}-1 ) n ( j_2 -1)\dots ( j_m-1 ) = c.\pi[i_0].\ ] ] now consider the segments @xmath200 $ ] and @xmath201 $ ] . if @xmath202 above , then the first letter of @xmath203 $ ] is the first letter of @xmath198 $ ] , less one . definition [ segment - pi - map ] shows that @xmath201 = c.\pi[i_0 - 1]$ ] in this case . if @xmath204 above , then the first letter of @xmath198 $ ] is @xmath178 and the first letter of @xmath203 $ ] is @xmath66 . another application of definition [ segment - pi - map ] shows that @xmath201 = c.\pi[i_0 - 1]$ ] in this case , as well . finally , the equality @xmath201 = c.\pi[i_0 - 1]$ ] and definition [ segment - pi - map ] make it clear that @xmath205 = c.\pi[i]$ ] for all @xmath206 . we are ready to prove our first equidistribution result . [ same - distribution - permutations ] let @xmath98 be a composition of @xmath66 . we have that @xmath207 the @xmath208-polynomials satisfy the recursion @xmath209.\ ] ] it is easy to see that @xmath176 satisfies the recursion in equation [ f - recursion ] . given an ordered set partition @xmath102 of shape @xmath210 , the block @xmath139 is involved in @xmath211 inversions . after selecting a number @xmath212 for @xmath213 , we have @xmath214 choices to complete the block @xmath139 . it follows that @xmath215 for all @xmath98 . to prove that @xmath216 , write @xmath217 and assume inductively that @xmath218 . for any ordered set partition @xmath84 of shape @xmath219 , let @xmath220 be the ordered set partition of type @xmath221 obtained by appending the singleton @xmath222 to the end of @xmath84 . clearly we have @xmath223 , so that by lemma [ minimaj - alternative ] , @xmath224 lemmas [ minimaj - alternative ] , [ cycle - commute - permutations ] , and [ cycle - major - permutations ] imply that for @xmath225 , @xmath226 this gives the recursion in equation [ f - recursion ] for @xmath175 when @xmath188 . for general @xmath227 , we apply lemma [ compress ] to see that for any @xmath24 , there are precisely @xmath228 ordered set partitions @xmath229 of @xmath58 $ ] of type @xmath98 satisfying @xmath230 . this shows that the recursion of equation [ f - recursion ] holds for @xmath175 . although our proof of theorem [ same - distribution - permutations ] is combinatorial , it is not bijective . j. remmel and a. t. wilson are preparing a bijective proof of theorem [ same - distribution - permutations ] . if we coarsen theorem [ same - distribution - permutations ] to consider ordered set partitions with @xmath119 blocks , we get the following corollary . [ same - distribution - stirling ] let @xmath231 . we have that @xmath232!_q { { \mathrm { stir}}}_{n , k}(q),\ ] ] where the @xmath18-stirling number @xmath233 is defined by the recursion @xmath234_q { { \mathrm { stir}}}_{n-1,k}(q)\ ] ] and the initial condition @xmath235 . steingrmsson ( * ? ? ? * theorem 4 ) proved that @xmath236!_q { { \mathrm { stir}}}_{n , k}(q)$ ] ( steingrmsson uses @xmath73 for our @xmath237 ) . now apply theorem [ same - distribution - permutations ] . in @xcite , remmel and wilson prove bijectively that @xmath237 is equidistributed on @xmath238 with a different @xmath239-like statistic on ordered set partitions due to steingrmsson @xcite . however , the statistics considered in @xcite are not equidistributed on the finer sets @xmath240 . relating corollary [ same - distribution - stirling ] to the delta conjecture yields the following result . [ valley - specializations ] the coefficients of the monomial quasisymmetric function @xmath241 in the monomial expansions of @xmath242 and @xmath243 are equal . corollary [ valley - specializations ] proves a conjecture of haglund , remmel , and wilson ( * ? ? ? * conjecture 4.1 ) and allows us to add @xmath244 to the list in theorem [ delta - q - t - zero - hrw ] . in the next section we will strengthen corollary [ valley - specializations ] by proving @xmath245 . if the delta conjecture is true , we would have the stronger symmetry @xmath246 . many definitions and results on ordered set partitions and permutations generalize naturally to ordered multiset partitions and words . however , we will discover a significant divergence in the behavior of the statistics @xmath79 and @xmath80 . for any weak composition @xmath65 , an _ ordered multiset partition of weight @xmath247 _ is a sequence @xmath248 of nonempty * sets * such that @xmath249 is the multiset union @xmath250 . the total number of letters is called the _ size _ of @xmath3 , the sets @xmath251 are called the _ blocks _ of @xmath3 , and the composition @xmath252 of set cardinalities is called the _ shape _ of @xmath3 . for example , we have that @xmath253 is an ordered multiset partition with @xmath127 blocks of size @xmath254 , weight @xmath255 , and shape @xmath256 . although letters can be repeated in an ordered multiset partition , no single block of an ordered multiset partition can have repeated letters . given integers @xmath100 , a weak composition @xmath72 , and a composition @xmath99 , we introduce the following families of ordered multiset partitions : @xmath257 let @xmath258 . as in the case of ordered set partitions , an _ inversion _ in @xmath3 is a pair @xmath259 such that @xmath105 and @xmath104 for some @xmath106 . the statistic @xmath69 counts the number of inversions of @xmath3 . if @xmath3 is the ordered multiset partition shown above , we have @xmath260 . given a weak composition @xmath261 , let @xmath262 denote the set of all words @xmath263 containing @xmath264 copies of @xmath195 , for all @xmath195 . for any ordered multiset partition @xmath265 , let @xmath74 be the set of words in @xmath262 obtained by rearranging the letters of @xmath3 within its blocks . as in section [ introduction ] , the @xmath80 statistic on ordered multiset partitions is @xmath266 as in section [ permutations ] , we introduce the following generating functions for @xmath79 and @xmath80 on ordered multiset partitions . @xmath267 in light of theorem [ same - distribution - permutations ] , the reader may guess that we have @xmath268 for any weak composition @xmath247 and any composition @xmath98 with @xmath269 . however , this statement is false . for example , consider @xmath270 and @xmath271 . we have @xmath272 we leave it for the reader to check that @xmath273 whereas @xmath274 despite this , we will prove the coarser equality @xmath275 for any @xmath72 and any @xmath276 . given a weak composition @xmath72 , let @xmath262 be the collection of words @xmath263 with @xmath264 copies of the letter @xmath195 for all @xmath195 . in particular , if @xmath277 we get @xmath278 . a _ @xmath119-segmented word _ is a pair @xmath279 , where @xmath280 is a word and @xmath99 is a composition with @xmath96 . we represent a @xmath119-segmented word @xmath279 as @xmath281 \cdot \ldots \cdot w[k]$ ] , were dots are placed after positions @xmath122 of the word @xmath51 . the subwords @xmath282 , w[2 ] , \dots , w[k]$ ] are called _ segments_. if @xmath130 is any statistic on words , we get a statistic on segmented words by @xmath283 . given any @xmath119-segmented word @xmath281 \cdot \ldots \cdot w[k]$ ] , we have a natural ordered multiset partition with @xmath119 blocks obtained by replacing dots with bars and deleting repeated letters . for example , the ordered multiset partition corresponding to @xmath284 is @xmath285 in particular , the length of a segmented word could be larger than the size of the associated ordered multiset partition . the length of a segmented word equals the size of the corresponding ordered multiset partition if and only if none of the segments have repeated letters . definition [ segment - pi - map ] can be repeated verbatim to get a function @xmath286 for example , we have @xmath287 lemma [ minimaj - alternative ] remains true in the presence of repeated letters . [ minimaj - alternative - word ] let @xmath3 be an ordered multiset partition with @xmath288 . the major index statistic @xmath153 achieves a unique minimum value on @xmath74 , and this value is achieved at @xmath51 . in particular , we have @xmath289 . for example , we have @xmath290 in this subsection we develop recursions for @xmath79 and @xmath80 on ordered multiset partitions . we will see that these recursions do not coincide , which explains why the generating functions for these statistics disagree on the sets @xmath291 . let @xmath187 be a composition and let @xmath292 be a weak composition . for any subset @xmath293 $ ] , let @xmath294 be the length @xmath295 indicator vector defined by @xmath296 the recursion for @xmath79 on ordered multiset partitions is as follows . [ inv - recursion - word ] preserve the notation from above . the generating function @xmath297 satisfies the following formula . @xmath298 where the sum is over all subsets @xmath293 $ ] such that @xmath299 and @xmath300 for all @xmath301 . consider a typical ordered multiset partition @xmath302 . writing @xmath303 , we have that @xmath304 . moreover , the addition of @xmath305 to the end of this ordered multiset partition contributes one inversion for each element of the sets @xmath251 ( @xmath141 ) which is @xmath306 . the recursion for @xmath80 is different and a bit more involved to prove . our starting point is the following generalization of lemma [ cycle - major - permutations ] from @xmath57 to to @xmath262 for @xmath72 with @xmath307 . as before , we let @xmath308 act on @xmath262 by decrementing all letters by @xmath178 modulo @xmath295 . [ cycle - major - words ] let @xmath309 where @xmath307 and @xmath310 . then @xmath311 . the map @xmath184 moves every descent occurring just before a maximal contiguous run of @xmath178 s in @xmath51 to the position at the end of this run . lemma [ cycle - commute - permutations ] generalizes to the setting of repeated letters as follows . [ cycle - commute - words ] let @xmath187 be a composition and let @xmath292 be a weak composition . assume that @xmath188 . we have that @xmath312 for any @xmath313 . similar to the proof of lemma [ cycle - commute - permutations ] . use lemma [ minimaj - alternative - word ] instead of lemma [ minimaj - alternative ] . since removing letters from an ordered multiset partition gives an ordered multiset partition ( provided that none of the blocks are emptied ) , there is no need to introduce standardization in the analog of lemma [ compress ] for ordered multiset partitions . [ compress - word ] let @xmath314 be an ordered multiset partition . we have @xmath315 similar to the proof of lemma [ compress ] . use lemma [ minimaj - alternative - word ] instead of lemma [ minimaj - alternative ] . in light of lemma [ compress - word ] , it is enough to state a recursion for @xmath316 when the last part of @xmath98 equals @xmath178 . [ basic - minimaj - recursion - word ] let @xmath187 be a composition with @xmath188 and let @xmath292 be a weak composition . we have @xmath317 without loss of generality , we may assume that @xmath261 is in fact a strict composition . by construction , we have that any ordered multiset partition of the form @xmath318 satisfies @xmath319 , so that lemma [ minimaj - alternative - word ] gives @xmath320 on the other hand , for @xmath53 , lemma [ cycle - commute - words ] and lemma [ cycle - major - words ] show that for a typical @xmath321 , we have @xmath322 the corresponding identity of generating functions follows . observe that the weight composition @xmath247 gets cycled in the recursion of lemma [ basic - minimaj - recursion - word ] , but that no such cycling appears in lemma [ inv - recursion - word ] . this is irrelevant in the permutation case @xmath277 , but in the case of words we get different behavior of @xmath79 and @xmath80 on @xmath323 . in order to prove that @xmath79 and @xmath80 are equidistributed on @xmath324 , we will show first that @xmath80 has the same distribution on @xmath324 and @xmath325 whenever @xmath326 is a rearrangement of @xmath247 . equivalently , we will show that the quasisymmetric function @xmath244 is symmetric in the @xmath327 variables . we will do this using a family of involutions on ordered multiset partitions called _ switch maps_. as the general definition of switch maps is a bit involved , let us first examine the special case of switch maps defined on words . let @xmath328 and let @xmath329 be a weak composition whose entries are a rearrangement of those of @xmath247 . our goal is to give a combinatorial proof that @xmath153 has the same distribution on the set of words @xmath262 as on the set of words @xmath330 . it is enough to consider the case @xmath331 for some @xmath53 . we define a map @xmath332 as follows . let @xmath309 . underline every consecutive pair of letters @xmath333 which appears in @xmath51 . now overline all maximal runs of not - underlined letters which are of the form @xmath334 for some @xmath335 . let @xmath336 be the word obtained by replacing every overlined run @xmath334 with the run @xmath337 . for example , we have @xmath338 [ bender - knuth - words ] let @xmath292 . for @xmath53 , the map @xmath332 is bijective and preserves descent sets , and hence major index . the @xmath339 are involutions , and so bijections . by construction , the @xmath339 preserve descent sets . we conclude that @xmath153 has the same distribution on @xmath262 and @xmath330 whenever @xmath326 is a rearrangement of @xmath247 . the operators @xmath340 satisfy the relations : @xmath341 the main task of this subsection is to generalize the @xmath339 maps from words to ordered multiset partitions . in particular , for any weak composition @xmath292 , any @xmath53 , and any @xmath342 , we will define a _ switch map _ @xmath343 . the switch maps will satisfy the relations of equation [ switch - relations ] . in particular , the relation @xmath344 will force the switch maps to be bijective . moreover , we will have that @xmath345 for any ordered multiset partition @xmath3 . lemma [ minimaj - alternative - word ] therefore implies that @xmath346 . in the all singletons case @xmath347 , the switch map @xmath339 will just be the map defined above . however , in the general case the switch map @xmath339 will not preserve shape ( and it * can not * ; see the example following corollary [ valley - symmetric ] below ) . in order to define the @xmath339 operators on ordered multiset partitions , we need to carefully consider the relative positions of the letters @xmath195 and @xmath348 in segmented words lying in the image of the map @xmath349segmented words@xmath350 . the following trichotomy will allow us to fruitfully generalize the notion of a contiguous pair of letters of the form @xmath333 . [ trichotomy ] let @xmath187 be a composition and let @xmath351 be an ordered multiset partition of shape @xmath98 . fix a letter @xmath195 and consider the @xmath119-segmented word @xmath352 \cdot \ldots \cdot w[k]$ ] . for each @xmath353 , exactly one of the following statements holds for the segment @xmath354 $ ] . 1 . the segment @xmath354 $ ] contains at most one letter from the set @xmath355 . the letters @xmath195 and @xmath348 both appear in @xmath354 $ ] , are adjacent , and occur in the order @xmath356 . 3 . the letters @xmath195 and @xmath348 both appear in @xmath354 $ ] , the letter @xmath348 is the first letter of @xmath354 $ ] , and the letter @xmath195 is the last letter of @xmath357 . moreover , we have that @xmath358 and the first letter of @xmath359 $ ] is @xmath195 . if @xmath360 , the segment @xmath361 $ ] consists of the letters in @xmath139 written in increasing order , and the claimed trichotomy holds . assume that @xmath362 and this trichotomy holds for the segment @xmath359 $ ] . let @xmath143 be the first letter of @xmath359 $ ] and write @xmath363 . by the definition of the map @xmath51 , the segment @xmath354 $ ] is @xmath364 , where @xmath295 is maximal such that @xmath365 . if @xmath366 , we have that @xmath367 is a contiguous subword of @xmath364 unless @xmath368 . if @xmath368 and @xmath366 , we get that @xmath369 and @xmath370 . we deduce that the desired trichotomy holds for the segment @xmath354 $ ] . in defining the @xmath339 operator on words , we froze all consecutive pairs of letters of the form @xmath333 . to extend the @xmath339 operators to ordered multiset partitions , we will need to expand the collection of subwords that get frozen . we capture this idea in the following definition of an _ @xmath195-drop_. the reader should compare this definition to lemma [ trichotomy ] . [ i - drop - def ] _ ( @xmath195-drops ) _ let @xmath281 \cdot \ldots \cdot w[k]$ ] be a @xmath119-segmented word and let @xmath195 be a letter @xmath195-drop _ in @xmath51 is a contiguous subword of the form @xmath371 , where * none of the letters @xmath372 are equal to @xmath195 or @xmath348 , and * either @xmath371 or @xmath373 is a segment of @xmath282 \cdot \ldots \cdot w[k]$ ] . we will consider @xmath195-drops in @xmath119-segmented words @xmath282 \cdot \ldots \cdot w[k]$ ] arising from ordered multiset partitions . for example , the @xmath254-segmented word which is the image under @xmath51 of the ordered multiset partition @xmath374 is shown below with all @xmath90-drops underlined : @xmath375 if @xmath376 is the length of @xmath51 , we recover the classical notion of a contiguous pair @xmath333 in a word @xmath51 . we next describe how to underline and overline the segmented word @xmath377 arising from an ordered multiset partition @xmath3 . [ word - decoration ] _ ( word decoration ) _ let @xmath292 , let @xmath53 , and let @xmath342 . let @xmath378 and write @xmath352 \cdot \ldots \cdot w[k]$ ] . @xmath195-decorated @xmath119-segmented word _ corresponding to @xmath3 is obtained from @xmath282 \cdot \ldots \cdot w[k]$ ] as follows . * underline every @xmath195-drop in @xmath377 , and then * overline every maximal contiguous subword of @xmath377 consisting entirely of @xmath195 s and @xmath379 s which are not underlined . continuing our running example , the @xmath90-decorated @xmath254-segmented word corresponding to the ordered multiset partition @xmath374 is @xmath380 in general , the overlined subwords in decorated words all have the same form . [ overlined - form ] every overlined subword in an @xmath195-decorated @xmath119-segmented word has the form @xmath334 for some @xmath335 . if not , then we can find an overlined subword with a contiguous pair of letters equal to @xmath333 . if these letters are in the same segment of @xmath352 \cdot \ldots \cdot w[k]$ ] , by lemma [ trichotomy ] this segment must equal @xmath333 , which would make @xmath333 an ( underlined ) @xmath195-drop , a contradiction . the letters @xmath379 and @xmath195 are therefore in different segments , forcing @xmath195 to be the first letter of its segment and @xmath379 to be the last letter of its segment . in turn , the definition of @xmath51 forces the segment of @xmath377 containing @xmath348 to have length @xmath178 , so that @xmath333 is again an @xmath195-drop , which is again a contradiction . we define the ordered set partition @xmath381 in terms of its @xmath119-segmented word @xmath382 . the word @xmath383 underlying the @xmath119-segmented word @xmath384 \cdot \ldots \cdot w'[k]$ ] is easy to describe : for every overlined subword in the @xmath195-decorated @xmath119-segmented word corresponding to @xmath377 , replace @xmath334 with @xmath337 . obtaining the correct segmentation @xmath385 \cdot \ldots \cdot w'[k]$ ] from the @xmath119-segmented word @xmath282 \cdot \ldots \cdot w[k]$ ] is more involved and depends on the local structure of @xmath377 near each overlined subword . [ switch - maps ] _ ( switch maps ) _ let @xmath292 , let @xmath53 , and let @xmath342 . we define an ordered set partition @xmath381 as follows . let @xmath386 be an ordered multiset partition . form the @xmath195-decorated @xmath119-segmented word @xmath352 \cdot \ldots \cdot w[k]$ ] corresponding to @xmath3 . we define a new @xmath119-segmented word @xmath387 \cdot \ldots \cdot w'[k]$ ] from this decorated word by altering the letters and segmentation in @xmath377 near each overlined subword of @xmath377 as follows . let @xmath334 be a typical overlined subword of @xmath377 . * * case 1 : * _ @xmath388 and @xmath389 . _ if the overlined run @xmath390 is not immediately preceded by an @xmath195-drop in @xmath377 , then trade every @xmath195 in this run for an @xmath348 and leave the segmentation at this run unchanged in @xmath383 . if the overlined run @xmath390 is immediately preceded by an @xmath195-drop in @xmath377 , then the structure of @xmath377 near this run must look like @xmath391 these expressions differ in a single dot before the leftmost @xmath195 . + trade these in @xmath383 for @xmath392 respectively . * * case 2 : * _ @xmath393 and @xmath394 . _ if the overlined run @xmath395 is not immediately preceded by an @xmath195-drop in @xmath377 , then trade every @xmath348 in this run for an @xmath195 and leave the segmentation of this run unchanged in @xmath383 . if the overlined run @xmath395 is immediately preceded by an @xmath195-drop in @xmath377 , then the structure of @xmath377 near this run must look like @xmath396 trade these in @xmath383 for @xmath397 respectively . * * case 3 : * _ @xmath388 and @xmath394 . _ the structure of @xmath377 near the run @xmath334 must look like @xmath398 trade these in @xmath383 for @xmath399 respectively . after applying the above procedure to every overlined run in @xmath377 , we get a @xmath119-segmented word @xmath387 \cdot \ldots \cdot w'[k]$ ] . define @xmath400 to be the ordered multiset partition obtained by letting the elements in the block @xmath401 be the letters in the segment @xmath402 $ ] . the operator @xmath339 is called a _ switch map _ on ordered multiset partitions . as definition [ switch - maps ] is elaborate , let us give an example of applying switch maps to ordered multiset partitions . we let @xmath403 and @xmath404 . we wish to compute @xmath405 . to do this , we first compute the @xmath90-decorated @xmath254-segmented word corresponding to @xmath3 to get @xmath406 \cdot \ldots \cdot w[11 ] = 712\overline{3 \cdot 34 } \cdot \underline{4 \cdot 3 } \cdot \overline{3 \cdot 4 } \cdot \underline{4673 } \cdot \overline{3 \cdot 3 } \cdot \underline{457 \cdot 3}56.\ ] ] now we alter the overlined subwords and the segmentation near them to get @xmath387 \cdot \ldots \cdot w'[11]$ ] . reading off from definition [ switch - maps ] , we get @xmath407 \cdot \ldots \cdot w'[11 ] = 71234 \cdot 4 \cdot 4 \cdot 3 \cdot 3 \cdot 4 \cdot 467 \cdot 3 4 \cdot 4 \cdot 457 \cdot 356.\ ] ] replacing segments with blocks , we get @xmath408 observe that we have @xmath409 that is , we have @xmath410 is precisely the @xmath254-segmented word @xmath387 \cdot \ldots \cdot w'[11]$ ] constructed in definition [ switch - maps ] . moreover , the @xmath90-decoration of @xmath410 is given by @xmath411 in particular , the positions of the underlined and overlined portions of this word ( ignoring segmentation ) are precisely the same as the corresponding positions in the @xmath90-decorated @xmath254-segmented word @xmath352 \cdot \ldots \cdot w[11]$ ] . if we apply the transformations of definition [ switch - maps ] to @xmath410 we get @xmath412 this is precisely the @xmath254-segmented word @xmath377 . in particular , we have that @xmath413 . the key facts about switch maps are collected in the following proposition . [ switch - well - defined ] let @xmath292 , let @xmath53 , and let @xmath342 . let @xmath386 . 1 . we have that @xmath381 is an ordered multiset partition in @xmath414 . the action of @xmath339 therefore gives a map @xmath415 2 . if @xmath387 \cdot \ldots \cdot w'[k]$ ] is the @xmath119-segmented word constructed in definition [ switch - maps ] , we have that @xmath384 \cdot \ldots \cdot w'[k]$ ] as @xmath119-segmented words . we have that @xmath345 . we have that @xmath416 . we have that @xmath417 . \(1 ) we first check that @xmath381 has the same size as @xmath3 . this is equivalent to showing that none of the segments in the @xmath119-segmented word @xmath387 \cdot \ldots \cdot w'[k]$ ] of definition [ switch - maps ] has repeated letters . to begin , notice that none of the segments of @xmath352 \cdot \ldots \cdot w[k]$ ] have repeated letters . consider forming the @xmath195-decorated @xmath119-segmented word corresponding to @xmath377 and let @xmath334 be a typical overlined subword . we need to show that none of the transformations in definition [ switch - maps ] induce repeated letters . * * case 1 : * _ @xmath388 and @xmath389 . _ if the overlined run @xmath390 is not immediately preceded by an @xmath195-drop , then * * the segment of @xmath377 containing the leftmost @xmath195 in this run can not contain @xmath379 , for otherwise this segment would be an ( underlined ) @xmath195-drop by lemma [ trichotomy ] , and * * the segment of @xmath377 containing the rightmost @xmath195 in this run can not contain @xmath379 , for otherwise lemma [ trichotomy ] implies that this rightmost @xmath195 must be immediately followed by @xmath379 and this @xmath379 can not be the first letter in an @xmath195-drop , contradicting the maximality of overlined runs . + we conclude that changing every @xmath195 to an @xmath348 and leaving segmentation preserved does not induce any repeated letters within segments . + if the overlined run @xmath390 is immediately preceded by an @xmath195-drop , then we apply either the left or right branch transformations in case 1 of definition [ switch - maps ] . in either situation , the reasoning of the last paragraph shows that the segment of @xmath377 containing the rightmost @xmath195 can not also contain an @xmath379 . it follows that neither of these transformations induce repeated letters within segments . * * case 2 : * _ @xmath393 and @xmath394 . _ if the overlined run @xmath395 is not immediately preceded by an @xmath195-drop , then * * the segment containing the leftmost @xmath379 in this run can not also contain an @xmath195 , for otherwise this segment would end in @xmath356 by lemma [ trichotomy ] . lemma [ trichotomy ] also implies that this @xmath195 can not be the end of an @xmath195-drop , contradicting the maximality of overlined runs , and * * the segment containing the rightmost @xmath379 can not also contain an @xmath195 , for otherwise this segment would be an ( underlined ) @xmath195-drop by lemma [ trichotomy ] . + we conclude that changing every @xmath348 to an @xmath195 and leaving segmentation preserved does not induce any repeated letters within segments . + if the overlined run @xmath395 is immediately preceded by an @xmath195-drop , then we apply either the left or right branch transformations of case 2 of definition [ switch - maps ] . the reasoning of the last paragraph shows that the segment containing the rightmost @xmath379 can not also contain an @xmath195 . moreover , the definition of an @xmath195-drop shows that none of the letters @xmath372 appearing in these braces equals @xmath195 . we conclude that neither of the transformations of these branches induces repeated letters within segments . * * case 3 : * _ @xmath418 . _ in this case we apply the either the left or right brach of case 3 of definition [ switch - maps ] to the overlined run @xmath334 . since @xmath418 it is evident that this transformation does not induce repeated letters within blocks . we conclude that none of the segments in the transformed word @xmath387 \cdot \ldots \cdot w'[k]$ ] contains repeated letters , so that @xmath381 has the same size as @xmath3 . it remains to show that @xmath419 . equivalently , we need to show that @xmath381 has @xmath119 blocks and weight @xmath420 . since none of the transformations of definition [ switch - maps ] changes the number of segments of a word ( just the lengths of these segments ) , we have that @xmath381 has the same number of blocks as @xmath3 . that is , the ordered multiset partition @xmath381 has @xmath119 blocks . since each underlined @xmath195-drop in @xmath377 contains precisely one @xmath195 and one @xmath379 , and each of the overlined @xmath334 runs is transformed to @xmath337 by definition [ switch - maps ] , we conclude that @xmath381 has weight @xmath420 . in summary , we have that @xmath381 is an ordered multiset partition in @xmath421 . \(2 ) write @xmath422 \cdot \ldots \cdot w''[k]$ ] and @xmath423 . we need to show that @xmath424 = w''[s]$ ] for all @xmath425 . definition [ switch - maps ] makes it clear that each segment @xmath426 $ ] is a rearrangement of the letters in the segment @xmath424 $ ] . it is therefore enough to show that the segments of @xmath385 \cdot \ldots \cdot w'[k]$ ] satisfy the recursive definition of the map @xmath51 applied to @xmath427 . consider a typical overlined run @xmath334 in the @xmath195-decorated @xmath119-segmented word corresponding to @xmath51 . we may inductively assume that the segmented words @xmath383 and @xmath428 agree to the right of this overlined word . * * case 1 : * _ @xmath388 and @xmath389 . _ the portion of the segmented word @xmath377 immediately to the right of this overlined run looks like @xmath429 where we could have @xmath430 . by the definition of @xmath51 , we have that @xmath431 . if @xmath432 , then the rightmost @xmath195 would be part of an @xmath195-drop . we conclude that @xmath433 or @xmath434 . the definition of @xmath51 and the maximality of overlined subwords imply that none of the letters @xmath435 lie in @xmath355 . moreover , the segment containing @xmath195 does not contain @xmath379 be lemma [ trichotomy ] . the transformations of case 1 change this portion of @xmath377 to @xmath436 perhaps altering the segmentation just to the left . this segmented subword agrees with the recursive definition of the map @xmath51 . * * case 2 : * _ @xmath393 and @xmath394 . _ the portion of the segmented word @xmath377 immediately to the right of this overlined run looks like @xmath437 where we could have @xmath430 . if @xmath368 , the rightmost @xmath379 would be part of an @xmath195-drop . by the definition of the map @xmath51 , we know that @xmath431 . we conclude that @xmath433 or @xmath434 . lemma [ trichotomy ] implies that none of the letters @xmath435 lie in @xmath355 . the transformations of case 2 change this portion of @xmath377 to @xmath438 perhaps altering the segmentation just to the left . this segmented subword agrees with the recursive definition of the map @xmath51 . * * case 3 : * _ @xmath418 . _ this case is easier and left to the reader . \(3 ) a glance at the transformations of definition [ switch - maps ] shows that none of them affects descent sets . now apply ( 2 ) . \(4 ) apply ( 3 ) together with lemma [ minimaj - alternative - word ] . \(5 ) consider the @xmath195-decorated @xmath119-segmented word @xmath352 \cdot \ldots \cdot w[k]$ ] corresponding to @xmath3 . we consider applying the transformations of definition [ switch - maps ] to @xmath377 twice . let @xmath387 \cdot \ldots \cdot w'[k]$ ] be the @xmath119-segmented word constructed in definition [ switch - maps ] and consider the @xmath195-decoration of @xmath383 . it is easy to see that the underlined and overlined portions of this @xmath195-decoration occur in precisely the same positions as those in @xmath377 . the transformation in the left branch of case 1 leads to the transformation in the left branch of case 2 , and vice versa . the transformation in the right branch of case 1 leads to the transformation of the right branch of case 2 , and vice versa . the transformation of either branch of case 3 leads to another transformation of the same branch . since the roles of @xmath439 and @xmath440 are interchanged in the second transformation , the application to two transformations recovers the @xmath119-segmented word @xmath377 . in particular , we have @xmath417 . it can be checked that the switch maps satisfy @xmath441 for @xmath442 , but we will not need this relation here . the most important consequence of proposition [ switch - well - defined ] for us is the following . [ rearrange ] let @xmath342 , let @xmath247 be a weak composition , and let @xmath326 be any weak composition obtained by rearranging the parts of @xmath247 . we have that @xmath443 for any @xmath195 , the map @xmath343 is a @xmath80-preserving bijection . as another immediate corollary of proposition [ switch - well - defined ] , we can deduce the symmetry of @xmath244 in the @xmath327 variables . it is unknown whether @xmath40 is symmetric . [ valley - symmetric ] let @xmath231 . the formal power series @xmath444 is symmetric in the variables @xmath1 , where the sum is over all ordered multiset partitions @xmath3 with @xmath445 blocks and size @xmath66 . corollary [ valley - symmetric ] is false if we instead sum over ordered set partitions @xmath3 with fixed shape . for example , we have @xmath446 it follows that the coefficient of @xmath447 in the quasisymmetric function @xmath448 is @xmath449 but the coefficient of @xmath450 is @xmath451 . proposition [ switch - well - defined ] can be used to prove something more refined than corollary [ valley - symmetric ] . namely , for any subset @xmath452 $ ] the quasisymmetric function @xmath453 is symmetric . i. gessel observed ( personal communication ) that when @xmath376 , the symmetry of @xmath454 follows from the fact that @xmath455 ( where @xmath456 is the complete homogeneous symmetric function of degree @xmath24 ) and the principle of inclusion - exclusion @xcite . the author is unaware of an analogous proof of the symmetry of @xmath457 . the author is also unaware of what relationship ( if any ) the polynomials @xmath458 have with the delta conjecture . we are ready to prove our equidistribution result for ordered multiset partitions . [ same - distribution - word ] let @xmath72 be a weak composition and let @xmath460 . we have that @xmath461 write @xmath292 and let @xmath187 with @xmath188 . lemma [ basic - minimaj - recursion - word ] says that @xmath462 sum both sides of equation [ same - distribution - word - first ] over all compositions @xmath463 of @xmath464 which have @xmath465 parts . this yields @xmath466 the first equality is equation [ same - distribution - word - first ] summed over all compositions @xmath467 with @xmath465 parts . the second equality interchanges the order of summation . the third equality evaluates the inner sum over all @xmath468 . the fourth equality is an application of corollary [ rearrange ] . the left hand side of equation [ main - chain ] is the generating function for @xmath80 on the collection of all @xmath119-block multiset partitions of weight @xmath247 whose last block has size @xmath178 . lemma [ compress - word ] shows that for general @xmath227 , @xmath469 where the sum on the left hand side is over all @xmath470-part compositions @xmath471 and the external sum on the right hand side is over all subsets @xmath293 $ ] of indices such that @xmath300 for all @xmath301 . lemma [ inv - recursion - word ] shows that @xmath472 satisfies the same recursion . the proof of theorem [ same - distribution - word ] proves a slightly stronger statement . namely , for any fixed weak composition @xmath247 and positive integer @xmath439 , we have that @xmath473 where the sums are over all @xmath119-block ordered multiset partitions @xmath3 of weight @xmath247 whose last block has size @xmath439 . the connection of this more refined equidistribution result to the delta conjecture is unclear . theorem [ valley - function - equality ] follows by combining theorems [ valley - interpretation ] and [ same - distribution - word ] . we restate it here . * theorem 1.3 . * _ for all @xmath28 , we have the equality @xmath48 consequently , the coefficients of the monomial quasisymmetric function @xmath45 are equal in each of the following : @xmath474 _ in light of the delta conjecture , it is natural to ask for the expansion of the symmetric functions @xmath245 in the schur basis @xmath475 . it turns out that @xmath243 is schur positive the coefficients in this expansion are polynomials in @xmath18 with nonnegative coefficients . an explicit formula for these coefficients follows immediately from the work of wilson @xcite . to give the schur expansion of @xmath243 , we will need some notation . given a partition @xmath476 , let @xmath477 denote the set of standard young tableaux of shape @xmath478 . for @xmath479 , a _ descent _ of @xmath480 is an index @xmath481 such that @xmath348 appears in a lower row of @xmath480 than @xmath195 . let @xmath482 denote the number of descents of @xmath480 . also let @xmath483 denote the sum of the descents of @xmath480 . for example , suppose that @xmath484 is the standard tableau 1 & 3 & 4 2 & 6 & 7 5 & 8 . the descents of @xmath480 are @xmath485 and @xmath486 so that @xmath487 and @xmath488 . the following corollary follows immediately from an insertion argument due to wilson @xcite and theorem [ valley - function - equality ] . we use the usual @xmath18-binomial @xmath489!_q}{[k]!_q [ n - k]!_q}$ ] . ( wilson @xcite ) [ valley - frobenius ] for a partition @xmath476 , we have that the coefficient of @xmath490 in @xmath491 equals @xmath492 in particular , we have that @xmath493 is schur positive . for @xmath494 , this follows from letting @xmath495 and taking the coefficient of @xmath496 in ( * ? ? ? * theorem 5.0.1 ) . now apply theorem [ valley - function - equality ] . the calculation @xmath497 shows that the coefficient of @xmath498 in @xmath499 is @xmath500 . the calculation @xmath501 shows that the coefficient of @xmath502 in @xmath499 is @xmath503 . since there are no ordered multiset partitions of weight @xmath504 with @xmath505 blocks , the coefficient of @xmath506 in @xmath499 is @xmath507 . we therefore have the monomial basis expansion of the symmetric function @xmath499 given by @xmath508 which leads to the schur basis expansion @xmath509 to see that this agrees with corollary [ valley - frobenius ] , one may check that the four standard young tableaux with three boxes _ _ 1 2 3 1 & 2 3 1 & 3 2 1 & 2 & 3 contribute ( from left to right ) @xmath510 and @xmath511 to the schur expansion of @xmath499 predicted by ( [ schur - expansion ] ) in contrast to the state of affairs regarding @xmath512 , it is known that the other quasisymmetric function @xmath513 appearing in the delta conjecture is both symmetric in the @xmath327-variables and schur positive @xcite . however , the proof of schur positivity relies on the positivity of llt polynomials a positivity result which lacks a combinatorial proof . wilson @xcite proved combinatorially that we have the identities @xmath514 it follows that the coefficient of @xmath490 in the schur basis expansion of @xmath515 or @xmath516 is also given by ( [ schur - expansion ] ) . a natural generalization of permutations can be obtained by coloring their entries . let @xmath517 and consider the alphabet @xmath518 we think of @xmath519 as the letter @xmath195 augmented with the ` color ' @xmath520 . the _ wreath product _ @xmath521 consists of all length @xmath66 words @xmath522 in @xmath523 which contain just one copy of the letter @xmath195 ( of any color ) for all @xmath524 . for example , we have @xmath525 . we can also think of elements in @xmath521 as pairs @xmath526 , where @xmath121 is the uncolored permutation and @xmath527 is the _ color sequence_. in this language , the colored permutation @xmath528 would be written as @xmath529 . as a group , the wreath product @xmath521 is isomorphic to the complex reflection group @xmath530 consisting of @xmath531 monomial complex matrices whose nonzero entries are @xmath532 roots of unity . we will have no occasion to use the group structure on @xmath521 . one extension of major index to colored permutations which has appeared in the literature is as follows . introduce the following total order @xmath533 on the set @xmath523 : @xmath534 let @xmath535 have color sequence @xmath536 . the _ major index _ of @xmath123 is @xmath537 this statistic is called the ` flag major index ' in @xcite . inside @xmath538 we have @xmath539 a _ @xmath521-ordered set partition _ is a sequence @xmath102 of nonempty subsets of @xmath523 such that , for all @xmath524 , precisely one copy of @xmath195 appears ( with any color ) in @xmath84 . as before , we call the sets @xmath540 the _ blocks _ of @xmath84 , we say that @xmath84 has _ @xmath119 blocks _ , and we call the composition @xmath187 the _ shape _ of @xmath84 . for example , we have that @xmath541 is a @xmath538-ordered set partition with @xmath90 blocks of shape @xmath542 . we have the collections of @xmath521-ordered set partitions : @xmath543 let @xmath102 be a @xmath521-ordered set partition . we define @xmath544 to be the set of elements of @xmath521 obtained by permuting the letters within the blocks of @xmath84 . for example , @xmath545 the set @xmath546 may be regarded as a parabolic coset in the complex reflection group @xmath521 . the @xmath80 statistic on @xmath547 is defined by @xmath548 in order to prove an analog of theorem [ same - distribution - permutations ] for colored ordered set partitions , we need to define a suitable generalization of @xmath79 on @xmath547 for @xmath549 . let @xmath550 $ ] be the decolorizing map given by @xmath551 and extend @xmath24 to a map @xmath552 in the obvious way . also define a statistic @xmath553 on @xmath547 by letting @xmath554 be the sum of the colors of the letters in @xmath84 . we define a statistic @xmath79 on @xmath547 by @xmath555 where @xmath556 is computed as in section [ permutations ] . for example , if @xmath557 , we have @xmath558 so that @xmath559 we have the usual host of generating functions : @xmath560 recall the polynomial @xmath81 from section [ permutations ] . we will prove a natural generalization of the equidistribution result of theorem [ same - distribution - permutations ] to colored permutations . our approach here will be to reduce the colored result to the uncolored case of theorem [ same - distribution - permutations ] . in the next subsection we will see that trying to mimic the proof of theorem [ same - distribution - permutations ] itself leads to a strange and difficult polynomial identity . [ same - distribution - colored ] let @xmath562 and let @xmath99 be a composition . we have @xmath563_q)^n f_{n,\alpha}(q^r).\ ] ] we start by proving that @xmath564_q)^n f_{\alpha}(q^r)$ ] . consider a fixed uncolored ordered set partition @xmath565 . we have that @xmath566_q)^n q^{r ( { { \mathrm { inv}}}(\sigma_0))}$ ] , where the sum is over all colored ordered set partitions @xmath567 satisfying @xmath568 . the identity @xmath564_q)^n f_{\alpha}(q^r)$ ] follows from summing over all @xmath565 and applying theorem [ same - distribution - permutations ] . next , we prove that @xmath569_q)^n f_{\alpha}(q^r)$ ] . to see this , we define a standardization map @xmath570 as follows . let @xmath567 be a colored ordered set partition and consider its elements with respect to the order @xmath533 on the alphabet @xmath571 . let @xmath572 be the unique element of @xmath240 which is order isomorphic to @xmath84 under @xmath533 . for example , we have @xmath573 let @xmath565 be an uncolored ordered set partition and let @xmath574 be a weak composition of @xmath66 of length @xmath143 . if @xmath567 satisfies @xmath575 and has @xmath576 letters of color @xmath195 for all @xmath195 , we have that @xmath577 for a fixed @xmath565 and a fixed color multiplicity sequence @xmath574 , how many ordered multiset partitions lie in the set @xmath578 for any color @xmath195 and any block @xmath579 , the number of entries in @xmath579 of color @xmath195 must equal the number of entries in the @xmath580 block of @xmath581 which lie in the interval @xmath582 $ ] . to determine @xmath84 , we need only assign @xmath576 entries in @xmath58 $ ] to have color @xmath195 in @xmath84 , for all @xmath583 . the number of ways to do this is the multinomial coefficient @xmath584 . we conclude that @xmath585_q)^n f_{n , \alpha}(q^r),\ ] ] where the second equality used the multinomial theorem together with theorem [ same - distribution - permutations ] . in light of theorem [ same - distribution - word ] , it is natural to expect an equidistribution result involving @xmath79 and @xmath80 on appropriately defined ` colored ordered multiset partitions ' with a fixed number of blocks and a fixed weight . the author has been unable to produce such a result . equidistribution fails to hold in small examples when one considers sequences of nonempty subsets of @xmath586 , e.g. @xmath587 equidistribution also fails in small examples when one considers sequences of nonempty subsets of @xmath586 where no set contains two copies of the same letter ( of any color ) , e.g. @xmath588 the reader may wonder whether the methods of section [ permutations ] can be used to prove theorem [ same - distribution - colored ] without relying on theorem [ same - distribution - permutations ] . attempting to do so leads to a strange and complicated polynomial identity whose truth is implied by theorem [ same - distribution - colored ] , but which the author does not know how to prove directly . lemma [ cycle - major - permutations ] generalizes naturally to the context of colored permutations . we have an action of @xmath589 on the alphabet @xmath523 given by the cycle @xmath590 viewing @xmath521 as the complex reflection group @xmath530 , we can think of @xmath184 as the regular element @xmath591 this action extends to an action @xmath592 on @xmath521 by setting @xmath593 for @xmath594 . the analog of lemma [ cycle - major - permutations ] continues to hold . [ cycle - major - colored - permutations ] let @xmath535 and assume that @xmath595 . then @xmath596 . if @xmath123 does not contain @xmath597 , the application of @xmath184 preserves the descent set of @xmath123 , sends @xmath598 to @xmath599 , and preserves all other signs . if @xmath123 contains @xmath597 , the application of @xmath184 moves the descent of @xmath123 ending in @xmath597 one unit to the right while decreasing the sum of signs by @xmath600 , resulting in a net increase of @xmath153 by @xmath178 . the map @xmath601 of section [ permutations ] extends easily to define a map @xmath602 for @xmath549 . given @xmath603 , the @xmath119-segmented word @xmath604 \cdot \ldots \cdot \pi[k ] \in c \wr s(b_1 | \dots | b_k)$ ] is defined using definition [ segment - pi - map ] with respect to the order @xmath533 on the alphabet @xmath523 . for example , if @xmath557 , we have @xmath605 \cdot \pi[2 ] \cdot \pi[3 ] \cdot \pi[4 ] = 1 ^ 1 4 ^ 0 2 ^ 2 \cdot 7 ^ 2 \cdot 9 ^ 2 8 ^ 1 \cdot 6 ^ 2 3 ^ 1 5 ^ 1.\ ] ] the analog of lemma [ minimaj - alternative ] is still true in this setting . [ minimaj - alternative - colored ] let @xmath84 be a @xmath521-ordered set partition . the statistic @xmath153 achieves a unique minimum on the set @xmath544 , and this value is achieved at @xmath192 . the analog of lemma [ compress ] also holds for colored set partitions . let @xmath156 be a sequence of nonempty subsets of @xmath523 with the property that at most one of @xmath606 appears among the sets @xmath607 , for all @xmath524 . let @xmath157 be the unique @xmath608-ordered set partition ( for some @xmath609 ) whose associated uncolored ordered set partition is order isomorphic to the uncolored sequence of sets @xmath156 , while preserving colors . for example , we have @xmath610 [ compress - colored ] let @xmath314 be a @xmath521-ordered set partition . write the elements of @xmath139 as @xmath611 and write @xmath612 for the color of @xmath264 for @xmath613 . we have that @xmath614 similar to the proof of lemma [ compress ] , except one must take into account the contribution of colors to the @xmath80 statistic . lemma [ cycle - commute - permutations ] generalizes in the obvious way . [ cycle - minimizers - colored ] let @xmath615 be a @xmath521-ordered set partition of type @xmath187 with @xmath188 . we have @xmath616 similar to the proof of lemma [ cycle - commute - permutations ] . let @xmath187 and let @xmath617 . by theorem [ same - distribution - colored ] , we have the recursion @xmath618_q)^{\alpha_k } \times \left [ { \alpha_k - 1 \choose \alpha_k - 1 } + { \alpha_k \choose \alpha_k - 1}q^r + \cdots + { n-1 \choose \alpha_k - 1 } q^{r(n-\alpha_k ) } \right ] \times m^r_{\overline{\alpha},n}(q).\ ] ] on the other hand , we can derive a recursion for @xmath619 combinatorially . fix a letter @xmath620 for @xmath524 and @xmath621 . let @xmath622 be a typical @xmath521-ordered set partition such that the minimum element @xmath213 ( with respect to @xmath533 ) is @xmath623 . the choices involved in the completion of the block @xmath139 are as follows : 1 . choose a subset @xmath624 of size @xmath20 ( for some @xmath625 ) . 2 . choose a subset @xmath626 of size @xmath627 . 3 . color the elements of @xmath305 with @xmath628 arbitrarily . 4 . color the elements of @xmath480 with @xmath629 arbitrarily . for a fixed choice of @xmath305 and @xmath480 ( and hence @xmath20 ) as above , the net contribution to @xmath630 coming from letter colors in @xmath631 will be @xmath632_q^{\alpha_k - t-1 } [ j+1]_q^t$ ] . on the other hand , lemmas [ cycle - major - colored - permutations ] , [ compress - colored ] , and [ cycle - minimizers - colored ] imply that the choice of @xmath633 contributes an additional @xmath634 to @xmath630 . we have @xmath635 choices for the set @xmath305 and @xmath636 choices for the set @xmath480 . putting all of this together , we get that @xmath637_q^{\alpha_k - t-1 } [ j+1]_q^t . \end{gathered}\ ] ] the following polynomial identity follows from ( and is equivalent to ) theorem [ same - distribution - colored ] . [ polynomial - identity ] for all @xmath638 and all @xmath639 we have @xmath640_q)^{\alpha_k } \times \left [ { \alpha_k - 1 \choose \alpha_k - 1 } + { \alpha_k \choose \alpha_k - 1}q^r + \cdots + { n-1 \choose \alpha_k - 1 } q^{r(n-\alpha_k ) } \right ] = \\ \sum_{i = 1}^n \sum_{j = 0}^{r-1 } \sum_{t = 0}^{\alpha_k-1 } { n - i \choose t } { i-1 \choose \alpha_k - t - 1 } q^{j(n-\alpha_k+1 ) + ( n - i - t ) } [ j]_q^{\alpha_k - t-1 } [ j+1]_q^t . \end{gathered}\ ] ] we challenge the reader to prove proposition [ polynomial - identity ] directly ! in this paper we have applied the combinatorics of ordered set partitions to obtain evidence for the delta conjecture of symmetric function theory . along the way to doing so , we discovered a new family of polynomials @xmath641 indexed by compositions @xmath187 . we pose the problem of finding an algebraic interpretation of these polynomials . consider the action of the symmetric group @xmath57 on the polynomial ring @xmath642 $ ] given by variable permutation . let @xmath643 be the ideal generated by @xmath57-invariant polynomials @xmath644 $ ] with vanishing constant term . the _ coinvariant algebra _ is the graded @xmath645-vector space @xmath646/i$ ] . the space @xmath647 carries a graded action of @xmath57 ; it can be shown that @xmath648 $ ] as @xmath57-representations . one natural @xmath645-basis of @xmath647 ( the so - called _ artin basis _ ) consists of those monomials @xmath649 whose exponent sequence @xmath650 satisfies @xmath651 . said differently , the multiplication map gives rise to an isomorphism of graded @xmath645-vector spaces @xmath652_{\leq 0 } \otimes { { \mathbb { c}}}[x_2]_{\leq 1 } \otimes \cdots \otimes { { \mathbb { c}}}[x_n]_{\leq n-1 } \xrightarrow{\sim } r_n.\ ] ] here @xmath653 denotes the subspace of a graded @xmath645-algebra @xmath654 consisting of elements of degree @xmath655 . this shows that the hilbert series @xmath656 of @xmath647 is @xmath58!_q = f_{n,(1^n)}(q)$ ] . for an arbitrary composition @xmath99 , we have that @xmath81 is the generating function for the degree statistic on monomials @xmath657 whose exponent sequences @xmath35 satisfy @xmath658 for all @xmath135 . said differently , the polynomial @xmath81 is the hilbert series of the graded @xmath645-vector space @xmath659_{\leq 0 } \otimes { { \mathbb { c}}}[x_{\alpha_1 + 1 } , \dots , x_{\alpha_1 + \alpha_2}]_{\leq \alpha_1 } \otimes \cdots \otimes { { \mathbb { c}}}[x_{n-\alpha_k+1 } , \dots , x_n]_{\leq n - \alpha_k}.\ ] ] the artin basis is one of several interesting bases for the coinvariant algebra @xmath647 . the _ descent monomial basis _ @xmath660 introduced by garsia and stanton @xcite has elements given by @xmath661 it is evident that the degree of the monomial @xmath662 is given by @xmath663 . the monomials @xmath664 may be extended to ordered set partitions by setting @xmath665 for any ordered set partition @xmath84 . it is immediate that the degree of @xmath666 is @xmath630 . a ubiquitous basis of @xmath647 which does _ not _ consist of monomials is the _ vandermonde basis _ whose elements are all of the nonzero polynomials which can be obtained by applying the partial derivative operators @xmath667 to the vandermonde polynomial @xmath668 . yet another important basis is the _ schubert basis _ which has elements given by all nonzero polynomials which can be obtained by applying the divided difference operators @xmath669 to the monomial @xmath670 . the degrees of vandermonde and schubert basis elements are closely related to the @xmath153 and @xmath79 statistics on the symmetric group . find analogs of the vandermonde and schubert basis for an arbitrary composition @xmath99 . find an analog @xmath671 of the ideal @xmath672 $ ] generated by homogeneous symmetric polynomials of positive degree . the multiplication map should give a graded @xmath645-vector space isomorphism @xmath673/i_{n,\alpha}$ ] . the analogs of the artin , descent monomial , vandermonde , and schubert bases should give bases of @xmath674 . the coinvariant algebra @xmath647 carries a graded action of @xmath57 whose graded frobenius character is the hall - littlewood polynomial @xmath675 . it is well known that for @xmath476 , the coefficient of @xmath490 in the schur expansion of @xmath675 equals @xmath676 . this coincides with the expression appearing in corollary [ valley - frobenius ] when @xmath376 . we ask for a delta conjecture - style generalization of the coinvariant module . for any @xmath276 , find a nice graded @xmath57-module @xmath677 whose graded frobenius character is @xmath245 ( after applying the involution @xmath678 which exchanges @xmath679 for @xmath26 and complementing @xmath18-degree ) . in the course of proving the equality @xmath245 it was necessary to prove that @xmath244 is symmetric in the @xmath327 variables . we accomplished this by introducing a family @xmath680 of involutive switch maps on ordered multiset partitions which preserve minimaj but permute weight compositions . the _ bender - knuth operators _ @xmath681 are a famous collection of involutions on semistandard young tableaux . given a ssyt @xmath480 , the operator @xmath682 acts on @xmath480 by freezing every instance of @xmath195 immediately above @xmath379 , and then interchanging the number of @xmath195 s and @xmath379 s in every maximal unfrozen horizontal run consisting entirely of @xmath195 s and @xmath379 s . for example , we have ( writing frozen entries in bold ) , , @xmath683 , 1 & 1 & * 2 * & 2 & 3 & 3 & 3 & 2 & * 3 * & 4 & 4 & 4 & 5 , , @xmath684 , 1 & 1 & * 2 * & 2 & 2 & 2 & 3 & 3 & * 3 * & 4 & 4 & 4 & 5 . since the operator @xmath682 interchanges the number of @xmath195 s and @xmath379 s in any ssyt , the bender - knuth operators define a family of involutions @xmath685 on words which preserve descent set ( and , in particular , major index ) while permuting weight . in particular , let @xmath280 be a word . we may apply robinson - schensted - knuth insertion to @xmath51 to get a pair @xmath686 , where @xmath687 and @xmath480 are tableaux of the same shape , the tableau @xmath687 is standard , the tableau @xmath480 is semistandard , and @xmath480 has content equal to the weight of @xmath51 . for any @xmath195 , let @xmath688 be the unique word whose rsk image is @xmath689 . the desired involutive and weight action properties of the @xmath690 are inherited from the corresponding properties of the @xmath682 . it turns out that the word operators @xmath339 and @xmath690 do not coincide . in fact , the switch maps @xmath339 do not even preserve the shape of a word under rsk . given the importance of the rsk algorithm , it would be interesting to extend the definition of the @xmath690 operators to ordered multiset partitions in such a way that * the @xmath690 act as involutions on ordered multiset partitions , * the @xmath690 preserve @xmath80 , and * the @xmath690 extend appropriately defined bender - knuth operators under the image of an appropriate ordered multiset partition version of rsk . the author is very grateful to nantel bergeron , jim haglund , ira gessel , jeff remmel , anne schilling , and andy wilson for many inspiring discussions and a great deal of constructive input on this paper . the author was partially supported by nsf grants dms-1068861 and dms-1500838 .

the delta conjecture of haglund , remmel , and wilson is a recent generalization of the shuffle conjecture in the field of diagonal harmonics . in this paper we give evidence for the delta conjecture by proving a pair of conjectures of wilson and haglund - remmel - wilson which give equidistribution results for statistics related to inversion count and major index on objects related to ordered set partitions . our results generalize the famous result of macmahon that major index and inversion number share the same distribution on permutations .

<s>[INST]the recently proven shuffle conjecture asserts a formula for the bigraded frobenius character of the module of diagonal harmonics in terms of a macdonald eigenoperator and the combinatorics of parking functions @xcite . the delta conjecture is a still - open generalization of the shuffle conjecture due to haglund , remmel , and wilson @xcite . this paper proves combinatorial results about statistics on ordered set partitions to obtain a specialization of the delta conjecture . we begin by reviewing the delta conjecture and then turn our attention to combinatorics ( where it will remain for the rest of the paper ) . let @xmath0 denote the ring of symmetric functions in the variable set @xmath1 with coefficients in the field @xmath2 . for any partition @xmath3 , let @xmath4 denote the corresponding modified macdonald symmetric function ; it is known that @xmath5 is a basis for @xmath0 . for any symmetric function @xmath6 , define the _ delta operator _ @xmath7 to be the macdonald eigenoperator given by @xmath8 \tilde{h}_{\mu}.\ ] ] here we are using the plethystic shorthand @xmath9 = f ( \dots , q^{i-1 } t^{j-1 } , \dots ) $ ] , where @xmath10 ranges over the matrix coordinates of all cells @xmath11 in the ( english ) young diagram of @xmath3 . for example , suppose @xmath12 is the partition whose young diagram is shown below . we have that @xmath13 \tilde{h}_{(3,2,1 ) } = f(q , q^2 , t , qt , t^2 ) \tilde{h}_{(3,2,1)},\ ] ] where we implicitly set @xmath14 in @xmath15 for all @xmath16 . @xmath17 & @xmath18 & @xmath19 @xmath20 & @xmath21 @xmath22 let @xmath23 denote the elementary symmetric function of degree @xmath24 . the delta conjecture ( ( * ? ? ? * conjecture 1.1 ) ) asserts a combinatorial formula for the application of @xmath25 to @xmath26 for all nonnegative integers @xmath27 . _ ( the delta conjecture ) _ for any integers @xmath28 , @xmath29 \\ & = \{z^{n - k-1}\ } \left [ \sum_{p \in \mathcal{ld}_n } q^{\mathrm{dinv}(p ) } t^{\mathrm{area}(p ) } \prod_{i \in \mathrm{val}(p ) } \left ( 1 + z / t^{d_i(p ) + 1 } \right ) x^p \right].\end{aligned}\ ] ] here the operator @xmath30 extracts the coefficient of @xmath31 . we will not need the set @xmath32 of labeled dyck paths , nor the statistics @xmath33 , @xmath34 , @xmath35 , @xmath36 , and @xmath37 that they carry ; for details on these objects see @xcite . for our purposes it will be enough to know that the delta conjecture asserts an equality of quasisymmetric functions in @xmath1 with coefficients depending on the parameters @xmath18 and @xmath20 . the two right hand sides of the delta conjecture display two quasisymmetric functions . following @xcite , we name these quantities as follows . @xmath38 , \\ { { \mathrm { val}}}_{n , k}(x ; q , t ) & : = \{z^{n - k-1}\ } \left [ \sum_{p \in \mathcal{ld}_n } q^{\mathrm{dinv}(p ) } t^{\mathrm{area}(p ) } \prod_{i \in \mathrm{val}(p ) } \left ( 1 + z / t^{d_i(p ) + 1 } \right ) x^p \right].\end{aligned}\ ] ] the notation here reflects the combinatorics ; @xmath39 is governed by rises of dyck paths and @xmath40 is governed by valleys of dyck paths ; see @xcite for details . when @xmath41 , the delta conjecture specializes to the shuffle conjecture of haglund , haiman , remmel , loehr , and ulyanov @xcite . the shuffle conjecture gives an expansion of the symmetric function @xmath42 into the fundamental basis of quasisymmetric functions , and therefore an expansion of the bigraded frobenius character of the module of diagonal harmonics into this quasisymmetric basis . it is an open problem to find a nice representation theoretic interpretation of @xmath43 for general @xmath27 . carlsson and mellit proved the shuffle conjecture using a dazzling and groundbreaking array of plethystic operators and combinatorial techniques @xcite . however , the delta conjecture remains open for general @xmath27 . various special cases of the delta conjecture were proven in @xcite . one of these special cases is as follows ; it concerns setting one of the variables @xmath44 equal to zero . [ delta - q - t - zero - hrw ] ( ( * ? ? ? * theorem 4.1 ) ) the coefficients of the monomial quasisymmetric function @xmath45 are equal in each of the following : @xmath46 not included in theorem [ delta - q - t - zero - hrw ] is the expression @xmath47 . in section [ words ] below , we will add it in by proving the following result . [ valley - function - equality ] for all @xmath28 , we have the equality @xmath48 consequently , we can append @xmath47 to the list in theorem [ delta - q - t - zero - hrw ] . theorem [ valley - function - equality ] proves a conjecture of a. t. wilson ( * ? ? ? * conjecture 1 ) as well as a related conjecture of haglund , remmel , and wilson ( * ? ? ? * conjecture 4.1 ) . our proof of theorem [ valley - function - equality ] will rely on equidistribution results for statistics on ordered set partitions and ordered multiset partitions which generalize statistics on permutations and words . let @xmath49 be any word in the alphabet @xmath50 . the _ inversion number _ of @xmath51 is @xmath52 a _ descent _ of @xmath51 is an index @xmath53 such that @xmath54 . the _ descent set _ of @xmath51 is @xmath55 finally , the _ major index _ of @xmath51 is @xmath56 the study of statistics on words ( and in particular permutations in the symmetric group @xmath57 on @xmath58 : = \{1 , 2 , \dots , n\}$ ] ) is a major facet of enumerative combinatorics . one of the foundational results on permutations statistics is due to macmahon @xcite ; in 1915 he proved that @xmath59!_q,\ ] ] where @xmath58!_q : = [ n]_q [ n-1]_q \cdots [ 1]_q$ ] and @xmath60_q : = 1 + q + \cdots + q^{r-1}$ ] . in his honor , any permutation statistic which shares this distribution is called _ mahonian_. in @xcite it was proven that @xmath39 and @xmath40 at @xmath61 or @xmath62 can be written using generalizations of permutation and word statistics to statistics on ordered set partitions and ordered multiset partitions . the result for @xmath63 is as follows . [ valley - interpretation ] ( @xcite ) for all @xmath28 , we have the equalities @xmath64 the outer sums in theorem [ valley - interpretation ] are over all weak compositions @xmath65 of @xmath66 . the inner sums in theorem [ valley - interpretation ] are over all @xmath67-block ordered multiset partitions @xmath3 of the multiset @xmath68 . the entries @xmath69 and @xmath70 appearing in the exponents are generalizations to ordered multiset partitions of the inversion and major index statistic on words . theorem [ valley - function - equality ] is therefore equivalent to proving that @xmath71 for any @xmath72 . this will be demonstrated in section [ words ] . the inversion statistic @xmath69 on ordered multiset partitions was studied by steingrmsson @xcite ( under the name @xmath73 ) and has received a fair amount of attention @xcite . the minimaj statistic @xmath70 is newer ; it first appeared in @xcite . given an ordered multiset partition @xmath3 , one considers the set of words @xmath74 obtained by permuting letters within the blocks of @xmath3 . for example , if @xmath75 , then @xmath76 the number @xmath70 is defined to be the minimum of the major index statistic over the set @xmath74 . in this example , we have @xmath77 so that @xmath78 . the rest of the paper is organized as follows . in * section [ permutations ] * we will study the @xmath79 and @xmath80 statistics on ordered set partitions . we will prove that they have the same distribution on ordered set partitions with a fixed shape , and calculate this distribution @xmath81 explicitly . the polynomials @xmath81 are nonstandard @xmath18-analogs of the multinomial coefficients @xmath82 . in * section [ words ] * we generalize from permutations and ordered set partitions to words and ordered multiset partitions . we will see that the theory of @xmath79 and @xmath80 behaves differently in the presence of repeated letters . in particular , these statistics are _ not _ equidistributed on ordered multiset partitions of the same weight and shape . on the other hand , these statistics _ are _ equidistributed on ordered multiset partitions of the same weight and with a fixed number of blocks . in * section [ colored ] * we generalize in another direction to colored permutations and colored ordered set partitions . as in the uncolored case , we will see that the statistics @xmath79 and @xmath80 share the same distribution on these sets . in fact , we will prove that this distribution is a natural generalization @xmath83_q)^n f_{n,\alpha}(q^r)$ ] of the polynomial @xmath81 . however , we will see that attempting to mimic the arguments of section [ permutations ] in the presence of colors results in a seemingly difficult polynomial identity ( proposition [ polynomial - identity ] ) . we close in * section [ closing ] * with some algebraic questions regarding the polynomial @xmath81 . a natural generalization of permutations is given by ordered set partitions . an _ ordered set partition _ @xmath84 of @xmath58 $ ] is a sequence @xmath85 of nonempty subsets of @xmath58 $ ] ( called _ blocks _ ) such that @xmath58 = b_1 \uplus \dots \uplus b_k$ ] . the sequence of cardinalities @xmath86 is called the _ shape _ of @xmath84 , so an ordered set partition of shape @xmath87 is just a permutation in @xmath57 . for example , we have that @xmath88 is an ordered set partition of @xmath89 $ ] with @xmath90 blocks and shape @xmath91 . we will adopt the shorthand of writing ordered set partitions @xmath92 by using vertical bars to demarcate blocks and writing entries within blocks in increasing order . our example ordered set partition is therefore @xmath93 recall that a _ weak composition of @xmath66 _ is a finite sequence @xmath94 of nonnegative integers satisfying @xmath95 . we say that @xmath96 . a _ composition of @xmath66 _ is a weak composition of @xmath66 without any zeros . we use the notation @xmath97 to mean that @xmath98 is a weak composition of @xmath66 and @xmath99 to mean that @xmath98 is a composition of @xmath66 . for any @xmath100 and @xmath99 , we introduce the following families of ordered set partitions : @xmath101 $ } \ } , \\ { { \mathcal{op}}}_{n , k } & : = \ { \text{all ordered set partitions of $ [ n]$ with $ k$ blocks } \ } , \\ { { \mathcal{op}}}_{n , \alpha } & : = \ { \text{all ordered set partitions of $ [ n]$ of shape $ \alpha$ } \}.\end{aligned}\ ] ] let @xmath102 be an ordered set partition . an _ inversion _ of @xmath84 is a pair @xmath103 such that @xmath104 and @xmath105 for some @xmath106 . the _ inversion count _ @xmath107 is the number of inversions of @xmath84 . for example , the inversions of @xmath108 are @xmath109 and @xmath110 and we have @xmath111 . the @xmath79 statistic on ordered set partitions was introduced by steingrmsson @xcite . for @xmath112 , let @xmath113 be the set of permutations in @xmath57 obtained by rearranging letters within the blocks of @xmath84 . for example , we have @xmath114 as @xmath84 varies over @xmath115 , the sets @xmath113 are precisely the parabolic cosets of the symmetric group @xmath57 . as in section [ introduction ] , we set @xmath116 for example , we have @xmath117 for any @xmath100 and @xmath99 , we introduce the generating functions for @xmath79 and @xmath80 . @xmath118 it will be convenient to consider permutations and words which carry a segmentation . formally , a _ @xmath119-segmented permutation _ of size @xmath66 is a pair @xmath120 where @xmath121 and @xmath99 has @xmath96 . we write @xmath120 by inserting dots between just after the positions @xmath122 of @xmath123 , resulting in a figure @xmath124 \cdot \pi[2 ] \cdot \ldots \cdot \pi[k]$ ] . the words @xmath125 , \pi[2 ] , \dots , \pi[k]$ ] are called the _ segments _ of @xmath120 . for example , we have that @xmath126 is a @xmath127-segmented permutation of size @xmath128 . we represent this pair as @xmath129 \cdot \pi[2 ] \cdot \pi[3 ] \cdot \pi[4 ] = 627 \cdot 3 \cdot 189 \cdot 45\ ] ] and we have the segments @xmath129 = 627 , \pi[2 ] = 3 , \pi[3 ] = 189 , \pi[4 ] = 45.\ ] ] for any permutation statistic @xmath130 , we have a natural extension of @xmath130 to segmented permutations given by forgetting the segmentation ; that is @xmath131 the role played by segmentation will be minor in this section , but segmentation will become very important in section [ words ] when we allow repetition of letters . segmented permutations can be used to give an alternative characterization of @xmath80 . in particular , we define a map @xmath132 as follows . [ segment - pi - map ] let @xmath133 . we define @xmath134 \cdot \pi[2 ] \cdot \ldots \cdot \pi[k]$ ] by the following recursive procedure . for @xmath135 , write @xmath136 * let the @xmath137 segment @xmath138 $ ] be the letters of @xmath139 written in increasing order : @xmath140 : = j_1^{(k ) } j_2^{(k ) } \cdots j_{\alpha_k}^{(k)}.\ ] ] * for @xmath141 , assume that the segment @xmath142 $ ] has been defined . let @xmath143 be the first letter in @xmath142 $ ] and let @xmath144 be the maximum index such that @xmath145 ( where we set @xmath146 ) . define the @xmath147 segment @xmath148 $ ] to be the sequence @xmath149 : = j_{m+1}^{(i ) } j_{m+2}^{(i ) } \cdots j_{\alpha_i}^{(i ) } j_1^{(i ) } j_2^{(i ) } \cdots j_m^{(i)}.\ ] ] for example , we have @xmath150 observe that if @xmath151 , we have that @xmath152 . the following alternative formulation of @xmath80 is easy to see ; its proof is left to the reader . [ minimaj - alternative ] let @xmath112 be an ordered set partition of @xmath58 $ ] and let @xmath151 . the major index statistic @xmath153 achieves a unique minimum value on @xmath113 , and this value is achieved at @xmath123 . in particular , we have @xmath154 for example , we may calculate @xmath155 given any sequence @xmath156 of nonempty , finite , and pairwise disjoint sets of integers , define the _ standardization _ @xmath157 to be the unique ordered set partition of @xmath158 $ ] which is order isomorphic to @xmath156 . for example , we have @xmath159 the @xmath80 statistic satisfies the following ` compression ' property . [ compress ] let @xmath160 be an ordered set partition . we have @xmath161 we have that @xmath162 coincides with @xmath134 \cdot \pi[2 ] \cdot \dots \cdot \pi[k]$ ] , except that its terminal segment @xmath138 $ ] is shortened to its first letter . moreover , the segment @xmath138 $ ] does not contain any descents . now apply lemma [ minimaj - alternative ] . for example , we have @xmath163 for a composition @xmath165 with @xmath96 , let @xmath81 be the following polynomial : @xmath166 for example , if @xmath167 we have @xmath168 \times \left [ { 1 \choose 1 } + { 2 \choose 1 } q + \cdots + { 6 \choose 1 } q^5 \right].\end{aligned}\ ] ] at the extremes , we have that @xmath169 and @xmath170!_q$ ] . we have that @xmath171 is the multinomial coefficient @xmath172 , but for general @xmath98 the polynomial @xmath81 is _ not _ the standard @xmath18-multinomial @xmath173!_q}{[\alpha_1]!_q \cdots [ \alpha_k]!_q}$ ] . in this subsection we will prove that @xmath174 coincides with both @xmath175 and @xmath176 . the strategy is to show that these three polynomials obey the same recursion . let @xmath177 act on permutations in @xmath57 by decrementing every letter by @xmath178 modulo @xmath66 . for example , if @xmath179 we have @xmath180 the following simple lemma will be crucial . [ cycle - major - permutations ] let @xmath181 and assume @xmath182 . we have @xmath183 the action of @xmath184 on @xmath123 preserves the descent set , except that the descent just before @xmath178 moves a single unit to the right . decrementing by @xmath178 modulo @xmath66 also defines an action of @xmath185 on ordered set partitions of @xmath58 $ ] . moreover , we have an action of @xmath185 on segmented permutations given by preserving segmentation : @xmath186 recall the map @xmath123 of definition [ segment - pi - map ] from ordered set partitions to segmented words . although @xmath123 does not commute with the action of @xmath185 in general , we have commutativity when we restrict to ordered set partitions whose terminal block size is @xmath178 . [ cycle - commute - permutations ] let @xmath187 and suppose that @xmath188 . let @xmath189 . we have that @xmath190 let @xmath191 be the block of @xmath84 containing @xmath178 . write the segments of @xmath192 and @xmath193 as @xmath134 \cdot \pi[2 ] \cdot \ldots \cdot \pi[k]$ ] and @xmath194 \cdot \pi'[2 ] \cdot \ldots \cdot \pi'[k]$ ] . we want to show that @xmath148 = c.\pi'[i]$ ] for all @xmath195 . this is true when @xmath196 because @xmath188 . definition [ segment - pi - map ] makes it clear that @xmath148 = c.\pi'[i]$ ] for @xmath197 . if @xmath198 = j_{m+1 } j_{m+2 } \dots j_{\alpha_{i_0 } } 1 j_2 \dots j_m$ ] , we see that @xmath199 = ( j_{m+1}-1 ) ( j_{m+2}-1 ) \dots ( j_{\alpha_{i_0}}-1 ) n ( j_2 -1)\dots ( j_m-1 ) = c.\pi[i_0].\ ] ] now consider the segments @xmath200 $ ] and @xmath201 $ ] . if @xmath202 above , then the first letter of @xmath203 $ ] is the first letter of @xmath198 $ ] , less one . definition [ segment - pi - map ] shows that @xmath201 = c.\pi[i_0 - 1]$ ] in this case . if @xmath204 above , then the first letter of @xmath198 $ ] is @xmath178 and the first letter of @xmath203 $ ] is @xmath66 . another application of definition [ segment - pi - map ] shows that @xmath201 = c.\pi[i_0 - 1]$ ] in this case , as well . finally , the equality @xmath201 = c.\pi[i_0 - 1]$ ] and definition [ segment - pi - map ] make it clear that @xmath205 = c.\pi[i]$ ] for all @xmath206 . we are ready to prove our first equidistribution result . [ same - distribution - permutations ] let @xmath98 be a composition of @xmath66 . we have that @xmath207 the @xmath208-polynomials satisfy the recursion @xmath209.\ ] ] it is easy to see that @xmath176 satisfies the recursion in equation [ f - recursion ] . given an ordered set partition @xmath102 of shape @xmath210 , the block @xmath139 is involved in @xmath211 inversions . after selecting a number @xmath212 for @xmath213 , we have @xmath214 choices to complete the block @xmath139 . it follows that @xmath215 for all @xmath98 . to prove that @xmath216 , write @xmath217 and assume inductively that @xmath218 . for any ordered set partition @xmath84 of shape @xmath219 , let @xmath220 be the ordered set partition of type @xmath221 obtained by appending the singleton @xmath222 to the end of @xmath84 . clearly we have @xmath223 , so that by lemma [ minimaj - alternative ] , @xmath224 lemmas [ minimaj - alternative ] , [ cycle - commute - permutations ] , and [ cycle - major - permutations ] imply that for @xmath225 , @xmath226 this gives the recursion in equation [ f - recursion ] for @xmath175 when @xmath188 . for general @xmath227 , we apply lemma [ compress ] to see that for any @xmath24 , there are precisely @xmath228 ordered set partitions @xmath229 of @xmath58 $ ] of type @xmath98 satisfying @xmath230 . this shows that the recursion of equation [ f - recursion ] holds for @xmath175 . although our proof of theorem [ same - distribution - permutations ] is combinatorial , it is not bijective . j. remmel and a. t. wilson are preparing a bijective proof of theorem [ same - distribution - permutations ] . if we coarsen theorem [ same - distribution - permutations ] to consider ordered set partitions with @xmath119 blocks , we get the following corollary . [ same - distribution - stirling ] let @xmath231 . we have that @xmath232!_q { { \mathrm { stir}}}_{n , k}(q),\ ] ] where the @xmath18-stirling number @xmath233 is defined by the recursion @xmath234_q { { \mathrm { stir}}}_{n-1,k}(q)\ ] ] and the initial condition @xmath235 . steingrmsson ( * ? ? ? * theorem 4 ) proved that @xmath236!_q { { \mathrm { stir}}}_{n , k}(q)$ ] ( steingrmsson uses @xmath73 for our @xmath237 ) . now apply theorem [ same - distribution - permutations ] . in @xcite , remmel and wilson prove bijectively that @xmath237 is equidistributed on @xmath238 with a different @xmath239-like statistic on ordered set partitions due to steingrmsson @xcite . however , the statistics considered in @xcite are not equidistributed on the finer sets @xmath240 . relating corollary [ same - distribution - stirling ] to the delta conjecture yields the following result . [ valley - specializations ] the coefficients of the monomial quasisymmetric function @xmath241 in the monomial expansions of @xmath242 and @xmath243 are equal . corollary [ valley - specializations ] proves a conjecture of haglund , remmel , and wilson ( * ? ? ? * conjecture 4.1 ) and allows us to add @xmath244 to the list in theorem [ delta - q - t - zero - hrw ] . in the next section we will strengthen corollary [ valley - specializations ] by proving @xmath245 . if the delta conjecture is true , we would have the stronger symmetry @xmath246 . many definitions and results on ordered set partitions and permutations generalize naturally to ordered multiset partitions and words . however , we will discover a significant divergence in the behavior of the statistics @xmath79 and @xmath80 . for any weak composition @xmath65 , an _ ordered multiset partition of weight @xmath247 _ is a sequence @xmath248 of nonempty * sets * such that @xmath249 is the multiset union @xmath250 . the total number of letters is called the _ size _ of @xmath3 , the sets @xmath251 are called the _ blocks _ of @xmath3 , and the composition @xmath252 of set cardinalities is called the _ shape _ of @xmath3 . for example , we have that @xmath253 is an ordered multiset partition with @xmath127 blocks of size @xmath254 , weight @xmath255 , and shape @xmath256 . although letters can be repeated in an ordered multiset partition , no single block of an ordered multiset partition can have repeated letters . given integers @xmath100 , a weak composition @xmath72 , and a composition @xmath99 , we introduce the following families of ordered multiset partitions : @xmath257 let @xmath258 . as in the case of ordered set partitions , an _ inversion _ in @xmath3 is a pair @xmath259 such that @xmath105 and @xmath104 for some @xmath106 . the statistic @xmath69 counts the number of inversions of @xmath3 . if @xmath3 is the ordered multiset partition shown above , we have @xmath260 . given a weak composition @xmath261 , let @xmath262 denote the set of all words @xmath263 containing @xmath264 copies of @xmath195 , for all @xmath195 . for any ordered multiset partition @xmath265 , let @xmath74 be the set of words in @xmath262 obtained by rearranging the letters of @xmath3 within its blocks . as in section [ introduction ] , the @xmath80 statistic on ordered multiset partitions is @xmath266 as in section [ permutations ] , we introduce the following generating functions for @xmath79 and @xmath80 on ordered multiset partitions . @xmath267 in light of theorem [ same - distribution - permutations ] , the reader may guess that we have @xmath268 for any weak composition @xmath247 and any composition @xmath98 with @xmath269 . however , this statement is false . for example , consider @xmath270 and @xmath271 . we have @xmath272 we leave it for the reader to check that @xmath273 whereas @xmath274 despite this , we will prove the coarser equality @xmath275 for any @xmath72 and any @xmath276 . given a weak composition @xmath72 , let @xmath262 be the collection of words @xmath263 with @xmath264 copies of the letter @xmath195 for all @xmath195 . in particular , if @xmath277 we get @xmath278 . a _ @xmath119-segmented word _ is a pair @xmath279 , where @xmath280 is a word and @xmath99 is a composition with @xmath96 . we represent a @xmath119-segmented word @xmath279 as @xmath281 \cdot \ldots \cdot w[k]$ ] , were dots are placed after positions @xmath122 of the word @xmath51 . the subwords @xmath282 , w[2 ] , \dots , w[k]$ ] are called _ segments_. if @xmath130 is any statistic on words , we get a statistic on segmented words by @xmath283 . given any @xmath119-segmented word @xmath281 \cdot \ldots \cdot w[k]$ ] , we have a natural ordered multiset partition with @xmath119 blocks obtained by replacing dots with bars and deleting repeated letters . for example , the ordered multiset partition corresponding to @xmath284 is @xmath285 in particular , the length of a segmented word could be larger than the size of the associated ordered multiset partition . the length of a segmented word equals the size of the corresponding ordered multiset partition if and only if none of the segments have repeated letters . definition [ segment - pi - map ] can be repeated verbatim to get a function @xmath286 for example , we have @xmath287 lemma [ minimaj - alternative ] remains true in the presence of repeated letters . [ minimaj - alternative - word ] let @xmath3 be an ordered multiset partition with @xmath288 . the major index statistic @xmath153 achieves a unique minimum value on @xmath74 , and this value is achieved at @xmath51 . in particular , we have @xmath289 . for example , we have @xmath290 in this subsection we develop recursions for @xmath79 and @xmath80 on ordered multiset partitions . we will see that these recursions do not coincide , which explains why the generating functions for these statistics disagree on the sets @xmath291 . let @xmath187 be a composition and let @xmath292 be a weak composition . for any subset @xmath293 $ ] , let @xmath294 be the length @xmath295 indicator vector defined by @xmath296 the recursion for @xmath79 on ordered multiset partitions is as follows . [ inv - recursion - word ] preserve the notation from above . the generating function @xmath297 satisfies the following formula . @xmath298 where the sum is over all subsets @xmath293 $ ] such that @xmath299 and @xmath300 for all @xmath301 . consider a typical ordered multiset partition @xmath302 . writing @xmath303 , we have that @xmath304 . moreover , the addition of @xmath305 to the end of this ordered multiset partition contributes one inversion for each element of the sets @xmath251 ( @xmath141 ) which is @xmath306 . the recursion for @xmath80 is different and a bit more involved to prove . our starting point is the following generalization of lemma [ cycle - major - permutations ] from @xmath57 to to @xmath262 for @xmath72 with @xmath307 . as before , we let @xmath308 act on @xmath262 by decrementing all letters by @xmath178 modulo @xmath295 . [ cycle - major - words ] let @xmath309 where @xmath307 and @xmath310 . then @xmath311 . the map @xmath184 moves every descent occurring just before a maximal contiguous run of @xmath178 s in @xmath51 to the position at the end of this run . lemma [ cycle - commute - permutations ] generalizes to the setting of repeated letters as follows . [ cycle - commute - words ] let @xmath187 be a composition and let @xmath292 be a weak composition . assume that @xmath188 . we have that @xmath312 for any @xmath313 . similar to the proof of lemma [ cycle - commute - permutations ] . use lemma [ minimaj - alternative - word ] instead of lemma [ minimaj - alternative ] . since removing letters from an ordered multiset partition gives an ordered multiset partition ( provided that none of the blocks are emptied ) , there is no need to introduce standardization in the analog of lemma [ compress ] for ordered multiset partitions . [ compress - word ] let @xmath314 be an ordered multiset partition . we have @xmath315 similar to the proof of lemma [ compress ] . use lemma [ minimaj - alternative - word ] instead of lemma [ minimaj - alternative ] . in light of lemma [ compress - word ] , it is enough to state a recursion for @xmath316 when the last part of @xmath98 equals @xmath178 . [ basic - minimaj - recursion - word ] let @xmath187 be a composition with @xmath188 and let @xmath292 be a weak composition . we have @xmath317 without loss of generality , we may assume that @xmath261 is in fact a strict composition . by construction , we have that any ordered multiset partition of the form @xmath318 satisfies @xmath319 , so that lemma [ minimaj - alternative - word ] gives @xmath320 on the other hand , for @xmath53 , lemma [ cycle - commute - words ] and lemma [ cycle - major - words ] show that for a typical @xmath321 , we have @xmath322 the corresponding identity of generating functions follows . observe that the weight composition @xmath247 gets cycled in the recursion of lemma [ basic - minimaj - recursion - word ] , but that no such cycling appears in lemma [ inv - recursion - word ] . this is irrelevant in the permutation case @xmath277 , but in the case of words we get different behavior of @xmath79 and @xmath80 on @xmath323 . in order to prove that @xmath79 and @xmath80 are equidistributed on @xmath324 , we will show first that @xmath80 has the same distribution on @xmath324 and @xmath325 whenever @xmath326 is a rearrangement of @xmath247 . equivalently , we will show that the quasisymmetric function @xmath244 is symmetric in the @xmath327 variables . we will do this using a family of involutions on ordered multiset partitions called _ switch maps_. as the general definition of switch maps is a bit involved , let us first examine the special case of switch maps defined on words . let @xmath328 and let @xmath329 be a weak composition whose entries are a rearrangement of those of @xmath247 . our goal is to give a combinatorial proof that @xmath153 has the same distribution on the set of words @xmath262 as on the set of words @xmath330 . it is enough to consider the case @xmath331 for some @xmath53 . we define a map @xmath332 as follows . let @xmath309 . underline every consecutive pair of letters @xmath333 which appears in @xmath51 . now overline all maximal runs of not - underlined letters which are of the form @xmath334 for some @xmath335 . let @xmath336 be the word obtained by replacing every overlined run @xmath334 with the run @xmath337 . for example , we have @xmath338 [ bender - knuth - words ] let @xmath292 . for @xmath53 , the map @xmath332 is bijective and preserves descent sets , and hence major index . the @xmath339 are involutions , and so bijections . by construction , the @xmath339 preserve descent sets . we conclude that @xmath153 has the same distribution on @xmath262 and @xmath330 whenever @xmath326 is a rearrangement of @xmath247 . the operators @xmath340 satisfy the relations : @xmath341 the main task of this subsection is to generalize the @xmath339 maps from words to ordered multiset partitions . in particular , for any weak composition @xmath292 , any @xmath53 , and any @xmath342 , we will define a _ switch map _ @xmath343 . the switch maps will satisfy the relations of equation [ switch - relations ] . in particular , the relation @xmath344 will force the switch maps to be bijective . moreover , we will have that @xmath345 for any ordered multiset partition @xmath3 . lemma [ minimaj - alternative - word ] therefore implies that @xmath346 . in the all singletons case @xmath347 , the switch map @xmath339 will just be the map defined above . however , in the general case the switch map @xmath339 will not preserve shape ( and it * can not * ; see the example following corollary [ valley - symmetric ] below ) . in order to define the @xmath339 operators on ordered multiset partitions , we need to carefully consider the relative positions of the letters @xmath195 and @xmath348 in segmented words lying in the image of the map @xmath349segmented words@xmath350 . the following trichotomy will allow us to fruitfully generalize the notion of a contiguous pair of letters of the form @xmath333 . [ trichotomy ] let @xmath187 be a composition and let @xmath351 be an ordered multiset partition of shape @xmath98 . fix a letter @xmath195 and consider the @xmath119-segmented word @xmath352 \cdot \ldots \cdot w[k]$ ] . for each @xmath353 , exactly one of the following statements holds for the segment @xmath354 $ ] . 1 . the segment @xmath354 $ ] contains at most one letter from the set @xmath355 . the letters @xmath195 and @xmath348 both appear in @xmath354 $ ] , are adjacent , and occur in the order @xmath356 . 3 . the letters @xmath195 and @xmath348 both appear in @xmath354 $ ] , the letter @xmath348 is the first letter of @xmath354 $ ] , and the letter @xmath195 is the last letter of @xmath357 . moreover , we have that @xmath358 and the first letter of @xmath359 $ ] is @xmath195 . if @xmath360 , the segment @xmath361 $ ] consists of the letters in @xmath139 written in increasing order , and the claimed trichotomy holds . assume that @xmath362 and this trichotomy holds for the segment @xmath359 $ ] . let @xmath143 be the first letter of @xmath359 $ ] and write @xmath363 . by the definition of the map @xmath51 , the segment @xmath354 $ ] is @xmath364 , where @xmath295 is maximal such that @xmath365 . if @xmath366 , we have that @xmath367 is a contiguous subword of @xmath364 unless @xmath368 . if @xmath368 and @xmath366 , we get that @xmath369 and @xmath370 . we deduce that the desired trichotomy holds for the segment @xmath354 $ ] . in defining the @xmath339 operator on words , we froze all consecutive pairs of letters of the form @xmath333 . to extend the @xmath339 operators to ordered multiset partitions , we will need to expand the collection of subwords that get frozen . we capture this idea in the following definition of an _ @xmath195-drop_. the reader should compare this definition to lemma [ trichotomy ] . [ i - drop - def ] _ ( @xmath195-drops ) _ let @xmath281 \cdot \ldots \cdot w[k]$ ] be a @xmath119-segmented word and let @xmath195 be a letter @xmath195-drop _ in @xmath51 is a contiguous subword of the form @xmath371 , where * none of the letters @xmath372 are equal to @xmath195 or @xmath348 , and * either @xmath371 or @xmath373 is a segment of @xmath282 \cdot \ldots \cdot w[k]$ ] . we will consider @xmath195-drops in @xmath119-segmented words @xmath282 \cdot \ldots \cdot w[k]$ ] arising from ordered multiset partitions . for example , the @xmath254-segmented word which is the image under @xmath51 of the ordered multiset partition @xmath374 is shown below with all @xmath90-drops underlined : @xmath375 if @xmath376 is the length of @xmath51 , we recover the classical notion of a contiguous pair @xmath333 in a word @xmath51 . we next describe how to underline and overline the segmented word @xmath377 arising from an ordered multiset partition @xmath3 . [ word - decoration ] _ ( word decoration ) _ let @xmath292 , let @xmath53 , and let @xmath342 . let @xmath378 and write @xmath352 \cdot \ldots \cdot w[k]$ ] . @xmath195-decorated @xmath119-segmented word _ corresponding to @xmath3 is obtained from @xmath282 \cdot \ldots \cdot w[k]$ ] as follows . * underline every @xmath195-drop in @xmath377 , and then * overline every maximal contiguous subword of @xmath377 consisting entirely of @xmath195 s and @xmath379 s which are not underlined . continuing our running example , the @xmath90-decorated @xmath254-segmented word corresponding to the ordered multiset partition @xmath374 is @xmath380 in general , the overlined subwords in decorated words all have the same form . [ overlined - form ] every overlined subword in an @xmath195-decorated @xmath119-segmented word has the form @xmath334 for some @xmath335 . if not , then we can find an overlined subword with a contiguous pair of letters equal to @xmath333 . if these letters are in the same segment of @xmath352 \cdot \ldots \cdot w[k]$ ] , by lemma [ trichotomy ] this segment must equal @xmath333 , which would make @xmath333 an ( underlined ) @xmath195-drop , a contradiction . the letters @xmath379 and @xmath195 are therefore in different segments , forcing @xmath195 to be the first letter of its segment and @xmath379 to be the last letter of its segment . in turn , the definition of @xmath51 forces the segment of @xmath377 containing @xmath348 to have length @xmath178 , so that @xmath333 is again an @xmath195-drop , which is again a contradiction . we define the ordered set partition @xmath381 in terms of its @xmath119-segmented word @xmath382 . the word @xmath383 underlying the @xmath119-segmented word @xmath384 \cdot \ldots \cdot w'[k]$ ] is easy to describe : for every overlined subword in the @xmath195-decorated @xmath119-segmented word corresponding to @xmath377 , replace @xmath334 with @xmath337 . obtaining the correct segmentation @xmath385 \cdot \ldots \cdot w'[k]$ ] from the @xmath119-segmented word @xmath282 \cdot \ldots \cdot w[k]$ ] is more involved and depends on the local structure of @xmath377 near each overlined subword . [ switch - maps ] _ ( switch maps ) _ let @xmath292 , let @xmath53 , and let @xmath342 . we define an ordered set partition @xmath381 as follows . let @xmath386 be an ordered multiset partition . form the @xmath195-decorated @xmath119-segmented word @xmath352 \cdot \ldots \cdot w[k]$ ] corresponding to @xmath3 . we define a new @xmath119-segmented word @xmath387 \cdot \ldots \cdot w'[k]$ ] from this decorated word by altering the letters and segmentation in @xmath377 near each overlined subword of @xmath377 as follows . let @xmath334 be a typical overlined subword of @xmath377 . * * case 1 : * _ @xmath388 and @xmath389 . _ if the overlined run @xmath390 is not immediately preceded by an @xmath195-drop in @xmath377 , then trade every @xmath195 in this run for an @xmath348 and leave the segmentation at this run unchanged in @xmath383 . if the overlined run @xmath390 is immediately preceded by an @xmath195-drop in @xmath377 , then the structure of @xmath377 near this run must look like @xmath391 these expressions differ in a single dot before the leftmost @xmath195 . + trade these in @xmath383 for @xmath392 respectively . * * case 2 : * _ @xmath393 and @xmath394 . _ if the overlined run @xmath395 is not immediately preceded by an @xmath195-drop in @xmath377 , then trade every @xmath348 in this run for an @xmath195 and leave the segmentation of this run unchanged in @xmath383 . if the overlined run @xmath395 is immediately preceded by an @xmath195-drop in @xmath377 , then the structure of @xmath377 near this run must look like @xmath396 trade these in @xmath383 for @xmath397 respectively . * * case 3 : * _ @xmath388 and @xmath394 . _ the structure of @xmath377 near the run @xmath334 must look like @xmath398 trade these in @xmath383 for @xmath399 respectively . after applying the above procedure to every overlined run in @xmath377 , we get a @xmath119-segmented word @xmath387 \cdot \ldots \cdot w'[k]$ ] . define @xmath400 to be the ordered multiset partition obtained by letting the elements in the block @xmath401 be the letters in the segment @xmath402 $ ] . the operator @xmath339 is called a _ switch map _ on ordered multiset partitions . as definition [ switch - maps ] is elaborate , let us give an example of applying switch maps to ordered multiset partitions . we let @xmath403 and @xmath404 . we wish to compute @xmath405 . to do this , we first compute the @xmath90-decorated @xmath254-segmented word corresponding to @xmath3 to get @xmath406 \cdot \ldots \cdot w[11 ] = 712\overline{3 \cdot 34 } \cdot \underline{4 \cdot 3 } \cdot \overline{3 \cdot 4 } \cdot \underline{4673 } \cdot \overline{3 \cdot 3 } \cdot \underline{457 \cdot 3}56.\ ] ] now we alter the overlined subwords and the segmentation near them to get @xmath387 \cdot \ldots \cdot w'[11]$ ] . reading off from definition [ switch - maps ] , we get @xmath407 \cdot \ldots \cdot w'[11 ] = 71234 \cdot 4 \cdot 4 \cdot 3 \cdot 3 \cdot 4 \cdot 467 \cdot 3 4 \cdot 4 \cdot 457 \cdot 356.\ ] ] replacing segments with blocks , we get @xmath408 observe that we have @xmath409 that is , we have @xmath410 is precisely the @xmath254-segmented word @xmath387 \cdot \ldots \cdot w'[11]$ ] constructed in definition [ switch - maps ] . moreover , the @xmath90-decoration of @xmath410 is given by @xmath411 in particular , the positions of the underlined and overlined portions of this word ( ignoring segmentation ) are precisely the same as the corresponding positions in the @xmath90-decorated @xmath254-segmented word @xmath352 \cdot \ldots \cdot w[11]$ ] . if we apply the transformations of definition [ switch - maps ] to @xmath410 we get @xmath412 this is precisely the @xmath254-segmented word @xmath377 . in particular , we have that @xmath413 . the key facts about switch maps are collected in the following proposition . [ switch - well - defined ] let @xmath292 , let @xmath53 , and let @xmath342 . let @xmath386 . 1 . we have that @xmath381 is an ordered multiset partition in @xmath414 . the action of @xmath339 therefore gives a map @xmath415 2 . if @xmath387 \cdot \ldots \cdot w'[k]$ ] is the @xmath119-segmented word constructed in definition [ switch - maps ] , we have that @xmath384 \cdot \ldots \cdot w'[k]$ ] as @xmath119-segmented words . we have that @xmath345 . we have that @xmath416 . we have that @xmath417 . \(1 ) we first check that @xmath381 has the same size as @xmath3 . this is equivalent to showing that none of the segments in the @xmath119-segmented word @xmath387 \cdot \ldots \cdot w'[k]$ ] of definition [ switch - maps ] has repeated letters . to begin , notice that none of the segments of @xmath352 \cdot \ldots \cdot w[k]$ ] have repeated letters . consider forming the @xmath195-decorated @xmath119-segmented word corresponding to @xmath377 and let @xmath334 be a typical overlined subword . we need to show that none of the transformations in definition [ switch - maps ] induce repeated letters . * * case 1 : * _ @xmath388 and @xmath389 . _ if the overlined run @xmath390 is not immediately preceded by an @xmath195-drop , then * * the segment of @xmath377 containing the leftmost @xmath195 in this run can not contain @xmath379 , for otherwise this segment would be an ( underlined ) @xmath195-drop by lemma [ trichotomy ] , and * * the segment of @xmath377 containing the rightmost @xmath195 in this run can not contain @xmath379 , for otherwise lemma [ trichotomy ] implies that this rightmost @xmath195 must be immediately followed by @xmath379 and this @xmath379 can not be the first letter in an @xmath195-drop , contradicting the maximality of overlined runs . + we conclude that changing every @xmath195 to an @xmath348 and leaving segmentation preserved does not induce any repeated letters within segments . + if the overlined run @xmath390 is immediately preceded by an @xmath195-drop , then we apply either the left or right branch transformations in case 1 of definition [ switch - maps ] . in either situation , the reasoning of the last paragraph shows that the segment of @xmath377 containing the rightmost @xmath195 can not also contain an @xmath379 . it follows that neither of these transformations induce repeated letters within segments . * * case 2 : * _ @xmath393 and @xmath394 . _ if the overlined run @xmath395 is not immediately preceded by an @xmath195-drop , then * * the segment containing the leftmost @xmath379 in this run can not also contain an @xmath195 , for otherwise this segment would end in @xmath356 by lemma [ trichotomy ] . lemma [ trichotomy ] also implies that this @xmath195 can not be the end of an @xmath195-drop , contradicting the maximality of overlined runs , and * * the segment containing the rightmost @xmath379 can not also contain an @xmath195 , for otherwise this segment would be an ( underlined ) @xmath195-drop by lemma [ trichotomy ] . + we conclude that changing every @xmath348 to an @xmath195 and leaving segmentation preserved does not induce any repeated letters within segments . + if the overlined run @xmath395 is immediately preceded by an @xmath195-drop , then we apply either the left or right branch transformations of case 2 of definition [ switch - maps ] . the reasoning of the last paragraph shows that the segment containing the rightmost @xmath379 can not also contain an @xmath195 . moreover , the definition of an @xmath195-drop shows that none of the letters @xmath372 appearing in these braces equals @xmath195 . we conclude that neither of the transformations of these branches induces repeated letters within segments . * * case 3 : * _ @xmath418 . _ in this case we apply the either the left or right brach of case 3 of definition [ switch - maps ] to the overlined run @xmath334 . since @xmath418 it is evident that this transformation does not induce repeated letters within blocks . we conclude that none of the segments in the transformed word @xmath387 \cdot \ldots \cdot w'[k]$ ] contains repeated letters , so that @xmath381 has the same size as @xmath3 . it remains to show that @xmath419 . equivalently , we need to show that @xmath381 has @xmath119 blocks and weight @xmath420 . since none of the transformations of definition [ switch - maps ] changes the number of segments of a word ( just the lengths of these segments ) , we have that @xmath381 has the same number of blocks as @xmath3 . that is , the ordered multiset partition @xmath381 has @xmath119 blocks . since each underlined @xmath195-drop in @xmath377 contains precisely one @xmath195 and one @xmath379 , and each of the overlined @xmath334 runs is transformed to @xmath337 by definition [ switch - maps ] , we conclude that @xmath381 has weight @xmath420 . in summary , we have that @xmath381 is an ordered multiset partition in @xmath421 . \(2 ) write @xmath422 \cdot \ldots \cdot w''[k]$ ] and @xmath423 . we need to show that @xmath424 = w''[s]$ ] for all @xmath425 . definition [ switch - maps ] makes it clear that each segment @xmath426 $ ] is a rearrangement of the letters in the segment @xmath424 $ ] . it is therefore enough to show that the segments of @xmath385 \cdot \ldots \cdot w'[k]$ ] satisfy the recursive definition of the map @xmath51 applied to @xmath427 . consider a typical overlined run @xmath334 in the @xmath195-decorated @xmath119-segmented word corresponding to @xmath51 . we may inductively assume that the segmented words @xmath383 and @xmath428 agree to the right of this overlined word . * * case 1 : * _ @xmath388 and @xmath389 . _ the portion of the segmented word @xmath377 immediately to the right of this overlined run looks like @xmath429 where we could have @xmath430 . by the definition of @xmath51 , we have that @xmath431 . if @xmath432 , then the rightmost @xmath195 would be part of an @xmath195-drop . we conclude that @xmath433 or @xmath434 . the definition of @xmath51 and the maximality of overlined subwords imply that none of the letters @xmath435 lie in @xmath355 . moreover , the segment containing @xmath195 does not contain @xmath379 be lemma [ trichotomy ] . the transformations of case 1 change this portion of @xmath377 to @xmath436 perhaps altering the segmentation just to the left . this segmented subword agrees with the recursive definition of the map @xmath51 . * * case 2 : * _ @xmath393 and @xmath394 . _ the portion of the segmented word @xmath377 immediately to the right of this overlined run looks like @xmath437 where we could have @xmath430 . if @xmath368 , the rightmost @xmath379 would be part of an @xmath195-drop . by the definition of the map @xmath51 , we know that @xmath431 . we conclude that @xmath433 or @xmath434 . lemma [ trichotomy ] implies that none of the letters @xmath435 lie in @xmath355 . the transformations of case 2 change this portion of @xmath377 to @xmath438 perhaps altering the segmentation just to the left . this segmented subword agrees with the recursive definition of the map @xmath51 . * * case 3 : * _ @xmath418 . _ this case is easier and left to the reader . \(3 ) a glance at the transformations of definition [ switch - maps ] shows that none of them affects descent sets . now apply ( 2 ) . \(4 ) apply ( 3 ) together with lemma [ minimaj - alternative - word ] . \(5 ) consider the @xmath195-decorated @xmath119-segmented word @xmath352 \cdot \ldots \cdot w[k]$ ] corresponding to @xmath3 . we consider applying the transformations of definition [ switch - maps ] to @xmath377 twice . let @xmath387 \cdot \ldots \cdot w'[k]$ ] be the @xmath119-segmented word constructed in definition [ switch - maps ] and consider the @xmath195-decoration of @xmath383 . it is easy to see that the underlined and overlined portions of this @xmath195-decoration occur in precisely the same positions as those in @xmath377 . the transformation in the left branch of case 1 leads to the transformation in the left branch of case 2 , and vice versa . the transformation in the right branch of case 1 leads to the transformation of the right branch of case 2 , and vice versa . the transformation of either branch of case 3 leads to another transformation of the same branch . since the roles of @xmath439 and @xmath440 are interchanged in the second transformation , the application to two transformations recovers the @xmath119-segmented word @xmath377 . in particular , we have @xmath417 . it can be checked that the switch maps satisfy @xmath441 for @xmath442 , but we will not need this relation here . the most important consequence of proposition [ switch - well - defined ] for us is the following . [ rearrange ] let @xmath342 , let @xmath247 be a weak composition , and let @xmath326 be any weak composition obtained by rearranging the parts of @xmath247 . we have that @xmath443 for any @xmath195 , the map @xmath343 is a @xmath80-preserving bijection . as another immediate corollary of proposition [ switch - well - defined ] , we can deduce the symmetry of @xmath244 in the @xmath327 variables . it is unknown whether @xmath40 is symmetric . [ valley - symmetric ] let @xmath231 . the formal power series @xmath444 is symmetric in the variables @xmath1 , where the sum is over all ordered multiset partitions @xmath3 with @xmath445 blocks and size @xmath66 . corollary [ valley - symmetric ] is false if we instead sum over ordered set partitions @xmath3 with fixed shape . for example , we have @xmath446 it follows that the coefficient of @xmath447 in the quasisymmetric function @xmath448 is @xmath449 but the coefficient of @xmath450 is @xmath451 . proposition [ switch - well - defined ] can be used to prove something more refined than corollary [ valley - symmetric ] . namely , for any subset @xmath452 $ ] the quasisymmetric function @xmath453 is symmetric . i. gessel observed ( personal communication ) that when @xmath376 , the symmetry of @xmath454 follows from the fact that @xmath455 ( where @xmath456 is the complete homogeneous symmetric function of degree @xmath24 ) and the principle of inclusion - exclusion @xcite . the author is unaware of an analogous proof of the symmetry of @xmath457 . the author is also unaware of what relationship ( if any ) the polynomials @xmath458 have with the delta conjecture . we are ready to prove our equidistribution result for ordered multiset partitions . [ same - distribution - word ] let @xmath72 be a weak composition and let @xmath460 . we have that @xmath461 write @xmath292 and let @xmath187 with @xmath188 . lemma [ basic - minimaj - recursion - word ] says that @xmath462 sum both sides of equation [ same - distribution - word - first ] over all compositions @xmath463 of @xmath464 which have @xmath465 parts . this yields @xmath466 the first equality is equation [ same - distribution - word - first ] summed over all compositions @xmath467 with @xmath465 parts . the second equality interchanges the order of summation . the third equality evaluates the inner sum over all @xmath468 . the fourth equality is an application of corollary [ rearrange ] . the left hand side of equation [ main - chain ] is the generating function for @xmath80 on the collection of all @xmath119-block multiset partitions of weight @xmath247 whose last block has size @xmath178 . lemma [ compress - word ] shows that for general @xmath227 , @xmath469 where the sum on the left hand side is over all @xmath470-part compositions @xmath471 and the external sum on the right hand side is over all subsets @xmath293 $ ] of indices such that @xmath300 for all @xmath301 . lemma [ inv - recursion - word ] shows that @xmath472 satisfies the same recursion . the proof of theorem [ same - distribution - word ] proves a slightly stronger statement . namely , for any fixed weak composition @xmath247 and positive integer @xmath439 , we have that @xmath473 where the sums are over all @xmath119-block ordered multiset partitions @xmath3 of weight @xmath247 whose last block has size @xmath439 . the connection of this more refined equidistribution result to the delta conjecture is unclear . theorem [ valley - function - equality ] follows by combining theorems [ valley - interpretation ] and [ same - distribution - word ] . we restate it here . * theorem 1.3 . * _ for all @xmath28 , we have the equality @xmath48 consequently , the coefficients of the monomial quasisymmetric function @xmath45 are equal in each of the following : @xmath474 _ in light of the delta conjecture , it is natural to ask for the expansion of the symmetric functions @xmath245 in the schur basis @xmath475 . it turns out that @xmath243 is schur positive the coefficients in this expansion are polynomials in @xmath18 with nonnegative coefficients . an explicit formula for these coefficients follows immediately from the work of wilson @xcite . to give the schur expansion of @xmath243 , we will need some notation . given a partition @xmath476 , let @xmath477 denote the set of standard young tableaux of shape @xmath478 . for @xmath479 , a _ descent _ of @xmath480 is an index @xmath481 such that @xmath348 appears in a lower row of @xmath480 than @xmath195 . let @xmath482 denote the number of descents of @xmath480 . also let @xmath483 denote the sum of the descents of @xmath480 . for example , suppose that @xmath484 is the standard tableau 1 & 3 & 4 2 & 6 & 7 5 & 8 . the descents of @xmath480 are @xmath485 and @xmath486 so that @xmath487 and @xmath488 . the following corollary follows immediately from an insertion argument due to wilson @xcite and theorem [ valley - function - equality ] . we use the usual @xmath18-binomial @xmath489!_q}{[k]!_q [ n - k]!_q}$ ] . ( wilson @xcite ) [ valley - frobenius ] for a partition @xmath476 , we have that the coefficient of @xmath490 in @xmath491 equals @xmath492 in particular , we have that @xmath493 is schur positive . for @xmath494 , this follows from letting @xmath495 and taking the coefficient of @xmath496 in ( * ? ? ? * theorem 5.0.1 ) . now apply theorem [ valley - function - equality ] . the calculation @xmath497 shows that the coefficient of @xmath498 in @xmath499 is @xmath500 . the calculation @xmath501 shows that the coefficient of @xmath502 in @xmath499 is @xmath503 . since there are no ordered multiset partitions of weight @xmath504 with @xmath505 blocks , the coefficient of @xmath506 in @xmath499 is @xmath507 . we therefore have the monomial basis expansion of the symmetric function @xmath499 given by @xmath508 which leads to the schur basis expansion @xmath509 to see that this agrees with corollary [ valley - frobenius ] , one may check that the four standard young tableaux with three boxes _ _ 1 2 3 1 & 2 3 1 & 3 2 1 & 2 & 3 contribute ( from left to right ) @xmath510 and @xmath511 to the schur expansion of @xmath499 predicted by ( [ schur - expansion ] ) in contrast to the state of affairs regarding @xmath512 , it is known that the other quasisymmetric function @xmath513 appearing in the delta conjecture is both symmetric in the @xmath327-variables and schur positive @xcite . however , the proof of schur positivity relies on the positivity of llt polynomials a positivity result which lacks a combinatorial proof . wilson @xcite proved combinatorially that we have the identities @xmath514 it follows that the coefficient of @xmath490 in the schur basis expansion of @xmath515 or @xmath516 is also given by ( [ schur - expansion ] ) . a natural generalization of permutations can be obtained by coloring their entries . let @xmath517 and consider the alphabet @xmath518 we think of @xmath519 as the letter @xmath195 augmented with the ` color ' @xmath520 . the _ wreath product _ @xmath521 consists of all length @xmath66 words @xmath522 in @xmath523 which contain just one copy of the letter @xmath195 ( of any color ) for all @xmath524 . for example , we have @xmath525 . we can also think of elements in @xmath521 as pairs @xmath526 , where @xmath121 is the uncolored permutation and @xmath527 is the _ color sequence_. in this language , the colored permutation @xmath528 would be written as @xmath529 . as a group , the wreath product @xmath521 is isomorphic to the complex reflection group @xmath530 consisting of @xmath531 monomial complex matrices whose nonzero entries are @xmath532 roots of unity . we will have no occasion to use the group structure on @xmath521 . one extension of major index to colored permutations which has appeared in the literature is as follows . introduce the following total order @xmath533 on the set @xmath523 : @xmath534 let @xmath535 have color sequence @xmath536 . the _ major index _ of @xmath123 is @xmath537 this statistic is called the ` flag major index ' in @xcite . inside @xmath538 we have @xmath539 a _ @xmath521-ordered set partition _ is a sequence @xmath102 of nonempty subsets of @xmath523 such that , for all @xmath524 , precisely one copy of @xmath195 appears ( with any color ) in @xmath84 . as before , we call the sets @xmath540 the _ blocks _ of @xmath84 , we say that @xmath84 has _ @xmath119 blocks _ , and we call the composition @xmath187 the _ shape _ of @xmath84 . for example , we have that @xmath541 is a @xmath538-ordered set partition with @xmath90 blocks of shape @xmath542 . we have the collections of @xmath521-ordered set partitions : @xmath543 let @xmath102 be a @xmath521-ordered set partition . we define @xmath544 to be the set of elements of @xmath521 obtained by permuting the letters within the blocks of @xmath84 . for example , @xmath545 the set @xmath546 may be regarded as a parabolic coset in the complex reflection group @xmath521 . the @xmath80 statistic on @xmath547 is defined by @xmath548 in order to prove an analog of theorem [ same - distribution - permutations ] for colored ordered set partitions , we need to define a suitable generalization of @xmath79 on @xmath547 for @xmath549 . let @xmath550 $ ] be the decolorizing map given by @xmath551 and extend @xmath24 to a map @xmath552 in the obvious way . also define a statistic @xmath553 on @xmath547 by letting @xmath554 be the sum of the colors of the letters in @xmath84 . we define a statistic @xmath79 on @xmath547 by @xmath555 where @xmath556 is computed as in section [ permutations ] . for example , if @xmath557 , we have @xmath558 so that @xmath559 we have the usual host of generating functions : @xmath560 recall the polynomial @xmath81 from section [ permutations ] . we will prove a natural generalization of the equidistribution result of theorem [ same - distribution - permutations ] to colored permutations . our approach here will be to reduce the colored result to the uncolored case of theorem [ same - distribution - permutations ] . in the next subsection we will see that trying to mimic the proof of theorem [ same - distribution - permutations ] itself leads to a strange and difficult polynomial identity . [ same - distribution - colored ] let @xmath562 and let @xmath99 be a composition . we have @xmath563_q)^n f_{n,\alpha}(q^r).\ ] ] we start by proving that @xmath564_q)^n f_{\alpha}(q^r)$ ] . consider a fixed uncolored ordered set partition @xmath565 . we have that @xmath566_q)^n q^{r ( { { \mathrm { inv}}}(\sigma_0))}$ ] , where the sum is over all colored ordered set partitions @xmath567 satisfying @xmath568 . the identity @xmath564_q)^n f_{\alpha}(q^r)$ ] follows from summing over all @xmath565 and applying theorem [ same - distribution - permutations ] . next , we prove that @xmath569_q)^n f_{\alpha}(q^r)$ ] . to see this , we define a standardization map @xmath570 as follows . let @xmath567 be a colored ordered set partition and consider its elements with respect to the order @xmath533 on the alphabet @xmath571 . let @xmath572 be the unique element of @xmath240 which is order isomorphic to @xmath84 under @xmath533 . for example , we have @xmath573 let @xmath565 be an uncolored ordered set partition and let @xmath574 be a weak composition of @xmath66 of length @xmath143 . if @xmath567 satisfies @xmath575 and has @xmath576 letters of color @xmath195 for all @xmath195 , we have that @xmath577 for a fixed @xmath565 and a fixed color multiplicity sequence @xmath574 , how many ordered multiset partitions lie in the set @xmath578 for any color @xmath195 and any block @xmath579 , the number of entries in @xmath579 of color @xmath195 must equal the number of entries in the @xmath580 block of @xmath581 which lie in the interval @xmath582 $ ] . to determine @xmath84 , we need only assign @xmath576 entries in @xmath58 $ ] to have color @xmath195 in @xmath84 , for all @xmath583 . the number of ways to do this is the multinomial coefficient @xmath584 . we conclude that @xmath585_q)^n f_{n , \alpha}(q^r),\ ] ] where the second equality used the multinomial theorem together with theorem [ same - distribution - permutations ] . in light of theorem [ same - distribution - word ] , it is natural to expect an equidistribution result involving @xmath79 and @xmath80 on appropriately defined ` colored ordered multiset partitions ' with a fixed number of blocks and a fixed weight . the author has been unable to produce such a result . equidistribution fails to hold in small examples when one considers sequences of nonempty subsets of @xmath586 , e.g. @xmath587 equidistribution also fails in small examples when one considers sequences of nonempty subsets of @xmath586 where no set contains two copies of the same letter ( of any color ) , e.g. @xmath588 the reader may wonder whether the methods of section [ permutations ] can be used to prove theorem [ same - distribution - colored ] without relying on theorem [ same - distribution - permutations ] . attempting to do so leads to a strange and complicated polynomial identity whose truth is implied by theorem [ same - distribution - colored ] , but which the author does not know how to prove directly . lemma [ cycle - major - permutations ] generalizes naturally to the context of colored permutations . we have an action of @xmath589 on the alphabet @xmath523 given by the cycle @xmath590 viewing @xmath521 as the complex reflection group @xmath530 , we can think of @xmath184 as the regular element @xmath591 this action extends to an action @xmath592 on @xmath521 by setting @xmath593 for @xmath594 . the analog of lemma [ cycle - major - permutations ] continues to hold . [ cycle - major - colored - permutations ] let @xmath535 and assume that @xmath595 . then @xmath596 . if @xmath123 does not contain @xmath597 , the application of @xmath184 preserves the descent set of @xmath123 , sends @xmath598 to @xmath599 , and preserves all other signs . if @xmath123 contains @xmath597 , the application of @xmath184 moves the descent of @xmath123 ending in @xmath597 one unit to the right while decreasing the sum of signs by @xmath600 , resulting in a net increase of @xmath153 by @xmath178 . the map @xmath601 of section [ permutations ] extends easily to define a map @xmath602 for @xmath549 . given @xmath603 , the @xmath119-segmented word @xmath604 \cdot \ldots \cdot \pi[k ] \in c \wr s(b_1 | \dots | b_k)$ ] is defined using definition [ segment - pi - map ] with respect to the order @xmath533 on the alphabet @xmath523 . for example , if @xmath557 , we have @xmath605 \cdot \pi[2 ] \cdot \pi[3 ] \cdot \pi[4 ] = 1 ^ 1 4 ^ 0 2 ^ 2 \cdot 7 ^ 2 \cdot 9 ^ 2 8 ^ 1 \cdot 6 ^ 2 3 ^ 1 5 ^ 1.\ ] ] the analog of lemma [ minimaj - alternative ] is still true in this setting . [ minimaj - alternative - colored ] let @xmath84 be a @xmath521-ordered set partition . the statistic @xmath153 achieves a unique minimum on the set @xmath544 , and this value is achieved at @xmath192 . the analog of lemma [ compress ] also holds for colored set partitions . let @xmath156 be a sequence of nonempty subsets of @xmath523 with the property that at most one of @xmath606 appears among the sets @xmath607 , for all @xmath524 . let @xmath157 be the unique @xmath608-ordered set partition ( for some @xmath609 ) whose associated uncolored ordered set partition is order isomorphic to the uncolored sequence of sets @xmath156 , while preserving colors . for example , we have @xmath610 [ compress - colored ] let @xmath314 be a @xmath521-ordered set partition . write the elements of @xmath139 as @xmath611 and write @xmath612 for the color of @xmath264 for @xmath613 . we have that @xmath614 similar to the proof of lemma [ compress ] , except one must take into account the contribution of colors to the @xmath80 statistic . lemma [ cycle - commute - permutations ] generalizes in the obvious way . [ cycle - minimizers - colored ] let @xmath615 be a @xmath521-ordered set partition of type @xmath187 with @xmath188 . we have @xmath616 similar to the proof of lemma [ cycle - commute - permutations ] . let @xmath187 and let @xmath617 . by theorem [ same - distribution - colored ] , we have the recursion @xmath618_q)^{\alpha_k } \times \left [ { \alpha_k - 1 \choose \alpha_k - 1 } + { \alpha_k \choose \alpha_k - 1}q^r + \cdots + { n-1 \choose \alpha_k - 1 } q^{r(n-\alpha_k ) } \right ] \times m^r_{\overline{\alpha},n}(q).\ ] ] on the other hand , we can derive a recursion for @xmath619 combinatorially . fix a letter @xmath620 for @xmath524 and @xmath621 . let @xmath622 be a typical @xmath521-ordered set partition such that the minimum element @xmath213 ( with respect to @xmath533 ) is @xmath623 . the choices involved in the completion of the block @xmath139 are as follows : 1 . choose a subset @xmath624 of size @xmath20 ( for some @xmath625 ) . 2 . choose a subset @xmath626 of size @xmath627 . 3 . color the elements of @xmath305 with @xmath628 arbitrarily . 4 . color the elements of @xmath480 with @xmath629 arbitrarily . for a fixed choice of @xmath305 and @xmath480 ( and hence @xmath20 ) as above , the net contribution to @xmath630 coming from letter colors in @xmath631 will be @xmath632_q^{\alpha_k - t-1 } [ j+1]_q^t$ ] . on the other hand , lemmas [ cycle - major - colored - permutations ] , [ compress - colored ] , and [ cycle - minimizers - colored ] imply that the choice of @xmath633 contributes an additional @xmath634 to @xmath630 . we have @xmath635 choices for the set @xmath305 and @xmath636 choices for the set @xmath480 . putting all of this together , we get that @xmath637_q^{\alpha_k - t-1 } [ j+1]_q^t . \end{gathered}\ ] ] the following polynomial identity follows from ( and is equivalent to ) theorem [ same - distribution - colored ] . [ polynomial - identity ] for all @xmath638 and all @xmath639 we have @xmath640_q)^{\alpha_k } \times \left [ { \alpha_k - 1 \choose \alpha_k - 1 } + { \alpha_k \choose \alpha_k - 1}q^r + \cdots + { n-1 \choose \alpha_k - 1 } q^{r(n-\alpha_k ) } \right ] = \\ \sum_{i = 1}^n \sum_{j = 0}^{r-1 } \sum_{t = 0}^{\alpha_k-1 } { n - i \choose t } { i-1 \choose \alpha_k - t - 1 } q^{j(n-\alpha_k+1 ) + ( n - i - t ) } [ j]_q^{\alpha_k - t-1 } [ j+1]_q^t . \end{gathered}\ ] ] we challenge the reader to prove proposition [ polynomial - identity ] directly ! in this paper we have applied the combinatorics of ordered set partitions to obtain evidence for the delta conjecture of symmetric function theory . along the way to doing so , we discovered a new family of polynomials @xmath641 indexed by compositions @xmath187 . we pose the problem of finding an algebraic interpretation of these polynomials . consider the action of the symmetric group @xmath57 on the polynomial ring @xmath642 $ ] given by variable permutation . let @xmath643 be the ideal generated by @xmath57-invariant polynomials @xmath644 $ ] with vanishing constant term . the _ coinvariant algebra _ is the graded @xmath645-vector space @xmath646/i$ ] . the space @xmath647 carries a graded action of @xmath57 ; it can be shown that @xmath648 $ ] as @xmath57-representations . one natural @xmath645-basis of @xmath647 ( the so - called _ artin basis _ ) consists of those monomials @xmath649 whose exponent sequence @xmath650 satisfies @xmath651 . said differently , the multiplication map gives rise to an isomorphism of graded @xmath645-vector spaces @xmath652_{\leq 0 } \otimes { { \mathbb { c}}}[x_2]_{\leq 1 } \otimes \cdots \otimes { { \mathbb { c}}}[x_n]_{\leq n-1 } \xrightarrow{\sim } r_n.\ ] ] here @xmath653 denotes the subspace of a graded @xmath645-algebra @xmath654 consisting of elements of degree @xmath655 . this shows that the hilbert series @xmath656 of @xmath647 is @xmath58!_q = f_{n,(1^n)}(q)$ ] . for an arbitrary composition @xmath99 , we have that @xmath81 is the generating function for the degree statistic on monomials @xmath657 whose exponent sequences @xmath35 satisfy @xmath658 for all @xmath135 . said differently , the polynomial @xmath81 is the hilbert series of the graded @xmath645-vector space @xmath659_{\leq 0 } \otimes { { \mathbb { c}}}[x_{\alpha_1 + 1 } , \dots , x_{\alpha_1 + \alpha_2}]_{\leq \alpha_1 } \otimes \cdots \otimes { { \mathbb { c}}}[x_{n-\alpha_k+1 } , \dots , x_n]_{\leq n - \alpha_k}.\ ] ] the artin basis is one of several interesting bases for the coinvariant algebra @xmath647 . the _ descent monomial basis _ @xmath660 introduced by garsia and stanton @xcite has elements given by @xmath661 it is evident that the degree of the monomial @xmath662 is given by @xmath663 . the monomials @xmath664 may be extended to ordered set partitions by setting @xmath665 for any ordered set partition @xmath84 . it is immediate that the degree of @xmath666 is @xmath630 . a ubiquitous basis of @xmath647 which does _ not _ consist of monomials is the _ vandermonde basis _ whose elements are all of the nonzero polynomials which can be obtained by applying the partial derivative operators @xmath667 to the vandermonde polynomial @xmath668 . yet another important basis is the _ schubert basis _ which has elements given by all nonzero polynomials which can be obtained by applying the divided difference operators @xmath669 to the monomial @xmath670 . the degrees of vandermonde and schubert basis elements are closely related to the @xmath153 and @xmath79 statistics on the symmetric group . find analogs of the vandermonde and schubert basis for an arbitrary composition @xmath99 . find an analog @xmath671 of the ideal @xmath672 $ ] generated by homogeneous symmetric polynomials of positive degree . the multiplication map should give a graded @xmath645-vector space isomorphism @xmath673/i_{n,\alpha}$ ] . the analogs of the artin , descent monomial , vandermonde , and schubert bases should give bases of @xmath674 . the coinvariant algebra @xmath647 carries a graded action of @xmath57 whose graded frobenius character is the hall - littlewood polynomial @xmath675 . it is well known that for @xmath476 , the coefficient of @xmath490 in the schur expansion of @xmath675 equals @xmath676 . this coincides with the expression appearing in corollary [ valley - frobenius ] when @xmath376 . we ask for a delta conjecture - style generalization of the coinvariant module . for any @xmath276 , find a nice graded @xmath57-module @xmath677 whose graded frobenius character is @xmath245 ( after applying the involution @xmath678 which exchanges @xmath679 for @xmath26 and complementing @xmath18-degree ) . in the course of proving the equality @xmath245 it was necessary to prove that @xmath244 is symmetric in the @xmath327 variables . we accomplished this by introducing a family @xmath680 of involutive switch maps on ordered multiset partitions which preserve minimaj but permute weight compositions . the _ bender - knuth operators _ @xmath681 are a famous collection of involutions on semistandard young tableaux . given a ssyt @xmath480 , the operator @xmath682 acts on @xmath480 by freezing every instance of @xmath195 immediately above @xmath379 , and then interchanging the number of @xmath195 s and @xmath379 s in every maximal unfrozen horizontal run consisting entirely of @xmath195 s and @xmath379 s . for example , we have ( writing frozen entries in bold ) , , @xmath683 , 1 & 1 & * 2 * & 2 & 3 & 3 & 3 & 2 & * 3 * & 4 & 4 & 4 & 5 , , @xmath684 , 1 & 1 & * 2 * & 2 & 2 & 2 & 3 & 3 & * 3 * & 4 & 4 & 4 & 5 . since the operator @xmath682 interchanges the number of @xmath195 s and @xmath379 s in any ssyt , the bender - knuth operators define a family of involutions @xmath685 on words which preserve descent set ( and , in particular , major index ) while permuting weight . in particular , let @xmath280 be a word . we may apply robinson - schensted - knuth insertion to @xmath51 to get a pair @xmath686 , where @xmath687 and @xmath480 are tableaux of the same shape , the tableau @xmath687 is standard , the tableau @xmath480 is semistandard , and @xmath480 has content equal to the weight of @xmath51 . for any @xmath195 , let @xmath688 be the unique word whose rsk image is @xmath689 . the desired involutive and weight action properties of the @xmath690 are inherited from the corresponding properties of the @xmath682 . it turns out that the word operators @xmath339 and @xmath690 do not coincide . in fact , the switch maps @xmath339 do not even preserve the shape of a word under rsk . given the importance of the rsk algorithm , it would be interesting to extend the definition of the @xmath690 operators to ordered multiset partitions in such a way that * the @xmath690 act as involutions on ordered multiset partitions , * the @xmath690 preserve @xmath80 , and * the @xmath690 extend appropriately defined bender - knuth operators under the image of an appropriate ordered multiset partition version of rsk . the author is very grateful to nantel bergeron , jim haglund , ira gessel , jeff remmel , anne schilling , and andy wilson for many inspiring discussions and a great deal of constructive input on this paper . the author was partially supported by nsf grants dms-1068861 and dms-1500838 .[/INST] the delta conjecture of haglund , remmel , and wilson is a recent generalization of the shuffle conjecture in the field of diagonal harmonics . in this paper we give evidence for the delta conjecture by proving a pair of conjectures of wilson and haglund - remmel - wilson which give equidistribution results for statistics related to inversion count and major index on objects related to ordered set partitions . our results generalize the famous result of macmahon that major index and inversion number share the same distribution on permutations . </s>

mrk 273 is an ultraluminous infrared galaxy with prominent merging signatures . 1 shows our scanned poss ii j - band image and a deep r - band image ( hibbard & yun 1999 , kindly made available to us by john hibbard ) of the mrk 273 field . these optical images reveal a long tail to the south and a faint plume to the northeast . the very large array ( vla ) continuum observations revealed extremely extended radio lobes up to more than 200 kpc in length extending further along the tip of the southern optical tail into southeast ( yun 1997 ; yun & hibbard 1999 ) . vla h 21 cm line observations show extended atomic gas associated with the southern optical tail as well ( hibbard & yun 1996 , 1999 ) . mrk 273 is also detected in the x - ray by rosat and asca ( turner et al . 1993 , 1997 , 1998 ; iwasawa 1998 ) . rosat hri image reveals an x - ray companion source of comparable brightness as mrk 273 , about @xmath0 to the northeast of mrk 273 . xia et al . ( 1998 ) named this source mrk 273x , and found an optically faint source coincident with the x - ray position ( cf . fig . 1 in xia et al . 1998 ; the position is marked here by ` x ' in fig . 1a and is very prominently shown in the deep r - band image in fig . all these optical features are also fairly prominent in the digitized sky survey ( dss ) image of mrk 273 . the core of mrk 273 has been resolved into two compact components in the radio and near - infrared ( condon et al . 1991 ; majewski et al . 1993 ; knapen et al . 1997 ) , which are believed to be the double nuclei of the two progenitor galaxies involved in the merging and at least one of them is a seyfert 2 nucleus ( sargent 1972 ; asatrian et al . 1990 ) . spectroscopic observations were carried out on the 2.16 m telescope at the beijing astronomical observatory ( bao ) to secure the redshift of mrk 273x and the bao spectrum indicates that an object ( thought to be mrk 273x ) at @xmath7 was detected ( xia et al . since the signal - to - noise ratio of this spectrum was low , further observations of mrk 273x were performed at the william herschel telescope ( wht ) for additional check . the new spectrum turned out to be different from the one obtained at bao . later examinations and further spectroscopic observations show that the object detected in the initial bao spectrum was not mrk 273x , but an object about @xmath8 to the northeast of mrk 273 ; we will call this diffuse object mrk 273d . the mis - identification was caused by incorrect slit positioning in previous observation at bao ( see section 2 ) . in this paper , we present the wht spectrum of mrk273x and new observations for mrk273d performed at bao . in addition , we re - examine all the original data analyzed by xia et al . we find that both mrk273x and mrk273d have intriguing properties . we show that the emission line widths and line ratios of mrk 273x resemble seyfert 2 galaxies . since mrk 273x turns out to be a distant background source , its x - ray and radio luminosities are one of the highest among seyfert 2 galaxies and yet it has a very low neutral hydrogen column density . mrk 273d consists of diffuse clumps at the same redshift as the ultraluminous galaxy mrk 273 and has quite unusual line ratios of / and /. these ratios are not easily produced by photoionization of o , b stars . we argue that the emission line ratios are better explained by shock excitation with precursors ( dopita & sutherland 1995 ) . the structure of the paper is as follows . in 2 , we describe the wht observation for mrk 273x and new observations for mrk 273d at bao . we also explain the original observational setup at bao . in 3 , we present the results of our spectral analysis . in 4 , we discuss the nature of mrk 273x and mrk 273d . and finally , a brief summary of the main results is given in 5 . throughout this paper , we use a hubble constant of @xmath9 and an einstein - de sitter ( @xmath10 ) cosmology . the observations carried out at bao used a zeiss universal spectrograph mounted on the 2.16 m telescope of bao . a tektronix 1024x1024 ccd was used as the detector . the original slit setup , for the bao observation on april 12 , 1997 , runs from the northeast to southwest passing through star s and source d , is illustrated in fig . the slit was approximately @xmath11 long and @xmath12 wide . this observational setup was intended to determine the redshift for mrk 273x ( source x in fig . unfortunately the slit missed the target due to a slight error in the slit orientation . this occurred because mrk 273x was too faint to be seen on the tv monitor , so the slit had to be rotated from an initial orientation ( which passed through the star ` s ' in fig . 1a ) by a prescribed angle such that it would pass through mrk273x . the amount of rotation required was calculated from several bright objects within the field . this technique of slit positioning for faint sources had been successfully employed previously at bao , so no extra check was enforced in the initial observations reported in xia et al . ( 1998 ) . in spite of the incorrect rotation angle used , by coincidence , an object other than star s was detected in the spectrum and was ( incorrectly ) identified as mrk273x . follow - up observations of mrk273x carried out at the william herschel telescope ( wht ) at la palma however yielded spectra that are completely different from that obtained at bao ( see below ) . a re - examination of the long - slit spectrum obtained at bao showed that the object detected in the spectrum was separated from the star s by 80@xmath13 rather than 20@xmath13 , the actual angular distance between mrk 273x and the star s. from the angular distance between the object detected in the bao spectrum and the star s , and from the fact that only two objects were seen in the spectrum , we were able to reconstruct the slit orientation as shown in fig . this slit orientation is well - constrained : a little more rotation to the southwest ( anti - clockwise ) the slit would enclose the bright southern tail of mrk 273 , while slightly more rotation to the opposition direction it would enclose no object other than the star s. it turned out that the slit passed through some bright clumps ( source d in fig . 1a ) , about @xmath14 to the nuclear region of mrk 273 ( knapen et al . while this slit re - construction seems convincing , as a double check , mrk273d was re - observed at bao on february 20 , 1999 with a different slit setup . the new observation yields a spectrum nearly identical to the one published by xia et al . the slit setup was recorded with photographs , which allowed us to determine the slit orientation reliably . this new slit is approximately @xmath11 long and @xmath15 wide and runs nearly vertically ( in the north south direction passing through stars s1 and s2 ) as shown in fig . both the previous and the new bao spectra cover a wavelength range of 3500 to 8100 with a grating of 195 / mm and a spectral resolution of 9.3 ( 2 pixels ) . wavelength calibration was carried out using an fe - he - ar lamp and standard stars were observed to perform flux calibrations . the wavelength calibration accuracy is better than 1 . mrk 273x ( source x in fig . 1 ) was first observed on june 19 , 1998 with the wht . since the resulting spectrum was different from the one obtained earlier at bao , another observation was attempted at the wht on june 26 , 1998 which yielded spectrum identical to the one obtained a week ago on june 19 . additional new spectrum for mrk 273x was also obtained using the bao 2.16 m telescope , confirming the results from the wht . the new bao spectrum for mrk 273x is not presented here given its lower signal - to - noise ratio . the wht spectra were obtained using the double spectrograph isis . the ccd detector used at the blue and red arm was respectively an eev chip of 2148@xmath164200 pixels with a 13.5@xmath17 m pixel size and a tek chip of 1124@xmath161124 pixels with a 24@xmath17 m pixel size . at the blue arm , a grating of 64 / mm centered at 4583 yielded a useful wavelength coverage from 32005300 . the violet end of the blue spectra was cut off by the atmosphere and by instrumental optics , while the red end was blocked out by the dichroic which had a half - power crossover wavelength of 5300 . for the red arm , a grating of 158 / mm dispersion covered the wavelength range 53008270 . three 2400s narrow - slit ( 0.8 ) exposures and one 1800s wide - slit spectra ( 6 ) were obtained for each arm . the full width at half maximum ( fwhm ) spectral resolution was 6.2 for the red arm and 3.28 for the blue arm , respectively . wavelength calibration was carried out using an ar - ne lamp ; the resulting wavelength accuracy is about 0.2 . the spectra were flux - calibrated using observations of the standard star bd+33@xmath182642 . all the optical spectral data reduction was performed at bao using iraf packages . the ccd data reduction includes standard procedures such as bias subtraction , flat fielding and cosmic ray removal . the measurements of emission lines were performed under the iraf environment using tasks `` splot '' and `` ngaussfit '' . we first show the wht optical spectrum for mrk 273x in fig . 2 . the spectrum combines both the red and blue arm data . , , , , , and mgii @xmath192796 , 2803 emission lines are all convincingly detected . the redshift determined from these emission lines is 0.458 . the measured fluxes for the identified lines are listed in table 1 . all detected lines have a fwhm of about @xmath20 . the optical b and r magnitudes for mrk 273x are respectively about 20.8 and 19.6 from the usno - a1.0 catalog ( monet 1996 ) . the absolute magnitude of mrk 273x is therefore @xmath21 , comparable to @xmath22 in the schechter luminosity function of galaxies ( e.g. , lin et al . this luminosity includes the contribution from both the central active galactic nucleus ( agn , see below ) and the host galaxy . in the short _ hubble space telescope ( hst ) _ wide field planetary camera 2 ( wfpc2 ) snapshot image , the underlying galaxy is visible but its outer faint contours are not well - detected . from the deep r - band image ( shown here in fig . 1b ) of hibbard & yun ( 1999 ) , the agn nucleus and the host galaxy seem to contribute comparable amount of light . as reported in xia et al . ( 1998 ) , mrk 273x is also luminous in the soft x - ray ( 0.12.4 kev ) band . the soft x - ray flux is @xmath23 , corresponding to an x - ray luminosity of @xmath24 . the soft x - ray spectrum of mrk 273x is well - fitted by a power - law , with a photon index of @xmath25 , a value typical for seyfert 2 galaxies . spectral fitting yielded a neutral hydrogen column density of @xmath26 . mrk 273x is also detected at the vla 21 cm continuum observations and appears to be consistent with a point - like source ( yun 1997 ; yun & hibbard 1999 ) . at this high redshift , mrk 273x falls into the class of powerful radio sources with @xmath27 . this single property sets mrk 273x into categories of agns , qsos , and starbursts and radio galaxies rather than normal galaxies . the high x - ray luminosity , strong radio emission and the emission line widths ( fwhm @xmath28 ) of mrk 273x imply that the main energy output mechanism is agn , and mrk 273x may be either a narrow - line seyfert 1 ( nls1 ) galaxy ( osterbrock & pogge 1985 ) or a seyfert 2 galaxy from the relatively narrow emission lines . below we explore each possibility in turn . nls1s are defined as seyfert galaxies which have fwhm for the line in the range of 500 - 2000 @xmath29 and with /@xmath303 . mrk 273x does not satisfy the second criterion since the ratio of the / is about 6 . furthermore , mrk 273x does not show prominent fe ii emission lines , which are strong in most ( but not all ) nls1 galaxies . also , the soft x - ray spectrum is well fitted by power - law with a photon index @xmath25 ( xia et al . 1998 ) and is not as steep as most nls1s . hence , mrk 273x does not fit in the definition of nls1 galaxies . the relatively narrow balmer and forbidden lines and the line ratios of / @xmath31 are consistent with mrk 273x being a seyfert 2 galaxy . turner et al . ( 1997 , 1998 ) and polletta et al . ( 1996 ) presented catalogs for several tens of seyfert 2 galaxies . in their catalogs , the soft x - ray luminosity for all but a few listed seyfert 2 galaxies are less than @xmath32 and the @xmath33 value is larger than @xmath34 . the combination of a low @xmath33 value together with powerful x - ray emission ( @xmath35 ) is therefore rare among seyfert 2 galaxies . this peculiarity is also supported by its quite high radio luminosity and multi - wavelength observations of mrk 273x . the flux ratios of mrk273x in the soft x - ray , b - band , and radio are @xmath36 ; such a spectral energy distribution is rarely seen in any other agns ( see xia et al . 1998 for more discussions ) . furthermore , the low @xmath33 value is not expected in the unified scheme of agns ( e.g. , dopita 1997 and references therein ) . in this picture , the broad - line regions of seyfert 2 galaxies are postulated to be obscured by a thick torus of gas and dust , which presumably gives rise to high @xmath33 values . to summarize , the optical emission line properties , the powerful x - ray and radio emission and the low neutral hydrogen absorption indicate that mrk 273x is a rare source that may provide a test of the unified picture of agns . the diffuse clumps ( mrk 273d , labeled as source d in fig . 1a ) are clearly seen in the j - film copy of poss ii and in the dss image , but they are visible neither in the near - infrared ( e.g. , smith et al . 1996 ) , most r - band images ( e.g. , yun & scoville 1995 ; mazzarella & boroson 1993 ) , nor in the hst wfpc2 f814 snapshot image , suggesting that they have quite blue colors . only the deep r - band image shown in fig . 1b ( hibbard & yun 1999 ) reveals some patches in the northeast plume corresponding to these dense knots . we extracted the bao spectra for the diffuse clumps in fig . 1a using an aperture window size of 4@xmath16 17 for the observation on april 12 , 1997 and 2.5@xmath16 17 for the observation on february 20 , 1999 . these aperture windows are indicated as the rectangles in fig . the spectra are shown in fig . 3 and the emission line fluxes are listed in table 1 . the old and new spectra are similar . the continuum is somewhat higher in the feb . 20 , 1999 observation . the difference may be real , as the two slits sampled slightly different regions , although the possibility of calibration uncertainties can not be completely ruled out . the emission line ratios are very similar from both spectra . the redshift for mrk 273d determined from the emission lines is the same as mrk 273 ( @xmath37 ) . therefore these clumps are physically associated with the major merger process of mrk 273 . yun & scoville ( 1995 ) suggest that mrk 273 is the merging product of a nearly edge - on gas - rich spiral and another more face - on spiral . the tidal plume in the northeast is from the face - on progenitor . so the physical association of mrk 273d with mrk 273 is expected . it is clear from fig . 3 and table 1 that the continuum emission from mrk 273d is very weak and the lines are strong compared to . more specifically , from the observation on april 12 , 1997 , the line ratio of the to is @xmath38 , while the line ratio of the to is @xmath39 ( the error bars are 1@xmath40 values ) . for the new observation , the ratio of the line to is @xmath41 while the ratio of line to is @xmath42 . note that these two line ratios are little affected by dust extinction since the two lines involved in the ratios are quite close in wavelength . 4 shows the standard diagnistic diagram of / versus / ( osterbrock 1989 ) for emission line galaxies . the hii , liner and seyfert galaxies occupy different regions in this diagram . for hii regions photoionized by o , b stars , @xmath43\thinspace\lambda5007/{\rm h}\beta < 5 $ ] for @xmath44\thinspace\lambda6584/{\rm h}\alpha \approx 0.3 - 0.4 $ ] ( see also fig . 12.1 in osterbrock 1989 ) . the / ratio of mrk 273d is clearly much higher than those typically found for photoionized h ii regions . in fact , mrk 273d is clearly located in the region occupied by seyfert 2 galaxies . the / and / line ratios of mrk 273d are also located in the seyfert 2 region ( cf . 12.2 , 12.3 , osterbrock 1989 and more discussions in xia et al . 1998 ) . to achieve these seyfert 2 like line ratios , the ionization source must be harder than the radiation provided by young massive stars . mrk 273d is , however , obviously not an agn given its diffuse morphology . we discuss further the mechanism of line excitations in mrk 273d in 4.2 . mrk 273x is a background object in the mrk 273 field ; it is at a much higher redshift ( @xmath45 ) than mrk 273 which has a redshift of 0.0376 . it is interesting to note that the x - ray companions of three nearest ultraluminous iras galaxies ( arp 220 , mrk 273 and mrk 231 ) are all background sources and are therefore not physically associated with the mergers themselves ( cf . xia et al . 1998 ) . mrk 273x has agn characteristics both optically and in the soft x - ray together with a high radio luminosity . the narrow emission lines and various line ratios are consistent with it being a seyfert 2 galaxy . its soft x - ray luminosity is one of the highest among seyfert 2 galaxies with a low neutral hydrogen column density . although many well known nearby seyferts ( including mrk 273 itself ) also host an energetically significant starburst , the low neutral hydrogen column density of @xmath46 appears to exclude the possibility of mrk 273x being a dusty luminous starburst galaxy . these observational facts show that mrk 273x is an unusual seyfert 2 galaxy that is not easy to explain using the unified scheme of agns . xia et al . ( 1998 ) examined the time variability of mrk 273x using the rosat data taken in may and june 1992 . while mrk 273x is fainter than mrk 273 by about 20% in the rosat pspc image , it is almost as bright as mrk 273 in the rosat hri image . a @xmath47 test however reveals that these changes are not statistically significant in the rosat data . from the 0.5 - 2 kev image of sis on board asca , iwasawa ( 1998 ) found that mrk 273x is at most 40 percent as bright as mrk 273 on dec . 27 , 1994 . since mrk 273 is not known to vary in the soft x - ray , these multi - epoch observations imply that mrk 273x has faded by a factor of 2 in two and a half years . cycle 1 axaf observations are planned to obtain a high - resolution map of mrk 273x and mrk 273 . these observations will provide further insights on their x - ray variability , higher energy behaviors and spatial distribution of the x - ray emissions . the diffuse clumps in mrk 273d in the northeast plume could directly come from the extreme outer regions of the face - on progenitor . it is also possible that mrk 273d was formed in the major merger process . this patchy object is unlikely to be a self - gravitating ( tidal ) dwarf galaxy since they are usually found far from the interacting parent galaxies and their spectra resemble typical photoionized h ii regions ( e.g. , duc & mirabel 1997 ) . furthermore , clumps formed close to the merger is liable to tidal disruption once they fall back to the merger . ( however , some observations indicate that clumps close to the merging pair do exist , e.g. , h ii regions in the ngc 4676a tail , hibbard & van gorkom 1996 . ) in contrast , mrk 273d is very close to ( @xmath6 kpc in projected distance from ) the main merging nuclei , and its spectrum differs significantly from photoionized h ii regions . although the spectrum of mrk 273d resembles that of a seyfert 2 galaxy , its diffuse morphology suggests that it is not a ( dwarf ) agn . in fact , the spectrum of mrk 273d is very similar to that of the soft x - ray nebula to the north of mrk 266 ( cf . fig . 5 in kollatschny & kowatsch 1998 ) . as pointed out by these authors , the @xmath48 color ( @xmath49 ) of the northern component is exceptionally blue due to the intense line emission . the diffuse gas clumps in mrk 273d are also very blue , since they are only seen in the b - band , but not in other bands redder than r. the blue color of mrk 273d is also due to the continuum being dominated by the line emission ( cf . fig . 3 ) . the spectrum of mrk 273d is also similar to the average spectrum of the northwest cone of ngc 2992 ( cf . 3a in allen et al . 1999 ) and the spectrum of diffuse ionized gas in ngc 891 ( rand 1997 , 1998 ) . as discussed by these authors , the likely excitation mechanism for these peculiar spectra is the shock plus precursor model ( dopita & sutherland 1995 ) . for a fast shock with velocity of several hundred @xmath29 , copious uv photons are produced in the shock front , which can in turn excite the gas of h ii regions in front of the shock , thus producing radiative precursors . the hardness of the uv radiation ( shock temperature ) depends on the velocity of the shock wave , and with suitable parameters , this scenario can produce the line ratios as seen in mrk 273d ( cf . 2a in dopita & sutherland 1995 ) . it is believed that starbursts can drive radial outflows ( wang , heckman & weaver 1997 ) . there is some evidence that such outflows ( superwinds ) indeed exist in several ultraluminous iras galaxies out to tens of kpc with velocities of a few hundred to 1000 @xmath29 , e.g. , in ngc 6240 , arp 299 , arp 220 ( heckman et al . 1987 , 1990 , 1996 , 1999 ; schulz et al . 1997 ; wang et al . since mrk 273 is also a major merger ultraluminous infrared galaxy and has extended soft x - ray emission and hi nebula , it is conceivable that such an outflow exists in mrk 273 . in this regard , mrk 266 is also a candidate since it is a luminous infrared merging galaxy with double nuclei ( @xmath50 kpc in projected separation ) and very extended ( about 150 kpc ) soft x - ray nebula . these observations suggest that the shock+precursor emission may be a common mechanism to excite gaseous nebulae in luminous infrared merging galaxies , in addition to the o , b star photoionization and agn excitation . wu et al . ( 1998 ) showed that many observed ultraluminous iras galaxies have mixture types in different line ratio diagnostic diagrams . goncalves et al . ( 1998 ) also suggested that most emission line galaxies with the so - called transition spectrum have composite spectra with simultaneous presence of seyfert , liner and h ii region contributions . perhaps these objects are not only just a mixture of agn and photoionized starburst regions ( genzel et al . 1998 ) , they may also contain shock+precursor regions , as seen in mrk 273d and the northern nebula of mrk 266 . this also provides a caution : a seyfert 2 like spectrum in high - redshift luminous infrared galaxies does not necessarily mean the presence of agns at their centers , instead such a spectrum could be induced by the shock+precursor excitation in the gas clumps in the mergers . we have presented optical spectroscopic observations for the x - ray companion source and the blue diffuse clumps in the northeast tidal debris surrounding the ultraluminous galaxy mrk 273 . their peculiar properties are discussed and explored together with soft x - ray and radio observations available . we summarize below the main points we have presented and addressed in this paper . mrk 273x , the x - ray companion @xmath0 to the northeast of the ultraluminous galaxy mrk 273 , is a background source at @xmath45 . its redshift is much higher than the redshift ( @xmath37 ) of mrk 273 . the soft x - ray spectrum for mrk 273x is typical of seyfert 2 galaxies . the x - ray luminosity of mrk 273x is exceptionally high for a seyfert 2 galaxy , @xmath1 . spectral fitting gives a low neutral hydrogen column density , @xmath3@xmath4 . all the optical emission lines detected for mrk 273x have a similar fwhm of @xmath51kms@xmath52 and the / ratio is about 6 , again typical for seyfert 2 galaxies . mrk 273x is also a powerful radio source with a radio luminosity @xmath2 . this adds more peculiarities to this energetically unusual seyfert 2 galaxy . the optical knots mrk 273d in the northeast tidal tail / plume @xmath6 kpc ( projected ) from the nuclear region of mrk 273 is at the same redshift as that of mrk 273 . they are diffuse gas clumps physically associated with the major merger . the spectrum of mrk 237d is dominated by strong emission from the [ o iii ] doublet . the strong line emission gives rise to the blue color of this object . the [ o iii]@xmath535007/h@xmath54 and [ n ii]@xmath536584/h@xmath55 line ratios are @xmath56 and 0.3 , respectively . these seyfert 2like line ratios for mrk 273d are likely excited by shocks plus precursor mechanism involved in the merging process . we are grateful to zheng zheng for assistance in observations and preliminary data reductions . we also thank simon white for advice and the anonymous referee and the scientific editor john huchra for valuable criticisms that have improved the paper . we appreciate very much for the deep r - band image kindly provided to us by john hibbard . this project was partially supported by the nsf of china and the exchange program between nsfc and dfg . y.g.s research at lai , dept . of astronomy is funded by nsf grants ast96 - 13999 and by the university of illinois . is also grateful to ernie seaquist for support at the university of toronto . allen , m. g. , dopita , m. a. , tsvetanov , z. i. , & sutherland , r. s. 1999 , apj , 511 , 686 asatrian , a.s . , petrosian , a.r . & borngen , f. 1990 , paired and interacting galaxies : iau colloquium no . 124 , eds . j. w. sulentic , w. c. keel , w.c . , & c. m. telesco , 201 condon , j. j. , huang , z .- p . , yin q. f. , & thuan , t. x. 1991 , apj , 278 , 65 dopita , m. a. 1997 , pasa , 14 , 230 dopita , m. a. , & sutherland , s. 1995 , apj , 455 , 468 duc , p .- a . , & mirabel , i. f. 1997 , preprint ( astro - ph/9711253 ) genzel , r. et al . 1998 , apj , 498 , 579 goncalves , a.c . , veron - cetty , m .- p . , & veron , p. 1998 , preprint ( astro - ph/9811342 ) heckman , t. m. , armus , l. , & miley , g. k. 1987 , aj , 92 , 276 heckman , t. m. , armus , l. , & miley , g. k. 1990 , apjs , 74 , 833 heckman , t. m. , dahlem , m. , eales , s. a. , fabbiano g. , & weaver , k.a . 1996 , apj , 457 , 616 heckman , t. m. , armus , l. , weaver , k. a. , & wang , j. 1999 , preprint ( astro - ph/9812317 ) hibbard , j. e. , & van gorkom , j. 1996 , aj , 111 , 655 hibbard , j. e. , & yun , m. s. 1996 , cold gas at high redshift , eds . m. n. bremer , p. p. van der werf , h.j.a . rttgering , & c.l . carilli ( doderecht : kluwer ) , 47 hibbard , j. e. , & yun , m. s. 1999 , in preparation hunsberger , s. d. , charlton , j. c. , & zarisky , d. 1996 , apj , 462 , 50 iwasawa , k. 1998 , preprint ( astro - ph/9808313 ) knapen , j. h. , laine , s. , yates , j. a. , robinson , a. , richards , a. m. s. , doyon , r. , & nadeau d. 1997 , apj , 490 , l29 kollatschny , w. , & kowatsch , p. , 1998 , a&a , l21 lin , h. , kirshner , r. p. , shectman , s. a. , landy , s. d. , oemler , a. , tucker , d. l. , & schechter , p. l. 1996 , apj , 464 , 60 majewski , s. r. , hereld , m. , koo , d.c . , illingworth , g.d . , & heckman , t. m. 1993 , apj , 402 , 125 mazzarella , j.m . & boroson , t.a . 1993 , apjs , 85 , 27 monet , d. 1996 , baas , 188 , 5404 mulchaey , j. s. , koratkar , a. , ward , m. j. , wilson , a. s. , whittle , m. , antonucci , r. j. , kinney , a. , & hurt , t. 1994 , apj , 436 , 586 osterbrock , d.e . , & pogge , r. 1985 , apj 297 , 166 osterbrock , d.e . 1989 , astrophysics of gaseous nebulae and active galactic nuclei ( mill valley : universe science books ) polletta , m. , bassani , l , malaguti , g. , palumbo , g. g. c. , & caroli , e. 1996 , apjs , 106 , 399 rand , r. 1997 , apj , 474 , 129 rand , r. 1998 , apj , 501 , 137 sargent , w. l. w. 1972 , apj , 173 , 7 schulz , h. , komossa , s. , berghfer , t. , & boer , b. 1998 , a&a , 330 , 823 smith , d.a . 1996 , apjs , 104 , 217 turner , t. j. , george , i. m. , & mushotzky , r. f. 1993 , apj , 412 , 72 turner , t. j. , george , i. m. , nandra , k. , & mushotzky , r. f. 1997 , apjs , 113 , 23 turner , t. j. , george , i. m. , nandra , k. , & mushotzky , r. f. 1998 , apj , 493 , 91 veilleux , s. , kim , d .- c . , sanders , d. b. , mazzarella , j. m. , & soifer , b. t. 1995 , apjs , 98 , 171 wang , j. , heckman , t. m. , & weaver , k. a. 1997 , apj , 474 , 659 wu , h. , zou , z .- xia , x .- y . , & deng , z .- g . 1998 , a&as 132 , 18 xia , x .- y . , boller , th . , wu , h. , deng , z .- g . , gao , y. , zou , z .- l . , mao , s. , & brner , g. 1998 , apj , 496 , l9 ; erratum , apj , 1998 , 507 , l99 yun , m.s . 1997 , private communication yun , m. s. , & scoville , n. z. 1995 , apj , 451 , l45 yun , m. s. , & hibbard , j. e. 1999 , in preparation lrrr & @xmath57 & @xmath58 & @xmath59 & @xmath60 & @xmath61 & @xmath62&&&@xmath63&@xmath64 & @xmath65 & @xmath66&@xmath67 & & & @xmath68 & & & @xmath67 & & & @xmath69 & @xmath70 & & & @xmath71 & @xmath72 & & @xmath73 & @xmath74 & & @xmath75 & @xmath76 & & @xmath77 & @xmath78

we present an optical spectrum for mrk 273x , the x - ray source @xmath0 to the northeast of mrk 273 . the new spectrum indicates that the object is at a much higher redshift ( 0.458 ) than the value ( 0.0376 ) previously reported by us . all the detected emission lines show properties of seyfert 2 galaxies . mrk273x has one of the highest x - ray and radio luminosities ( @xmath1 , @xmath2 ) among seyfert 2 galaxies , yet it has a low neutral hydrogen column density , @xmath3@xmath4 . these properties seem difficult to explain in the unified scheme of active galactic nuclei . the spectrum which we previously used to identify the redshift for mrk 273x turns out to be for diffuse clumps in the northeast tail / plume about @xmath5 ( @xmath6 kpc in projected distance ) from the nuclear region of mrk 273 . a new spectrum for this region was obtained ; this spectrum is essentially the same as the previous one . these observations indicate that these clumps have the same redshift as mrk273 and are physically associated with the merger . the spectrum is dominated by strong emission from the [ o iii ] doublet with seyfert 2-like line ratios , which indicate that these northeast clumps are probably excited by the shock plus precursor mechanism during the merging process . this mechanism may be operating in other ultraluminous iras galaxies as well . # 1#2=.5 = .5 # 1*(#1 ) *

<s>[INST]mrk 273 is an ultraluminous infrared galaxy with prominent merging signatures . 1 shows our scanned poss ii j - band image and a deep r - band image ( hibbard & yun 1999 , kindly made available to us by john hibbard ) of the mrk 273 field . these optical images reveal a long tail to the south and a faint plume to the northeast . the very large array ( vla ) continuum observations revealed extremely extended radio lobes up to more than 200 kpc in length extending further along the tip of the southern optical tail into southeast ( yun 1997 ; yun & hibbard 1999 ) . vla h 21 cm line observations show extended atomic gas associated with the southern optical tail as well ( hibbard & yun 1996 , 1999 ) . mrk 273 is also detected in the x - ray by rosat and asca ( turner et al . 1993 , 1997 , 1998 ; iwasawa 1998 ) . rosat hri image reveals an x - ray companion source of comparable brightness as mrk 273 , about @xmath0 to the northeast of mrk 273 . xia et al . ( 1998 ) named this source mrk 273x , and found an optically faint source coincident with the x - ray position ( cf . fig . 1 in xia et al . 1998 ; the position is marked here by ` x ' in fig . 1a and is very prominently shown in the deep r - band image in fig . all these optical features are also fairly prominent in the digitized sky survey ( dss ) image of mrk 273 . the core of mrk 273 has been resolved into two compact components in the radio and near - infrared ( condon et al . 1991 ; majewski et al . 1993 ; knapen et al . 1997 ) , which are believed to be the double nuclei of the two progenitor galaxies involved in the merging and at least one of them is a seyfert 2 nucleus ( sargent 1972 ; asatrian et al . 1990 ) . spectroscopic observations were carried out on the 2.16 m telescope at the beijing astronomical observatory ( bao ) to secure the redshift of mrk 273x and the bao spectrum indicates that an object ( thought to be mrk 273x ) at @xmath7 was detected ( xia et al . since the signal - to - noise ratio of this spectrum was low , further observations of mrk 273x were performed at the william herschel telescope ( wht ) for additional check . the new spectrum turned out to be different from the one obtained at bao . later examinations and further spectroscopic observations show that the object detected in the initial bao spectrum was not mrk 273x , but an object about @xmath8 to the northeast of mrk 273 ; we will call this diffuse object mrk 273d . the mis - identification was caused by incorrect slit positioning in previous observation at bao ( see section 2 ) . in this paper , we present the wht spectrum of mrk273x and new observations for mrk273d performed at bao . in addition , we re - examine all the original data analyzed by xia et al . we find that both mrk273x and mrk273d have intriguing properties . we show that the emission line widths and line ratios of mrk 273x resemble seyfert 2 galaxies . since mrk 273x turns out to be a distant background source , its x - ray and radio luminosities are one of the highest among seyfert 2 galaxies and yet it has a very low neutral hydrogen column density . mrk 273d consists of diffuse clumps at the same redshift as the ultraluminous galaxy mrk 273 and has quite unusual line ratios of / and /. these ratios are not easily produced by photoionization of o , b stars . we argue that the emission line ratios are better explained by shock excitation with precursors ( dopita & sutherland 1995 ) . the structure of the paper is as follows . in 2 , we describe the wht observation for mrk 273x and new observations for mrk 273d at bao . we also explain the original observational setup at bao . in 3 , we present the results of our spectral analysis . in 4 , we discuss the nature of mrk 273x and mrk 273d . and finally , a brief summary of the main results is given in 5 . throughout this paper , we use a hubble constant of @xmath9 and an einstein - de sitter ( @xmath10 ) cosmology . the observations carried out at bao used a zeiss universal spectrograph mounted on the 2.16 m telescope of bao . a tektronix 1024x1024 ccd was used as the detector . the original slit setup , for the bao observation on april 12 , 1997 , runs from the northeast to southwest passing through star s and source d , is illustrated in fig . the slit was approximately @xmath11 long and @xmath12 wide . this observational setup was intended to determine the redshift for mrk 273x ( source x in fig . unfortunately the slit missed the target due to a slight error in the slit orientation . this occurred because mrk 273x was too faint to be seen on the tv monitor , so the slit had to be rotated from an initial orientation ( which passed through the star ` s ' in fig . 1a ) by a prescribed angle such that it would pass through mrk273x . the amount of rotation required was calculated from several bright objects within the field . this technique of slit positioning for faint sources had been successfully employed previously at bao , so no extra check was enforced in the initial observations reported in xia et al . ( 1998 ) . in spite of the incorrect rotation angle used , by coincidence , an object other than star s was detected in the spectrum and was ( incorrectly ) identified as mrk273x . follow - up observations of mrk273x carried out at the william herschel telescope ( wht ) at la palma however yielded spectra that are completely different from that obtained at bao ( see below ) . a re - examination of the long - slit spectrum obtained at bao showed that the object detected in the spectrum was separated from the star s by 80@xmath13 rather than 20@xmath13 , the actual angular distance between mrk 273x and the star s. from the angular distance between the object detected in the bao spectrum and the star s , and from the fact that only two objects were seen in the spectrum , we were able to reconstruct the slit orientation as shown in fig . this slit orientation is well - constrained : a little more rotation to the southwest ( anti - clockwise ) the slit would enclose the bright southern tail of mrk 273 , while slightly more rotation to the opposition direction it would enclose no object other than the star s. it turned out that the slit passed through some bright clumps ( source d in fig . 1a ) , about @xmath14 to the nuclear region of mrk 273 ( knapen et al . while this slit re - construction seems convincing , as a double check , mrk273d was re - observed at bao on february 20 , 1999 with a different slit setup . the new observation yields a spectrum nearly identical to the one published by xia et al . the slit setup was recorded with photographs , which allowed us to determine the slit orientation reliably . this new slit is approximately @xmath11 long and @xmath15 wide and runs nearly vertically ( in the north south direction passing through stars s1 and s2 ) as shown in fig . both the previous and the new bao spectra cover a wavelength range of 3500 to 8100 with a grating of 195 / mm and a spectral resolution of 9.3 ( 2 pixels ) . wavelength calibration was carried out using an fe - he - ar lamp and standard stars were observed to perform flux calibrations . the wavelength calibration accuracy is better than 1 . mrk 273x ( source x in fig . 1 ) was first observed on june 19 , 1998 with the wht . since the resulting spectrum was different from the one obtained earlier at bao , another observation was attempted at the wht on june 26 , 1998 which yielded spectrum identical to the one obtained a week ago on june 19 . additional new spectrum for mrk 273x was also obtained using the bao 2.16 m telescope , confirming the results from the wht . the new bao spectrum for mrk 273x is not presented here given its lower signal - to - noise ratio . the wht spectra were obtained using the double spectrograph isis . the ccd detector used at the blue and red arm was respectively an eev chip of 2148@xmath164200 pixels with a 13.5@xmath17 m pixel size and a tek chip of 1124@xmath161124 pixels with a 24@xmath17 m pixel size . at the blue arm , a grating of 64 / mm centered at 4583 yielded a useful wavelength coverage from 32005300 . the violet end of the blue spectra was cut off by the atmosphere and by instrumental optics , while the red end was blocked out by the dichroic which had a half - power crossover wavelength of 5300 . for the red arm , a grating of 158 / mm dispersion covered the wavelength range 53008270 . three 2400s narrow - slit ( 0.8 ) exposures and one 1800s wide - slit spectra ( 6 ) were obtained for each arm . the full width at half maximum ( fwhm ) spectral resolution was 6.2 for the red arm and 3.28 for the blue arm , respectively . wavelength calibration was carried out using an ar - ne lamp ; the resulting wavelength accuracy is about 0.2 . the spectra were flux - calibrated using observations of the standard star bd+33@xmath182642 . all the optical spectral data reduction was performed at bao using iraf packages . the ccd data reduction includes standard procedures such as bias subtraction , flat fielding and cosmic ray removal . the measurements of emission lines were performed under the iraf environment using tasks `` splot '' and `` ngaussfit '' . we first show the wht optical spectrum for mrk 273x in fig . 2 . the spectrum combines both the red and blue arm data . , , , , , and mgii @xmath192796 , 2803 emission lines are all convincingly detected . the redshift determined from these emission lines is 0.458 . the measured fluxes for the identified lines are listed in table 1 . all detected lines have a fwhm of about @xmath20 . the optical b and r magnitudes for mrk 273x are respectively about 20.8 and 19.6 from the usno - a1.0 catalog ( monet 1996 ) . the absolute magnitude of mrk 273x is therefore @xmath21 , comparable to @xmath22 in the schechter luminosity function of galaxies ( e.g. , lin et al . this luminosity includes the contribution from both the central active galactic nucleus ( agn , see below ) and the host galaxy . in the short _ hubble space telescope ( hst ) _ wide field planetary camera 2 ( wfpc2 ) snapshot image , the underlying galaxy is visible but its outer faint contours are not well - detected . from the deep r - band image ( shown here in fig . 1b ) of hibbard & yun ( 1999 ) , the agn nucleus and the host galaxy seem to contribute comparable amount of light . as reported in xia et al . ( 1998 ) , mrk 273x is also luminous in the soft x - ray ( 0.12.4 kev ) band . the soft x - ray flux is @xmath23 , corresponding to an x - ray luminosity of @xmath24 . the soft x - ray spectrum of mrk 273x is well - fitted by a power - law , with a photon index of @xmath25 , a value typical for seyfert 2 galaxies . spectral fitting yielded a neutral hydrogen column density of @xmath26 . mrk 273x is also detected at the vla 21 cm continuum observations and appears to be consistent with a point - like source ( yun 1997 ; yun & hibbard 1999 ) . at this high redshift , mrk 273x falls into the class of powerful radio sources with @xmath27 . this single property sets mrk 273x into categories of agns , qsos , and starbursts and radio galaxies rather than normal galaxies . the high x - ray luminosity , strong radio emission and the emission line widths ( fwhm @xmath28 ) of mrk 273x imply that the main energy output mechanism is agn , and mrk 273x may be either a narrow - line seyfert 1 ( nls1 ) galaxy ( osterbrock & pogge 1985 ) or a seyfert 2 galaxy from the relatively narrow emission lines . below we explore each possibility in turn . nls1s are defined as seyfert galaxies which have fwhm for the line in the range of 500 - 2000 @xmath29 and with /@xmath303 . mrk 273x does not satisfy the second criterion since the ratio of the / is about 6 . furthermore , mrk 273x does not show prominent fe ii emission lines , which are strong in most ( but not all ) nls1 galaxies . also , the soft x - ray spectrum is well fitted by power - law with a photon index @xmath25 ( xia et al . 1998 ) and is not as steep as most nls1s . hence , mrk 273x does not fit in the definition of nls1 galaxies . the relatively narrow balmer and forbidden lines and the line ratios of / @xmath31 are consistent with mrk 273x being a seyfert 2 galaxy . turner et al . ( 1997 , 1998 ) and polletta et al . ( 1996 ) presented catalogs for several tens of seyfert 2 galaxies . in their catalogs , the soft x - ray luminosity for all but a few listed seyfert 2 galaxies are less than @xmath32 and the @xmath33 value is larger than @xmath34 . the combination of a low @xmath33 value together with powerful x - ray emission ( @xmath35 ) is therefore rare among seyfert 2 galaxies . this peculiarity is also supported by its quite high radio luminosity and multi - wavelength observations of mrk 273x . the flux ratios of mrk273x in the soft x - ray , b - band , and radio are @xmath36 ; such a spectral energy distribution is rarely seen in any other agns ( see xia et al . 1998 for more discussions ) . furthermore , the low @xmath33 value is not expected in the unified scheme of agns ( e.g. , dopita 1997 and references therein ) . in this picture , the broad - line regions of seyfert 2 galaxies are postulated to be obscured by a thick torus of gas and dust , which presumably gives rise to high @xmath33 values . to summarize , the optical emission line properties , the powerful x - ray and radio emission and the low neutral hydrogen absorption indicate that mrk 273x is a rare source that may provide a test of the unified picture of agns . the diffuse clumps ( mrk 273d , labeled as source d in fig . 1a ) are clearly seen in the j - film copy of poss ii and in the dss image , but they are visible neither in the near - infrared ( e.g. , smith et al . 1996 ) , most r - band images ( e.g. , yun & scoville 1995 ; mazzarella & boroson 1993 ) , nor in the hst wfpc2 f814 snapshot image , suggesting that they have quite blue colors . only the deep r - band image shown in fig . 1b ( hibbard & yun 1999 ) reveals some patches in the northeast plume corresponding to these dense knots . we extracted the bao spectra for the diffuse clumps in fig . 1a using an aperture window size of 4@xmath16 17 for the observation on april 12 , 1997 and 2.5@xmath16 17 for the observation on february 20 , 1999 . these aperture windows are indicated as the rectangles in fig . the spectra are shown in fig . 3 and the emission line fluxes are listed in table 1 . the old and new spectra are similar . the continuum is somewhat higher in the feb . 20 , 1999 observation . the difference may be real , as the two slits sampled slightly different regions , although the possibility of calibration uncertainties can not be completely ruled out . the emission line ratios are very similar from both spectra . the redshift for mrk 273d determined from the emission lines is the same as mrk 273 ( @xmath37 ) . therefore these clumps are physically associated with the major merger process of mrk 273 . yun & scoville ( 1995 ) suggest that mrk 273 is the merging product of a nearly edge - on gas - rich spiral and another more face - on spiral . the tidal plume in the northeast is from the face - on progenitor . so the physical association of mrk 273d with mrk 273 is expected . it is clear from fig . 3 and table 1 that the continuum emission from mrk 273d is very weak and the lines are strong compared to . more specifically , from the observation on april 12 , 1997 , the line ratio of the to is @xmath38 , while the line ratio of the to is @xmath39 ( the error bars are 1@xmath40 values ) . for the new observation , the ratio of the line to is @xmath41 while the ratio of line to is @xmath42 . note that these two line ratios are little affected by dust extinction since the two lines involved in the ratios are quite close in wavelength . 4 shows the standard diagnistic diagram of / versus / ( osterbrock 1989 ) for emission line galaxies . the hii , liner and seyfert galaxies occupy different regions in this diagram . for hii regions photoionized by o , b stars , @xmath43\thinspace\lambda5007/{\rm h}\beta < 5 $ ] for @xmath44\thinspace\lambda6584/{\rm h}\alpha \approx 0.3 - 0.4 $ ] ( see also fig . 12.1 in osterbrock 1989 ) . the / ratio of mrk 273d is clearly much higher than those typically found for photoionized h ii regions . in fact , mrk 273d is clearly located in the region occupied by seyfert 2 galaxies . the / and / line ratios of mrk 273d are also located in the seyfert 2 region ( cf . 12.2 , 12.3 , osterbrock 1989 and more discussions in xia et al . 1998 ) . to achieve these seyfert 2 like line ratios , the ionization source must be harder than the radiation provided by young massive stars . mrk 273d is , however , obviously not an agn given its diffuse morphology . we discuss further the mechanism of line excitations in mrk 273d in 4.2 . mrk 273x is a background object in the mrk 273 field ; it is at a much higher redshift ( @xmath45 ) than mrk 273 which has a redshift of 0.0376 . it is interesting to note that the x - ray companions of three nearest ultraluminous iras galaxies ( arp 220 , mrk 273 and mrk 231 ) are all background sources and are therefore not physically associated with the mergers themselves ( cf . xia et al . 1998 ) . mrk 273x has agn characteristics both optically and in the soft x - ray together with a high radio luminosity . the narrow emission lines and various line ratios are consistent with it being a seyfert 2 galaxy . its soft x - ray luminosity is one of the highest among seyfert 2 galaxies with a low neutral hydrogen column density . although many well known nearby seyferts ( including mrk 273 itself ) also host an energetically significant starburst , the low neutral hydrogen column density of @xmath46 appears to exclude the possibility of mrk 273x being a dusty luminous starburst galaxy . these observational facts show that mrk 273x is an unusual seyfert 2 galaxy that is not easy to explain using the unified scheme of agns . xia et al . ( 1998 ) examined the time variability of mrk 273x using the rosat data taken in may and june 1992 . while mrk 273x is fainter than mrk 273 by about 20% in the rosat pspc image , it is almost as bright as mrk 273 in the rosat hri image . a @xmath47 test however reveals that these changes are not statistically significant in the rosat data . from the 0.5 - 2 kev image of sis on board asca , iwasawa ( 1998 ) found that mrk 273x is at most 40 percent as bright as mrk 273 on dec . 27 , 1994 . since mrk 273 is not known to vary in the soft x - ray , these multi - epoch observations imply that mrk 273x has faded by a factor of 2 in two and a half years . cycle 1 axaf observations are planned to obtain a high - resolution map of mrk 273x and mrk 273 . these observations will provide further insights on their x - ray variability , higher energy behaviors and spatial distribution of the x - ray emissions . the diffuse clumps in mrk 273d in the northeast plume could directly come from the extreme outer regions of the face - on progenitor . it is also possible that mrk 273d was formed in the major merger process . this patchy object is unlikely to be a self - gravitating ( tidal ) dwarf galaxy since they are usually found far from the interacting parent galaxies and their spectra resemble typical photoionized h ii regions ( e.g. , duc & mirabel 1997 ) . furthermore , clumps formed close to the merger is liable to tidal disruption once they fall back to the merger . ( however , some observations indicate that clumps close to the merging pair do exist , e.g. , h ii regions in the ngc 4676a tail , hibbard & van gorkom 1996 . ) in contrast , mrk 273d is very close to ( @xmath6 kpc in projected distance from ) the main merging nuclei , and its spectrum differs significantly from photoionized h ii regions . although the spectrum of mrk 273d resembles that of a seyfert 2 galaxy , its diffuse morphology suggests that it is not a ( dwarf ) agn . in fact , the spectrum of mrk 273d is very similar to that of the soft x - ray nebula to the north of mrk 266 ( cf . fig . 5 in kollatschny & kowatsch 1998 ) . as pointed out by these authors , the @xmath48 color ( @xmath49 ) of the northern component is exceptionally blue due to the intense line emission . the diffuse gas clumps in mrk 273d are also very blue , since they are only seen in the b - band , but not in other bands redder than r. the blue color of mrk 273d is also due to the continuum being dominated by the line emission ( cf . fig . 3 ) . the spectrum of mrk 273d is also similar to the average spectrum of the northwest cone of ngc 2992 ( cf . 3a in allen et al . 1999 ) and the spectrum of diffuse ionized gas in ngc 891 ( rand 1997 , 1998 ) . as discussed by these authors , the likely excitation mechanism for these peculiar spectra is the shock plus precursor model ( dopita & sutherland 1995 ) . for a fast shock with velocity of several hundred @xmath29 , copious uv photons are produced in the shock front , which can in turn excite the gas of h ii regions in front of the shock , thus producing radiative precursors . the hardness of the uv radiation ( shock temperature ) depends on the velocity of the shock wave , and with suitable parameters , this scenario can produce the line ratios as seen in mrk 273d ( cf . 2a in dopita & sutherland 1995 ) . it is believed that starbursts can drive radial outflows ( wang , heckman & weaver 1997 ) . there is some evidence that such outflows ( superwinds ) indeed exist in several ultraluminous iras galaxies out to tens of kpc with velocities of a few hundred to 1000 @xmath29 , e.g. , in ngc 6240 , arp 299 , arp 220 ( heckman et al . 1987 , 1990 , 1996 , 1999 ; schulz et al . 1997 ; wang et al . since mrk 273 is also a major merger ultraluminous infrared galaxy and has extended soft x - ray emission and hi nebula , it is conceivable that such an outflow exists in mrk 273 . in this regard , mrk 266 is also a candidate since it is a luminous infrared merging galaxy with double nuclei ( @xmath50 kpc in projected separation ) and very extended ( about 150 kpc ) soft x - ray nebula . these observations suggest that the shock+precursor emission may be a common mechanism to excite gaseous nebulae in luminous infrared merging galaxies , in addition to the o , b star photoionization and agn excitation . wu et al . ( 1998 ) showed that many observed ultraluminous iras galaxies have mixture types in different line ratio diagnostic diagrams . goncalves et al . ( 1998 ) also suggested that most emission line galaxies with the so - called transition spectrum have composite spectra with simultaneous presence of seyfert , liner and h ii region contributions . perhaps these objects are not only just a mixture of agn and photoionized starburst regions ( genzel et al . 1998 ) , they may also contain shock+precursor regions , as seen in mrk 273d and the northern nebula of mrk 266 . this also provides a caution : a seyfert 2 like spectrum in high - redshift luminous infrared galaxies does not necessarily mean the presence of agns at their centers , instead such a spectrum could be induced by the shock+precursor excitation in the gas clumps in the mergers . we have presented optical spectroscopic observations for the x - ray companion source and the blue diffuse clumps in the northeast tidal debris surrounding the ultraluminous galaxy mrk 273 . their peculiar properties are discussed and explored together with soft x - ray and radio observations available . we summarize below the main points we have presented and addressed in this paper . mrk 273x , the x - ray companion @xmath0 to the northeast of the ultraluminous galaxy mrk 273 , is a background source at @xmath45 . its redshift is much higher than the redshift ( @xmath37 ) of mrk 273 . the soft x - ray spectrum for mrk 273x is typical of seyfert 2 galaxies . the x - ray luminosity of mrk 273x is exceptionally high for a seyfert 2 galaxy , @xmath1 . spectral fitting gives a low neutral hydrogen column density , @xmath3@xmath4 . all the optical emission lines detected for mrk 273x have a similar fwhm of @xmath51kms@xmath52 and the / ratio is about 6 , again typical for seyfert 2 galaxies . mrk 273x is also a powerful radio source with a radio luminosity @xmath2 . this adds more peculiarities to this energetically unusual seyfert 2 galaxy . the optical knots mrk 273d in the northeast tidal tail / plume @xmath6 kpc ( projected ) from the nuclear region of mrk 273 is at the same redshift as that of mrk 273 . they are diffuse gas clumps physically associated with the major merger . the spectrum of mrk 237d is dominated by strong emission from the [ o iii ] doublet . the strong line emission gives rise to the blue color of this object . the [ o iii]@xmath535007/h@xmath54 and [ n ii]@xmath536584/h@xmath55 line ratios are @xmath56 and 0.3 , respectively . these seyfert 2like line ratios for mrk 273d are likely excited by shocks plus precursor mechanism involved in the merging process . we are grateful to zheng zheng for assistance in observations and preliminary data reductions . we also thank simon white for advice and the anonymous referee and the scientific editor john huchra for valuable criticisms that have improved the paper . we appreciate very much for the deep r - band image kindly provided to us by john hibbard . this project was partially supported by the nsf of china and the exchange program between nsfc and dfg . y.g.s research at lai , dept . of astronomy is funded by nsf grants ast96 - 13999 and by the university of illinois . is also grateful to ernie seaquist for support at the university of toronto . allen , m. g. , dopita , m. a. , tsvetanov , z. i. , & sutherland , r. s. 1999 , apj , 511 , 686 asatrian , a.s . , petrosian , a.r . & borngen , f. 1990 , paired and interacting galaxies : iau colloquium no . 124 , eds . j. w. sulentic , w. c. keel , w.c . , & c. m. telesco , 201 condon , j. j. , huang , z .- p . , yin q. f. , & thuan , t. x. 1991 , apj , 278 , 65 dopita , m. a. 1997 , pasa , 14 , 230 dopita , m. a. , & sutherland , s. 1995 , apj , 455 , 468 duc , p .- a . , & mirabel , i. f. 1997 , preprint ( astro - ph/9711253 ) genzel , r. et al . 1998 , apj , 498 , 579 goncalves , a.c . , veron - cetty , m .- p . , & veron , p. 1998 , preprint ( astro - ph/9811342 ) heckman , t. m. , armus , l. , & miley , g. k. 1987 , aj , 92 , 276 heckman , t. m. , armus , l. , & miley , g. k. 1990 , apjs , 74 , 833 heckman , t. m. , dahlem , m. , eales , s. a. , fabbiano g. , & weaver , k.a . 1996 , apj , 457 , 616 heckman , t. m. , armus , l. , weaver , k. a. , & wang , j. 1999 , preprint ( astro - ph/9812317 ) hibbard , j. e. , & van gorkom , j. 1996 , aj , 111 , 655 hibbard , j. e. , & yun , m. s. 1996 , cold gas at high redshift , eds . m. n. bremer , p. p. van der werf , h.j.a . rttgering , & c.l . carilli ( doderecht : kluwer ) , 47 hibbard , j. e. , & yun , m. s. 1999 , in preparation hunsberger , s. d. , charlton , j. c. , & zarisky , d. 1996 , apj , 462 , 50 iwasawa , k. 1998 , preprint ( astro - ph/9808313 ) knapen , j. h. , laine , s. , yates , j. a. , robinson , a. , richards , a. m. s. , doyon , r. , & nadeau d. 1997 , apj , 490 , l29 kollatschny , w. , & kowatsch , p. , 1998 , a&a , l21 lin , h. , kirshner , r. p. , shectman , s. a. , landy , s. d. , oemler , a. , tucker , d. l. , & schechter , p. l. 1996 , apj , 464 , 60 majewski , s. r. , hereld , m. , koo , d.c . , illingworth , g.d . , & heckman , t. m. 1993 , apj , 402 , 125 mazzarella , j.m . & boroson , t.a . 1993 , apjs , 85 , 27 monet , d. 1996 , baas , 188 , 5404 mulchaey , j. s. , koratkar , a. , ward , m. j. , wilson , a. s. , whittle , m. , antonucci , r. j. , kinney , a. , & hurt , t. 1994 , apj , 436 , 586 osterbrock , d.e . , & pogge , r. 1985 , apj 297 , 166 osterbrock , d.e . 1989 , astrophysics of gaseous nebulae and active galactic nuclei ( mill valley : universe science books ) polletta , m. , bassani , l , malaguti , g. , palumbo , g. g. c. , & caroli , e. 1996 , apjs , 106 , 399 rand , r. 1997 , apj , 474 , 129 rand , r. 1998 , apj , 501 , 137 sargent , w. l. w. 1972 , apj , 173 , 7 schulz , h. , komossa , s. , berghfer , t. , & boer , b. 1998 , a&a , 330 , 823 smith , d.a . 1996 , apjs , 104 , 217 turner , t. j. , george , i. m. , & mushotzky , r. f. 1993 , apj , 412 , 72 turner , t. j. , george , i. m. , nandra , k. , & mushotzky , r. f. 1997 , apjs , 113 , 23 turner , t. j. , george , i. m. , nandra , k. , & mushotzky , r. f. 1998 , apj , 493 , 91 veilleux , s. , kim , d .- c . , sanders , d. b. , mazzarella , j. m. , & soifer , b. t. 1995 , apjs , 98 , 171 wang , j. , heckman , t. m. , & weaver , k. a. 1997 , apj , 474 , 659 wu , h. , zou , z .- xia , x .- y . , & deng , z .- g . 1998 , a&as 132 , 18 xia , x .- y . , boller , th . , wu , h. , deng , z .- g . , gao , y. , zou , z .- l . , mao , s. , & brner , g. 1998 , apj , 496 , l9 ; erratum , apj , 1998 , 507 , l99 yun , m.s . 1997 , private communication yun , m. s. , & scoville , n. z. 1995 , apj , 451 , l45 yun , m. s. , & hibbard , j. e. 1999 , in preparation lrrr & @xmath57 & @xmath58 & @xmath59 & @xmath60 & @xmath61 & @xmath62&&&@xmath63&@xmath64 & @xmath65 & @xmath66&@xmath67 & & & @xmath68 & & & @xmath67 & & & @xmath69 & @xmath70 & & & @xmath71 & @xmath72 & & @xmath73 & @xmath74 & & @xmath75 & @xmath76 & & @xmath77 & @xmath78[/INST] we present an optical spectrum for mrk 273x , the x - ray source @xmath0 to the northeast of mrk 273 . the new spectrum indicates that the object is at a much higher redshift ( 0.458 ) than the value ( 0.0376 ) previously reported by us . all the detected emission lines show properties of seyfert 2 galaxies . mrk273x has one of the highest x - ray and radio luminosities ( @xmath1 , @xmath2 ) among seyfert 2 galaxies , yet it has a low neutral hydrogen column density , @xmath3@xmath4 . these properties seem difficult to explain in the unified scheme of active galactic nuclei . the spectrum which we previously used to identify the redshift for mrk 273x turns out to be for diffuse clumps in the northeast tail / plume about @xmath5 ( @xmath6 kpc in projected distance ) from the nuclear region of mrk 273 . a new spectrum for this region was obtained ; this spectrum is essentially the same as the previous one . these observations indicate that these clumps have the same redshift as mrk273 and are physically associated with the merger . the spectrum is dominated by strong emission from the [ o iii ] doublet with seyfert 2-like line ratios , which indicate that these northeast clumps are probably excited by the shock plus precursor mechanism during the merging process . this mechanism may be operating in other ultraluminous iras galaxies as well . # 1#2=.5 = .5 # 1*(#1 ) * </s>

microlensing is sensitive to planets orbiting low - mass stars and brown dwarfs ( bds ) that are difficult to detect by other methods , such as the radial velocity and transit method . although faint low - mass stars such as m dwarfs comprise @xmath11 of stars in the solar neighborhood and the galaxy @xcite , it is difficult to detect distant m dwarfs due to their low luminosity . however , microlensing depends on the mass of the lens , not the luminosity , and thus it is not affected by the distance and luminosity of the lens . hence , microlensing is the best method to probe faint m dwarfs in the galaxy . a majority of host stars of 52 extrasolar planets detected by microlensing are m dwarfs , and they are distributed within a wide range of distances about @xmath12 . until now a large number of bds @xcite have been discovered by various methods including radial velocity @xcite , transit @xcite , and direct imaging @xcite , and most of them are young @xcite . there exist various scenarios of bd formation based on these plentiful bd samples . since microlensing provides different bd samples from other methods , the microlensing bd samples will play an important role to constrain the various bd formation scenarios . 17 bds have been detected with microlensing so far . only two of them , ogle-2007-blg-224l @xcite and ogle-2015-blg-1268l @xcite , are isolated bds , while most of the others , ogle-2006-blg-277 lb @xcite , ogle-2008-blg-510lb / moa-2008-blg-369l @xcite , moa-2009-blg-411 lb @xcite , moa-2010-blg-073 lb @xcite , moa-2011-blg-104lb / ogle-2011-blg-0172 @xcite , moa-2011-blg-149 lb @xcite , ogle-2013-blg-0102 lb @xcite , and ogle-2013-blg-0578 lb @xcite , are binary companions orbiting m dwarf stars . this is because binary lens events ( i.e. , events with anomalies in the light curve ) have a larger chance to measure masses of the lens than single lens events , such as isolated bd events . the key problem in detecting " isolated bds is that in general , we do not know whether they are detected " or not , since all that we obtain from observed events is the einstein timescale @xmath13 , which is the crossing time of the einstein radius of the lens . with the observed @xmath13 , we can only make a very rough estimate of the lens mass and so can not distinguish potential bds from stars . to measure the masses of isolated bds in the isolated bds events , two parameters are required : the angular einstein radius @xmath14 and microlens parallax @xmath15 . this is because @xcite @xmath16 and @xmath17 where @xmath18 here @xmath19 is the lens mass , and @xmath20 and @xmath21 are the distances to the lens and the source from the observer , respectively . however , it is usually quite difficult to measure the two parameters @xmath14 and @xmath15 . in general , @xmath14 is obtained from the measurement of the normalized source radius @xmath22 , where @xmath23 is an angular radius of the source . the @xmath6 measurement is limited to well - covered caustic - crossing events and high - magnification events in which the source passes close to the lens , while @xmath23 is usually well measured through the color and brightness of the source . because isolated bd events are almost always quite short , @xmath15 can usually be measured only via so - called terrestrial parallax @xcite . terrestrial parallax measurements are limited to well - covered high - magnification events . as a result , it is very hard to measure masses of isolated bds from the ground @xcite . the best way to measure @xmath15 is a simultaneous observation of an event from earth and a satellite @xcite . fortunately , since 2014 , the _ spitzer _ satellite has been regularly observing microlensing events toward the galactic bulge in order to measure the microlens parallax . the _ spitzer _ observations suggest a new opportunity to obtain the mass function of bds from the simultaneous observation from earth and _ spitzer _ , although they are not dedicated to bds @xcite . the simultaneous observation from the two observatories with sufficiently wide projected separation @xmath24 allows to measure the microlens parallax vector @xmath25 from the difference in the light curves as seen from the two observatories , @xmath26 where @xmath27 is the lens - source relative proper motion and @xmath28 where @xmath29 here @xmath30 is the time of the closest source approach to the lens ( peak time of the event ) and @xmath31 is the separation between the lens and the source at time @xmath30 ( impact parameter ) . the subscripts of @xmath32 and @xmath33 indicate the parameters as measured from the satellite and earth , respectively . thus , @xmath34 and @xmath35 represent the difference in @xmath30 and @xmath31 as measured from the two observatories . parallax measurements made by such comparisons between the light curves are subject to a well - known four - fold degeneracy , which comes from four possible values of @xmath35 including ( @xmath36 ) and ( @xmath37 ) . however , there is only a two - fold degeneracy in the amplitude of @xmath25 because @xmath38 and @xmath39 . the only exception to the four - fold degeneracy would be if one of the two observatories has @xmath31 consistent with zero , while the other has @xmath31 inconsistent with zero . in this case , the four - fold degeneracy reduces to a two - fold degeneracy . for example , if @xmath40 ( within errors ) , then @xmath41 ( and similarly for @xmath42 ) . then , since @xmath43 , there is no degeneracy in the mass ( see e.g. , @xcite ) . this case is very important for point - lens mass measurements since the lens always passes very close to or over the source as seen by one observatory , so @xmath44 , whether or not it is strictly consistent with zero . here we report the fifth isolated - star measurement derived from microlensing measurements of @xmath6 and @xmath15 . in contrast to the previous four measurements , this one has a discrete degeneracy in @xmath6 and therefore in mass . we trace the origin of this degeneracy to the fact that only a single point is affected by finite - source effects , and we argue that it may occur frequently in future space - based microlensing mass measurements , including bds . we show how this degeneracy can be broken by future high - resolution imaging , regardless of whether the lens is dark or luminous . this paper is organized as follows . in section 2 , the observation of the event ogle-2015-blg-1482 is summarized , and we describe the analysis of the light curve in section 3 . with the results of section 3 , we derive physical properties of the source and lens in section 4 and then we discuss the results in section 5 . finally , we conclude in section 6 . the gravitational microlensing event ogle-2015-blg-1482 was discovered by the optical gravitational lensing experiment ( ogle ) ( udalski 2003 ) , and it was also observed by _ spitzer _ and korea microlensing telescope network ( kmtnet , @xcite ) . the microlensed source star of the event is located at ( @xmath45,@xmath46 ) = ( @xmath47 ) in equatorial coordinates and ( @xmath48,@xmath49 ) = ( @xmath50 ) in galactic coordinates . ogle observations were carried out using a 1.3 m warsaw telescope with a field of view of 1.4 square degrees at the las campanas observatory in chile . the event lies in the ogle field blg534 with a cadence of about @xmath51 in @xmath52 band . the einstein timescale is quite short , @xmath53days , and the ogle baseline of this event is slightly variable on long timescales at about the 0.02 mag level . thus , we used only 2015 season data for light curve modeling . kmtnet observations were conducted using 1.6 m telescopes with fields of view of 4.0 square degrees at each of three different sites , cerro tololo inter - american observatory ( ctio ) in chile , the south african astronomical observatory ( saao ) in south africa , and siding spring observatory ( sso ) in australia . the scientific observations at the ctio , saao , and sso were initiated on 3 february , 19 february , and 6 june in 2015 , respectively . ogle-2015-blg-1482 was observed with @xmath54 minute cadence at the three sites and the exposure time was 60 s. the ctio , saao , and sso observations were made in @xmath52-band filter , and for determining the color of the source star , the ctio observations with a typical good seeing were also made in @xmath55-band filter . thus , the light curve of the event was well covered by the three kmtnet observation data sets . the kmtnet data were reduced by the difference image analysis ( dia ) photometry pipeline @xcite . _ spitzer _ observations in 2015 were carried out under an 832-hour program whose principal scientific goal was to measure the galactic distribution of planets @xcite . the event selection and observational cadences were decided strictly by the protocols of @xcite , according to which events could be selected either subjectively " or objectively " . events that meet specified objective criteria _ must _ be observed according to a specified cadence . in this case all planets discovered , whether before or after _ spitzer _ observations are triggered , ( as well as all planet sensitivity ) can be included in the analysis . events that do not meet these criteria can still be chosen subjectively " . in this case , planets ( and planet sensitivity ) can only be included in the galactic - distribution analysis based on data that become available after the decision . like objective events , events selected subjectively must continue to be observed according to the specified cadence and stopping criteria ( although those may be specified as different from the standard , objective values at the time of selection ) . because the current paper is not about planets or planet sensitivities , the above considerations play no direct role . however , they play a crucial indirect role . figure 1 shows that despite the event s very short timescale @xmath53days , and despite the fact that it peaked as seen from _ slightly before it peaked from earth , observations began about 1 day prior to the peak . this is remarkable because , as discussed in detail by @xcite ( see their figure 1 ) , there is a delay between the selection of a target and the start of the _ spitzer _ observations . targets can only be uploaded to the spacecraft once per week , and it takes some time to prepare the target uploads . therefore , _ spitzer _ observations begin a minimum of three days after the final decision is made to observe the event with _ spitzer _ , and that decision is generally based on data taken the night before , i.e. about four days prior to the first _ spitzer _ observations . hence , at the time that the decision was made to observe ogle-2015-blg-1482 , the source was significantly outside the einstein ring . it is notoriously difficult to predict the future course of such events . therefore , such events can not meet objective criteria that far from the peak , but selecting themsubjectively " would require a commitment to continue observing them for several more weeks of the campaign , which risks wasting a large number of observations if the event turns out to be very low - magnification with almost zero planet sensitivity ( the most likely scenario ) . at the same time , if the event timescale is short , it could be over before the next opportunity to start observations with _ spitzer _ ( 10 days later ) hence , @xcite also specified the possibility of so - called secret alerts " . for these , an observational sequence would be uploaded to _ spitzer _ for a given week , but no announcement would be made . if the event looked promising later ( after upload ) , then it could be chosen subjectively . in this case , _ spitzer _ data taken after the public alert could be included in the parallax measurement ( needed to enter the galactic - distribution sample ) but _ spitzer _ data taken before this date could not . if the event was subsequently regarded as unpromising , it would not be subjectively alerted , in which case the observations could be halted the next week without violating the @xcite protocols . this was exactly the case for ogle-2015-blg-1482 ( see figure 1 ) . it was @xmath56secretly " alerted at the upload for observations to begin at hjd@xmath57 = hjd-2450000 = 7206.73 . it was only because of this secret alert that an observation was made near peak , which became the basis for the current paper . in fact , its subsequent rise was so fast ( due to its short timescale ) that it was subjectively alerted just prior to the near - peak _ spitzer _ observation . at the next week s upload , it met the objective criteria . note , however , that if we had waited for the event to become objective before triggering observations , we would not have been able to make the mass measurement reported here , even though the planet sensitivity analysis would have been almost identically the same ( provided that parallax could still be measured with the remaining _ spitzer _ observations ) . this is the first _ microlensing event for which a secret alert " played a crucial role . _ spitzer _ observations were made in @xmath58 m channel on the irac camera from hjd@xmath57 = hjd - 2450000 = 7206.73 to 7221.04 . the data were reduced using specialized software developed specifically for this program @xcite . even though the _ spitzer _ data are relatively sparse , there is one point near the peak , which proves to be essential to determine the normalized source radius @xmath6 . event ogle-2015-blg-1482 was densely , and almost continuously covered by ground - based data , but showed no significant anomalies ( see figure 1 ) . this has two very important implications . first , it means that the ground - based light curve can be analyzed as a point lens . second , it implies that it is very likely ( but not absolutely guaranteed ) that the _ spitzer _ light curve can likewise be analyzed as a point lens . the reason that the latter conclusion is not absolutely secure is that the _ spitzer _ and ground - based light curves are separated in the einstein ring by @xmath59 . thus , even though we can be quite certain that the ground - based source trajectory did not go through ( or even near ) any caustics of significant size , it is still possible that the source as seen from _ did pass through a significant caustic , but that this caustic was just too small to affect the ground - based light curve . nevertheless , since the closest _ point to peak has impact parameter @xmath60 and it is quite rare for events to show caustic anomalies at such separations when there are no anomalies seen in densely sampled data @xmath61 , we proceed under the assumption that the event can be analyzed as a point lens from both earth and _ spitzer_. thus , we conduct the single lens modeling of the observed light curve by minimizing @xmath62 over parameter space . for the @xmath62 minimization , we use the markov chain monte carlo ( mcmc ) method . thanks to the simultaneous observation from the earth and satellite , we are able to measure the microlens parallax @xmath63 , which are the north and east components of the parallax vector @xmath25 , respectively . the _ spitzer _ light curve has a point near the peak of the light curve , and thus we can also measure the normalized source radius @xmath6 . hence , we put three single lensing parameters of @xmath30 , @xmath31 , and @xmath13 , the parallax parameters of @xmath64 and @xmath65 , and the normalized source radius @xmath6 as free parameters in the modeling . in addition , there are two flux parameters for each of the 5 observatories ( _ spitzer _ , ogle , kmt ctio , kmt saao , kmt sso ) . one represents the source flux @xmath66 as seen from the @xmath67th observatory , while the other , @xmath68 is the blended flux within the aperture that does not participate in the event . that is , the five observed fluxes @xmath69 at epochs @xmath70 are simultaneously modeled by @xmath71 where @xmath72 is the magnification as a function of time at the @xmath67th observatory . in principle , these magnifications may differ because the observatories are at different locations . however , in this event the separations of the observatories on earth are so small compared to the projected size of the einstein ring that we ignore them and consider all earth - based observations as being made from earth s center . that is , we ignore so - called terrestrial parallax `` . at the same time , the distance between the earth and _ spitzer _ remains highly significant , so @xmath73 is different from @xmath74 . as is customary ( e.g. , @xcite ) , we determine the parameters in the @xmath56geocentric '' frame at the peak of the event as observed from earth @xcite , and likewise adopt the sign conventions shown in figure 4 of @xcite . in addition , we conduct the modeling for the point - source / point - lens , because only a single point of _ spitzer _ contributes to the finite - source effect . we find that the @xmath75 between the best - fit models of the point- and finite - sources is @xmath76 . hence , ogle-2015-blg-1482 strongly favors the finite - source model . as we will show , the lens either transits or passes very close to the source as seen by _ , which induces finite - source effects near the peak of the _ spitzer _ light curve . to account for this , we adopt a limb - darkened brightness profile for the source star of the form @xmath77,\ ] ] where @xmath78 is the mean surface brightness of the source , @xmath79 is the total flux at wavelength @xmath80 , @xmath81 is the limb darkening coefficient , and @xmath82 is the angle between the normal to the surface of the source star and the line of sight @xcite . based on the estimated color and magnitude of the source , which is discussed in section 4 , assuming an effective temperature @xmath83 , solar metallicity , surface gravity @xmath84 , and microturbulent velocity @xmath85 km / s , we adopt @xmath86 from @xcite . as discussed in section 1 , space - based parallax measurements for point lenses generically give rise to four solutions , which can be highly degenerate . however , in cases for which one of two observations has @xmath88 , while the other has @xmath89 , the four solutions reduce to two solutions . since for event ogle-2015-blg-1482 , @xmath90 has @xmath91 , we expect the event to have two degenerate solutions , @xmath92 and @xmath93 . however , what we see in table 1 is not two degenerate solutions but four . for each of the two expected degenerate solutions [ @xmath94 , there are two solutions with different values of @xmath6 ( @xmath95 and @xmath96 ) . figure 1 shows the best - fit light curve of the event ogle-2015-blg-1482 with the ogle , kmt , and _ spitzer _ data sets . the best - fit solution is @xmath97 solution for @xmath95 , which means @xmath92 and @xmath91 . the biggest @xmath75 between the four solutions is @xmath98 . we should expect the two - fold parallax to be very severe in this case . this two - fold degeneracy would be exact in the approximations that 1 ) earth and _ spitzer _ are in rectilinear motion and 2 ) they have zero relative projected velocity @xcite . for events that are very short compared to a year ( like this one ) , the approximation of rectilinear motion is excellent . and while earth and _ spitzer _ had relative projected motion of order @xmath99 , this must be compared to the lens - source projected velocity @xmath100 , @xmath101 hence , these two solutions are almost perfectly degenerate . on the other hand , the @xmath6 degeneracy was completely unexpected . it is also very severe . the origins of the @xmath6 degeneracy are discussed in section 5 . to illustrate the @xmath6 degeneracy , the light curve of the best - fit model @xmath97 for @xmath96 is also presented in figure 1 . in table 1 , we present the parameters of all the four solutions . the color and magnitude of the source are estimated from the observed @xmath102 source color and best - fit modeling of the light curve , but they are affected by extinction and reddening due to the interstellar dust along the line of sight . the dereddened color and magnitude of the source can be determined by comparing to the color and magnitude of the red clump giant ( rc ) under the assumption that the source and rc experience the same amount of reddening and extinction @xcite . figure 2 shows the instrumental kmt ctio color - magnitude diagram ( cmd ) of stars in the observed field . the color and magnitude of the rc are obtained from the position of the rc on the cmd , which correspond to @xmath103_{\rm rc } = [ 1.67 , 17.15]$ ] . we adopt the intrinsic color and magnitude of the rc with @xmath104 = 1.06 @xcite and @xmath105 = 14.50 @xcite . the instrumental source color obtained from a regression is @xmath106 and the magnitude of the source obtained from the best - fit model is @xmath107 . the measured offset between the source and the rc is @xmath108 = [ 0.07 , 0.22]$ ] . here we note that there exists an offset between the instrumental magnitudes of ogle and kmtnet as @xmath109 mag . thus , we should consider the offset when we estimate the dereddened magnitude of the source . as a result , we find the dereddened color and magnitude of the source @xmath103_{\rm s,0 } = [ 1.13 , 14.76]$ ] . the dereddened @xmath110 source color by using the color - color relation of @xcite is @xmath111 . then adopting @xmath112 to the the color - surface brightness relation of @xcite , we determine the source angular radius @xmath113 . the estimated color and magnitude of the source suggest that the source is a k type giant . the error in @xmath114 includes the uncertainty in the source flux , the uncertainty in the conversion from the observed @xmath102 color to the surface brightness , and the uncertainty of centroiding the rc . the uncertainty in the source flux is about @xmath115 and the uncertainty of the microlensing color is @xmath116 mag , which contributes @xmath117 error in @xmath114 measurement . the scatter of the source angular radius relation in @xmath112 is @xmath118 @xcite , and centroiding the rc contributes @xmath119 to the radius uncertainty @xcite . as mentioned above , since the degeneracy between two different @xmath6 solutions is very severe as @xmath120 , we should consider both @xmath6 solutions . the two @xmath6 values yield two different einstein radii , @xmath121 because of the two different einstein radii , all the physical parameters related to the lens take on two discrete values . the relative proper motions of the lens and source are , @xmath122 the mass and distance of the lens can be obtained from the measured einstein radius @xmath14 and microlens parallax @xmath15 . as discussed in the introduction , the four - fold degeneracy in @xmath25 usually leads to a two - fold degeneracy in its amplitude @xmath15 . however , in the case of events that are much higher magnification ( much lower @xmath31 ) as seen from one observatory than the other , the two - fold degeneracy collapses as well . this is because , under these conditions , @xmath123 . the present case is consistent with the lens passing exactly over the center of the source as seen by _ ( to our ability to measure it ) . then , according to equation , we measure the lens mass , @xmath124 the lens - source relative parallax for the two cases is @xmath125 these values of @xmath126 are very small compared to the source parallax @xmath127mas . this implies that the distance between the lens and the source is determined much more precisely than the distance to the lens or the source separately . that is , @xmath128 @xmath129 since the source is almost certainly a bulge clump star ( from its position on the cmd ) , and the lens is @xmath130 kpc from the source , it is likewise almost certainly in the bulge . thus , this is the first isolated low - mass object that has been determined to lie in the galactic bulge . event ogle-2015-blg-1482 has a very severe two - fold degeneracy in @xmath6 , in which the @xmath75 between the two solutions ( @xmath95 and @xmath96 ) is @xmath131 . for the solutions with @xmath92 and @xmath93 , the microlens parallax vectors @xmath25 are different from one another , but they have almost the same amplitude @xmath15 . therefore , the two solutions yield almost the same physical parameters of the lens . however , each of the two solutions also has two degenerate @xmath6 solutions : @xmath95 and @xmath96 . each @xmath6 solution yields different physical parameters of the lens , in particular the lens mass . for @xmath95 , the lens is a very low - mass star , while for @xmath96 it is a brown dwarf . the degeneracy of the lens mass due to the two @xmath6 can be resolved from direct lens imaging by using instruments with high spatial resolution ( han & chang 2003 ; henderson et al . 2014 ) , such as the visao camera of the 6.5 m magellan telescope with the resolution @xmath132 in the @xmath133 band @xcite band images , which gives hope for optical ao . however , it is premature to claim that this technique can be applied to faint stars in the galactic bulge ] and the gmtifs of the 24.5 m giant magellan telescope ( gmt ) with resolution @xmath134 in the nir @xcite . in general , direct imaging requires 1 ) that the lens be luminous , and 2 ) that it be sufficiently far from the source to be separately resolved . in the present case , ( 1 ) clearly fails for the bd solution . hence , the way that high - resolution imaging would resolve the degeneracy is to look for the luminous ( but faint ) m dwarf predicted by the other solution at its predicted orientation ( either almost due north or due south of the source since @xmath135 ) and with its predicted separation @xmath136 . if the m dwarf fails to appear at one of these two expected positions , the bd solution is correct . since the source is a clump giant , and hence roughly @xmath137 times brighter than the m dwarf , it is likely that the two can not be separately resolved until they are separated by at least 2.5 fwhm . this requires to wait until @xmath138 for magellan or @xmath139 for gmt . the degeneracy in @xmath6 was completely unexpected . indeed we discovered it accidentally because @xmath6 had one value in one of two degenerate parallax solutions and the other value in another one . originally , this led us to think that it was somehow connected to the parallax degeneracy . however , by seeding both solutions with both values of @xmath6 we discovered that it was completely independent of the parallax degeneracy . in retrospect , the reason for this degeneracy is `` obvious '' . there is only a single point that is strongly impacted by the finite size of the source . the value of @xmath140 at this time is well predicted by the rest of the light curve , in particular because _ spitzer _ data begin before peak ( see section 2 ) , @xmath141 hence , the magnification ( for point - lens / point - source geometry in a high magnification event ) is also known @xmath142 . moreover , both @xmath143 and @xmath144 for _ spitzer _ are also well measured , so that the measured flux at the near - peak point @xmath145 directly yields an empirical magnification @xmath146 ( i.e. the magnification in the presence of finite - source effects ) . following @xcite , the ratio of @xmath147 and @xmath148 can therefore be derived directly from the light curve @xmath149 as shown by figure 1 of @xcite , @xmath150 reaches a peak at @xmath151 , with @xmath152 . therefore , if one inverts a measurement of @xmath150 to infer a value of @xmath153 , there are respectively one , two and zero solutions for @xmath154 , @xmath155 , and @xmath156 . since this event is a high - magnification event only for _ spitzer _ , i.e. , the finite - source effect is only seen by _ spitzer _ , only the trajectory of _ spitzer _ is considered . figure 3 ( adapted from @xcite ) shows the finite - source effect function @xmath150 as a function of @xmath153 . for this event , @xmath157 at the nearest point to the peak , which is indicated by the horizontal dotted line in the figure . as shown in figure 3 , the function @xmath158 is satisfied at two different values of @xmath159 and @xmath160 , which implies ( as outlined above ) that there are two @xmath6 values . the two @xmath153 values yield two normalized source radii of @xmath161 ( for @xmath162 ) and @xmath163 ( for @xmath164 ) . these two derived @xmath6 values are almost the same as those obtained numerically from the best - fit solutions . because high - magnification events can be alerted in real time , the high - magnification events observed from earth are often well covered around the peak by intensive follow - up observations , and thus @xmath6 is almost always well measured if there are significant finite - source effects ( i.e. , @xmath165 for some points ) . this means that the @xmath6 degeneracy will often be resolved in high - magnification events observed from the ground . on the other hand , since the observation cadence of _ spitzer _ is much lower than those of ground - based observations , the @xmath6 degeneracy can occur frequently in high - magnification events observed by _ spitzer_. note that , in contrast to figure 1 of @xcite , our figure 3 shows @xmath150 with and without the effects of limb darkening . the effect is hardly distinguishable by eye , in particular because limb darkening at @xmath166 m is very weak . nevertheless this effect should be included . if finite - source effects are reliably detected from a single measurement near peak , how often will @xmath6 be ambiguous , and if it is ambiguous , how often will the value fall in the upper versus lower allowed ranges ? we might judge there to be areliable detection " of finite - source effects from a single point if @xmath167 , where @xmath168 might be taken as 5% . for high - magnification events including the limb darkening effect , we can taylor expand @xmath169 for @xmath170 ( see appendix ) @xmath171 where @xmath81 is the limb darkening coefficient , as mentioned in section 3 . truncating at the second term , we have @xmath172 . for _ spitzer _ @xmath173 , so we can ignore it . then @xmath174 . thus , @xmath175 , i.e. , @xmath176 , implies @xmath177 ( for @xmath178 ) . to next order , @xmath179 which is very close to the numerical value , 1.7 hence , we have three ranges of recognizable finite - source effects . the ranges are presented in table 3 . table 3 shows that @xmath180 of the finite - source effects will be unambiguous . and of the times they are ambiguous @xmath181 will have the higher value of @xmath6 . figure 4 shows the @xmath62 distribution of @xmath182 versus @xmath6 from the mcmc chains of the four degenerate solutions in table 1 . the figure shows that the distribution is centered on @xmath183 and thus the four solutions are consistent with @xmath183 , although there is scatter . therefore , it is correct to label @xmath182 as 0 " . the figure also shows that the nearest point to the peak of _ spitzer _ light curve favors @xmath184 , but can accommodate other values of @xmath182 , up to about 0.03 at @xmath185 . in this case , the bigger @xmath182 makes @xmath150 bigger because @xmath186 , and so allowing values of @xmath153 between the two best - fit values . at the nearest point to the peak , @xmath187 . then , @xmath188 since @xmath189 from figure 3 , @xmath190 , and it is the maximum value allowed @xmath169 , and thus the maximum allowed @xmath182 . the allowed maximum @xmath191 yields @xmath192 and @xmath193 and hence two @xmath6 values , @xmath194 and @xmath195 . thus , @xmath96 solutions have the lower limit of @xmath196 , while @xmath95 solutions have the upper limit of @xmath195 . ogle-2015-blg-0763 is the only other event with a single lens mass measurement based on finite - source effects observed by _ spitzer _ @xcite . as with ogle-2016-blg-1482 , the _ spitzer _ light curve shows only one point that is strongly affected by finite - source effects ( i.e. , @xmath165 ) . @xcite report @xmath197 , @xmath198days and their solution implies @xmath199 and @xmath200 . therefore , the three points closest to peak @xcite at @xmath201days , have respectively , @xmath202 . since the measurement was derived primarily from the highest point , one may infer @xmath203 . inspection of figure 3 shows that this implies @xmath204 , which ( since @xmath205 ) implies that there is another solution at @xmath206 and therefore with @xmath207 . we can then derive for the two solutions @xmath208 ( adopted ) and @xmath209 ( other ) . these yield values of @xmath169 ( from figure 3 ) of @xmath210 ( adopted ) and @xmath211 ( other ) . that is , for ogle-2015-blg-0763 , the two nearest points to the peak will both be about 0.08 mag brighter in the adopted solution than in the other solution . since the _ spitzer _ photometric errors are small compared to these inferred differences ( figure 2 of @xcite ) , we expect that , in the case of ogle-2015-blg-0763 ( and in contrast to ogle-2015-blg-1482 ) , the near - peak points resolve the degeneracy between the two solutions . armed with the above understanding , which was derived without any detailed modeling , we reanalyze ogle-2015-blg-0763 and find only an upper limit of 0.01 for the second @xmath6 . however , as discussed in @xcite , solutions of the second @xmath6 result in inconsistency with observations , and thus they are not physically correct . as a result , there is no @xmath6 degeneracy for the event ogle-2015-blg-0763 . as mentioned before , this is because of the near - peak points . this implies that although for events in which the finite - source effect is seen only in the _ spitzer _ the @xmath6 degeneracy can occur frequently due to low observation cadence of the _ spitzer _ , it can be resolved by a few data points near the peak . the error in the @xmath6 measurement of the event ogle-2015-blg-1482 is @xmath212 for @xmath95 and @xmath213 for @xmath96 . these errors are quite big relative to measurements in high - magnification events from the ground . we therefore study the source of these errors in @xmath6 both to determine why they are so different and to make sure that we are properly incorporating all sources of error in this measurement . as outlined above , the train of information is basically captured by @xmath214 where @xmath215 is the inverse of @xmath150 and both @xmath140 and @xmath169 can be regarded approximately as measured " quantities . it is instructive to further expand this expression @xmath216 in this form , it is clear that the contribution from an error in determining @xmath140 tends to be suppressed if @xmath217 ( i.e. , @xmath218 , so @xmath96 in our case ) , and it tends to be enhanced if @xmath219 . hence , this feature of equation goes in the direction of explaining the larger error in the @xmath95 case . second , if we for the moment ignore the error in @xmath140 , then equation implies @xmath220 . for the two cases , @xmath221 , we have @xmath222 , @xmath223 and so @xmath224 . hence , this aspect also favors larger errors for the smaller @xmath6 ( larger @xmath153 ) solution . this is intuitively clear from figure 3 : the shallow slope of @xmath150 toward large @xmath153 makes it difficult to estimate @xmath153 from a measurement of @xmath169 . hence , the fact that the fractional error in @xmath6 is much larger for the large @xmath153 ( small @xmath6 ) solution is well understood . ignoring blending , we can write @xmath225 . the error in @xmath145 ( i.e. , the flux measurement at the high point ) is uncorrelated with any other error . since in our case , @xmath226 , we can write @xmath227 , and so @xmath228 since @xmath30 is known extremely well , and @xmath229 is known essentially perfectly , there would appear to be essentially no error in @xmath230 . the denominator is a near - invariant in high - magnification events @xcite . that is , the errors in this product are generally much smaller than the errors in either one separately . this means that the error in @xmath169 ( and so @xmath215 ) is dominated by the flux measurement error of the single point that is affected by finite - source effects . nevertheless , it is important to recognize that @xcite derived their conclusion regarding the invariance of @xmath231 under conditions that the error in @xmath143 is completely dominated by the model , and not by the flux measurement errors . indeed , as a rather technical , but very relevant point , it is customary practice to ignore the role of flux measurement errors in the determination of @xmath143 . that is , @xmath143 and @xmath144 are normally _ not _ included as chain variables when modeling microlensing events . instead , the magnification is determined at each point along the light curve from microlens parameters that are in the chain , and then the two flux parameters ( from each observatory ) are determined from a linear fit . this is a perfectly valid approach for the overwhelming majority of microlensing events because the errors arising from this fit ( which are returned but usually not reported from the linear fit routine ) are normally tiny compared to the error in @xmath143 due to the model . moreover , there are usually many observatories contributing to the light curve , and if all the flux parameters were incorporated in the chain , it would increase the convergence time exponentially . however , in the present case @xmath232 is essentially determined from ground - based data , which are both numerous and very high precision , while @xmath143 is determined from just 16 _ spitzer _ points ( i.e. , all the points save the one near peak ) . if the usual ( linear fit ) procedure were applied , it would seriously underestimate the error in @xmath143 and so overestimate its degree anticorrelation with @xmath232 . we therefore include @xmath233 as chain parameters and remodel this event . the result of the remodeling is presented in table 2 . by comparing to runs in which we treat these flux parameters in the usual way , we find that including these parameters in the chain contributes about 41% to the @xmath6 error compared to all other sources of @xmath6 error combined . that is , in the end , this does not dramatically increase the final error , since @xmath234 . nevertheless , it is important to treat @xmath233 in a formally proper way since this contribution could easily be the dominant one in other cases . the @xmath6 degeneracy was not realized until now for several reasons . first of all , although single lens finite - source events have been routinely detected from ground - based observations , they are not scientifically very interesting without the measurement of @xmath15 . however , @xmath15 measurements of single lens events based on ground - based data alone are intrinsically rare and technically difficult @xcite . second , prior to the establishment of second - generation microlensing surveys , observations of high - magnification microlensing events were usually conducted under the survey+followup mode , which was first suggested by @xcite . high - magnification events with their nearly 100% sensitivity to planets @xcite were therefore often followed up with intensive ( @xmath2351 min cadence ) observations , which could easily resolve this @xmath6 degeneracy , if it exists . the @xmath6 degeneracy is nevertheless important for the science of second - generation ground - based and future space - based microlensing surveys . the majority of events found by these surveys will not be followed up at all , and thus the @xmath6 degeneracy can appear because the typical source radius crossing time , @xmath236 , is comparable to the observing cadences that these surveys adopt . here @xmath237 where @xmath238as is the angular source size of a sun - like star in the bulge , and 7 @xmath239 is the typical value for lens - source relative proper motion of disk lenses . for second - generation microlensing surveys like ogle - iv and kmtnet , although a few fields are observed once every @xmath240 min , the majority of fields are observed at @xmath241 hr cadences . therefore , the single lens finite - source events in these relatively low - cadence fields are likely to have one single data point probing the finite - source effect , and thus the @xmath6 degeneracy appears . fortunately , however , the result of event ogle-2015-blg-0763 showed that a few additional data points ( before / after crossing the source ) around the peak play a crucial role in resolving the @xmath6 degeneracy . when we observe typical microlensing events with a cadence of 1 hr , we can obtain 2 more data points right before and after crossing the source , except one source - crossing data point . in this case , the @xmath6 degeneracy will be resolved as in the event ogle-2015-blg-0763 . this implies that 1 hr is the upper limit of the observing cadence to resolve the @xmath6 degeneracy in typical single lens events to be observed from the second - generation ground - based surveys , whereas for events with high @xmath27 , such as events caused by a fast moving lens object or a high - velocity source star , it is not enough to resolve the @xmath6 degeneracy . since about half of kmtnet fields have @xmath242 hr cadences and these fields have higher probability of detecting events than the other fields with cadences of @xmath243 hr , the @xmath6 degeneracy will be resolved in the majority of single high - magnification events to be observed by kmtnet . although @xmath15 is still intrinsically hard to measure even with second - generation surveys , the fraction of events with finite - source effects can be used as an indicator of the properties of the lens population , which is especially important for validating the short - timescale events such as the population of free - floating planets ( ffps ) @xcite . _ the wide - field infrared survey telescope _ ( _ wfirst _ ) is likely to have six microlensing campaigns , each with 72 days observing a @xmath2353 deg@xmath244 microlensing field at 15 min cadence @xcite . _ wfirst _ microlensing is expected to detect thousands of bound planets and hundreds of ffps . at first sight , the 15 min cadence that _ wfirst _ microlensing is currently adopting suggests that it will not be affected by the @xmath6 degeneracy . however , since _ wfirst _ will go much fainter than ground - based surveys , most of the sources for _ wfirst _ events will be m dwarfs , which are a half or even a quarter the size of sun . then the typical @xmath236 for _ wfirst _ events is @xmath23515 min , which is the same as the adopted cadence . hence , as mentioned above , although the @xmath6 degeneracy can be usually resolved by obtaining more than 2 data points around the peak , it will be severe for a significant fraction of events with high @xmath27 . what makes this @xmath6 degeneracy more important for _ wfirst _ is that @xmath15 can be measured relatively easily once ground - based observations are taken simultaneously @xcite . therefore , the degeneracy in @xmath6 will directly lead to a degeneracy in the mass determination of isolated objects , including ffps , bds , and stellar - mass black holes . as discussed in section 3 , it is possible that the deviation of the highly magnified _ point might be caused by a caustic structure rather than being entirely due to finite - source effects . it is easy to show qualitatively that this could affect the exact nature of the system , but is unlikely to significantly change the conclusion that the lens is a low - mass object in the bulge . first , if there were a caustic perturbation , there would be a second body in the lens system . however , we do not see any evidence for the second body in the ground - based light curve , and therefore the dominant lensing effect still comes from a single star . second , consider the effect on the inferred physical properties of the lens ( e.g. , mass and distance ) . if there were a caustic structure , then it is likely to be small since it does not affected the ground - based data . in that case @xmath6 would be smaller and therefore @xmath14 would be larger . at the same time , @xmath13 is clearly determined from the dense , ground - based observations , so if @xmath14 is larger , @xmath27 must also be larger . however , @xmath27 is already 9 @xmath239 for the smaller @xmath6 solution . larger values of @xmath27 are increasingly improbable and will eventually become unphysical . hence , ogle-2015-blg-1482 is likely an event caused by the single lens star . however , since a binary lens system could simultaneously reproduce the single lens - like light curve from ground - based observations and the poorly sampled light curve from _ spitzer _ , we conduct binary lens modeling . as a result , we find that the best - fit binary lens solution is the bd binary lens system composed of a primary star @xmath245 and a secondary star @xmath246 with their projected separation 19 au , which correspond to lensing parameters of the mass ratio between the binary components @xmath247 and the projected separation in units of @xmath14 of the lens system @xmath248 . the estimated distance to the bd binary is 7.5 kpc , and thus it is also located in the galactic bulge . although @xmath62 of the binary lens model is smaller than that of the single lens model by 35 , it is a very wide binary system with large @xmath249 , and thus it is extremely closely related to ( in fact , a variety of ) the single lens solution with @xmath95 . it is important to understand the reason for this close relation . the key point is that the high point of _ spitzer _ is explained by finite - source effects on the tiny caustic of the very wide bd binary that `` replaces '' the point caustic of the point lens in the single lens solution . but the @xmath62 improvement for the binary solution comes entirely from ground - based data , while the @xmath62 of the _ spitzer _ becomes slightly worse than that of the single lens model ( see figure 1 ) . thus , the _ spitzer _ high point is not caused by the binary , as we originally sought to test . the @xmath62 improvement could in principle be due to a distant companion . however , low - level systematics can also easily produce @xmath250 improvements in microlensing light curves , which could then mistakenly be attributed to planets , binaries , etc . for this reason , @xcite and @xcite already set a threshold at @xmath251 for the detection of a planet based on experience with several dozen carefully analyzed events . thus , all we can say about ogle-2015-blg-1482 is that the lens is consistent with being isolated but that we can not rule out that it has a distant companion . and that the evidence " for such a companion is consistent with the systematic effects often seen in microlensing events . in order to find out whether there is a binary solution for which the high point of _ spitzer _ is actually explained by the caustic of a binary , we also conduct binary lens modeling in which @xmath252 . from this , we find that there is no valid binary lens solution with small @xmath6 . this is because although we find two solutions with better @xmath62 relative to the single lens model , the best fit lens - source relative proper motions are @xmath253 and @xmath254 for the @xmath255 and @xmath256 solutions , respectively . these are very large ( as anticipated in the previous paragraph ) to the extent that they are unphysical . one of the two solutions ( for @xmath255 ) is the binary system composed of a primary star @xmath257 and a planet @xmath258 with their projected separation 9.3 au , while for the other solution ( for @xmath256 ) it is the binary system composed of a primary star @xmath259 and a planet @xmath260 with the separation 14.7 au , and these binaries are respectively located at 3.7 kpc and 1.6 kpc . the very large proper motion is due to large @xmath14 , while @xmath13 is clearly determined from dense ground - based observations , as mentioned in the previous paragraph . moreover , the @xmath62 of the _ spitzer _ data for the two binary lens models becomes worse . we analyzed the single lens event ogle-2015-blg-1482 simultaneously observed from two ground - based surveys and from _ spitzer_. the _ spitzer _ data exhibit the finite - source effect due to the passage of the lens directly over the surface of the source star as seen from _ spitzer_. thanks to the finite - source effect and the simultaneous observation from earth and _ spitzer _ , we were able to measure the mass of the lens . from this analysis , we found that the lens of ogle-2015-blg-1482 is a very low - mass star with the mass @xmath0 or a brown dwarf with the mass @xmath261 , which are respectively located at @xmath2 and @xmath3 , and thus it is the first isolated low - mass object located in the galactic bulge . the degeneracy between the two solutions is very severe ( @xmath5 ) . the fundamental reason for the degeneracy is that the finite - source effect is seen only in a single data point from _ spitzer _ and this data point has the finite - source effect function @xmath262 , where @xmath263 . we showed that whenever @xmath264 , there are two solutions for @xmath153 and hence for @xmath265 . because the @xmath6 degeneracy can be resolved only by relatively high cadence observations around the peak , while the _ spitzer _ cadence is typically @xmath266 , we expect that events where the finite - source effect is seen only in the _ spitzer _ data may frequently exhibit the @xmath6 degeneracy . in the case of ogle-2015-blg-1482 , the lens - source relative proper motion for the low - mass star is @xmath8 , while for the brown dwarf it is @xmath267 . hence , the severe degeneracy can be resolved within @xmath268 from direct lens imaging by using next - generation instruments with high spatial resolution . work by s .- chung was supported by the kasi ( korea astronomy and space science institute ) grant 2017 - 1 - 830 - 03 . work by w.z . and a.g . was supported by jpl grant 1500811 . work by c.h . was supported by the creative research initiative program ( 2009 - 0081561 ) of national research foundation of korea . this research has made use of the kmtnet system operated by kasi and the data were obtained at three host sites of ctio in chile , saao in south africa , and sso in australia . the ogle has received funding from the national science centre , poland , grant maestro 2014/14/a / st9/00121 to a.u . the ogle team thanks professors m. kubiak , g. pietrzynski , and .wyrzykowski for their contribution to the collection of the ogle photometric data over the past years . alard , c. , & lupton , r. h. 1998 , , 503 , 325 albrow , m. d. , an , j. , beaulieu , j .- p . , et al . 2001 , , 556 , l113 albrow , m. d. , horne , k. , bramich , d. m. , et al . 2009 , , 397 , 2099 an , j. h. , albrow , m. d. , beaulieu j .- p . , et al . 2002 , , 572 , 521 bachelet , e. , fouqu , p. , han , c. , et al . 2012 , , 547 , 55 bensby , t. , adn , d. , melndez , et al . 2011 , 533 , 134 bessell , m. s. , & brett , j. m. 1988 , , 100 , 1134 bozza , v. , dominik , m. , rattenbury , n. j. , et al . 2012 , , 424 , 902 calchi novati , s. , gould , a. , yee , j. c. , et al . 2015 , , 814 , 92 choi , j .- y . , han , c. , udalski , a. , et al . 2013 , , 768 , 129 claret , a. 2000 , , 363,1081 claret , a. , & bloemen , s. 2011 , , 529 , a75 close , l. m. , males , j. r. , morzinski , k. , et al . 2013 , , 774 , 94 deleuil , m. , deeg , h. j. , alonso , r. , et al . 2008 , , 491 , 889 daz , r. f. , damiani , c. , deleuil , m. , et al . 2013 , , 551 , l9 dong , s. , udalski , a. , gould , a. , et al . 2007 , , 664 , 862 gaudi , b. s. , albrow , m. d. , an , j. , et al . 2002 , 566 , 463 gould , a. 1992 , 392 , 442 gould , a. , & loeb a. 1992 , 396 , 104 gould , a. 1994a , 421 , l71 gould , a. 1994b , 421 , l75 gould , a. 1995 , 441 , l21 gould , a. 1997 , 480 , 188 gould , a. 2000 , 542 , 785 gould , a. 2004 , 606 , 319 gould , a. 2008 , 681 , 1593 gould , a. , udalski , a. , monard , b. , et al . 2009 , 698 , l147 gould , a. & yee , j. c. 2012 , 755 , l17 gould , a. & yee , j. c. 2013 , 764 , 107 gould , a. , carey , s. , & yee , j. 2014 , spitzer proposal id#11006 griest , k. & safizadeh , n. 1998 , 500 , 37 han , c. & chang , h .- y . 2003 , , 338 , 637 han , c. , jung , y. k. , udalski , a. , et al . , 2016 , , 822 , 75 henderson , c. b. , gaudi , b. s. , han , c. et al . 2014 , , 794 , 52 johnson , j. a. , apps , k. , gazak , j. z. , et al . 2011 , 730 , 79 jung , y. k. , udalski , a. , sumi , t. , et al . 2015 , 798 , 123 kervella , p. , thvenin , f. , di folco , e. , sgransan , d. 2004 , , 426 , 297 kervella , p. , & fouqu , p. 2008 , , 491 , 855 kim , s .- l . , lee , c .- u . , park , b .- , et al . 2016 , jkas , 49 , 37 lafrenire , d. , doyon , r. , marois , c. , et al . 2007 , , 670 , 1367 laureijs , r. , amiaux , j. , arduini , s. , et al . 2011 , arxiv:1110.3193 luhman , k. l. 2012 , , 50 , 65 mcgregor , p. j. , bloxham , g. j. , boz , r. , et al . 2012 , , 8446 , 84461i moutou , c. , bonomo , a. s. , bruno , g. , et al . 2013 , , 558 , l6 nataf , d. h. , gould , a. , fouqu , p. et al . 2013 , , 769 , 88 park , h. , udalski , a. , han , c. , et al . 2013 , , 778 , 134 park , h. , udalski , a. , han , c. , et al . 2015 , , 805 , 117 refsdal , s. 1966 , 134 , 315 sahlmann , j. , sgransan , d. , queloz , d. , et al . 2011 , , 525 , a95 shin , i .- g . , choi , j .- y . , park , s .- y . , et al . 2012a , , 746 , 127 shin , i .- , han , c. , gould , a. , et al . 2012b , , 760 , 116 shin , i .- g . , ryu , y .- h . , udalski , a. , et al . 2016 , jkas , 49 , 73 siverd , r. j. , beatty , t. g. , pepper , j. , et al . 2012 , , 761 , 123 skowron j. , shin , i .- , udalski , a. , et al . 2015 , , 804 , 33 spergel , d. , gehrels , n. , baltay , c. , et al . 2015 , arxiv:1503.03757v2 street , r. a. , choi , j .- y . , tsapras , y. , et al . 2013 , , 763 , 67 sumi , t. , kamiya , k. , bennett , d. p. , et al . 2011 , nature , 473 , 349 udalski , a. 2003 , aca , 53 , 291 udalski , a. , yee , j. c. , gould , a. , et al . 2015 , , 799 , 237 yee , j. c. , udalski , a. , sumi , t. , et al . 2009 , , 703 , 2082 yee , j. c. , shvartzvald , y. , gal - yam , a. , et al . 2012 , , 755 , 102 yee , j. c. 2013 , , 770 , l31 yee , j. c. , udalski , a. , calchi novati , s. , et al . 2015a , , 802 , 76 yee , j. c. , gould , a. , beichman , c. , et al . 2015b , , 810 , 155 yoo , j. , depoy , d. l. , gal - yam , a. , et al . 2004 , , 603 , 139 zhu , w. , & gould , a. 2016 , jkas , 49 , 93 zhu , w. , calchi novati , s. , gould , a. , et al . 2016 , , 825 , 60 in the high - magnification limit , the magnification of a point source is @xmath269 . considering the limb darkening effect in high - magnification events , the ratio between the magnifications with and without the finite - source effect is expressed as @xmath270\over \pi\rho^2},\ ] ] where @xmath140 is the normalized separation between the lens and the center of the source , @xmath271 , and @xmath272 and @xmath82 are the position vector and the position angle of a point on the source surface with the respect to the source center , respectively ( see @xcite ) . changing variables to @xmath273 , @xmath274 \over \pi } \nonumber \\ & = & { \int_0 ^ 1 dx\,x \left[1 - \gamma(1 - 1.5\sqrt{1-x^2})\right ] \int_0^{2\pi}d\theta \left[1 + 2(x / z)\cos\theta + ( x / z)^2\right]^{-1/2}\over \pi}.\end{aligned}\ ] ] here we change @xmath275 , and taylor expand the first factor in the integrand , @xmath276 then , keeping terms only to @xmath277 , @xmath278\end{gathered}\ ] ] @xmath279 \\ & = & 2\pi\left(1 + { 1\over 4}q^2 + { 9\over 64}q^4\right ) .\end{aligned}\ ] ] with @xmath280 , equation ( a2 ) becomes @xmath281 \\ & = \int_0 ^ 1 dy \left(1 + { 1\over 4}{y\over z^2 } + { 9\over 64}{y^2\over z^4}\right)- \gamma\int_0 ^ 1 dy\left[\left(1 - 1.5(1-y)^{1/2}\right)\left(1 + { 1\over 4}{y\over z^2 } + { 9\over 64}{y^2\over z^4}\right)\right].\end{aligned}\ ] ] noting that @xmath282 , we get @xmath283 \\ & = 1 + { 1\over 8}{1\over z^2 } + { 3\over 64}{1\over z^4 } -\gamma\left({1\over 40}{1\over z^2 } + { 33\over { 64\times35}}{1\over z^4}\right).\end{aligned}\ ] ] then , we finally get @xmath284 color - magnitude diagram ( cmd ) of stars in the observed field . the field stars are taken from kmtnet ctio data . we note that there exists an offset between the instrumental magnitudes of ogle and kmtnet as @xmath109 mag . the red and blue circles mark the centroid of the red clump giant and the microlensed source star , respectively . , width=566 ] ratio between the actual magnification including finite - source effects to the magnification of a point source , @xmath150 , as a function of @xmath285 , i.e. , the ratio of the lens - source projected separation to the source radius . in contrast to @xcite from which this figure is adapted , we show the magnification both with ( solid ) and without ( dashed ) limb darkening . the horizontal dotted line indicates @xmath158 . , width=566 ] cccrcccccccccccc & & 8360.63/8367 & @xmath286 & @xmath287 & @xmath288 & @xmath289 & @xmath290 & @xmath291 & @xmath292 & @xmath293 + & & 8360.92/8367 & @xmath286 & @xmath294 & @xmath295 & @xmath296 & @xmath297 & @xmath298 & @xmath299 & @xmath300 + + & & 8360.95/8367 & @xmath286 & @xmath301 & @xmath288 & @xmath302 & @xmath303 & @xmath304 & @xmath292 & @xmath305 + & & 8361.15/8367 & @xmath286 & @xmath306 & @xmath307 & @xmath308 & @xmath309 & @xmath310 & @xmath311 & @xmath305 + cccccccccccccccc & & 8361.00/8367 & @xmath312 & @xmath287 & @xmath313 & @xmath314 & @xmath315 & @xmath316 & @xmath317 & @xmath318 + & & 8361.20/8367 & @xmath319 & @xmath294 & @xmath320 & @xmath321 & @xmath322 & @xmath323 & @xmath324 & @xmath325 + + & & 8361.08/8367 & @xmath312 & @xmath301 & @xmath326 & @xmath327 & @xmath328 & @xmath329 & @xmath330 & @xmath331 + & & 8361.27/8367 & @xmath312 & @xmath306 & @xmath332 & @xmath333 & @xmath334 & @xmath335 & @xmath330 & @xmath331 + lccc + range ( b ) & @xmath336 & @xmath337 & @xmath338 + range ( z ) & @xmath339 & @xmath340 & @xmath341 + length ( z ) & 0.51 & 0.34 & 0.79 + @xmath6 solution & single & two ( higher @xmath6 ) & two ( lower @xmath6 ) + +

we analyze the single microlensing event ogle-2015-blg-1482 simultaneously observed from two ground - based surveys and from _ spitzer_. the _ spitzer _ data exhibit finite - source effects due to the passage of the lens close to or directly over the surface of the source star as seen from _ spitzer_. such finite - source effects generally yield measurements of the angular einstein radius , which when combined with the microlens parallax derived from a comparison between the ground - based and the _ spitzer _ light curves , yields the lens mass and lens - source relative parallax . from this analysis , we find that the lens of ogle-2015-blg-1482 is a very low - mass star with the mass @xmath0 or a brown dwarf with the mass @xmath1 , which are respectively located at @xmath2 and @xmath3 , where @xmath4 is the distance between the lens and the source , and thus it is the first isolated low - mass microlens that has been decisively located in the galactic bulge . the degeneracy between the two solutions is severe ( @xmath5 ) . the fundamental reason for the degeneracy is that the finite - source effect is seen only in a single data point from _ spitzer _ and this single data point gives rise to two solutions for @xmath6 , the angular size of the source in units of the angular einstein ring radius . because the @xmath6 degeneracy can be resolved only by relatively high cadence observations around the peak , while the _ spitzer _ cadence is typically @xmath7 , we expect that events for which the finite - source effect is seen only in the _ spitzer _ data may frequently exhibit this @xmath6 degeneracy . for ogle-2015-blg-1482 , the relative proper motion of the lens and source for the low - mass star is @xmath8 , while for the brown dwarf it is @xmath9 . hence , the degeneracy can be resolved within @xmath10 from direct lens imaging by using next - generation instruments with high spatial resolution .

<s>[INST]microlensing is sensitive to planets orbiting low - mass stars and brown dwarfs ( bds ) that are difficult to detect by other methods , such as the radial velocity and transit method . although faint low - mass stars such as m dwarfs comprise @xmath11 of stars in the solar neighborhood and the galaxy @xcite , it is difficult to detect distant m dwarfs due to their low luminosity . however , microlensing depends on the mass of the lens , not the luminosity , and thus it is not affected by the distance and luminosity of the lens . hence , microlensing is the best method to probe faint m dwarfs in the galaxy . a majority of host stars of 52 extrasolar planets detected by microlensing are m dwarfs , and they are distributed within a wide range of distances about @xmath12 . until now a large number of bds @xcite have been discovered by various methods including radial velocity @xcite , transit @xcite , and direct imaging @xcite , and most of them are young @xcite . there exist various scenarios of bd formation based on these plentiful bd samples . since microlensing provides different bd samples from other methods , the microlensing bd samples will play an important role to constrain the various bd formation scenarios . 17 bds have been detected with microlensing so far . only two of them , ogle-2007-blg-224l @xcite and ogle-2015-blg-1268l @xcite , are isolated bds , while most of the others , ogle-2006-blg-277 lb @xcite , ogle-2008-blg-510lb / moa-2008-blg-369l @xcite , moa-2009-blg-411 lb @xcite , moa-2010-blg-073 lb @xcite , moa-2011-blg-104lb / ogle-2011-blg-0172 @xcite , moa-2011-blg-149 lb @xcite , ogle-2013-blg-0102 lb @xcite , and ogle-2013-blg-0578 lb @xcite , are binary companions orbiting m dwarf stars . this is because binary lens events ( i.e. , events with anomalies in the light curve ) have a larger chance to measure masses of the lens than single lens events , such as isolated bd events . the key problem in detecting " isolated bds is that in general , we do not know whether they are detected " or not , since all that we obtain from observed events is the einstein timescale @xmath13 , which is the crossing time of the einstein radius of the lens . with the observed @xmath13 , we can only make a very rough estimate of the lens mass and so can not distinguish potential bds from stars . to measure the masses of isolated bds in the isolated bds events , two parameters are required : the angular einstein radius @xmath14 and microlens parallax @xmath15 . this is because @xcite @xmath16 and @xmath17 where @xmath18 here @xmath19 is the lens mass , and @xmath20 and @xmath21 are the distances to the lens and the source from the observer , respectively . however , it is usually quite difficult to measure the two parameters @xmath14 and @xmath15 . in general , @xmath14 is obtained from the measurement of the normalized source radius @xmath22 , where @xmath23 is an angular radius of the source . the @xmath6 measurement is limited to well - covered caustic - crossing events and high - magnification events in which the source passes close to the lens , while @xmath23 is usually well measured through the color and brightness of the source . because isolated bd events are almost always quite short , @xmath15 can usually be measured only via so - called terrestrial parallax @xcite . terrestrial parallax measurements are limited to well - covered high - magnification events . as a result , it is very hard to measure masses of isolated bds from the ground @xcite . the best way to measure @xmath15 is a simultaneous observation of an event from earth and a satellite @xcite . fortunately , since 2014 , the _ spitzer _ satellite has been regularly observing microlensing events toward the galactic bulge in order to measure the microlens parallax . the _ spitzer _ observations suggest a new opportunity to obtain the mass function of bds from the simultaneous observation from earth and _ spitzer _ , although they are not dedicated to bds @xcite . the simultaneous observation from the two observatories with sufficiently wide projected separation @xmath24 allows to measure the microlens parallax vector @xmath25 from the difference in the light curves as seen from the two observatories , @xmath26 where @xmath27 is the lens - source relative proper motion and @xmath28 where @xmath29 here @xmath30 is the time of the closest source approach to the lens ( peak time of the event ) and @xmath31 is the separation between the lens and the source at time @xmath30 ( impact parameter ) . the subscripts of @xmath32 and @xmath33 indicate the parameters as measured from the satellite and earth , respectively . thus , @xmath34 and @xmath35 represent the difference in @xmath30 and @xmath31 as measured from the two observatories . parallax measurements made by such comparisons between the light curves are subject to a well - known four - fold degeneracy , which comes from four possible values of @xmath35 including ( @xmath36 ) and ( @xmath37 ) . however , there is only a two - fold degeneracy in the amplitude of @xmath25 because @xmath38 and @xmath39 . the only exception to the four - fold degeneracy would be if one of the two observatories has @xmath31 consistent with zero , while the other has @xmath31 inconsistent with zero . in this case , the four - fold degeneracy reduces to a two - fold degeneracy . for example , if @xmath40 ( within errors ) , then @xmath41 ( and similarly for @xmath42 ) . then , since @xmath43 , there is no degeneracy in the mass ( see e.g. , @xcite ) . this case is very important for point - lens mass measurements since the lens always passes very close to or over the source as seen by one observatory , so @xmath44 , whether or not it is strictly consistent with zero . here we report the fifth isolated - star measurement derived from microlensing measurements of @xmath6 and @xmath15 . in contrast to the previous four measurements , this one has a discrete degeneracy in @xmath6 and therefore in mass . we trace the origin of this degeneracy to the fact that only a single point is affected by finite - source effects , and we argue that it may occur frequently in future space - based microlensing mass measurements , including bds . we show how this degeneracy can be broken by future high - resolution imaging , regardless of whether the lens is dark or luminous . this paper is organized as follows . in section 2 , the observation of the event ogle-2015-blg-1482 is summarized , and we describe the analysis of the light curve in section 3 . with the results of section 3 , we derive physical properties of the source and lens in section 4 and then we discuss the results in section 5 . finally , we conclude in section 6 . the gravitational microlensing event ogle-2015-blg-1482 was discovered by the optical gravitational lensing experiment ( ogle ) ( udalski 2003 ) , and it was also observed by _ spitzer _ and korea microlensing telescope network ( kmtnet , @xcite ) . the microlensed source star of the event is located at ( @xmath45,@xmath46 ) = ( @xmath47 ) in equatorial coordinates and ( @xmath48,@xmath49 ) = ( @xmath50 ) in galactic coordinates . ogle observations were carried out using a 1.3 m warsaw telescope with a field of view of 1.4 square degrees at the las campanas observatory in chile . the event lies in the ogle field blg534 with a cadence of about @xmath51 in @xmath52 band . the einstein timescale is quite short , @xmath53days , and the ogle baseline of this event is slightly variable on long timescales at about the 0.02 mag level . thus , we used only 2015 season data for light curve modeling . kmtnet observations were conducted using 1.6 m telescopes with fields of view of 4.0 square degrees at each of three different sites , cerro tololo inter - american observatory ( ctio ) in chile , the south african astronomical observatory ( saao ) in south africa , and siding spring observatory ( sso ) in australia . the scientific observations at the ctio , saao , and sso were initiated on 3 february , 19 february , and 6 june in 2015 , respectively . ogle-2015-blg-1482 was observed with @xmath54 minute cadence at the three sites and the exposure time was 60 s. the ctio , saao , and sso observations were made in @xmath52-band filter , and for determining the color of the source star , the ctio observations with a typical good seeing were also made in @xmath55-band filter . thus , the light curve of the event was well covered by the three kmtnet observation data sets . the kmtnet data were reduced by the difference image analysis ( dia ) photometry pipeline @xcite . _ spitzer _ observations in 2015 were carried out under an 832-hour program whose principal scientific goal was to measure the galactic distribution of planets @xcite . the event selection and observational cadences were decided strictly by the protocols of @xcite , according to which events could be selected either subjectively " or objectively " . events that meet specified objective criteria _ must _ be observed according to a specified cadence . in this case all planets discovered , whether before or after _ spitzer _ observations are triggered , ( as well as all planet sensitivity ) can be included in the analysis . events that do not meet these criteria can still be chosen subjectively " . in this case , planets ( and planet sensitivity ) can only be included in the galactic - distribution analysis based on data that become available after the decision . like objective events , events selected subjectively must continue to be observed according to the specified cadence and stopping criteria ( although those may be specified as different from the standard , objective values at the time of selection ) . because the current paper is not about planets or planet sensitivities , the above considerations play no direct role . however , they play a crucial indirect role . figure 1 shows that despite the event s very short timescale @xmath53days , and despite the fact that it peaked as seen from _ slightly before it peaked from earth , observations began about 1 day prior to the peak . this is remarkable because , as discussed in detail by @xcite ( see their figure 1 ) , there is a delay between the selection of a target and the start of the _ spitzer _ observations . targets can only be uploaded to the spacecraft once per week , and it takes some time to prepare the target uploads . therefore , _ spitzer _ observations begin a minimum of three days after the final decision is made to observe the event with _ spitzer _ , and that decision is generally based on data taken the night before , i.e. about four days prior to the first _ spitzer _ observations . hence , at the time that the decision was made to observe ogle-2015-blg-1482 , the source was significantly outside the einstein ring . it is notoriously difficult to predict the future course of such events . therefore , such events can not meet objective criteria that far from the peak , but selecting themsubjectively " would require a commitment to continue observing them for several more weeks of the campaign , which risks wasting a large number of observations if the event turns out to be very low - magnification with almost zero planet sensitivity ( the most likely scenario ) . at the same time , if the event timescale is short , it could be over before the next opportunity to start observations with _ spitzer _ ( 10 days later ) hence , @xcite also specified the possibility of so - called secret alerts " . for these , an observational sequence would be uploaded to _ spitzer _ for a given week , but no announcement would be made . if the event looked promising later ( after upload ) , then it could be chosen subjectively . in this case , _ spitzer _ data taken after the public alert could be included in the parallax measurement ( needed to enter the galactic - distribution sample ) but _ spitzer _ data taken before this date could not . if the event was subsequently regarded as unpromising , it would not be subjectively alerted , in which case the observations could be halted the next week without violating the @xcite protocols . this was exactly the case for ogle-2015-blg-1482 ( see figure 1 ) . it was @xmath56secretly " alerted at the upload for observations to begin at hjd@xmath57 = hjd-2450000 = 7206.73 . it was only because of this secret alert that an observation was made near peak , which became the basis for the current paper . in fact , its subsequent rise was so fast ( due to its short timescale ) that it was subjectively alerted just prior to the near - peak _ spitzer _ observation . at the next week s upload , it met the objective criteria . note , however , that if we had waited for the event to become objective before triggering observations , we would not have been able to make the mass measurement reported here , even though the planet sensitivity analysis would have been almost identically the same ( provided that parallax could still be measured with the remaining _ spitzer _ observations ) . this is the first _ microlensing event for which a secret alert " played a crucial role . _ spitzer _ observations were made in @xmath58 m channel on the irac camera from hjd@xmath57 = hjd - 2450000 = 7206.73 to 7221.04 . the data were reduced using specialized software developed specifically for this program @xcite . even though the _ spitzer _ data are relatively sparse , there is one point near the peak , which proves to be essential to determine the normalized source radius @xmath6 . event ogle-2015-blg-1482 was densely , and almost continuously covered by ground - based data , but showed no significant anomalies ( see figure 1 ) . this has two very important implications . first , it means that the ground - based light curve can be analyzed as a point lens . second , it implies that it is very likely ( but not absolutely guaranteed ) that the _ spitzer _ light curve can likewise be analyzed as a point lens . the reason that the latter conclusion is not absolutely secure is that the _ spitzer _ and ground - based light curves are separated in the einstein ring by @xmath59 . thus , even though we can be quite certain that the ground - based source trajectory did not go through ( or even near ) any caustics of significant size , it is still possible that the source as seen from _ did pass through a significant caustic , but that this caustic was just too small to affect the ground - based light curve . nevertheless , since the closest _ point to peak has impact parameter @xmath60 and it is quite rare for events to show caustic anomalies at such separations when there are no anomalies seen in densely sampled data @xmath61 , we proceed under the assumption that the event can be analyzed as a point lens from both earth and _ spitzer_. thus , we conduct the single lens modeling of the observed light curve by minimizing @xmath62 over parameter space . for the @xmath62 minimization , we use the markov chain monte carlo ( mcmc ) method . thanks to the simultaneous observation from the earth and satellite , we are able to measure the microlens parallax @xmath63 , which are the north and east components of the parallax vector @xmath25 , respectively . the _ spitzer _ light curve has a point near the peak of the light curve , and thus we can also measure the normalized source radius @xmath6 . hence , we put three single lensing parameters of @xmath30 , @xmath31 , and @xmath13 , the parallax parameters of @xmath64 and @xmath65 , and the normalized source radius @xmath6 as free parameters in the modeling . in addition , there are two flux parameters for each of the 5 observatories ( _ spitzer _ , ogle , kmt ctio , kmt saao , kmt sso ) . one represents the source flux @xmath66 as seen from the @xmath67th observatory , while the other , @xmath68 is the blended flux within the aperture that does not participate in the event . that is , the five observed fluxes @xmath69 at epochs @xmath70 are simultaneously modeled by @xmath71 where @xmath72 is the magnification as a function of time at the @xmath67th observatory . in principle , these magnifications may differ because the observatories are at different locations . however , in this event the separations of the observatories on earth are so small compared to the projected size of the einstein ring that we ignore them and consider all earth - based observations as being made from earth s center . that is , we ignore so - called terrestrial parallax `` . at the same time , the distance between the earth and _ spitzer _ remains highly significant , so @xmath73 is different from @xmath74 . as is customary ( e.g. , @xcite ) , we determine the parameters in the @xmath56geocentric '' frame at the peak of the event as observed from earth @xcite , and likewise adopt the sign conventions shown in figure 4 of @xcite . in addition , we conduct the modeling for the point - source / point - lens , because only a single point of _ spitzer _ contributes to the finite - source effect . we find that the @xmath75 between the best - fit models of the point- and finite - sources is @xmath76 . hence , ogle-2015-blg-1482 strongly favors the finite - source model . as we will show , the lens either transits or passes very close to the source as seen by _ , which induces finite - source effects near the peak of the _ spitzer _ light curve . to account for this , we adopt a limb - darkened brightness profile for the source star of the form @xmath77,\ ] ] where @xmath78 is the mean surface brightness of the source , @xmath79 is the total flux at wavelength @xmath80 , @xmath81 is the limb darkening coefficient , and @xmath82 is the angle between the normal to the surface of the source star and the line of sight @xcite . based on the estimated color and magnitude of the source , which is discussed in section 4 , assuming an effective temperature @xmath83 , solar metallicity , surface gravity @xmath84 , and microturbulent velocity @xmath85 km / s , we adopt @xmath86 from @xcite . as discussed in section 1 , space - based parallax measurements for point lenses generically give rise to four solutions , which can be highly degenerate . however , in cases for which one of two observations has @xmath88 , while the other has @xmath89 , the four solutions reduce to two solutions . since for event ogle-2015-blg-1482 , @xmath90 has @xmath91 , we expect the event to have two degenerate solutions , @xmath92 and @xmath93 . however , what we see in table 1 is not two degenerate solutions but four . for each of the two expected degenerate solutions [ @xmath94 , there are two solutions with different values of @xmath6 ( @xmath95 and @xmath96 ) . figure 1 shows the best - fit light curve of the event ogle-2015-blg-1482 with the ogle , kmt , and _ spitzer _ data sets . the best - fit solution is @xmath97 solution for @xmath95 , which means @xmath92 and @xmath91 . the biggest @xmath75 between the four solutions is @xmath98 . we should expect the two - fold parallax to be very severe in this case . this two - fold degeneracy would be exact in the approximations that 1 ) earth and _ spitzer _ are in rectilinear motion and 2 ) they have zero relative projected velocity @xcite . for events that are very short compared to a year ( like this one ) , the approximation of rectilinear motion is excellent . and while earth and _ spitzer _ had relative projected motion of order @xmath99 , this must be compared to the lens - source projected velocity @xmath100 , @xmath101 hence , these two solutions are almost perfectly degenerate . on the other hand , the @xmath6 degeneracy was completely unexpected . it is also very severe . the origins of the @xmath6 degeneracy are discussed in section 5 . to illustrate the @xmath6 degeneracy , the light curve of the best - fit model @xmath97 for @xmath96 is also presented in figure 1 . in table 1 , we present the parameters of all the four solutions . the color and magnitude of the source are estimated from the observed @xmath102 source color and best - fit modeling of the light curve , but they are affected by extinction and reddening due to the interstellar dust along the line of sight . the dereddened color and magnitude of the source can be determined by comparing to the color and magnitude of the red clump giant ( rc ) under the assumption that the source and rc experience the same amount of reddening and extinction @xcite . figure 2 shows the instrumental kmt ctio color - magnitude diagram ( cmd ) of stars in the observed field . the color and magnitude of the rc are obtained from the position of the rc on the cmd , which correspond to @xmath103_{\rm rc } = [ 1.67 , 17.15]$ ] . we adopt the intrinsic color and magnitude of the rc with @xmath104 = 1.06 @xcite and @xmath105 = 14.50 @xcite . the instrumental source color obtained from a regression is @xmath106 and the magnitude of the source obtained from the best - fit model is @xmath107 . the measured offset between the source and the rc is @xmath108 = [ 0.07 , 0.22]$ ] . here we note that there exists an offset between the instrumental magnitudes of ogle and kmtnet as @xmath109 mag . thus , we should consider the offset when we estimate the dereddened magnitude of the source . as a result , we find the dereddened color and magnitude of the source @xmath103_{\rm s,0 } = [ 1.13 , 14.76]$ ] . the dereddened @xmath110 source color by using the color - color relation of @xcite is @xmath111 . then adopting @xmath112 to the the color - surface brightness relation of @xcite , we determine the source angular radius @xmath113 . the estimated color and magnitude of the source suggest that the source is a k type giant . the error in @xmath114 includes the uncertainty in the source flux , the uncertainty in the conversion from the observed @xmath102 color to the surface brightness , and the uncertainty of centroiding the rc . the uncertainty in the source flux is about @xmath115 and the uncertainty of the microlensing color is @xmath116 mag , which contributes @xmath117 error in @xmath114 measurement . the scatter of the source angular radius relation in @xmath112 is @xmath118 @xcite , and centroiding the rc contributes @xmath119 to the radius uncertainty @xcite . as mentioned above , since the degeneracy between two different @xmath6 solutions is very severe as @xmath120 , we should consider both @xmath6 solutions . the two @xmath6 values yield two different einstein radii , @xmath121 because of the two different einstein radii , all the physical parameters related to the lens take on two discrete values . the relative proper motions of the lens and source are , @xmath122 the mass and distance of the lens can be obtained from the measured einstein radius @xmath14 and microlens parallax @xmath15 . as discussed in the introduction , the four - fold degeneracy in @xmath25 usually leads to a two - fold degeneracy in its amplitude @xmath15 . however , in the case of events that are much higher magnification ( much lower @xmath31 ) as seen from one observatory than the other , the two - fold degeneracy collapses as well . this is because , under these conditions , @xmath123 . the present case is consistent with the lens passing exactly over the center of the source as seen by _ ( to our ability to measure it ) . then , according to equation , we measure the lens mass , @xmath124 the lens - source relative parallax for the two cases is @xmath125 these values of @xmath126 are very small compared to the source parallax @xmath127mas . this implies that the distance between the lens and the source is determined much more precisely than the distance to the lens or the source separately . that is , @xmath128 @xmath129 since the source is almost certainly a bulge clump star ( from its position on the cmd ) , and the lens is @xmath130 kpc from the source , it is likewise almost certainly in the bulge . thus , this is the first isolated low - mass object that has been determined to lie in the galactic bulge . event ogle-2015-blg-1482 has a very severe two - fold degeneracy in @xmath6 , in which the @xmath75 between the two solutions ( @xmath95 and @xmath96 ) is @xmath131 . for the solutions with @xmath92 and @xmath93 , the microlens parallax vectors @xmath25 are different from one another , but they have almost the same amplitude @xmath15 . therefore , the two solutions yield almost the same physical parameters of the lens . however , each of the two solutions also has two degenerate @xmath6 solutions : @xmath95 and @xmath96 . each @xmath6 solution yields different physical parameters of the lens , in particular the lens mass . for @xmath95 , the lens is a very low - mass star , while for @xmath96 it is a brown dwarf . the degeneracy of the lens mass due to the two @xmath6 can be resolved from direct lens imaging by using instruments with high spatial resolution ( han & chang 2003 ; henderson et al . 2014 ) , such as the visao camera of the 6.5 m magellan telescope with the resolution @xmath132 in the @xmath133 band @xcite band images , which gives hope for optical ao . however , it is premature to claim that this technique can be applied to faint stars in the galactic bulge ] and the gmtifs of the 24.5 m giant magellan telescope ( gmt ) with resolution @xmath134 in the nir @xcite . in general , direct imaging requires 1 ) that the lens be luminous , and 2 ) that it be sufficiently far from the source to be separately resolved . in the present case , ( 1 ) clearly fails for the bd solution . hence , the way that high - resolution imaging would resolve the degeneracy is to look for the luminous ( but faint ) m dwarf predicted by the other solution at its predicted orientation ( either almost due north or due south of the source since @xmath135 ) and with its predicted separation @xmath136 . if the m dwarf fails to appear at one of these two expected positions , the bd solution is correct . since the source is a clump giant , and hence roughly @xmath137 times brighter than the m dwarf , it is likely that the two can not be separately resolved until they are separated by at least 2.5 fwhm . this requires to wait until @xmath138 for magellan or @xmath139 for gmt . the degeneracy in @xmath6 was completely unexpected . indeed we discovered it accidentally because @xmath6 had one value in one of two degenerate parallax solutions and the other value in another one . originally , this led us to think that it was somehow connected to the parallax degeneracy . however , by seeding both solutions with both values of @xmath6 we discovered that it was completely independent of the parallax degeneracy . in retrospect , the reason for this degeneracy is `` obvious '' . there is only a single point that is strongly impacted by the finite size of the source . the value of @xmath140 at this time is well predicted by the rest of the light curve , in particular because _ spitzer _ data begin before peak ( see section 2 ) , @xmath141 hence , the magnification ( for point - lens / point - source geometry in a high magnification event ) is also known @xmath142 . moreover , both @xmath143 and @xmath144 for _ spitzer _ are also well measured , so that the measured flux at the near - peak point @xmath145 directly yields an empirical magnification @xmath146 ( i.e. the magnification in the presence of finite - source effects ) . following @xcite , the ratio of @xmath147 and @xmath148 can therefore be derived directly from the light curve @xmath149 as shown by figure 1 of @xcite , @xmath150 reaches a peak at @xmath151 , with @xmath152 . therefore , if one inverts a measurement of @xmath150 to infer a value of @xmath153 , there are respectively one , two and zero solutions for @xmath154 , @xmath155 , and @xmath156 . since this event is a high - magnification event only for _ spitzer _ , i.e. , the finite - source effect is only seen by _ spitzer _ , only the trajectory of _ spitzer _ is considered . figure 3 ( adapted from @xcite ) shows the finite - source effect function @xmath150 as a function of @xmath153 . for this event , @xmath157 at the nearest point to the peak , which is indicated by the horizontal dotted line in the figure . as shown in figure 3 , the function @xmath158 is satisfied at two different values of @xmath159 and @xmath160 , which implies ( as outlined above ) that there are two @xmath6 values . the two @xmath153 values yield two normalized source radii of @xmath161 ( for @xmath162 ) and @xmath163 ( for @xmath164 ) . these two derived @xmath6 values are almost the same as those obtained numerically from the best - fit solutions . because high - magnification events can be alerted in real time , the high - magnification events observed from earth are often well covered around the peak by intensive follow - up observations , and thus @xmath6 is almost always well measured if there are significant finite - source effects ( i.e. , @xmath165 for some points ) . this means that the @xmath6 degeneracy will often be resolved in high - magnification events observed from the ground . on the other hand , since the observation cadence of _ spitzer _ is much lower than those of ground - based observations , the @xmath6 degeneracy can occur frequently in high - magnification events observed by _ spitzer_. note that , in contrast to figure 1 of @xcite , our figure 3 shows @xmath150 with and without the effects of limb darkening . the effect is hardly distinguishable by eye , in particular because limb darkening at @xmath166 m is very weak . nevertheless this effect should be included . if finite - source effects are reliably detected from a single measurement near peak , how often will @xmath6 be ambiguous , and if it is ambiguous , how often will the value fall in the upper versus lower allowed ranges ? we might judge there to be areliable detection " of finite - source effects from a single point if @xmath167 , where @xmath168 might be taken as 5% . for high - magnification events including the limb darkening effect , we can taylor expand @xmath169 for @xmath170 ( see appendix ) @xmath171 where @xmath81 is the limb darkening coefficient , as mentioned in section 3 . truncating at the second term , we have @xmath172 . for _ spitzer _ @xmath173 , so we can ignore it . then @xmath174 . thus , @xmath175 , i.e. , @xmath176 , implies @xmath177 ( for @xmath178 ) . to next order , @xmath179 which is very close to the numerical value , 1.7 hence , we have three ranges of recognizable finite - source effects . the ranges are presented in table 3 . table 3 shows that @xmath180 of the finite - source effects will be unambiguous . and of the times they are ambiguous @xmath181 will have the higher value of @xmath6 . figure 4 shows the @xmath62 distribution of @xmath182 versus @xmath6 from the mcmc chains of the four degenerate solutions in table 1 . the figure shows that the distribution is centered on @xmath183 and thus the four solutions are consistent with @xmath183 , although there is scatter . therefore , it is correct to label @xmath182 as 0 " . the figure also shows that the nearest point to the peak of _ spitzer _ light curve favors @xmath184 , but can accommodate other values of @xmath182 , up to about 0.03 at @xmath185 . in this case , the bigger @xmath182 makes @xmath150 bigger because @xmath186 , and so allowing values of @xmath153 between the two best - fit values . at the nearest point to the peak , @xmath187 . then , @xmath188 since @xmath189 from figure 3 , @xmath190 , and it is the maximum value allowed @xmath169 , and thus the maximum allowed @xmath182 . the allowed maximum @xmath191 yields @xmath192 and @xmath193 and hence two @xmath6 values , @xmath194 and @xmath195 . thus , @xmath96 solutions have the lower limit of @xmath196 , while @xmath95 solutions have the upper limit of @xmath195 . ogle-2015-blg-0763 is the only other event with a single lens mass measurement based on finite - source effects observed by _ spitzer _ @xcite . as with ogle-2016-blg-1482 , the _ spitzer _ light curve shows only one point that is strongly affected by finite - source effects ( i.e. , @xmath165 ) . @xcite report @xmath197 , @xmath198days and their solution implies @xmath199 and @xmath200 . therefore , the three points closest to peak @xcite at @xmath201days , have respectively , @xmath202 . since the measurement was derived primarily from the highest point , one may infer @xmath203 . inspection of figure 3 shows that this implies @xmath204 , which ( since @xmath205 ) implies that there is another solution at @xmath206 and therefore with @xmath207 . we can then derive for the two solutions @xmath208 ( adopted ) and @xmath209 ( other ) . these yield values of @xmath169 ( from figure 3 ) of @xmath210 ( adopted ) and @xmath211 ( other ) . that is , for ogle-2015-blg-0763 , the two nearest points to the peak will both be about 0.08 mag brighter in the adopted solution than in the other solution . since the _ spitzer _ photometric errors are small compared to these inferred differences ( figure 2 of @xcite ) , we expect that , in the case of ogle-2015-blg-0763 ( and in contrast to ogle-2015-blg-1482 ) , the near - peak points resolve the degeneracy between the two solutions . armed with the above understanding , which was derived without any detailed modeling , we reanalyze ogle-2015-blg-0763 and find only an upper limit of 0.01 for the second @xmath6 . however , as discussed in @xcite , solutions of the second @xmath6 result in inconsistency with observations , and thus they are not physically correct . as a result , there is no @xmath6 degeneracy for the event ogle-2015-blg-0763 . as mentioned before , this is because of the near - peak points . this implies that although for events in which the finite - source effect is seen only in the _ spitzer _ the @xmath6 degeneracy can occur frequently due to low observation cadence of the _ spitzer _ , it can be resolved by a few data points near the peak . the error in the @xmath6 measurement of the event ogle-2015-blg-1482 is @xmath212 for @xmath95 and @xmath213 for @xmath96 . these errors are quite big relative to measurements in high - magnification events from the ground . we therefore study the source of these errors in @xmath6 both to determine why they are so different and to make sure that we are properly incorporating all sources of error in this measurement . as outlined above , the train of information is basically captured by @xmath214 where @xmath215 is the inverse of @xmath150 and both @xmath140 and @xmath169 can be regarded approximately as measured " quantities . it is instructive to further expand this expression @xmath216 in this form , it is clear that the contribution from an error in determining @xmath140 tends to be suppressed if @xmath217 ( i.e. , @xmath218 , so @xmath96 in our case ) , and it tends to be enhanced if @xmath219 . hence , this feature of equation goes in the direction of explaining the larger error in the @xmath95 case . second , if we for the moment ignore the error in @xmath140 , then equation implies @xmath220 . for the two cases , @xmath221 , we have @xmath222 , @xmath223 and so @xmath224 . hence , this aspect also favors larger errors for the smaller @xmath6 ( larger @xmath153 ) solution . this is intuitively clear from figure 3 : the shallow slope of @xmath150 toward large @xmath153 makes it difficult to estimate @xmath153 from a measurement of @xmath169 . hence , the fact that the fractional error in @xmath6 is much larger for the large @xmath153 ( small @xmath6 ) solution is well understood . ignoring blending , we can write @xmath225 . the error in @xmath145 ( i.e. , the flux measurement at the high point ) is uncorrelated with any other error . since in our case , @xmath226 , we can write @xmath227 , and so @xmath228 since @xmath30 is known extremely well , and @xmath229 is known essentially perfectly , there would appear to be essentially no error in @xmath230 . the denominator is a near - invariant in high - magnification events @xcite . that is , the errors in this product are generally much smaller than the errors in either one separately . this means that the error in @xmath169 ( and so @xmath215 ) is dominated by the flux measurement error of the single point that is affected by finite - source effects . nevertheless , it is important to recognize that @xcite derived their conclusion regarding the invariance of @xmath231 under conditions that the error in @xmath143 is completely dominated by the model , and not by the flux measurement errors . indeed , as a rather technical , but very relevant point , it is customary practice to ignore the role of flux measurement errors in the determination of @xmath143 . that is , @xmath143 and @xmath144 are normally _ not _ included as chain variables when modeling microlensing events . instead , the magnification is determined at each point along the light curve from microlens parameters that are in the chain , and then the two flux parameters ( from each observatory ) are determined from a linear fit . this is a perfectly valid approach for the overwhelming majority of microlensing events because the errors arising from this fit ( which are returned but usually not reported from the linear fit routine ) are normally tiny compared to the error in @xmath143 due to the model . moreover , there are usually many observatories contributing to the light curve , and if all the flux parameters were incorporated in the chain , it would increase the convergence time exponentially . however , in the present case @xmath232 is essentially determined from ground - based data , which are both numerous and very high precision , while @xmath143 is determined from just 16 _ spitzer _ points ( i.e. , all the points save the one near peak ) . if the usual ( linear fit ) procedure were applied , it would seriously underestimate the error in @xmath143 and so overestimate its degree anticorrelation with @xmath232 . we therefore include @xmath233 as chain parameters and remodel this event . the result of the remodeling is presented in table 2 . by comparing to runs in which we treat these flux parameters in the usual way , we find that including these parameters in the chain contributes about 41% to the @xmath6 error compared to all other sources of @xmath6 error combined . that is , in the end , this does not dramatically increase the final error , since @xmath234 . nevertheless , it is important to treat @xmath233 in a formally proper way since this contribution could easily be the dominant one in other cases . the @xmath6 degeneracy was not realized until now for several reasons . first of all , although single lens finite - source events have been routinely detected from ground - based observations , they are not scientifically very interesting without the measurement of @xmath15 . however , @xmath15 measurements of single lens events based on ground - based data alone are intrinsically rare and technically difficult @xcite . second , prior to the establishment of second - generation microlensing surveys , observations of high - magnification microlensing events were usually conducted under the survey+followup mode , which was first suggested by @xcite . high - magnification events with their nearly 100% sensitivity to planets @xcite were therefore often followed up with intensive ( @xmath2351 min cadence ) observations , which could easily resolve this @xmath6 degeneracy , if it exists . the @xmath6 degeneracy is nevertheless important for the science of second - generation ground - based and future space - based microlensing surveys . the majority of events found by these surveys will not be followed up at all , and thus the @xmath6 degeneracy can appear because the typical source radius crossing time , @xmath236 , is comparable to the observing cadences that these surveys adopt . here @xmath237 where @xmath238as is the angular source size of a sun - like star in the bulge , and 7 @xmath239 is the typical value for lens - source relative proper motion of disk lenses . for second - generation microlensing surveys like ogle - iv and kmtnet , although a few fields are observed once every @xmath240 min , the majority of fields are observed at @xmath241 hr cadences . therefore , the single lens finite - source events in these relatively low - cadence fields are likely to have one single data point probing the finite - source effect , and thus the @xmath6 degeneracy appears . fortunately , however , the result of event ogle-2015-blg-0763 showed that a few additional data points ( before / after crossing the source ) around the peak play a crucial role in resolving the @xmath6 degeneracy . when we observe typical microlensing events with a cadence of 1 hr , we can obtain 2 more data points right before and after crossing the source , except one source - crossing data point . in this case , the @xmath6 degeneracy will be resolved as in the event ogle-2015-blg-0763 . this implies that 1 hr is the upper limit of the observing cadence to resolve the @xmath6 degeneracy in typical single lens events to be observed from the second - generation ground - based surveys , whereas for events with high @xmath27 , such as events caused by a fast moving lens object or a high - velocity source star , it is not enough to resolve the @xmath6 degeneracy . since about half of kmtnet fields have @xmath242 hr cadences and these fields have higher probability of detecting events than the other fields with cadences of @xmath243 hr , the @xmath6 degeneracy will be resolved in the majority of single high - magnification events to be observed by kmtnet . although @xmath15 is still intrinsically hard to measure even with second - generation surveys , the fraction of events with finite - source effects can be used as an indicator of the properties of the lens population , which is especially important for validating the short - timescale events such as the population of free - floating planets ( ffps ) @xcite . _ the wide - field infrared survey telescope _ ( _ wfirst _ ) is likely to have six microlensing campaigns , each with 72 days observing a @xmath2353 deg@xmath244 microlensing field at 15 min cadence @xcite . _ wfirst _ microlensing is expected to detect thousands of bound planets and hundreds of ffps . at first sight , the 15 min cadence that _ wfirst _ microlensing is currently adopting suggests that it will not be affected by the @xmath6 degeneracy . however , since _ wfirst _ will go much fainter than ground - based surveys , most of the sources for _ wfirst _ events will be m dwarfs , which are a half or even a quarter the size of sun . then the typical @xmath236 for _ wfirst _ events is @xmath23515 min , which is the same as the adopted cadence . hence , as mentioned above , although the @xmath6 degeneracy can be usually resolved by obtaining more than 2 data points around the peak , it will be severe for a significant fraction of events with high @xmath27 . what makes this @xmath6 degeneracy more important for _ wfirst _ is that @xmath15 can be measured relatively easily once ground - based observations are taken simultaneously @xcite . therefore , the degeneracy in @xmath6 will directly lead to a degeneracy in the mass determination of isolated objects , including ffps , bds , and stellar - mass black holes . as discussed in section 3 , it is possible that the deviation of the highly magnified _ point might be caused by a caustic structure rather than being entirely due to finite - source effects . it is easy to show qualitatively that this could affect the exact nature of the system , but is unlikely to significantly change the conclusion that the lens is a low - mass object in the bulge . first , if there were a caustic perturbation , there would be a second body in the lens system . however , we do not see any evidence for the second body in the ground - based light curve , and therefore the dominant lensing effect still comes from a single star . second , consider the effect on the inferred physical properties of the lens ( e.g. , mass and distance ) . if there were a caustic structure , then it is likely to be small since it does not affected the ground - based data . in that case @xmath6 would be smaller and therefore @xmath14 would be larger . at the same time , @xmath13 is clearly determined from the dense , ground - based observations , so if @xmath14 is larger , @xmath27 must also be larger . however , @xmath27 is already 9 @xmath239 for the smaller @xmath6 solution . larger values of @xmath27 are increasingly improbable and will eventually become unphysical . hence , ogle-2015-blg-1482 is likely an event caused by the single lens star . however , since a binary lens system could simultaneously reproduce the single lens - like light curve from ground - based observations and the poorly sampled light curve from _ spitzer _ , we conduct binary lens modeling . as a result , we find that the best - fit binary lens solution is the bd binary lens system composed of a primary star @xmath245 and a secondary star @xmath246 with their projected separation 19 au , which correspond to lensing parameters of the mass ratio between the binary components @xmath247 and the projected separation in units of @xmath14 of the lens system @xmath248 . the estimated distance to the bd binary is 7.5 kpc , and thus it is also located in the galactic bulge . although @xmath62 of the binary lens model is smaller than that of the single lens model by 35 , it is a very wide binary system with large @xmath249 , and thus it is extremely closely related to ( in fact , a variety of ) the single lens solution with @xmath95 . it is important to understand the reason for this close relation . the key point is that the high point of _ spitzer _ is explained by finite - source effects on the tiny caustic of the very wide bd binary that `` replaces '' the point caustic of the point lens in the single lens solution . but the @xmath62 improvement for the binary solution comes entirely from ground - based data , while the @xmath62 of the _ spitzer _ becomes slightly worse than that of the single lens model ( see figure 1 ) . thus , the _ spitzer _ high point is not caused by the binary , as we originally sought to test . the @xmath62 improvement could in principle be due to a distant companion . however , low - level systematics can also easily produce @xmath250 improvements in microlensing light curves , which could then mistakenly be attributed to planets , binaries , etc . for this reason , @xcite and @xcite already set a threshold at @xmath251 for the detection of a planet based on experience with several dozen carefully analyzed events . thus , all we can say about ogle-2015-blg-1482 is that the lens is consistent with being isolated but that we can not rule out that it has a distant companion . and that the evidence " for such a companion is consistent with the systematic effects often seen in microlensing events . in order to find out whether there is a binary solution for which the high point of _ spitzer _ is actually explained by the caustic of a binary , we also conduct binary lens modeling in which @xmath252 . from this , we find that there is no valid binary lens solution with small @xmath6 . this is because although we find two solutions with better @xmath62 relative to the single lens model , the best fit lens - source relative proper motions are @xmath253 and @xmath254 for the @xmath255 and @xmath256 solutions , respectively . these are very large ( as anticipated in the previous paragraph ) to the extent that they are unphysical . one of the two solutions ( for @xmath255 ) is the binary system composed of a primary star @xmath257 and a planet @xmath258 with their projected separation 9.3 au , while for the other solution ( for @xmath256 ) it is the binary system composed of a primary star @xmath259 and a planet @xmath260 with the separation 14.7 au , and these binaries are respectively located at 3.7 kpc and 1.6 kpc . the very large proper motion is due to large @xmath14 , while @xmath13 is clearly determined from dense ground - based observations , as mentioned in the previous paragraph . moreover , the @xmath62 of the _ spitzer _ data for the two binary lens models becomes worse . we analyzed the single lens event ogle-2015-blg-1482 simultaneously observed from two ground - based surveys and from _ spitzer_. the _ spitzer _ data exhibit the finite - source effect due to the passage of the lens directly over the surface of the source star as seen from _ spitzer_. thanks to the finite - source effect and the simultaneous observation from earth and _ spitzer _ , we were able to measure the mass of the lens . from this analysis , we found that the lens of ogle-2015-blg-1482 is a very low - mass star with the mass @xmath0 or a brown dwarf with the mass @xmath261 , which are respectively located at @xmath2 and @xmath3 , and thus it is the first isolated low - mass object located in the galactic bulge . the degeneracy between the two solutions is very severe ( @xmath5 ) . the fundamental reason for the degeneracy is that the finite - source effect is seen only in a single data point from _ spitzer _ and this data point has the finite - source effect function @xmath262 , where @xmath263 . we showed that whenever @xmath264 , there are two solutions for @xmath153 and hence for @xmath265 . because the @xmath6 degeneracy can be resolved only by relatively high cadence observations around the peak , while the _ spitzer _ cadence is typically @xmath266 , we expect that events where the finite - source effect is seen only in the _ spitzer _ data may frequently exhibit the @xmath6 degeneracy . in the case of ogle-2015-blg-1482 , the lens - source relative proper motion for the low - mass star is @xmath8 , while for the brown dwarf it is @xmath267 . hence , the severe degeneracy can be resolved within @xmath268 from direct lens imaging by using next - generation instruments with high spatial resolution . work by s .- chung was supported by the kasi ( korea astronomy and space science institute ) grant 2017 - 1 - 830 - 03 . work by w.z . and a.g . was supported by jpl grant 1500811 . work by c.h . was supported by the creative research initiative program ( 2009 - 0081561 ) of national research foundation of korea . this research has made use of the kmtnet system operated by kasi and the data were obtained at three host sites of ctio in chile , saao in south africa , and sso in australia . the ogle has received funding from the national science centre , poland , grant maestro 2014/14/a / st9/00121 to a.u . the ogle team thanks professors m. kubiak , g. pietrzynski , and .wyrzykowski for their contribution to the collection of the ogle photometric data over the past years . alard , c. , & lupton , r. h. 1998 , , 503 , 325 albrow , m. d. , an , j. , beaulieu , j .- p . , et al . 2001 , , 556 , l113 albrow , m. d. , horne , k. , bramich , d. m. , et al . 2009 , , 397 , 2099 an , j. h. , albrow , m. d. , beaulieu j .- p . , et al . 2002 , , 572 , 521 bachelet , e. , fouqu , p. , han , c. , et al . 2012 , , 547 , 55 bensby , t. , adn , d. , melndez , et al . 2011 , 533 , 134 bessell , m. s. , & brett , j. m. 1988 , , 100 , 1134 bozza , v. , dominik , m. , rattenbury , n. j. , et al . 2012 , , 424 , 902 calchi novati , s. , gould , a. , yee , j. c. , et al . 2015 , , 814 , 92 choi , j .- y . , han , c. , udalski , a. , et al . 2013 , , 768 , 129 claret , a. 2000 , , 363,1081 claret , a. , & bloemen , s. 2011 , , 529 , a75 close , l. m. , males , j. r. , morzinski , k. , et al . 2013 , , 774 , 94 deleuil , m. , deeg , h. j. , alonso , r. , et al . 2008 , , 491 , 889 daz , r. f. , damiani , c. , deleuil , m. , et al . 2013 , , 551 , l9 dong , s. , udalski , a. , gould , a. , et al . 2007 , , 664 , 862 gaudi , b. s. , albrow , m. d. , an , j. , et al . 2002 , 566 , 463 gould , a. 1992 , 392 , 442 gould , a. , & loeb a. 1992 , 396 , 104 gould , a. 1994a , 421 , l71 gould , a. 1994b , 421 , l75 gould , a. 1995 , 441 , l21 gould , a. 1997 , 480 , 188 gould , a. 2000 , 542 , 785 gould , a. 2004 , 606 , 319 gould , a. 2008 , 681 , 1593 gould , a. , udalski , a. , monard , b. , et al . 2009 , 698 , l147 gould , a. & yee , j. c. 2012 , 755 , l17 gould , a. & yee , j. c. 2013 , 764 , 107 gould , a. , carey , s. , & yee , j. 2014 , spitzer proposal id#11006 griest , k. & safizadeh , n. 1998 , 500 , 37 han , c. & chang , h .- y . 2003 , , 338 , 637 han , c. , jung , y. k. , udalski , a. , et al . , 2016 , , 822 , 75 henderson , c. b. , gaudi , b. s. , han , c. et al . 2014 , , 794 , 52 johnson , j. a. , apps , k. , gazak , j. z. , et al . 2011 , 730 , 79 jung , y. k. , udalski , a. , sumi , t. , et al . 2015 , 798 , 123 kervella , p. , thvenin , f. , di folco , e. , sgransan , d. 2004 , , 426 , 297 kervella , p. , & fouqu , p. 2008 , , 491 , 855 kim , s .- l . , lee , c .- u . , park , b .- , et al . 2016 , jkas , 49 , 37 lafrenire , d. , doyon , r. , marois , c. , et al . 2007 , , 670 , 1367 laureijs , r. , amiaux , j. , arduini , s. , et al . 2011 , arxiv:1110.3193 luhman , k. l. 2012 , , 50 , 65 mcgregor , p. j. , bloxham , g. j. , boz , r. , et al . 2012 , , 8446 , 84461i moutou , c. , bonomo , a. s. , bruno , g. , et al . 2013 , , 558 , l6 nataf , d. h. , gould , a. , fouqu , p. et al . 2013 , , 769 , 88 park , h. , udalski , a. , han , c. , et al . 2013 , , 778 , 134 park , h. , udalski , a. , han , c. , et al . 2015 , , 805 , 117 refsdal , s. 1966 , 134 , 315 sahlmann , j. , sgransan , d. , queloz , d. , et al . 2011 , , 525 , a95 shin , i .- g . , choi , j .- y . , park , s .- y . , et al . 2012a , , 746 , 127 shin , i .- , han , c. , gould , a. , et al . 2012b , , 760 , 116 shin , i .- g . , ryu , y .- h . , udalski , a. , et al . 2016 , jkas , 49 , 73 siverd , r. j. , beatty , t. g. , pepper , j. , et al . 2012 , , 761 , 123 skowron j. , shin , i .- , udalski , a. , et al . 2015 , , 804 , 33 spergel , d. , gehrels , n. , baltay , c. , et al . 2015 , arxiv:1503.03757v2 street , r. a. , choi , j .- y . , tsapras , y. , et al . 2013 , , 763 , 67 sumi , t. , kamiya , k. , bennett , d. p. , et al . 2011 , nature , 473 , 349 udalski , a. 2003 , aca , 53 , 291 udalski , a. , yee , j. c. , gould , a. , et al . 2015 , , 799 , 237 yee , j. c. , udalski , a. , sumi , t. , et al . 2009 , , 703 , 2082 yee , j. c. , shvartzvald , y. , gal - yam , a. , et al . 2012 , , 755 , 102 yee , j. c. 2013 , , 770 , l31 yee , j. c. , udalski , a. , calchi novati , s. , et al . 2015a , , 802 , 76 yee , j. c. , gould , a. , beichman , c. , et al . 2015b , , 810 , 155 yoo , j. , depoy , d. l. , gal - yam , a. , et al . 2004 , , 603 , 139 zhu , w. , & gould , a. 2016 , jkas , 49 , 93 zhu , w. , calchi novati , s. , gould , a. , et al . 2016 , , 825 , 60 in the high - magnification limit , the magnification of a point source is @xmath269 . considering the limb darkening effect in high - magnification events , the ratio between the magnifications with and without the finite - source effect is expressed as @xmath270\over \pi\rho^2},\ ] ] where @xmath140 is the normalized separation between the lens and the center of the source , @xmath271 , and @xmath272 and @xmath82 are the position vector and the position angle of a point on the source surface with the respect to the source center , respectively ( see @xcite ) . changing variables to @xmath273 , @xmath274 \over \pi } \nonumber \\ & = & { \int_0 ^ 1 dx\,x \left[1 - \gamma(1 - 1.5\sqrt{1-x^2})\right ] \int_0^{2\pi}d\theta \left[1 + 2(x / z)\cos\theta + ( x / z)^2\right]^{-1/2}\over \pi}.\end{aligned}\ ] ] here we change @xmath275 , and taylor expand the first factor in the integrand , @xmath276 then , keeping terms only to @xmath277 , @xmath278\end{gathered}\ ] ] @xmath279 \\ & = & 2\pi\left(1 + { 1\over 4}q^2 + { 9\over 64}q^4\right ) .\end{aligned}\ ] ] with @xmath280 , equation ( a2 ) becomes @xmath281 \\ & = \int_0 ^ 1 dy \left(1 + { 1\over 4}{y\over z^2 } + { 9\over 64}{y^2\over z^4}\right)- \gamma\int_0 ^ 1 dy\left[\left(1 - 1.5(1-y)^{1/2}\right)\left(1 + { 1\over 4}{y\over z^2 } + { 9\over 64}{y^2\over z^4}\right)\right].\end{aligned}\ ] ] noting that @xmath282 , we get @xmath283 \\ & = 1 + { 1\over 8}{1\over z^2 } + { 3\over 64}{1\over z^4 } -\gamma\left({1\over 40}{1\over z^2 } + { 33\over { 64\times35}}{1\over z^4}\right).\end{aligned}\ ] ] then , we finally get @xmath284 color - magnitude diagram ( cmd ) of stars in the observed field . the field stars are taken from kmtnet ctio data . we note that there exists an offset between the instrumental magnitudes of ogle and kmtnet as @xmath109 mag . the red and blue circles mark the centroid of the red clump giant and the microlensed source star , respectively . , width=566 ] ratio between the actual magnification including finite - source effects to the magnification of a point source , @xmath150 , as a function of @xmath285 , i.e. , the ratio of the lens - source projected separation to the source radius . in contrast to @xcite from which this figure is adapted , we show the magnification both with ( solid ) and without ( dashed ) limb darkening . the horizontal dotted line indicates @xmath158 . , width=566 ] cccrcccccccccccc & & 8360.63/8367 & @xmath286 & @xmath287 & @xmath288 & @xmath289 & @xmath290 & @xmath291 & @xmath292 & @xmath293 + & & 8360.92/8367 & @xmath286 & @xmath294 & @xmath295 & @xmath296 & @xmath297 & @xmath298 & @xmath299 & @xmath300 + + & & 8360.95/8367 & @xmath286 & @xmath301 & @xmath288 & @xmath302 & @xmath303 & @xmath304 & @xmath292 & @xmath305 + & & 8361.15/8367 & @xmath286 & @xmath306 & @xmath307 & @xmath308 & @xmath309 & @xmath310 & @xmath311 & @xmath305 + cccccccccccccccc & & 8361.00/8367 & @xmath312 & @xmath287 & @xmath313 & @xmath314 & @xmath315 & @xmath316 & @xmath317 & @xmath318 + & & 8361.20/8367 & @xmath319 & @xmath294 & @xmath320 & @xmath321 & @xmath322 & @xmath323 & @xmath324 & @xmath325 + + & & 8361.08/8367 & @xmath312 & @xmath301 & @xmath326 & @xmath327 & @xmath328 & @xmath329 & @xmath330 & @xmath331 + & & 8361.27/8367 & @xmath312 & @xmath306 & @xmath332 & @xmath333 & @xmath334 & @xmath335 & @xmath330 & @xmath331 + lccc + range ( b ) & @xmath336 & @xmath337 & @xmath338 + range ( z ) & @xmath339 & @xmath340 & @xmath341 + length ( z ) & 0.51 & 0.34 & 0.79 + @xmath6 solution & single & two ( higher @xmath6 ) & two ( lower @xmath6 ) + +[/INST] we analyze the single microlensing event ogle-2015-blg-1482 simultaneously observed from two ground - based surveys and from _ spitzer_. the _ spitzer _ data exhibit finite - source effects due to the passage of the lens close to or directly over the surface of the source star as seen from _ spitzer_. such finite - source effects generally yield measurements of the angular einstein radius , which when combined with the microlens parallax derived from a comparison between the ground - based and the _ spitzer _ light curves , yields the lens mass and lens - source relative parallax . from this analysis , we find that the lens of ogle-2015-blg-1482 is a very low - mass star with the mass @xmath0 or a brown dwarf with the mass @xmath1 , which are respectively located at @xmath2 and @xmath3 , where @xmath4 is the distance between the lens and the source , and thus it is the first isolated low - mass microlens that has been decisively located in the galactic bulge . the degeneracy between the two solutions is severe ( @xmath5 ) . the fundamental reason for the degeneracy is that the finite - source effect is seen only in a single data point from _ spitzer _ and this single data point gives rise to two solutions for @xmath6 , the angular size of the source in units of the angular einstein ring radius . because the @xmath6 degeneracy can be resolved only by relatively high cadence observations around the peak , while the _ spitzer _ cadence is typically @xmath7 , we expect that events for which the finite - source effect is seen only in the _ spitzer _ data may frequently exhibit this @xmath6 degeneracy . for ogle-2015-blg-1482 , the relative proper motion of the lens and source for the low - mass star is @xmath8 , while for the brown dwarf it is @xmath9 . hence , the degeneracy can be resolved within @xmath10 from direct lens imaging by using next - generation instruments with high spatial resolution . </s>

SECTION 1. SHORT TITLE. This Act may be cited as the ``Medicare Diabetes Self-Management Training Act of 2007''. SEC. 2. FINDINGS. Congress makes the following findings: (1) Diabetes is widely recognized as one of the top public health threats currently facing the United States. Approximately 21,000,000 people in the United States are currently living with diabetes, and another 54,000,000 people in the United States have pre-diabetes, dramatically raising their risk of developing diabetes, heart disease, and stroke. Diabetes is the 6th leading cause of death in the United States, causing at least 224,000 deaths annually. The prevalence of the most common type of diabetes has tripled in the last 30 years, and approximately 2,200 people are diagnosed with diabetes each day. (2) Diabetes self-management training, also called diabetes education, provides critical knowledge and skills training to patients with diabetes, helping them identify barriers, facilitate problem solving, and develop coping skills to effectively manage their diabetes. A certified diabetes educator is a health care professional, often a nurse, dietitian, or pharmacist, who specializes in helping people with diabetes develop the self-management skills needed to stay healthy and avoid costly acute complications and emergency care, as well as debilitating secondary conditions caused by diabetes. (3) Diabetes self-management training has been proven effective in helping to reduce the risks and complications of diabetes. In 2002, the Diabetes Prevention Program study conducted by the National Institutes of Health and the Centers for Disease Control and Prevention found that participants (all of whom were at increased risk of developing type 2 diabetes) who made lifestyle changes reduced their risk of getting type 2 diabetes by 58 percent. Lifestyle intervention worked in all of the groups but it worked particularly well in people aged 60 and older, reducing the development of diabetes by 71 percent. Similarly, studies have found that patients under the care of a certified diabetes educator are better able to control their diabetes and report improvement in their health status. (4) Lifestyle changes, such as those taught by certified diabetes educators, directly contribute to better glycemic control and reduced complications from diabetes. Evidence shows that the potential for prevention of the most serious medical complications caused by diabetes to be as high as 90 percent (blindness), 85 percent (amputations), and 50 percent (heart disease and stroke) with proper medical treatment and active self-management. (5) There are currently more than 20,000 diabetes educators in the United States, most of whom are certified diabetes educators credentialed by the National Certification Board for Diabetes Educators. Eligibility for certification as a diabetes educator by the National Certification Board for Diabetes Educators requires prerequisite qualifying professional credentials in specific health care professions and professional practice experience that includes a minimum number of hours and years of experience in diabetes self-management training. Diabetes educators certified by the National Certification Board for Diabetes Educators must also pass a rigorous national examination and periodically renew their credentials. Diabetes educators certified by the National Certification Board for Diabetes Educators, and licensed by a State as a health professional, are uniquely qualified to provide diabetes self-management training under the Medicare program. SEC. 3. RECOGNITION OF CERTIFIED DIABETES EDUCATORS AS CERTIFIED PROVIDERS FOR PURPOSES OF MEDICARE DIABETES OUTPATIENT SELF-MANAGEMENT TRAINING SERVICES. (a) In General.--Section 1861(qq) of the Social Security Act (42 U.S.C. 1395x(qq)) is amended-- (1) in paragraph (1), by inserting ``or by a certified diabetes educator (as defined in paragraph (3))'' after ``paragraph (2)(B)''; and (2) by adding at the end the following new paragraphs: ``(3) For purposes of paragraph (1), the term `certified diabetes educator' means an individual who-- ``(A) is licensed or registered by the State in which the services are performed as a health care professional; ``(B) specializes in teaching individuals with diabetes to develop the necessary skills and knowledge to manage the individual's diabetic condition; and ``(C) is certified as a diabetes educator by a recognized certifying body (as defined in paragraph (4)). ``(4)(A) For purposes of paragraph (3)(B), the term `recognized certifying body' means-- ``(i) the National Certification Board for Diabetes Educators, or ``(ii) a certifying body for diabetes educators, which is recognized by the Secretary as authorized to grant certification of diabetes educators for purposes of this subsection pursuant to standards established by the Secretary, if the Secretary determines such Board or body, respectively, meets the requirement of subparagraph (B). ``(B) The National Certification Board for Diabetes Educators or a certifying body for diabetes educators meets the requirement of this subparagraph, with respect to the certification of an individual, if the Board or body, respectively, is incorporated and registered to do business in the United States and requires as a condition of such certification each of the following: ``(i) The individual has a qualifying credential in a specified health care profession. ``(ii) The individual has professional practice experience in diabetes self-management training that includes a minimum number of hours and years of experience in such training. ``(iii) The individual has successfully completed a national certification examination offered by such entity. ``(iv) The individual periodically renews certification status following initial certification.''. (b) GAO Study and Report.-- (1) Study.--The Comptroller General of the United States shall conduct a study to identify the barriers that exist for Medicare beneficiaries with diabetes in accessing diabetes self-management training services under the Medicare program, including economic and geographic barriers and availability of appropriate referrals and access to adequate and qualified providers. (2) Report.--Not later than 1 year after the date of the enactment of this Act, the Comptroller General of the United States shall submit to Congress a report on the study conducted under paragraph (1). (c) AHRQ Development of Recommendations for Outreach Methods and Report.-- (1) Development of recommendations.--The Director of the Agency for Healthcare Research and Quality shall, through use of a workshop and other appropriate means, develop a series of recommendations on effective outreach methods to educate primary care physicians and the public about the benefits of diabetes self-management training in order to promote better health outcomes for patients with diabetes. (2) Report.--Not later than 1 year after the date of the enactment of this Act, the Director of the Agency for Healthcare Research and Quality shall submit to Congress a report on the recommendations developed under paragraph (1). (d) Effective Date.--The amendments made by subsection (a) shall apply to diabetes outpatient self-management training services furnished on or after the first day of the first calendar year that is at least 6 months after the date of the enactment of this Act.

Medicare Diabetes Self-Management Training Act of 2007- Amends title XVIII (Medicare) of the Social Security Act to provide for the recognition of state- licensed or registered health care professionals who are certified diabetes educators as Medicare providers of diabetes outpatient self-management training services. Directs the Comptroller General to study and report to Congress on the barriers that exist for Medicare beneficiaries with diabetes in accessing diabetes self-management training services under the Medicare program. Directs the Director of the Agency for Health Care Research and Quality to develop a series of recommendations on effective outreach methods to educate primary care physicians and the public about the benefits of diabetes self-management training.

<s>[INST]SECTION 1. SHORT TITLE. This Act may be cited as the ``Medicare Diabetes Self-Management Training Act of 2007''. SEC. 2. FINDINGS. Congress makes the following findings: (1) Diabetes is widely recognized as one of the top public health threats currently facing the United States. Approximately 21,000,000 people in the United States are currently living with diabetes, and another 54,000,000 people in the United States have pre-diabetes, dramatically raising their risk of developing diabetes, heart disease, and stroke. Diabetes is the 6th leading cause of death in the United States, causing at least 224,000 deaths annually. The prevalence of the most common type of diabetes has tripled in the last 30 years, and approximately 2,200 people are diagnosed with diabetes each day. (2) Diabetes self-management training, also called diabetes education, provides critical knowledge and skills training to patients with diabetes, helping them identify barriers, facilitate problem solving, and develop coping skills to effectively manage their diabetes. A certified diabetes educator is a health care professional, often a nurse, dietitian, or pharmacist, who specializes in helping people with diabetes develop the self-management skills needed to stay healthy and avoid costly acute complications and emergency care, as well as debilitating secondary conditions caused by diabetes. (3) Diabetes self-management training has been proven effective in helping to reduce the risks and complications of diabetes. In 2002, the Diabetes Prevention Program study conducted by the National Institutes of Health and the Centers for Disease Control and Prevention found that participants (all of whom were at increased risk of developing type 2 diabetes) who made lifestyle changes reduced their risk of getting type 2 diabetes by 58 percent. Lifestyle intervention worked in all of the groups but it worked particularly well in people aged 60 and older, reducing the development of diabetes by 71 percent. Similarly, studies have found that patients under the care of a certified diabetes educator are better able to control their diabetes and report improvement in their health status. (4) Lifestyle changes, such as those taught by certified diabetes educators, directly contribute to better glycemic control and reduced complications from diabetes. Evidence shows that the potential for prevention of the most serious medical complications caused by diabetes to be as high as 90 percent (blindness), 85 percent (amputations), and 50 percent (heart disease and stroke) with proper medical treatment and active self-management. (5) There are currently more than 20,000 diabetes educators in the United States, most of whom are certified diabetes educators credentialed by the National Certification Board for Diabetes Educators. Eligibility for certification as a diabetes educator by the National Certification Board for Diabetes Educators requires prerequisite qualifying professional credentials in specific health care professions and professional practice experience that includes a minimum number of hours and years of experience in diabetes self-management training. Diabetes educators certified by the National Certification Board for Diabetes Educators must also pass a rigorous national examination and periodically renew their credentials. Diabetes educators certified by the National Certification Board for Diabetes Educators, and licensed by a State as a health professional, are uniquely qualified to provide diabetes self-management training under the Medicare program. SEC. 3. RECOGNITION OF CERTIFIED DIABETES EDUCATORS AS CERTIFIED PROVIDERS FOR PURPOSES OF MEDICARE DIABETES OUTPATIENT SELF-MANAGEMENT TRAINING SERVICES. (a) In General.--Section 1861(qq) of the Social Security Act (42 U.S.C. 1395x(qq)) is amended-- (1) in paragraph (1), by inserting ``or by a certified diabetes educator (as defined in paragraph (3))'' after ``paragraph (2)(B)''; and (2) by adding at the end the following new paragraphs: ``(3) For purposes of paragraph (1), the term `certified diabetes educator' means an individual who-- ``(A) is licensed or registered by the State in which the services are performed as a health care professional; ``(B) specializes in teaching individuals with diabetes to develop the necessary skills and knowledge to manage the individual's diabetic condition; and ``(C) is certified as a diabetes educator by a recognized certifying body (as defined in paragraph (4)). ``(4)(A) For purposes of paragraph (3)(B), the term `recognized certifying body' means-- ``(i) the National Certification Board for Diabetes Educators, or ``(ii) a certifying body for diabetes educators, which is recognized by the Secretary as authorized to grant certification of diabetes educators for purposes of this subsection pursuant to standards established by the Secretary, if the Secretary determines such Board or body, respectively, meets the requirement of subparagraph (B). ``(B) The National Certification Board for Diabetes Educators or a certifying body for diabetes educators meets the requirement of this subparagraph, with respect to the certification of an individual, if the Board or body, respectively, is incorporated and registered to do business in the United States and requires as a condition of such certification each of the following: ``(i) The individual has a qualifying credential in a specified health care profession. ``(ii) The individual has professional practice experience in diabetes self-management training that includes a minimum number of hours and years of experience in such training. ``(iii) The individual has successfully completed a national certification examination offered by such entity. ``(iv) The individual periodically renews certification status following initial certification.''. (b) GAO Study and Report.-- (1) Study.--The Comptroller General of the United States shall conduct a study to identify the barriers that exist for Medicare beneficiaries with diabetes in accessing diabetes self-management training services under the Medicare program, including economic and geographic barriers and availability of appropriate referrals and access to adequate and qualified providers. (2) Report.--Not later than 1 year after the date of the enactment of this Act, the Comptroller General of the United States shall submit to Congress a report on the study conducted under paragraph (1). (c) AHRQ Development of Recommendations for Outreach Methods and Report.-- (1) Development of recommendations.--The Director of the Agency for Healthcare Research and Quality shall, through use of a workshop and other appropriate means, develop a series of recommendations on effective outreach methods to educate primary care physicians and the public about the benefits of diabetes self-management training in order to promote better health outcomes for patients with diabetes. (2) Report.--Not later than 1 year after the date of the enactment of this Act, the Director of the Agency for Healthcare Research and Quality shall submit to Congress a report on the recommendations developed under paragraph (1). (d) Effective Date.--The amendments made by subsection (a) shall apply to diabetes outpatient self-management training services furnished on or after the first day of the first calendar year that is at least 6 months after the date of the enactment of this Act.[/INST]Medicare Diabetes Self-Management Training Act of 2007- Amends title XVIII (Medicare) of the Social Security Act to provide for the recognition of state- licensed or registered health care professionals who are certified diabetes educators as Medicare providers of diabetes outpatient self-management training services. Directs the Comptroller General to study and report to Congress on the barriers that exist for Medicare beneficiaries with diabetes in accessing diabetes self-management training services under the Medicare program. Directs the Director of the Agency for Health Care Research and Quality to develop a series of recommendations on effective outreach methods to educate primary care physicians and the public about the benefits of diabetes self-management training.</s>